Search for Long-lived Chargino with
Anomaly-Mediated Supersymmetry√ Breaking
Scenarios in pp Collisions at s = 7 TeV

A dissertation submitted to
Department of Physics,
Graduate School of Science,
the University of Tokyo
in partial fulfillment of the requirements for the Degree of Doctor of Philosophy

Yuya Azuma
Department of Physics, Graduate School of Science, The University of Tokyo
December 18, 2012

Abstract
A search for long-lived charginos in anomaly-mediated√supersymmetry breaking (AMSB) mod−1
els is performed using 4.7 fb data of pp collisions at s = 7 TeV with the ATLAS detector.
In the AMSB models, the wino is the lightest gaugino and the lightest chargino and neutralino(as the lightest supersymmetric particle) are dominantly composed of the charged and neutral
winos, respectively. Furthermore, the masses of the charged and neutral winos are highly degenerate, which results in a significant lifetime of the chargino. The lightest chargino decays
into a neutralino and a soft charged pion. Due to the mass degeneracy, the momentum of thepion originating from the chargino decay is too soft to be reconstructed in collider experiments.
The neutralino escapes detection, therefore, the decaying chargino could be identified as a highmomentum track breaking up in the tracking volume (disappearing track).
In this dissertation, a method for detecting such chargino tracks is newly developed. The transition radiation tracker (TRT) employed as one of the ATLAS inner detectors, consisting of alot of drift tubes, is used for the identification of the disappearing track. A large number ofassociated hits in the TRT detector for the stable charged particles while a smaller number is
expected for decaying charginos. By requiring a small number of TRT hits along a track, thechargino track is discriminated to the track of the SM particles.
After the application of selection requirements, three hundred and four candidate tracks remain.
The background and signal yields are determined by an unbinned maximum likelihood fit on thept of the tracks. The pT spectrum of the candidate tracks is consistent with the background-only
hypothesis and no excess of data is found.
New constraints on the chargino properties and the AMSB model parameters are then set.
A chargino having a lifetime τχ̃±1 = 1 ns is excluded up to mχ̃±1 ∼ 120 GeV in the region
m 23 > 2000 GeV at 95% Confidence Level (CL). For a chargino having a lifetime τχ̃±1 = 0.3 ns,
a constraint of mχ̃±1 > 100 GeV in the region m 23 > 2000 GeV is set at 95% CL.

This thesis is dedicated to my dear family, especially to my late grandparents Shizu
Hatakenaka, Tadao Hatakenaka and Sadao Azuma.

Acknowledgments
I wold like to express my gratitude to many people for writing up my dissertation. I think I
could not accomplish this study without instruction, help and encouragement from a number ofpeople.
I wish deliver an address of thanks to my supervisor, Prof. Shoji Asai. While I have been a
student of the graduate school, I have learned a lot from a particle physics to an attitude for the
research. He always indicates the right way which I should go and his powerful voice roused
me into activity. It is my great fortune that I have been spent my doctorate course.
I deeply appreciate Prof. Shimpei Yamamoto for his eager instruction, technical supportand encouragement in my Ph.D period. He gave me a variety of important advices and great
encouragement on my study. I really appreciate him for teaching me kindly. Without his help,
my dissertation would never have completed.
I would like to express my thanks to Prof. Osamu Jinnouchi for his advice. Since I wasin master course, he gave me zealous instruction on the physics analysis and the Monte Calrosimulations. When I was stumbled by a difficulty, he gave me kind and patient assistance.
I would like to express my appreciation to Prof. Tomio Kobayashi, Prof. Katsuo Tokushuku
and Prof. Takahiko Kondo for giving me the golden opportunity to participate in the ATLAS
experiment. I am very grateful to the all staff of ICEPP at CERN, Prof. Tatsuo Kawamoto,Prof. Naoko Kanaya, Prof. Junichi Tanaka, Prof Ikuo Ueda, Prof. Koji Terashi, Prof. Yousuke
Kataoka, Dr. Taiki Yamamura, Prof. Koji Nakamura and Dr. Tatsuya Masubuchi. They gave mesincere advice about basic techniques for data analysis or an excellent computing environment.
I also would like to thank Prof. Tetsuro Mashimo, Prof. Yoshizumi Inoue, Prof. Hiroyuki
Matsunaga, Prof. Tadaaki Isobe, Prof. Tomoaki Nakamura and Mr. Nagataka Matsui forproviding me a marvelous computing environment at Tokyo.
I want to express my gratitude to Ms. Kuniko Kono and secretaries of ICEPP, Ms. Ritsuko
Anbiru, Ms. Masako Shiota, Ms. Yoko Takemoto, Ms. Akiko Miyazono, Ms. Yoshie Tezuka,
Ms. Megumi Suzuki, Ms. Chieko Morita, Ms. Naoko Kataoka, Ms. Eiko Yuno and Ms. Hiroko
Yakushi. They have helped me a lot on paperwork and gave me secretarial supports. I want tothank all of ATLAS secretaries for their sincere help with administrative supports.
It is my great honor to express my gratitude to the members of the ATLAS collaboration
for giving me a opportunity to join in this experiment. Furthermore, I would like to express mythanks to all the LHC crews for providing us a excellent data.
I appreciate the conveners and the collaborators of the SUSY working group. The convenersof the SUSY working group, Prof. George Redlinger, Prof. Pascal Pralavorio and Prof. Andreas Hoecker gave me incisive comments and excellent suggestion for physics analysis. I also
3would like to express my appreciation to the conveners and collaborators of the SUSY RPVLL
working group. The conveners of RPVLL working group, Prof. David Milstead and Prof. Paul
Douglas Jackson were always taking care of my research. I appreciate Prof. Christian Ohm
and Prof. Nick Barlow for providing me the ATLAS data dedicated for my research. I would
like to express my thanks to the conveners and the collaborators of the TRT working group. I
appreciate Dr. Christoph Rembser for giving me a good opportunity to participate in this group.
I’m very happy to have many friends who participate in the ATLAS experiments in the same
period. I would like to express my thanks Mr. Kohei Kessoku, Mr. Ginga Akimoto, Mr. Takuya
Suzuki, Mr. Hiroshi Yamaguchi, Mr. Takeshi Dohmae, Dr. Takashi Yamanaka, Mr. Minoru
Hirose, Mr. Kanno Takayuki, Mr. Yu Suzuki, Mr. Satoshi Hasegawa, Dr. Takashi Hayakawa,Mr. Tatsuma Meguro and Mr. Matthew King. We went out to play or held a party to take ourmind off our work on holidays and sometimes have discussions on physics. Especially, Kohei
and I are called “doublet” since we are always hanging out and telling a joke with each other.
He seriously listen to my worries and gave me sincere advice. Furthermore, Takeshi is also mybest playmate and we hanged out many times. He gave me many help in my life at CERN.
I’m also very happy to have many friends in the same period in the University of Tokyo. I
appreciate Dr. Takayuki Yamazaki, Mr. Hideyuki Oide, Mr. Daisuke Kaneko and Ms. Xue Bai.
We made a crack with each other or discussed physics.
I would like to express my gratitude to Dr. Takashi Kubota, Dr. Yasuyuki Okumura and
Dr. Yuta Takahashi. They are my great seniors. I have enjoyed talking or making discussions
with them. I also would like to express my thanks to Dr. Michiru Kaneda and Dr. Hidetoshi
Otono. They are also my great seniors. Michiru gave me sincere advice about data analysis
and kind support in life at CERN. I will never forget the memory of going to see the Tour deFrance together. Hidetoshi also gave me a lot of help and encouraged me. He gave me a brilliant
opportunity to know ICEPP and I could decide to advance to the University of Tokyo in order
to search for SUSY thanks to him.
I want to thank Ms. Katarina Bendtz, Mr. Yoichi Ninomiya and Mr. Ikuo Otani. Yoichi,
who is one of the “triplet” (the others are Kohei and me), is my good junior in study and a goodfriends of mine. Ikuo is also my junior in study and telling a joke with each other. Mr. Shingo
Kazama, Mr. Keisuke Yoshihara and Mr. Youhei Yamaguchi have been my good room matesin the CERN office. Mr. Ryo Katayama have also been my good room mates in the office at
ICEPP. I appreciate my colleagues in the same laboratory, Prof. Akira Ishida, Mr. Yoshifumi
Takeichi, Mr. Yuichi Sasaki, Mr. Akira Miyazaki, Mr. Takashi Goto, Mr. Masahiro Morinaga,
Mr. Kenta Owada, Ms. Maya Okawa and Mr. Yuki Kawanishi. I want to express my gratitude
to Mr. Toyonobu Okuyama, Mr. Yuto Komori, Mr. Wataru Okamura and Mr. Takuya Nobe.
They have encouraged me a lot in CERN life.
I appreciate to Ms. Nelly Bernard and Mr. Jean-François Bernard, the landlords in France
for providing me a comfortable place. I regret that I could not tell her a accomplishment of mydissertation during her lifetime.
I also would like to express my thanks to my friends in Kyoto University, Mr. Takahiko
Masuda, Dr. Mitsuru Matsumura, Dr. Yoshiyuki Inoue and Mr. Satoru Iwaki. They are friends
who have been studying hard together in my undergraduate periods and I could make up mymind to advance to the doctorates course thanks to them.
4This work is supported by JSPS with Research Fellowship for Young Scientists program
and the Global COE Program.
My greatest gratitude goes to my family, Tazunu Azuma, Michiko Azuma and Yoshie
Azuma. Furthermore, I deeply appreciate my sister’s family and my aunt’s family. They gave
me many supports and have been encouraged me. Finally, this thesis is dedicate to my lategrandparents Shizu Hatakenaka, Tadao Hatakenaka and Sadao Azuma.
I’m very happy to have a marvelous opportunity to making a research with a lot of help
from such excellent people. There are many people who encouraged and support me except forpeople I mentioned here. I’m sure that my research had not been completed without their help.
It may be time to say “Goodbye (to the) Yellow Brick Road”. I’m willing to make use of
my “Gold Experience” of this research in my life.
Yuya Azuma
Tokyo, Japan
December, 20125

CONTENTS

Contents
1 Introduction
1.1 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 History of Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Issues in Physics and Supersymmetry . . . . . . . . . . . . . . . . . .
1.3.3 Particles of the Standard Model and Their Superpartner . . . . . . . . .
1.3.4 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.5 Supersymmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.6 Masses of Sparticles . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.7 Production of Sparticles . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.8 Decays of Sparticles . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Anomaly-Mediated Supersymmetry Breaking . . . . . . . . . . . . . . . . . .
1.4.1 Recent Results of the Long-lived Charginos . . . . . . . . . . . . . . .
1.5 Outline of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Experimental Apparatus
2.1 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Injection Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Main Machine Layout . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 The LHC Performance . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 ATLAS Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Magnet System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Forward Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.7 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . .

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3 Performance of TRT Detector
3.1 Performance of TRT with Cosmic Data . . . . . . . . . . . . . . . . . . . . .
3.1.1 Occupancy Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Efficiency Study . . . . . . . . . . . .√. . . . . . . . . . . . . . . . .
3.2 Performance of TRT with pp Collision data of s = 7 TeV . . . . . . . . . . .

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3.2.1
3.2.2

Occupancy Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Efficiency Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Analysis Overview
4.1 Event Topologies of the AMSB Model . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Production Processes . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Characteristics of the Chargino Signal in the ATLAS Experiment . . .

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5 Dataset and Monte Carlo Simulation
5.1 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Analysis Framework . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Software Chain in the Data Preparation . . . . . . . . . . . . . . . . .
5.2 Object Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Calorimeter Cluster Reconstruction . . . . . . . . . . . . . . . . . . .
5.2.4 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.5 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.6 Muon Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.7 Missing Transverse Energy Reconstruction . . . . . . . . . . . . . . .
5.3 Collision Data and Monte Carlo Simulation . . . . . . . . . . . . . . . . . . .
5.3.1 Collision Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Signal Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Background simulation . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Event Selection
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6.1 Object Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.1 Criteria for Resolving Object Overlapping . . . . . . . . . . . . . . . . 95
6.2 TRT Hits Association to a Track . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.3 Kinematic Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.4 Selection Criteria for Chargino Candidate Track . . . . . . . . . . . . . . . . . 96
6.5 Monte Calro Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Backgrounds
101
7.1 Category of Background Tracks . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1.1 Studies on Background Tracks . . . . . . . . . . . . . . . . . . . . . . 102
7.2 Control Regions for Background Tracks . . . . . . . . . . . . . . . . . . . . . 107
7.3 Extraction of Background Track Shapes . . . . . . . . . . . . . . . . . . . . . 109
8 Systematic Uncertainties
113
8.1 Systematic Uncertainties on Backgrounds . . . . . . . . . . . . . . . . . . . . 113
8.2 Systematic Uncertainties on Signal Normalization . . . . . . . . . . . . . . . . 113
8.2.1 Uncertainty on the Theoretical Cross Section . . . . . . . . . . . . . . 113
8.2.2 Uncertainty on the Jet Energy Scale . . . . . . . . . . . . . . . . . . . 114
8.2.3 Uncertainty on the Track Reconstruction Efficiency . . . . . . . . . . . 115
8.2.4 Uncertainty on the Integrated Luminosity . . . . . . . . . . . . . . . . 115
7

CONTENTS
8.2.5
8.2.6

Uncertainty on the Pile-up Modeling . . . . . . . . . . . . . . . . . . . 116
Uncertainty on the Trigger Efficiency . . . . . . . . . . . . . . . . . . 116

9 Background Estimation and Signal Extraction
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9.1 Estimation of Background and Signal Yields . . . . . . . . . . . . . . . . . . . 118
9.1.1 Unbinned Maximum Likelihood Fit . . . . . . . . . . . . . . . . . . . 118
9.2 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.3.1 The Background Shape with Alternative Functions . . . . . . . . . . . 121
9.3.2 Validation of the Signal Extraction Method . . . . . . . . . . . . . . . 121
9.3.3 Distributions of Candidate Tracks . . . . . . . . . . . . . . . . . . . . 123
10 Results and Discussion
127
10.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.1.1 Model Independent Limits . . . . . . . . . . . . . . . . . . . . . . . . 127±
10.1.2 Constraints on the Production Cross Section and the Properties of χ̃1 . 127
10.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
11 Summary

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A Luminosity Determination
142
A.1 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
A.2 Luminosity Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A.3 Luminosity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B Details of Concepts for Tracking
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B.1 Pattern Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.1.1 Histogramming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.1.2 Hough Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.2 Track Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.2.1 Global χ2 Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B.2.2 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B.2.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.2.4 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.2.5 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C Hypothesis Test
149
C.1 Maximum Likelihood Method . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.2 P-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3 The Profile Likelihood Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8LIST OF FIGURES

List of Figures
1.1

1.2
1.3
1.4
1.5
1.6
1.7

The inverse of coupling constants as a function of the energy scale. The unification of the coupling constants is failed if only the SM is assumed. Gauge
coupling constants are unified in the MSSM [15]. . . . . . . . . . . . . . . . .
Feynman diagrams for gluino pair production process. . . . . . . . . . . . . .
Feynman diagrams for gluino squark associate production process. . . . . . . .
Feynman diagrams for squark pair production process. . . . . . . . . . . . . .
The lifetime of the lightest chargino as a function of the mass difference ∆Mχ[18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The constraint on long-lived chargino obtained by combination of the results of
LEP2 experiments[22]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The constraint on the chargino mass and lifetime with 1.0 fb−1 data. The observed bound is set at 95% CL and a chargino having a mass mχ̃±1 < 92 GeVand
lifetime 0.5 < τχ̃±1 < 2.0 ns is excluded [23]. . . . . . . . . . . . . . . . . . . .

2.1
2.2
2.3
2.4
2.5
2.6
2.7

Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The LHC injector complex. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The layout of the LHC lattice. . . . . . . . . . . . . . . . . . . . . . . . . . .
The overview of the ATLAS detector. . . . . . . . . . . . . . . . . . . . . . .
The overview of ATLAS magnet system. . . . . . . . . . . . . . . . . . . . . .
The central solenoid magnet of ATLAS. . . . . . . . . . . . . . . . . . . . . .
Dependencies for r and z of the radial and axial magnetic field components in
the inner detector cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Toroid magnets of the ATLAS. (a) is barrel toroid magnet and (b) is end-cap
toroid magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Predicted magnetic field integral as a function of |η| from the innermost to theoutermost MDT layer in one toroid octant. The red and black lines corresponds
to φ = 0 and φ = π/8, respectively. . . . . . . . . . . . . . . . . . . . . . . . .
2.10 The overview of Inner Detector. . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 The cross section of the Inner Detector on r-z plane. Each of the major detector
elements with its active dimensions and envelops is shown. . . . . . . . . . . .
2.12 Drawing of the sensors and the structural elements traversed by a charged trackof 10 GeV in the barrel region (|η| = 0.3). . . . . . . . . . . . . . . . . . . . .
2.13 Drawing of the sensors and the structural elements traversed by a charged trackof 10 GeV in the end-cap region (|η| = 1.4 and 2.2). . . . . . . . . . . . . . . .
2.14 Photograph of the pixel detector. (a) and (b) are the barrel module and theend-cap module, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . .
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LIST OF FIGURES
2.15 Photographs of the SCT. (a) and (b) are the barrel module and the end-cap
module, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Photographs of the TRT. (a) is the barrel detector of the TRT. (b) shows a endcap disc of the TRT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.17 Layout of a barrel module. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 The cross-section of the barrel detector. . . . . . . . . . . . . . . . . . . . . .
2.19 The pulse height of the TRT drift tube. (a) shows the pulse height of the
20 GeVpions while (b) shows that of the 20 GeVelectrons. . . . . . . . . . . .
2.20 The overview of calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.21 A cross section of LAr electromagnetic calorimeter. . . . . . . . . . . . . . . .
2.22 The geometry of LAr electromagnetic calorimeter at η=0. The accordion geometry is chosen for the electromagnetic calorimeter of ATLAS. . . . . . . . .
2.23 Schematic showing of the tile calorimeter. . . . . . . . . . . . . . . . . . . . .
2.24 Tile calorimeter of the ATLAS. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.25 Photograph of the assembled LAr hadronic end-cap calorimeter. . . . . . . . .
2.26 Schematic view of the LAr hadronic end-cap calorimeter. A cutaway shows thereadout and active pad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.27 Schematic view of the LAr hadronic end-cap calorimeter. A cutaway shows thereadout and active pad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.28 The structure of the electrode of FCal1. The Moliére radius which is represented
R M is shown with magenta disk. . . . . . . . . . . . . . . . . . . . . . . . . .
2.29 The overview of Muon Spectrometer of ATLAS. . . . . . . . . . . . . . . . .
2.30 The cross section of Muon Spectrometer on r-z plane. . . . . . . . . . . . . . .
2.31 Photograph of the RPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.32 Cut-away view of the barrel muon system. RPC is marked with color. . . . . .
2.33 The photograph of drift tubes of MDT. . . . . . . . . . . . . . . . . . . . . . .
2.34 The photograph of the big wheels of the muon spectrometer. . . . . . . . . . .
2.35 The structure of TGC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.36 A small wheel of the muon spectrometer. The inner and outer detector mounted
on the small wheel are the CSC and the MDT, respectively. . . . . . . . . . . .
2.37 The diagram of data acquisition system. . . . . . . . . . . . . . . . . . . . . .
2.38 The diagram of L1 trigger flow. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.1

Event display of the cosmic ray obtained in the commissioning runs. . . . . . .
Occupancy distributions in cosmic runs. . . . . . . . . . . . . . . . . . . . . .
The average occupancy of the barrel module in cosmic runs. . . . . . . . . . .
The average occupancy in each straw layers. (a) and (b) shows the average
numbers of the module of A-side and C-side, respectively. . . . . . . . . . . .
The residual of the track position. . . . . . . . . . . . . . . . . . . . . . . . .
TRT hits efficiency with or without residual selections. . . . . . . . . . . . . .
TRT hits efficiency for different barrel modules. . . . . . . . . . . . . . . . . .
Average number of hit occupancy in each straw layer of the barrel module. . . .
TRT efficiency as a function of a distance from track to the wire. . . . . . . . .
The track reconstruction efficiency for the decaying charginos as a function of
the radial distance of the decay point. . . . . . . . . . . . . . . . . . . . . . .
10

45
45
46
47
48
49
49
49
51
51
52
52
53
53
54
55
56
56
57
57
58
59
62
63
66
67
67
67
69
69
69
70
71
73

LIST OF FIGURES
4.2

4.3
4.4
4.5

5.1

5.2
5.3
6.1

6.2

6.3
6.4

6.5

7.1

Distribution of the chargino track pT and the minimum ∆R between the chargino
and other tracks in various AMSB models. The normalization of AMSB signals
is not taken into account. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Decaying chargino in the TRT detector. . . . . . . . . . . . . . . . . . . . . . 75
The number of TRT hits of reconstructed chargino tracks with |η| < 0.63 as afunction of its decay R. TRT is instrumented between R = 563 mm and 1066 mm. 76
outerdistribution of reconstructed chargino tracks with |η| < 0.63. BlackThe NTRT
line shows all the reconstructed chargino track.Magenta shaded and blue shaded
histograms are the tracks which decay before the TRT Type-3 module and thetracks which penetrates the whole TRT detector, respectively.When charginos
outerdecay before reaching (after penetrating) the TRT type-3 module, NTRT
gives
nearly zero (fifteen). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Illustration of the ambiguity solving in the SCT module.Tracks a,b and c arefound by the seeded track finding. Module hit of the SCT detector is scoredrelatively higher. Hits in a overlap region for track b are high scored.On theother hand, holes where hits are expected results in a penalty. . . . . . . . . . .
Cumulative luminosity delivered from the LHC (green) and recorded by the
ATLAS detector (yellow) during stable beam. . . . . . . . . . . . . . . . . . .
Various parameters of the AMSB models on the m0 -m 23 plane. (a), (b) and (c)√show the mχ̃±1 ,mχ̃±1 − mχ̃01 and cross-section at s = 7 TeV, respectively. . . . . .
The distributions of track parameters. The black point show the data obtainedwith jet triggers while the red lines show the MC expectation with P QCD
samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A sketch of the TRT hits association to track. The track position on a detector
surface is calculated by the ATLAS extrapolator. If the track distance from awire of drift tube is less than the radius of drift tube, the TRT hits is associatedto the track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ETmiss and jet pT distributions after the lepton veto. The selection boundaries
are indicated by arrows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
outer
The NTRT
distributions for data and signal events (LL01, τχ̃±1 = 1 ns). The
signal events are shown by the hatched histogram with the high-pT isolated
track selection. In the signal events, the contribution of chargino tracks decayed
before the TRT outer module (r < 863 mm) is indicated by the filled histogram.
outer
For these tracks, NTRTis expected to have a value near zero. On the otherouterhand, charged particles traversing the TRT typically have NTRT
' 15. The
selection boundary is indicated by the arrow. The expectation from QCD multijet background MC events, normalized to the number of observed events, is also
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acceptance cut for chargino track candidates. Only the tracks expected to penetrate the all active layers of the TRT detector are selected. Tracks which is
passing inactive region at the center of the TRT or is not penetrating the alllayers are rejected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81
87
90

93

96
97

98

99

Origins of disappearing tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
11

LIST OF FIGURES
7.2

Example of a interacting hadron track. A high-pT momentum track makes interaction with TRT detector material. From the point of the interaction in thedetector, many of secondary particles is generated. . . . . . . . . . . . . . . . 102
7.3 The breakdown of the interacting hadron tracks in the TRT detector. (a) and(b) show the truth and the reconstructed pT distributions, respectively. The top
figure shows pT spectra of non-interacting charged pions, interacting elasticallyand inelastically, and decaying into µ + ν in single charged pion MC events ofa flat pT distribution. The bottom figure shows the ratios with respect to the
non-interacting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
P
7.4 The ∆R<0.1 ETclus /ptrack
distributions for chargino (solid line), high-pT interactT
ing hadron (dashed line) and bad tracks (dotted line) derived from MC events. . 104
7.5 the pT distribution of reconstructed tracks as a function of ptrue
T . . . . . . . . . . 105
7.6 Event display of the badly reconstructed track candidate. The corresponding
track is shown as a red line. There is continuous TRT hits of a low momentum
particle near to the badly reconstructed track. . . . . . . . . . . . . . . . . . . 105
7.7 The pT distribution of badly reconstructed tracks for (a) 0 < ptrue< 1 GeV ,
T
true
true
(b) 1 < ptrue
<
2
GeV,
(c)
2
<
p
<
3
GeV,
(d)
3
<
p
<
4
GeV
and (e)TT
Ttrue
4 < pT < 5 GeV. Each distribution is normalized to unity. The ratio of the
distribution of each selection (see the text) to that of no selection is also shownat the bottom of each figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.8 The pT distribution of badly reconstructed tracks. The distributions are normalized by the number of tracks with pT above 50 GeV. . . . . . . . . . . . . . . . 107
7.9 The NPixel distributions of correctly and badly reconstructed tracks in QCD MC
events. Correctly reconstructed track is defined as |σ(pT )| < 0.5 while badly
reconstructed track is defined as σ(pT ) > 3 or σ(pT ) > 5. . . . . . . . . . . . . 108
7.10 The top figure shows pT distribution of interacting hadron track in the control
sample. The data and the fitted line are shown by solid circles and a line, respectively. The bottom figure is the significance of the data-model difference
on a bin-by-bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.11 The top figure shows pT distribution of badly reconstructed track control sample. The data and the fitted line are shown by solid circles and a line, respectively. The significance of the data-model difference on a bin-by-bin are also
shown in the bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.12 The pT distributions of badly reconstructed tracks in events with various NPV . . 112
8.1

8.2
9.1

The distributions of ETmiss and the first leading jet pT distributions of signal sample after kinematic selections with the nominal value and ±σ variations. The
black, red and blue shows the nominal value, +1σ and −1σ variations, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Trigger efficiencies for data and MC events as a function of ETmiss . . . . . . . . 117
Probability density functions employed for the background estimation and thesignal extraction. The dotted line is the shape of the pT distribution in the control sample of the interacting hadron tracks. The dashed line is the shape of thebadly reconstructed tracks. The hatched histogram is the pT distribution of thesignal Monte Carlo (LL01). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
12

LIST OF FIGURES
9.2

9.3
9.4

9.5

9.6

The pT distribution of candidate tracks with the best-fit shape of the ’signal+ background’ and ’background only’ model. The signal point of LL01 andτχ̃±1 = 1 ns are used, but the best-fit signal contribution is found to be zero. . . . 121
Best-fit form of alternative functions for interacting hadron track shape. . . . . 122
The fitted parameters of fbad (a) and µ (b) as a function of true fbad derived frompseudo-experiments observing 304 events including signals (LL01). The pull
distributions of fbad (c) for various true values are also shown. . . . . . . . . . . 124
The fitted parameters of fbad (a) and µ (b) as a function of true fbad derived frompseudo-experiments observing 304 events with the only backgrounds. The pull
distributions of fbad (c) for various true values are also shown. . . . . . . . . . . 125
The distributions of the number of hits in the TRT module. The background expectations are derived from the control samples and normalized to the observed
number of tracks. (a) and (b) show the distributions of hits in the inner moduleand the middle module, respectively. . . . . . . . . . . . . . . . . . . . . . . 126

10.1 Model-independent upper limits on the cross section times the acceptance foran non-SM physics production with an isolated disappearing track with pT > p0T
as a function of p0T . The observed bound at 95% CL and the expected boundwith an integrated luminosity of 4.71 fb−1 are shown. The background estimate
is derived from the background-only fit in the region 10 < pT ≤ 50 GeV. . . . . 128
10.2 The observed and expected upper limits on the signal cross section as a functionof chargino lifetime at 95% CL for mχ̃±1 = 90.2 GeV. The band and dotted line
indicate the range where the limit is expected to lie, assuming no signal. Theline of 6.79 × 10−2 pb corresponds to the theoretical cross section of the LL01
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
10.3 The observed and expected upper limits on the cross section as a function of thechargino lifetime at 95% CL for mχ̃±1 = 117.8 GeV. The line of 8.66 × 10−3 pb
corresponds to the theoretical cross section of the LL02 model. . . . . . . . . . 129
10.4 The observed and expected upper limits on the cross section as a function of thechargino lifetime at 95% CL for mχ̃±1 = 147.7 GeV. The line of 1.16 × 10−3 pb
corresponds to the theoretical cross section of the LL03 model. . . . . . . . . . 129
10.5 The constraint on the chargino mass and lifetime with 4.7fb−1 data. The observed bound is set at 95% CL. The black line shows the observed bound andthe dashed blue line shows the expected bound. The constraint on chargino
mass up to nearly 118 GeV with the lifetime of 1 ∼ 2 ns is set. . . . . . . . . . 130
10.6 The constraint on the AMSB models in the m0 -m 32 plane. (a) shows the observed
and expected upper limits. (b) shows the only observed excluded region. The
black line and the dashed blue line show the observed and the expected upper
limits for chargino having a lifetime τχ̃±1 = 1 ns at 95% CL, respectively. The
red line and the dashed orange line show the obserbed and the expected upper
limits for chargino having a lifetime τχ̃±1 = 0.3 ns at 95% CL, respectively. The
red region is theoretically excluded because the sfermion becomes a tachyon
due to a small m0 . The green region is also theoletically excluded due to noelectroweak symmetry breaking. The mass of chargino in the gray region is
below 92 GeVand is experimentally excluded by the LEP2. . . . . . . . . . . . 131

13

LIST OF TABLES

List of Tables
1.1
1.2
1.3

Quarks and leptons in the Standard Model.S,Q,T 3 and Y are Spin, charge, thethird component of weak isospin and weak hypercharge, respectively. . . . . .
Gauge bosons in the Standard Model. . . . . . . . . . . . . . . . . . . . . . .
Particles in the minimal supersymmetric standard model . . . . . . . . . . . .

2.1
2.2
2.3
2.4
2.5
2.6

LHC design parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters of the central solenoid . . . . . . . . . . . . . . . . . . . . . . . .
Parameters of barrel and end-cap toroid magnets . . . . . . . . . . . . . . . . .
Parameters of the pixel detector . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters of SCT barrel cylinder layer and the numbers of modules per layer.
Nominal |z| positions of SCT end-cap disk and the number of SCT modules per
disk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Parameters of TRT detector. The innermost nine layers of Type-1 is inactive inthe region |z| < 400 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 The main parameters of EM calorimeter of the ATLAS. . . . . . . . . . . . . .
2.9 The main parameters of scintillator tile calorimeter of the ATLAS. . . . . . . .
2.10 The main parameters of LAr hadronic calorimeter of the ATLAS. . . . . . . . .
2.11 The main parameters of forward calorimeter of the ATLAS. . . . . . . . . . . .
2.12 Parameters of the four sub-detector of muon spectrometer. . . . . . . . . . . .
5.1
5.2
5.3
5.4
5.5

6.1
6.2

17
17
20
36
39
40
43
44
45
47
50
52
52
54
55

Track parameters at perigee . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Track characteristics in the track scoring. . . . . . . . . . . . . . . . . . . . . 80
Parameters of signal Monte Carlo samples.The NLO+NLL cross sections include only g̃g̃, q̃g̃ and q̃q̃ production process. . . . . . . . . . . . . . . . . . . 88
Mass spectrum for each benchmark point of AMSB signal. The values are in
the unit of GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Standard Model background Monte Carlo samples. The cross sections of LO
values are shown for QCD jets, while NLO with NLL and NNLO values are
given for tt¯ and boson production processes respectively. p̂T represents the transverse momentum of the two partons in the hard scattering process used in P. 91
The definition of variables used in medium selection for electrons. . . . . . . .
Summary of kinematic selection cuts and data reduction. The selection efficiencies for each AMSB signal model are also shown. . . . . . . . . . . . . . . . .

14

94
96

LIST OF TABLES
6.3

6.4

Summary of selection requirements, the data reduction and the selection efficiencies of the AMSB signals. The purities of chargino tracks are also shownin parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
The breakdown of the SM background process after applying the high-pT isolated track selection criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.1

Selection criteria for the control samples of interacting hadron track and badly
reconstructed track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.1
8.2

The uncertainties on the theoretical cross section of the AMSB signals. . . . . . 114
Summary of systematic uncertainties in the signal normalization. . . . . . . . . 117

9.1
9.2

Summary of the fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Corresponding χ2 values for the interacting hadron track. . . . . . . . . . . . . 122

15

CHAPTER 1. INTRODUCTION

Chapter 1
Introduction
1.1 Symmetry
Symmetry is the most important concept in physics[1, 2] and is the property that the descriptionof the system is invariant under some transformations. Many physicists have been attracted tosymmetry as ever. Emmy Nöther is one of the greatest mathematicians. The Nöther’s theorem
disclaims that some conserved currents exists if the system is invariant under a continuoustransformation. For example, the conservation of energy is equivalent to the time transformation
symmetry. Moreover, the momentum conservation and the angular momentum conservation
follow from the space transformation symmetry and the space rotation symmetry respectively.
Symmetry is important also in the particle physics. The Standard Model (SM) describes thethree interactions: the electromagnetic interaction, the weak interaction and the strong interaction. The SM is the theory based on the internal symmetry of S U(3) × S U(2) × U(1). Furthermore, Peter Higgs put forward a model that Spontaneous Symmetry Breaking gives masses
to gauge bosons. In the Weinberg-Salam theory, the gauge symmetry is broken by considering“wine bottle potential ”and weak bosons achieve masses due to this breaking. As physics beyond SM, Supersymmetry is introduced for the SM. Supersymmetry is the symmetry relating
fermions and bosons and expected to exist because some problems in physics are solved if thesymmetry exists.
This dissertation is devoted the search for a supersymmetry particle inspired by a supersymmetry model.

1.2 The Standard ModelAll of the matters in the world consist of elementary particles[3]. Elementary particles containquarks, leptons and gauge bosons.
Table 1.1 shows the summary of quarks and leptons. They have spin- 12 and are categorized
as fermions. Baryons such as protons or neutrons, and mesons such as pions are called hadrons.
Quarks are elements of hadrons. Electrons, muons, taus and neutrinos are categorized as leptons. Quarks and leptons are divided into three generations. Table 1.2 shows the summary ofgauge bosons. The gauge boson is a carrier of force:the gluon (g) carries the strong interaction,

16

CHAPTER 1. INTRODUCTION

Table 1.1: Quarks and leptons in the Standard Model.S,Q,T 3 and Y are Spin, charge, the third
component of weak isospin and weak hypercharge, respectively.
ParticlesS
Q !
T3 ! Y
!
!
!
1
2
u
c
t
1
1
3
2
1
3
d L
−3
− 12
s L
b L 2
1
2
1
4
Quarks
uR
sR
tR
2
3
2
3
1
1
1
2
dR !
cR !
bR !
−
−
−
2
3 !
2 !
3
1
νe
νµ
ντ
0
1
2
−1
e− L
µ− L
τ− L 2−1− 12
Leptons
1
τ−R
µ−R
-1
0
-2
e−R
2
weak bosons (W ± and Z 0 ) carry the weak interaction and photons (γ) carry the electromagnetic
interaction. The graviton considered as a carrier of gravity but is not yet discovered. Furthermore, Higgs boson which is the origin of mass is expected to be discovered at the LHC.1
Table 1.2: Gauge bosons in the Standard Model.
S Q T3 Y
gluino
g 1 0
0 0
±
W
1 ±1 ±1 0
Weak boson
0
Z
1 0
0 0
photonγ 1 0
0 0

1.3 Supersymmetry
Supersymmetry is a symmetry between bosonic and fermionic degrees of freedom[6, 7, 8, 9].
Various problems in the modern physics are expected to be solved if supersymmetry exists.

1.3.1 History of Supersymmetry
The first concept of supersymmetry is put forward by H.Miyazawa in 1966[10]. This idea
is the symmetry on mesons and baryons. However, this concept did not attract physicists’attention of those days. It is in the 1970s that the idea of supersymmetry on elementary particle are published. Supersymmetry is proposed by Yu.A.Golfand and E.P.Likhtman (1971)[11], D.V.Volkov and V.P.Akulov (1972)[12], and J.Wess and B.Zumino(1974) [13]. In 1981,
H.Georgi and S.Dimopoulos extends the Standard Model minimally with the concept of supersymmetry[14].
This model is called the Minimal Supersymmetric Standard Model or the MSSM for short.
1

In the summer of 2012 , ATLAS and CMS which are experiments at LHC claimed the discovery of Higgsboson like particle[4, 5].

17CHAPTER 1. INTRODUCTION

1.3.2 Issues in Physics and Supersymmetry
There are some of benefits for existing supersymmetry. Various issues are expected to be solvedby the supersymmetry.
• Unification of gauge coupling
Gauge couplings changes with energy and the all gauge couplings are expected to beunified in high energy region, which is called GUT scale. However, the unification of
couplings is impossible if only the Standard Model is considered. By assuming TeV scale
SUSY, the slope of coupling constant changes. As a result, the unification is achieved in
the supersymmetric model. Figure 1.1 shows the evolution of the coupling constants in
the Standard Model and the model with the supersymmetry assumption [15].

Figure 1.1: The inverse of coupling constants as a function of the energy scale. The unificationof the coupling constants is failed if only the SM is assumed. Gauge coupling constants are
unified in the MSSM [15].
• Hierarchy problem
This is the problem that there is a huge difference between the Planck scale and theelectroweak scale. The electroweak sector of the Standard Model have a parameter called
the vacuum expectation value. This parameter sets the scale of masses of bosons. The
mass of the W± is given by1(1.1)
MW = vg,2
where v is the vacuum expectation value of the neutral Higgs field and g is the S U(2)gauge coupling constant. The mass of the Higgs boson is given by√
MH = v −2λ,(1.2)
where λ is the strength of the Higgs self-interaction in the Higgs potential. This is the
only discussion at tree level and by considering one-loop correction. If the Higgs field
couples to a Dirac fermion f with a term in the Lagrangian −λ f H f¯ f , where λ f is the18CHAPTER 1. INTRODUCTION
Yukawa coupling constant, the quadratic correction from a loop of a fermion added toMH2 is expressed as1
δMH2 = − 2 |λ f |2 ΛUV ,(1.3)
8π
where ΛUV is an ultraviolet momentum cutoff. If there is none of new physics up to
Planck scale and ΛUV is set at the Planck mass
1

M p = (GNewton ) 2 ≈ 1.2 × 1019 GeV,

(1.4)

the correction is extremely greater than O((100 GeV)2 ). Therefore,fine-tuning is needed
to lead the electroweak scale with a remarkable cancellation.
If there is a heavy complex scalar particle S having a mass mS that couples to the Higgs
with a Lagrangian term −λS |H|2 |S |2 ,
δMH2 = 2

1
λS ΛUV ,
16π2

(1.5)

If mass correction from the both of fermions and bosons with λS = |λ f |2 , the contributions
from ΛUV is clearly canceled out.
• A good candidate of the dark matter
Experimental cosmology suggests the existence of the dark matter. The dark matterscarcely make interaction with other matter. A good candidate of the dark matter is thelightest supersymmetric particle (LSP).

1.3.3 Particles of the Standard Model and Their Superpartner
In the supersymmetric model, there are supersymmetric particles which correspond to the Standard Model particles. They are called superpartner. The Standard Model particles and thesupersymmetric particles, which is also called sparticles for short, are summarized in the Table
1.3.
Partners of fermions in the Standard Model such as quarks or leptons has spin-0. Their namehave “s”as a prefix. For example, the bosonic partner of quarks and leptons are called squarks
and sleptons. The bosonic partner of fermions is also called sfermions. On the other hand, thenames of fermionic partner of bosons in the Standard Model have “ino”as a suffix. Fermionic
partners of gauge boson, Higgs boson and Graviton are gaugino, higgsino and gravitino, respectively. Gaugino and higgsino has spin- 21 while gravitino has spin- 23 .
In the supersymmetric model, there are two complex Higgs S U(2)L doublets:
!
Hu+
(1.6)
Hu =
Hu0
and
Hd =

Hd0
Hd−

!
.

(1.7)

Hu+ , Hu0 , Hd0 and Hd− are complex numbers. Hence, there are eight real scalar degrees of freedom
in the Higgs doublet. Three of them become the longitudinal modes of the massive vector
19

CHAPTER 1. INTRODUCTION
bosons W ± and Z 0 . The mass eigenstates of the other five are referred as H,h,A and H ± . The
lightest higgs h has a properties similar to the SM higgs and the other four higgs have heavier
masses.
Gauginos are wino(W̃ 0 ,W̃ ± ), bino( B̃0 ) and gravitino(g̃) The electroweak gauge symmetry
S U(2)L × U(1)Y is associated with spin-1 gauge bosons W 0 , W + , W − and B0 . Mass eigenstates
γ (photon), Z 0 (Z-boson) are given by mixing of the W 0 ,B0 after the electroweak symmetry
braking. The superpartners of gauge eigenstates W 0 and B0 are W̃ 0 and B̃0 . Neutral gauginos(W̃ 0 and B̃0 ) and neutral higgsinos (H̃10 ,H̃20 ) make mixing and result in neutralinos (χ̃01 , χ̃02 , χ̃03 ,χ̃04 ). Charged winos and charged higgsinos are also mixed to charginos (χ̃±1 , χ̃±2 ).
Table 1.3: Particles in the minimal supersymmetric standard model
The Standard Model particles
Supersymmetric particles
Names
Spin
Names
Spin
1
˜
quarks (u, d, s, c, b, t)
squarks (ũ, d̃, s̃, c̃, b̃, t)0
2
1
leptons (e, µ, τ,νe , νµ , ντ )sleptons
(ẽ,
µ̃,
τ̃,
ν
˜
,
ν
˜
,
ν
˜
)
0
e µ τ
2
1
± 0
0
0
±
gauge bosons (γ,W ,Z ,g)1gauginos ( B̃ ,W̃ ,W̃ ,g̃)
2
1
±
0
0
±
Higgs bosons (H, h, A, H )0higgsinos (H̃1 ,H̃2 ,H̃ )2
3graviton (G)2gravitino (G̃)
2

1.3.4 R-parity
In the MSSM, the new symmetry which is called R-parity is postulated. Using baryon number(B), lepton number (L) and spin (S), R-parity, PR is defined as
PR = (−1)3(B−L)+2S .

(1.8)

The Standard Model particles have PR = +1 while sparticles have PR = −1.
If R-parity is conserved, there is no mixing between the SM particles and sparticles. Furthermore, the number of sparticles is even in every interaction vertex. Additionally, some ofimportant consequences are obtained. Firstly, the lightest supersymmetric particle, which isalso called LSP must be stable. Secondly, sparticles except for LSP decay to the state that
there is an odd number of LSPs. Thirdly, an even number of sparticles are produced in collider
experiments.
In the most of supersymmetric models, this symmetry is assumed from the point of view ofproton decay constraints or good candidate for the dark matter.

1.3.5 Supersymmetry Breaking
If there is exact invariance under supersymmetry, there expected to be a particle having thesame mass and the same quantum number with a different spin by one-half. However, suchparticles is not observed in nature. It means that the our world is not exactly invariant under thesupersymmetry. The superpartner of the SM particle are expected to have a heavier mass thanthe SM particles due to this reason.
There are various models depending on mechanisms of the supersymmetry breaking. The
supersymmetry breaking is considered to come to our world through some interactions from the20

CHAPTER 1. INTRODUCTION
origin of the supersymmetry breaking, which is called Hidden Sector. The major models arelisted below:• Supergravity-Mediated Supersymmetry Breaking (SUGRA)The supersymmetry breaking is mediated by the gravity from the hidden sector to ourobservable world in this model. It is assumed that the all scalar particles have a common
mass at GUT scale. In this model, the lightest gaugino is bino. Therefore, The LSP is a0bino-like χ̃1 .
• Gauge-Mediated Supersymmetry Breaking (GMSB)
Gauge interactions communicates the effects of supersymmetry breaking in this models.
There is another set of fields that has both SM gauge interactions and a couplings with ahidden sector. This sector is referred as Messenger Sector. G̃ is a the LSP in this model.
0
In some case, τ̃ or χ̃1 become the NLSP and they have a long lifetime. In the case thatτ̃ is the NLSP, the decay of τ̃ is τ̃ → τG̃. The lifetime of τ̃ is expected to be long enoughto penetrate whole detector. The τ̃ is expected to be detected as a Massive Stable Particle
00
00or Kink Track. In the case that χ̃1 is the NLSP, the decay of χ̃1 is χ̃1 → γG̃. The χ̃1 signal
is expected to be detected as Non-Pointing Photon.
• Anomaly-Mediated Supersymmetry Breaking (AMSB)
The supersymmetry breaking is mediated by a conformal anomaly. This model is a simple
model because it does not require such as Messenger Sector in GMSB. However, themodel require m0 for the masses of sfermions in order to prevent sfermions becoming
tachyons. The details on this model are described in Section 1.4.

1.3.6 Masses of Sparticles
Parameters in the MSSM
There are many parameters in the MSSM. In various supersymmetric models, some assumptions
are introduced and the number of parameters is lessen. The parameters widely used in theseveral models are listed here.
1. m0 : Mass of scalar particle at GUT scale.
2. m 21 : Gaugino mass at GUT scale.
3. m 23 : Gravitino mass.
4. µ : Higgsino mass parameter.
5. tan β : the ratio of the vacuum expectation values of doublet.
Moreover,three gaugino mass parameters are widely used: M1 , M2 and M3 are bino mass, winomass and gluino mass, respectively.

21

CHAPTER 1. INTRODUCTION
Gluino Mass
The gluino is the only color octet fermion and can not mix with any other fermion because
S U(3) is unbroken. The mass of the gluino at tree level is simplymg̃ = M3 .

(1.9)

Chargino Mass
The higgsinos and electroweak gauginos (wino and bino) mix with each other. The positively
charged pair (W̃ + , H̃u+ ) mix to form two eigenstates with charge +1. On the other hand, the negatively charged pair (W̃ − , H̃d− ) mix to form two eigenstates with charge −1. Using the eigenstatebasis ψ± = (W̃ + , H̃u+ , W̃ − , H̃d− ), the mass term of charginos is1− (ψ± )T Mψ± ,
2
where
M=

0 XT
X 0

with
X=

√ M2
2 cos βmW

(1.10)!

√!
2 sin βmW.
µ(1.11)(1.12)

From here, (m2χ̃± , m2χ̃± ) is obtained,
1
2
 

q

 2   1
2
2
2
2
2
2
2
2
 mχ̃±   2 (M2 + |µ| + 2mW ) − (M2 + |µ| + 2mW ) − 4|µM2 − mW sin 2β| 
 2 1  =    . (1.13)
q
 1
mχ̃±
2
2
2
2

2 + 2m2 ) − 4|µM − m2 sin 2β|2 
(M
+
|µ|
+
2m
)
+
(M
+
|µ|
2
2
W
2
W
W
2
2
By assuming M2 and µ is real and M2 < µ, the eigenvalues are given by mχ̃±1 ≈ M2 and mχ̃±2 ≈ µ.
±±
In this assumption, χ̃1 becomes wino-like and χ̃2 becomes higgsino-like.
Neutralino Mass
The neutral higgsinos (H̃u0 , H̃d0 ) and the neutral gauginos ( B̃, W̃ 0 ) combine to form four mass
eigenvalues. Using the gauge-eigenstate basis ψ0 = ( B̃, W̃ 0 , H̃u0 , H̃d0 ),1− (ψ0 )T Mψ0 ,2(1.14)

where



M1
0
− cos β sin θW mZ sin β sin θW mZ 


0
M2
cos β cos θW mZ − sin β cos θW mZ 
M = 
 .
0
−µ

 − cos β sin θW mZ cos β cos θW mZ
cos β sin θW mZ − sin β cos θW mZ−µ
0(1.15)The mass matrix M is diagonalized by a unitary matrix N in order to obtain mass eigenstates,χ̃0i = Ni j ψ0j .
By the calculation similarly to the chargino case, the eigenvalue of M is obtained.
22(1.16)

CHAPTER 1. INTRODUCTION
Squarks and Sleptons
In many models such as SUGRA or GMSB, their running masses can be given as,
m2ũL ,d̃L = m2c̃L , s̃L = m20 + K3 + K2 +

1
K1 ,
36

(1.17)

4m2ũR = m2c̃R = m20 + K3 + K1 ,91
m2d̃R = m2s̃R = m20 + K3 + K1 ,91m2ν̃eL ,ẽL = m2ν̃µL ,µ̃L = m20 + K2 + K1 ,4
2
2
2
mẽR = mµ̃R = m0 + K2 + K1 ,(1.18)(1.19)(1.20)(1.21)

where K1 , K2 and K3 are mentioned as the renormalization gauge equation (RGE) contributions
which are corresponding to the square gaugino mass. Roughly, the RGE contributions are,K1 ∼ 0.15m21 , K2 ∼ 0.5m21 , K3 ∼ (4.5 ≈ 6.5)m21 .
2

2(1.22)

2

On the other hand, the sfermion mass in the AMSB model is expressed as,
m2f˜ = −{· · · }m23 + m20 ,(1.23)

2

where the m23 term is the anomaly-mediated contribution to the scalar mass parameter. As men2

tioned before, the sfermion mass is amended by adding m20 in order to make sfermion masses
positive.

1.3.7 Production of Sparticles
Production process of QCD strength
Reactions of QCD strength at the hadron collider are
gg → g̃g̃,(1.24)

gq → g̃q̃,(1.25)

gg → q̃q̃,(1.26)

qq → q̃q̃.

(1.27)The process in (1.24) is gluino pair production process and Feynman diagrams of this process are shown in Figure 1.2. Gluino squark associate production process is shown as (1.25)
and in Figure 1.3. The process in (1.26) and (1.27) is known as squark pair production process
and diagrams of this process is shown in Figure 1.4.
Hard collision of partons is needed in order to produce heavy particles such as sparticle.
Contributions from gluon-gluon collision, gluon-quark collision and quark-quark collision arelarge at proton-proton collider like LHC. There are also contributions from quark-antiquark
collision and these processes are important at proton-antiproton collider like Tevatron.
23

CHAPTER 1. INTRODUCTION

g
g

g̃
g

g

g̃

g

g̃

g̃
g̃

g

g̃
g̃

g

(b)

(a)

g̃

(c)

Figure 1.2: Feynman diagrams for gluino pair production process.

g̃
q
g

q̃
q

q

q

q̃

q̃
g̃

q̃

g

g

g̃

q̃

(a)

(b)

(c)

Figure 1.3: Feynman diagrams for gluino squark associate production process.

24CHAPTER 1. INTRODUCTION

g
g

g

q̃

g

q̃

q̃

q̃

g

g

q̃

q̃
g

q̃

(a)

q̃

(b)

q

(c)

q

q̃

q̃

g̃
q

g̃
q

q̃

(d)

q̃

(e)

Figure 1.4: Feynman diagrams for squark pair production process.

25

CHAPTER 1. INTRODUCTION
Production Process of Electroweak Strength
Reactions in (1.28) - (1.33) are production process of sparticles are via parton collisions ofelectroweak strength.
qq̄ → χ̃+i χ̃−j , χ̃0i χ̃0j(1.28)
ud̄ → χ̃+i χ̃0j(1.29)

dū → χ̃−i χ̃0j(1.30)

qq̄ → l˜i+ l˜−j , ν̃i ν̃ j

(1.31)

ud̄ → l˜+L ν̃l(1.32)

dū → l˜−L ν̃l(1.33)

These reactions have contributions from electroweak gauge bosons in s-channel and fromsquark exchange in t-channel. These process are important at the Tevatron collider.

1.3.8 Decays of Sparticles
In this section, the decay pattern of sparticles in the MSSM is shown. By assuming that R-parity
is conserved, the decays of gluino, squarks, sleptons, charginos and neutralinos are described
qualitatively.
Gluino Decays
The gluino decays can be occurred via either on-shell squarks or virtual squarks. When the
two-body decay, g̃ → qq̃ is possible, this process is dominant.
If the mass of the all squarks is heavier than the gluino mass, then the two-body decay isimpossible. In this case, the three-body decay through virtual squarks occurs: g̃ → qq0 χ̃0 org̃ → qq0 χ̃± .
Squarks Decays
If the two-body decay, q̃ → qg̃ is possible, this process is dominant. If this is not the case,squarks decay to charginos or neutralinos, that is, q̃ → qχ̃± or q̃ → qχ̃0 . In this case, The direct
decay to the LSP such as χ̃01 is favored. For instance, in the case bino is the lightest in somemodels such as mSUGRA, right-handed squarks (q̃R ) decay to χ̃01 (q̃R → qχ̃01 ) dominantly.
However, left-handed squarks (q̃L ) tend to decay to heavier charginos or neutralinos (q̃L →qχ̃02 or q̃L → qχ̃±1 ) because the squark-quark-wino coupling is much bigger than squark-quarkbino coupling. The squark decay to higgsino-like charginos and neutralinos is not very important except for the case stops or sbottoms decay. Stops and sbottoms have sizable Yukawa
couplings.
If two-body decay such as t˜1 → tg̃ or t˜1 → tχ̃01 is open, then the lighter stop may makes twobody decay to chargino (t˜1 → bχ̃± ) or the three-body decay to neutralino (t˜1 → bW χ̃0 ). Even if
these decays are kinematically forbidden, flavor-suppressed decay to charm quarks (t˜1 → bχ̃0 )or four-body decay (t˜1 → b f f 0 χ̃0 ) can be happened. In this case, these decays can be occurredin late and the lighter stop is quasi-stable and hadronized into bound state.
26

CHAPTER 1. INTRODUCTION
Slepton decays
Sleptons decay to leptons plus charginos or neutralinos: l˜ → lχ̃0i , l˜ → νχ̃±i , ν̃ → νχ̃0i andν̃ → lχ̃±i . These decay modes have strength of weak interaction. The direct decays to the lightest
neutralino (l˜ → lχ̃01 and ν̃ → νχ̃01 ) is kinematically allowed when χ̃01 is the LSP. Furthermore,modes of two-body decay to the heavier charginos or neutralinos such as l˜ → lχ̃02 , l˜ → νχ̃±1 ,ν̃ → νχ̃02 and ν̃ → lχ̃±1 also have to be considered.
Right-handed sleptons do not have the coupling to SU(2)L gauginos. For that reason, twobody decay of these sleptons (l˜R → lχ̃01 ) occurs when χ̃01 is the LSP and bino-like. On the other
hand, left-handed sleptons decay to χ̃±1 or χ̃02 if these decay modes are kinematically allowedand χ̃±1 or χ̃02 are wino-like.
Chargino Decays
Charginos are admixtures of charged wino and charged higgsino. Charginos decay to the lighter
chargino or neutralino plus Higgs boson or electroweak gauge bosons (χ̃±i → W ± χ̃0j , χ̃±i →Z 0 χ̃±1 and χ̃±i → h0 χ̃±1 ). Additionally, if sleptons or squarks are sufficiently light, the decays ofcharginos to lepton plus slepton or to quarks plus squarks are open (χ̃±i → lν̃, χ̃±i → νl˜ andχ̃±i → qq̃0 ). However, decay modes to heavier Higgs such as χ̃±i → A0 χ̃±1 ,χ̃±i → H 0 χ̃±1 andχ̃±i → H ± χ̃0j are unlikely because h0 is required to be light
One or more of decay modes of the heavier chargino χ̃±2 is kinematically allowed. Furthermore, if the decay of the chargino which has sizable component of higgsino to third-generation
quark plus squarks are open, this mode is enhanced by top-quark Yukawa coupling.
When two-body decay are forbidden, chargino makes three-body decay such as χ̃±i → f f 0 χ̃0jand χ̃±2 → f f 0 χ̃01 .
Neutralino Decays
Neutralinos are admixtures of bino, neutral wino and neutral higgsino. Hence, decays of neutralinos can be considered in the same way as chargino. Possible decay modes of neutralinoare,• Two-body decays to lighter neutralino or chargino plus Higgs boson or electroweak gaugebosonχ̃0i → Z 0 χ̃0j , χ̃0i → W ± χ̃∓j and χ̃0i → h0 χ̃01
• Two-body decays to sleptons or squarks in the case sleptons or squarks are lightχ̃0 → ll,˜ χ̃0 → νν̃ and χ̃0 → qq̃
iii• Three-body decays when two-body decays are forbidden
χ̃0i → f f χ̃0j and χ̃0i → f f 0 χ̃±j .

27

CHAPTER 1. INTRODUCTION

1.4 Anomaly-Mediated Supersymmetry Breaking
Anomaly mediation of supersymmetry breaking [16, 17] is very attractive for the anomaly mediation is the simplest mechanism since the mediation of supersymmetry breaking. This mechanism occurs in any supersymmetry models.
In the minimal anomaly mediated supersymmetry breaking models, three gaugino masses(M1 ,M2 and M3 ) can be given with the gravitino mass and the gauge coupling at TeV scale:M1 =g21 33( m 3 ),
16π2 5 2(1.34)

g22(m 3 ),(1.35)
16π2 2g2
M3 = 3 2 (−3m 32 ),(1.36)
16π
where g1 ,g2 and g3 are the gauge coupling constants of U(1),S U(2) and S U(3) gauge groups,
respectively. The wino mass is the lightest of the three gaugino mass. Therefore, the lightest
neutralino and chargino are expected to be wino-like. The charged wino becomes slightly heavier than the neutral wino by radiative correction. So the LSP is the lightest wino-like neutralino(χ̃01 ) and the NLSP is the lightest wino-like chargino(χ̃±1 ). The wino-like chargino and neutralinowith near-degeneracy indicate the important phenomenological feature [18]. Near-degenerateparticles are not unusual in SUSY phenomenology. The small mass difference ∆Mχ = Mχ̃±1 −Mχ̃01
leads to the long lifetime of the lightest chargino. The lightest chargino may have a lifetime
long enough to be reconstructed as a charged track with a detector. Figure 1.5 shows the lifeM2 =Figure 1.5: The lifetime of the lightest chargino as a function of the mass difference ∆Mχ [18].
28CHAPTER 1. INTRODUCTION
time of the lightest chargino as a function of the mass difference ∆Mχ . A lifetime of the lightest
chargino having the mass difference which is around the pion mass (140 MeV) corresponds toO(0.1) ∼ O(1) ns. The chargino mass in this analysis is assumed to be around 100 GeV and themass difference of this chargino corresponds to about the pion mass. Hence, the analysis for
AMSB charginos relies on the search for tracks of the lightest charginos.
In this case, χ̃±1 decays into χ̃01 with low-momentum charged particles:χ̃±1 → χ̃01 + π± ,(1.37)

χ̃+1 → χ̃01 + e+ ν (χ̃−1 → χ̃01 + e− ν̄)(1.38)

Neutralino or low-momentum charged particles is hard to be detected. The signal of decaying
chargino in the tracking volume is expected to be exotic. The methods for identifying chargino
track is mentioned in Chapter 4.
In the AMSB scenarios, the universal scalar mass at GUT scale needs to be large otherwise
the scalar leptons becomes tachyons.
Then all of sfermions becomes too heavy to be produced√
in proton-proton collisions at s = 7 TeV. Due to the relatively large masses of squarks, avery precise fine-tuning of parameters is needed to obtain the correct electroweak symmetry
breaking, which solves many serious problems of the standard SUSY models. First, the flavorchanging neutral current and CP-violation problems become very milder thanks to the larger
masses of squarks and sleptons. Second, AMSB gives a natural explanation to no discovery of
proton decay induced by dimension-five operators.

1.4.1 Recent Results of the Long-lived Charginos
The recent search for the long-lived charginos was performed by experiments at LEP2 [19, 20,21]. These analyses are based on the search for events with the ISR photon. The combined
results in the LEP2 search excludes chargino having a mass < 92 GeV[22]. Figure 1.6 shows
the constraint on a long-lived charginos obtained by the combination of the results of the LEP2
experiments.A chargino having a mass Mχ̃±1 < 92 GeV for ∆M ≡ Mχ̃±1 − Mχ̃01 of about 150 MeV
is excluded.
The long-lived chargino search is also performed with the ATLAS detector with 1.0 fb−1 data[23]. The analysis with 1.0 fb−1 data is also based on the search for the chargino track. The
results presented in this dissertation are obtained by the extension of the analysis of 1.0 fb−1 data.
Figure 1.7 shows the constraint on the chargino mass and lifetime with 1.0 fb−1 data. A chargino
having a mass mχ̃±1 < 92 GeVand lifetime 0.5 < τχ̃± < 2.0 ns is excluded in the framework ofminimal AMSB model by the analysis of 1.0 fb−1 data and the results comparable to the LEP2
search are obtained.

1.5 Outline of Dissertation• Chapter 1
In this chapter, physics motivation of this study presented in this dissertation is described.
The recent results concerning to this study is also shown.

29

CHAPTER 1. INTRODUCTION

Figure 1.6: The constraint on long-lived chargino obtained by combination of the results of
LEP2 experiments[22].

301mχ∼± [GeV]

CHAPTER 1. INTRODUCTION

95( mAMSB: m <32TeV, m0<1.5TeV, tanβ=5, µ >0 )
3/2

94

ATLAS
s=7TeV,∫

Observed 95% CL limit-1

Ldt = 1.02 fb

Expected 95% CL limit

93
92
91
90

10-1

1

10

102
τχ∼± [ns]1

Figure 1.7: The constraint on the chargino mass and lifetime with 1.0 fb−1 data. The observed
bound is set at 95% CL and a chargino having a mass mχ̃±1 < 92 GeVand lifetime 0.5 < τχ̃±1 <2.0 ns is excluded [23].
• Chapter 2
The details of the experimental apparatus√in this research are shown. This analysis is performed by using data of pp collision at s = 7 TeV provided by Large Hadron Collider.
The data is collected by the ATLAS detector.
• Chapter 3
As a contributions to the ATLAS collaboration, performance study of the TRT using
cosmic data is performed. The studies of TRT detector are shown here.
• Chapter 4
The methods dedicated for identifying chargino track are newly developed. The characterof chargino track, the methods for identification of chargino and the event topology of
AMSB events are described.
• Chapter 5
The details of object reconstruction of ATLAS data are summarized here. The dataset
and Monte Carlo simulation are also described.
• Chapter 6
In accordance with the event topology, the selection in this search is summarized.
• Chapter 7
The studies on the backgrounds in this analysis are described. The properties of backgrounds are investigated. The control samples extracted by using these properties are
made use of estimation of backgrounds and extraction of signal yields.
31

CHAPTER 1. INTRODUCTION• Chapter 8
The systematic uncertainties in this analysis are investigated.
• Chapter 9
In this chapter, background estimation and signal extraction are performed. For the estimation, simultaneous fitting method is employed. The details of fitting method, fitting
results and validation of the fitting are shown.
• Chapter 10
Using the results of the analysis, the physical interpretation is given in this chapter.
• Chapter 11
The summary of this dissertation is described.

32

CHAPTER 2. EXPERIMENTAL APPARATUS

Chapter 2
Experimental Apparatus
2.1 Large Hadron Collider
Large Hadron Collider (LHC) [24] is a two-ring√superconducting pp accelerator collider which
is designed to have the center-of-mass energy s = 14 TeVand the luminosity is 1034 cm−2 s−1 .
It is installed in the tunnel which is 26.7km long. The main goal of the LHC is the discovery of
the physics beyond the Standard Model.
Various experiments are held at the LHC. Two high luminosity experiments are ATLAS[25] and CMS [26]. These experiments are operated at peak luminosity L = 1034 cm−2 s−1
for proton-proton collision. Two low luminosity experiments are LHCb[27] and TOTEM [28].
LHCb is operated at peak luminosity L = 1032 cm−2 s−1 . TOTEM is operated at peak luminosity
L = 2 ×1029 cm−2 s−1 . Moreover, one heavy ion experiment is ALICE [29]. ALICE is operated atpeak luminosity L = 1027 cm−2 s−1 for lead-lead ion collision. The energy of Pb ions 2.8 TeVper
nucleon.

Figure 2.1: Large Hadron Collider

33

CHAPTER 2. EXPERIMENTAL APPARATUS

2.1.1 Injection Chain
The LHC is supplied with proton beams by the injector chain shown in Figure 2.2. The injector
chain consists of LINAC2, Proton Synchrotron Booster (PSB), Proton Synchrotron (PS) andSuper Proton Synchrotron (SPS).
In the early stage of the injector chain, protons are accelerated by linear accelerator whichis called LINAC2. The proton sources is a duoplasmon. Protons from duoplasmon are sent to
LINAC2, which is a linear accelerator of protons. LINAC2 accelerates protons up to 50 MeV.
Beam current results in 180 mA. Proton beam is sent to the PSB.
The PSB is a synchrotron which consists of four superposed rings of 25m radius. It accelerates protons from LINAC2 up to 1.4 GeVand send them to the PS.
The PS is also a synchrotron which is about 628m circumference. In the PS protons areaccelerated up to 25 GeV.
Proton beam from the PS is sent to the SPS. The SPS is a synchrotron of approximately 7km
circumference. It accelerates protons up to 450 GeVand sent to the LHC ring. The SPS was
running as a proton-antiproton collider called Spp̄S in 1980’s. It contributed to the discovery of
W and Z bosons[30, 31, 32, 33].

Figure 2.2: The LHC injector complex.

34

CHAPTER 2. EXPERIMENTAL APPARATUS

2.1.2 Main Machine Layout
The LHC main ring is installed in the LEP tunnel. LHC consists of eight arcs and eight straightsections. The straight section is 528m long and has experimental insertions. The layout of LHC
lattice is shown in Figure 2.3. Two high luminosity experiments are arranged on the opposite
points:ATLAS is located at Point 1 and CMS is located at Point 5. ALICE and LHCb are locatedat Point 2 and Point 8, respectively. At the remaining four sections there are no beam crossings.
There are two collimation systems at each Point 3 and 7. The insertion at Point 4 are two RF
systems. There are beam dump insertions at Point 6. An arc of LHC consists of 23 arc cells. An
arc cell is 106.9m long and is separated to two half cells of 53.45m long. Each half cell contains
three 14.3m dipole magnet, cryostat and a short straight section (SSS). Two aperture of Ring 1
and Ring 2 are separated by 194mm.
The LHC uses superconducting magnets similarly to the other large accelerator such as
Tevatron or RHIC. The LHC magnet system uses NiTi cables, cools magnets to approximately
4.2K by superfluid helium and operates at magnetic fields above 8T. Almost all of the superconducting magnet is two-in-one structure due to space limitation. The LHC ring has 1232 main
dipole magnets.

Figure 2.3: The layout of the LHC lattice.

2.1.3 The LHC Performance
The designed parameter of the LHC is summarized in Table 2.1.
The number of bunches is 2808. The number of protons per bunches is 1.15 × 1011 . Bunch
length is 7.55cm. Bunch spacing is 25ns.
35

CHAPTER 2. EXPERIMENTAL APPARATUS

Table 2.1: LHC design parameters
Maximum proton energy
7 TeV
Number of bunches
2808
Bunch length (r.m.s)
7.5 cmCircumference of ring
26658.883 m
Frequency of bunch collision
25 ns
Number of collision point
4
Injection energy
450 GeV
Number of particles per bunch
1.15 × 1011
Luminosity
1034 cm−2 s−1
The main goal of the LHC is revealing physics beyond the Standard Model. The LHC
is designed to achieve the center of mass energies of 14 TeV. Designed peak luminosity is1034 cm−2 s−1 . The LHC is operated with the center of mass energies of 7 TeVin 2011.

2.2 The ATLAS Detector
The ATLAS (A Toroidal LHC Apparatus) detector [34, 35] is one of the multi purpose detector
at LHC experiments. Discovery of Higgs particle or the particle which is beyond the Standard
Model such as supersymmetry model is expected in this experiment. The ATLAS detector
covers nearly 4π around the collision point. The height is 25m and the length is 44m. The
overview of the ATLAS detector is shown in Figure 2.4.

Figure 2.4: The overview of the ATLAS detector.

36

CHAPTER 2. EXPERIMENTAL APPARATUS

2.2.1 ATLAS Coordinate
ATLAS uses a right-handed coordinate system. The origin is the nominal interaction point (IP)which is the center of the detector. The z-axis is along with the beam-pipe and the x-axis points
to the center on the LHC-ring.
Cylindrical coordinate (r, φ, z) are used in the transverse plane. The definition of the r,φ ispr = x 2 + y2 ,(2.1)
yφ = arctan( ).
x

(2.2)

Furthermore, the polar angle θ is defined as,rθ = arctan( ).
z

(2.3)

1 E + pzyrap ≡ ln(),
2 E − pz

(2.4)

The rapidity yrap is defined aswhere E and pz are the energy and the momentum in z-direction of a particle.
The pseudo-rapidity η is also often used in collider physics. This variable is the limit of therapidity as the mass of a particle approaches zero and expressed with the polar angle asθη = −ln(tan( )).
2

(2.5)

The region that η > 0 is called A-side, on the other side the region that η < 0 is called c-side.
Furthermore, the distance in the η-φ plane is frequently used in analyses. This variable isdefined as,q∆R ≡(ηi − η j )2 + (φi − φ j )2 ,(2.6)

where ηi( j) and φi( j) are pseudo-rapidity and azimuthal angle of i( j)-th object.

2.2.2 Magnet System
ATLAS has four superconductive magnet subsystem. The magnet system is 22 m in diameterand 26 m in length. A stored energy is 1.6 GJ.
The spacial arrangement of the magnet system is shown in Figure 2.5. The ATLAS magnet
system consists of a central solenoid magnet, a barrel toroid magnet and two end-cap toroid
magnets. A barrel solenoid is aligned on the beam axis. It provides a 2 T axial magnetic field
for the inner detector. A barrel toroid and two end-cap toroids produce a toroidal magnetic
fields of around 0.5 ∼ 1 T for the muon spectrometers.

37

CHAPTER 2. EXPERIMENTAL APPARATUS

Figure 2.5: The overview of ATLAS magnet system.
Central Solenoid Magnet

Field (Tesla)

Figure 2.6 displays the central solenoid. The central solenoid magnet is designed for trackingof charged particles with the inner detector. It is surrounding the inner detector and is alongwith beam axis.
Figure 2.7 shows the dependencies for r and z of the radial and axial magnetic field components. It provides a 2T axial magnetic field for the Inner Detector. The solenoid magnetic
fields drops steeply from nearly 1.8 T at z = 1.7 m to 0.9 T at the end of the cavity of the innerdetector. The flux is returned by the steel of the ATLAS hadronic calorimeter. The inner and2
1.5

Bz at R=1.058 m
Br at R=1.058 m
Bz at R=0.538 m

1

Br at R=0.538 m
Bz at R=0.118 m

0.5

Br at R=0.118 m

0
-0.5
-3

-2

-1

0

1

2

3
z (m)

Figure 2.6: The central solenoid magnet of AT- Figure 2.7: Dependencies for r and z of the radial and axial magnetic field components in the
LAS.
inner detector cavity.
outer diameters of solenoid are 2.46 and 2.56 m, respectively. Its axial length is 5.8 m. The
single layer coil is wound with a NbTi conductor. The radiation length of the magnet results in∼ 0.66 at nominal incidence. The parameters of the central solenoid magnet is shown in Table
2.2.

38

CHAPTER 2. EXPERIMENTAL APPARATUS

Table 2.2: Parameters of the central solenoid
Inner diameter
2.46 mOuter diameter
2.56 mAxial length
5.8 m
Number of coils
1
Mass
5.7 t
Turns per coil
1154
Nominal current
7.73 kAStored energy
0.04 GJ
Peak field in the windings
2.6 T
Field range in the bore
0.9-2.0 T
Toroid Magnet
Figure 2.8 (a) and (b) show the barrel and end-cap magnets, respectively. Table 2.3 is thesummary of the parameters of the toroid magnets.
This system is designed for the precise measurement of muons. The toroidal magnet fields
enable to measure the momentum for low-pT muon by bending for θ-direction. Magnetic field
made by the toroid magnetic system is not uniform. The toroidal magnetic field has not only φcomponent but also z component.

(a) Barrel toroid magnet(b) End-cap toroid magnet

Figure 2.8: Toroid magnets of the ATLAS. (a) is barrel toroid magnet and (b) is end-cap toroid
magnet.
Figure 2.9 shows the field integral as a function of |η| from the innermost to the outermost
MDT layer in one toroid octant. A good magnetic field covers up to |η| ∼ 2.6.
Barrel Toroid The barrel toroid system is shown in Figure 2.8 (a). The overall size of thesystem is 25.3 m length, the inner diameter of 9.4 m and the outer diameter of 20.1 m.
This system consists of eight coils encased in racetrack-shaped and stainless-steel vacuum
vessel. The barrel toroid system is arranged with eight-fold rotational symmetry for beam-axis.

39

CHAPTER 2. EXPERIMENTAL APPARATUS

8

Transition region∫B dl (T ⋅ m)

Table 2.3: Parameters of barrel and end-cap toroid magnets
Property
Barrel toroid End-cap toroid
Inner diameter
9.4 m
1.65 mOuter diameter
20.1 m10.7 mAxial length25.3 m
5.0 m
Number of coils
8
2×8
Mass
830 t
2×239 tTurns per coil
120
116
Nominal current
20.5 kA
20.5 kAStored energy
1.08 GJ
2×0.25 GJ
Peak field in the windings
3.9 T
4.1 T
Field range in the bore
0.2-2.5 T
0.2-3.5 T

Barrel region
6
4

φ=π/8

2

φ=0

End-cap
region

0
-2
0

0.5

1

1.5

2

2.5

|η|

Figure 2.9: Predicted magnetic field integral as a function of |η| from the innermost to theoutermost MDT layer in one toroid octant. The red and black lines corresponds to φ = 0 andφ = π/8, respectively.

40

CHAPTER 2. EXPERIMENTAL APPARATUS
End-cap Toroid The main parameters are listed in Table 2.3 and the end-cap toroid is shownin Figure 2.8 (b). The end-cap toroid system is 5.0 m length, the inner diameter of 1.65 m andthe outer diameter of 10.7 m.
This system is also arranged with eight-fold rotational symmetry.

2.2.3 Inner Detector
The Inner Detector [36, 37] is the innermost detector of the ATLAS detector. The Inner Detector
is designed for the tracking of the charged particles.
Figure 2.10 shows the side-view of the Inner Detector of the ATLAS. The Inner Detector
consists of three sub-detectors, that is, pixel detector, Semiconductor Tracker (SCT) and Transition radiation Tracker (TRT). Figure 2.11 shows the cross section of the Inner Detector. The
Inner Detector is contained within a cylindrical envelope of length ±3512 mm and of radius
1150mm. The Inner Detector is surrounded by the solenoid magnet. The magnetic field up to
the 2T is applied for the Inner Detector in order to track charged particles. The detail of thesolenoid magnet is described in Section 2.2.2.

Figure 2.10: The overview of Inner Detector.
Figure 2.12 and 2.13 show the sensors and structural elements traversed by 10 GeV tracks
in the barrel and end-cap regions, respectively. The charged track at |η| = 0.3 traverses successively the beam-pipe, the three cylindrical pixel layers, the four cylindal double layers ofbarrel SCT and approximately 36 straws contained in the barrel TRT modules. The charged
track at |η| = 1.4 traverses successively the beam-pipe, the three cylindrical pixel layers, four ofthe disks with double layers of the end-cap SCT and approximately 40 straws contained in theend-cap TRT. The track at |η| = 2.2 traverses successively the beam-pipe, only the first of thecylindrical pixel layers, two end-cap pixel disks and the last four disks of the end-cap SCT.

41

CHAPTER 2. EXPERIMENTAL APPARATUS

ID end-plate

3512

CryostatSolenoid coil
PPF1
R1150

712

Radius(mm)

R1066

848

PPB1

2710
R1004

TRT(end-cap)

TRT(barrel)
1

R563
R514
R443
R371
R299

R122.5
R88.5
R50.5
0

2

3

4

5

6

7

8

9 10 11 12

1

2

3

Cryostat
4

5

6

7

8

R644
R560

SCT(barrel)

SCT (end-cap)

R408

R438.8Pixel
support tube

R337.6

Pixel PP1

R275

R229

Beam-pipe

Pixel

R34.3
1299.9934749
400.5 580
1399.7495 650 853.8 1091.5

01771.42115.22505

2720.2z(mm)Envelopes

Pixel

Pixel

45.5<R<242mm|Z|<3092mm

SCT barrel

255<R<549mm|Z|<805mm

SCT end-cap

251<R<610mm
810<|Z|<2797mm

R149.6

R122.5
R88.5

R88.8

R50.5

TRT barrel

554<R<1082mm|Z|<780mm

TRT end-cap

617<R<1106mm
827<|Z|<2744mm

0
0

400.5

495

580 650

Figure 2.11: The cross section of the Inner Detector on r-z plane. Each of the major detector
elements with its active dimensions and envelops is shown.

Figure 2.12: Drawing of the sensors and the structural elements traversed by a charged track of
10 GeV in the barrel region (|η| = 0.3).

42CHAPTER 2. EXPERIMENTAL APPARATUS

Figure 2.13: Drawing of the sensors and the structural elements traversed by a charged track of
10 GeV in the end-cap region (|η| = 1.4 and 2.2).
Pixel Detector
The nearest detector to the beam-pipe is the Pixel detector. The pixel detector has fine granularity. The parameters of the Pixel detector are summarized in Table 2.4.
All 1744 pixel sensors on each module are identical. Operating voltage is about 150V.
Nominal size of each pixel is 50 × 400µ m and there are 47232 pixels on each sensor. However,there are ganged pixels on the sensor due to the reason for the space. The total number ofreadout channels are 46080. In or PbSn are used for bump bonds by which pixel sensors areconnected to the readout channels. The pixel sensor is 63.4 × 24.4mm2 and of approximately
250µm thick.
The pixel detector has three layers in the barrel region and three disks in the end-cap region
on each side. The innermost layer is also called b-layer.
Figure 2.14 (a) and (b) show the barrel stave and the end-cap disk of the Pixel detector,
respectively. There are 112 staves in total for the barrel. 13 pixel modules are mounted on eachstave For the end-cap region, a total of 48 sectors exists and each disk has eight sectors. Six
pixel modules are mounted on each sectors. Totally, there are 144 pixel modules on each side
for the end-cap region.

BarrelLayer-0
Layer-1
Layer-2End-cap (×2)
Disk 1
Disk 2
Disk 3Barrel and both end-cap

Table 2.4: Parameters of the pixel detectorr(mm) Number of staves Number of modules
50.5
22
286
88.5
38
494
122.5
52
676
|z|(mm) Number of sectors Number of modules
495
8×2
48 × 2580
8×2
48 × 2650
8×2
48 × 2
1744

Number of pixels
13.2 × 106
22.8 × 106
31.2 × 106
Number of pixels
2.2 × 106 × 2
2.2 × 106 × 2
2.2 × 106 × 2
80.4 × 106

Particle position can be measured with the accuracy of 12µm on the r − φ plane and the 110µm on z−direction by using Pixel detector.
43

CHAPTER 2. EXPERIMENTAL APPARATUS(a) Barrel module(b) End-cap module

Figure 2.14: Photograph of the pixel detector. (a) and (b) are the barrel module and the end-cap
module, respectively.
Semiconductor Tracker
The Semiconductor Tracker (SCT) is the silicon strip detector. Figure 2.15 show the SCT barrel
module and the end-cap module. SCT sensors are operated at ≈150 V bias voltage. The sensor
thickness is 285 ± 15 µm. Strip pitch of sensor for the barrel is 80 µm while that for the end-cap
varies from 56.9 to 90.4 µm. SCT module is composed of four sensors. There are two sensors
each on the top and bottom side. Two sensor layers of a SCT module are rotated with theirhybrid assemblies by ±20 mrad around the geometrical center of the module. The identificationof a particle position is enabled by two sensor layers of a SCT module.
Table 2.5 is the summary of the parameters of SCT barrel modules. SCT for the barrel
consists of four coaxial cylindrical layers, which are called ID layers 3≈6. The SCT module isarranged on cylindrical layers tilting about 11 degrees. The parameters of the end-cap modules
are also summarized in Table 2.6. SCTs for the end-cap consists of each nine disks. There are2112 barrel module and 1976 end-cap module.
Nominal resolution is ≈ 17µm in lateral plane (r-φ) and ≈ 580µm in longitudinal (z or r).
Table 2.5: Parameters of SCT barrel cylinder layer and the numbers of modules per layer.
ID layers r(mm) Full length (mm) Module tilt angle (degrees) Number of modules
3
299
1498
11.00
384
4
371
1498
11.00
480
5
443
1498
11.25
576
6
514
1498
11.25
672
Total
2112

Transition Radiation Tracker
Transition Radiation Tracker (TRT) [38, 39, 40] consists of many proportional drift tubes. In
addition, TRT can perform particle identification by using Transition Radiation (TR). Figure
2.16 (a) and (b) show the photographs of the TRT detector.
44

CHAPTER 2. EXPERIMENTAL APPARATUS(a) Barrel module(b) End-cap module

Figure 2.15: Photographs of the SCT. (a) and (b) are the barrel module and the end-cap module,
respectively.

Table 2.6: Nominal |z| positions of SCT end-cap disk and the number of SCT modules per disk.
Disk
1
2
3
4
5
6
7
8
9
|z|(mm) 853.8 934.0 1091.5 1299.9 1399.7 1771.4 2115.2 2505.0 2720.2
Outer
52
Middle
40
None
Inner
None
40
None

(a) Barrel detector(b) End-cap disc

Figure 2.16: Photographs of the TRT. (a) is the barrel detector of the TRT. (b) shows a end-cap
disc of the TRT.

45

CHAPTER 2. EXPERIMENTAL APPARATUS
Transition Radiation [41, 42, 43, 44] is a phenomenon that a relativistic particle emits photons when it passes through a boundary of materials whose dielectric constants are different.
When a relativistic particle pass through the boundary of vacuum and the medium with a plasma
frequency ωp , it emits the energy W,
1
WTR = αωp γ,(2.7)
3
where α is the fine structure constant and γ is the Lorentz factor of the particle. The plasma
frequency ωp is defined as,
s
Ne e2
,
0 me

ωp =

(2.8)

where, Ne , 0 and me are the electron density of the medium, the dielectric constant and theelectron mass, respectively. WTR is proportional to the Lorentz factor of a charged particle.
Transition radiation is made use of the identification of electron which has a large γ. Transition
radiation is extremely forward peaked within an angle θ0 ∼ 1/γ.
The diameter of a drift tube is 4 mm. Anode wire is tungsten of 30 µm diameter which isgold-plated of about 0.5 µm thickness. Cathode is a tube of approximately 60 µm thickness
which is made from carbon, aluminum and Kapton. The straw cathodes is operated at a highvoltage of 1530 V with the gas mixture of Xe : CO2 : O2 = 70 : 27 : 3. A gas gain is
2.5 × 104 . Polypropylene is used for the radiator of TRT. Figure 2.17 shows a layout of a barrel
module. In barrel region, the radiator consists of the sheet of 3mm thickness which is made fromradiator fiber of approximately 19 µm diameter. The density of the sheet is about 0.06 g/cm3 .
These sheets are made holes in accordance with the geometry of TRT drift tubes and drift tubes
penetrates these sheets. On the other hand, the radiator in the end-cap region is made by pilingup foils made by polypropylene of 17 µm thickness.

Figure 2.17: Layout of a barrel module.
Table 2.7 shows the main parameters of the TRT detector. In the barrel region, drift tubes
are arranged along with z-axis. 1441mm drift tube is divided at its center in order to reduce46

CHAPTER 2. EXPERIMENTAL APPARATUS
an occupancy. Figure 2.18 shows the cross-section of the TRT barrel detector. There are three
types of modules which are called Type-1, Type-2 and Type-3. They are consists of 19, 24, 30
drift tube layers, respectively. Moreover, they are divided into 32 modules in φ-direction. The
innermost nine layers are not active in |z| < 400 mm of the Type-1 module in order to reduce an
occupancy.
In this analysis, Type-1, Type-2 and Type-3 are referred as inner module, middle moduleand outer module, respectively.

Figure 2.18: The cross-section of the barrel detector.
TRT in the end-cap region consists of disks in which drift tubes are arranged along withr-direction. There are two types for the end-cap detector. They are called Type-A and Type-B.
They differ in the z spacing of these plates. In both modules each of these layers contains 768
straws of approximately 37 cm length. Both Type-A and Type-B module consists of eight disks
layers.
Table 2.7: Parameters of TRT detector. The innermost nine layers of Type-1 is inactive in theregion |z| < 400 mm.
|z|min |z|max
rmin
rmax Number of Number of straws per(mm) (mm) (mm) (mm)moduleslayersmoduleBarrel
0
780
554
1082
96
73
52544
Type-1(inner) 400 712.1 563
624
32
9
329
Type-1(outer)
7.5
712.1 625
694
10Type-2
7.5
712.1 697
860
32
24
520
Type-37.5
712.1 863
1066
32
30
793
End-cap
827
2744
615
1106
20
160
122880Type-A
848
1705
644
1004
12
8
6144
Type-B
1740 2710
644
1004
8
8
6144
Figure 2.19 (a) and (b) show the pulse height of the drift tubes for 20 GeVpions and electrons, respectively. There is a bump around 7 keVfor electrons. It corresponds to the X-ray
due to the transition radiation. There are two threshold in TRT for particle identification. The
first is for discriminating a energy loss of a particle ionization. The value of the threshold is47

CHAPTER 2. EXPERIMENTAL APPARATUS(a) Pions(b) Electrons

Figure 2.19: The pulse height of the TRT drift tube. (a) shows the pulse height of the
20 GeVpions while (b) shows that of the 20 GeVelectrons.
about 0.2 keV. The second is for identifying electrons which emits TR photons. The value ofthe threshold is set at about 6 keV.
The studies for the TRT performance using cosmic data is mentioned in Chapter 3.

2.2.4 Calorimetry
Figure 2.20 shows the cutaway view of the calorimeter system of the ATLAS detector. Calorimeters are surrounding the Inner Detector and these system covers the range |η| < 4.9. Calorimeter system of the ATLAS has three calorimeters, that is, electromagnetic (EM) calorimeter,
hadronic calorimeter and forward calorimeter.
Electromagnetic Calorimeter
The electromagnetic(EM) calorimeter are divided into three parts, a barrel part (|η| < 1.475)
and two end-cap parts (1.375 < |η| < 3.2). The total thickness of the EM calorimeter is morethan 22 radiation length (X0 ) in the barrel regions and more than 24X0 in the end-cap region.
The geometry of the electromagnetic calorimeter for absorber and electrode is a particulargeometry. The electromagnetic calorimeter has an accordion geometry for both the barrel andend-cap electromagnetic calorimeter as shown in Figure 2.21. This geometry enables to achieve
full coverage in φ direction. In the barrel, the accordion waves are axial and run in φ-direction,on the other hand, in the end-cap the accordion waves are parallel to the radial direction and run
axially. The barrel electromagnetic calorimeter separates to two half-barrels.
The main parameters of EM calorimeter is summarized in the Table 2.8. One half-barrel
covers a region z > 0, 0 < η < 1.475 and the other half-barrel covers a region z < 0, −1.475 <η < 0. The length of a half-barrel is 3.2m and the inner and outer diameters are 2.8m and 4m,
48

CHAPTER 2. EXPERIMENTAL APPARATUS

Figure 2.20: The overview of calorimeter.

Figure 2.21: A cross section of LAr electromagnetic calorimeter.

49

Figure 2.22: The geometry of LAr electromagnetic calorimeter at η=0. The accordion geometry is chosen for the electromagnetic calorimeter of ATLAS.

CHAPTER 2. EXPERIMENTAL APPARATUS

Table 2.8: The main parameters of EM calorimeter of the ATLAS.
BarrelEnd-cap
η coverage
Presampler|η| < 1.52
1.5 < |η| < 1.8
Calorimeter 1st layer|η| < 1.475
1.375 < |η| < 3.2
Calorimeter 2nd layer|η| < 1.475
1.375 < |η| < 3.2
Calorimeter 3rd layer|η| < 1.35
1.5 < |η| < 2.5
Granularity ∆η × ∆φ versus η
Presampler
0.025×0.1|η| < 1.52
0.025×0.1
1.5 < |η| < 1.8
Calorimeter 1st layer
0.025/8×0.1|η| < 1.40
0.050×0.1 1.375 < |η| < 1.425
0.025×0.025 1.40 < |η| < 1.475
0.025×0.1
1.425 < |η| < 1.5
0.025/8×0.1
1.5 < |η| < 1.8
0.025/6×0.1
1.8 < |η| < 2.0
0.025/4×0.1
2.0 < |η| < 2.4
0.025 ×0.1
2.4 < |η| < 2.5
0.1 ×0.1
2.5 < |η| < 3.2
Calorimeter 2nd layer 0.025×0.025|η| < 1.40 0.050×0.025 1.375 < |η| < 1.425
0.075×0.025 1.40 < |η| < 1.475 0.025×0.025
1.425 < |η| < 2.5
0.1×0.1
2.5 < |η| < 3.2
Calorimeter 3rd layer 0.050×0.025|η| < 1.35 0.050×0.025
1.5 < |η| < 2.5
respectively. The accordion-shape absorber are made of lead plates. A half-barrel consists of1024 absorbers and readout electrodes. The electrode is placed in the middle of gap with thehoneycomb spacers. Each half-barrel is divided into 16 modules for φ and covers a ∆φ = 22.5◦ .
The total-thickness is of a module is at least 22X0 . For 0 < |η| < 0.8 the total thickness is from
22X0 to 33X0 and for 0.8 < |η| < 1.3 from 24X0 to 33X0 . A module has three layers in depth(front, middle and back) as shown in Figure 2.22.
Presampler is s separated thin liquid-argon layer. It is 11m in depth. It provides shower
sampling in front of the electromagnetic calorimeter. This is made of 64 azimuthal sectors(32sectors per half-barrel). Each sector is 3.1m long and provides a covering ∆η × ∆φ of 1.52 ×
0.2.
The EM end-cap calorimeters consist of two wheels. Each wheel is 63 cm thick and the innerand outer radii are 330 m and 2098 mm. It covers the region 1.375 < |η| < 3.2. Each end-cap
is made of two co-axial wheels. Furthermore, this end-cap is divided into eight wedge-shaped
modules. Each end-cap in the outer wheel has 768 absorbers with the electrodes interleaved
and each end-cap in the inner wheel has 256 absorbers. The total thickness is greater than 24 X0
except for the region |η| < 1.475. The total thickness is from 24 X0 to 38 X0 for 1.475 < |η| < 2.5
and from 26X0 to 36X0 for 2.5 < |eta| < 3.8. Each end-cap presampler consists of 32 identicalsectors. The granularity of the presampler is ∆η × ∆φ = 0.025 × 0.1. This presampler is madeof two, 2mm thick, active liquid-argon layers.

50

CHAPTER 2. EXPERIMENTAL APPARATUS
Hadronic Calorimeter
Hadronic calorimeter has two calorimeter systems; tile calorimeter and LAr hadronic end-cap
calorimeter. Hadronic calorimeter system is placed at the outer region of the electromagnetic
calorimeter in order to measure the energy of hadrons.
The tile calorimeter consists of three parts; one central barrel and two extended barrels. The
tile calorimeter covers the range 0 < |η| < 1.7. For the range 1.7 < |η|, the LAr hadronic end-cap
calorimeter is arranged.
Tile Calorimeter The tile calorimeter is placed outside the EM calorimeter. Figure 2.24
shows the tile calorimeter. The tile barrel calorimeter covers the range |η| < 0.8 and the tile

Figure 2.23: Schematic showing of the tile Figure 2.24: Tile calorimeter of the ATLAS.
calorimeter.
extended barrel covers the range 0.8 < |η| < 1.7. The tile calorimeter consists of steel andscintillating tile. Steel is used as the absorber and scintillating tile is used as the active material.
The inner radius is 2.28m and the outer radius is 4.25m. This calorimeter is divided into
three parts in layers in depth. These layers of tile barrel are roughly 1.5λ, 4.1λ and 1.8λ thickand these of tile extended barrel are roughly 1.5λ, 2.6λ and 3.3λ thick. The total thickness oftile calorimeter at η = 0 is 9.7λ.
The geometry of the assembled module is sketched in the Figure 2.23. The tile scintillator isoriented radially and normal to the beam axis. This scintillator is combined with a wavelengthshifting tube on the edge of tile. The scintillating tile is read out from two sides with wavelength
shifting fiber and into two photomultiplier tubes.
This calorimeter is a sampling calorimeter.
LAr Hadronic End-cap Calorimeter The hadronic end-cap calorimeter is shown in Figure
2.25. This calorimeter consists of two parts of detector. It uses copper as the absorber andliquid argon as the active material. The hadronic end-cap calorimeter (HEC) is a copper and
LAr sampling calorimeter. It covers the range 1.5 < |η| < 3.2.

51

CHAPTER 2. EXPERIMENTAL APPARATUS

Table 2.9: The main parameters of scintillator tile calorimeter of the ATLAS.
Barrel Extended barrel
η coverage|η| < 1.0
0.8 < |η| < 1.7
Number of layers
33
Granularity ∆η × ∆φ 0.1 × 0.1
0.1 × 0.1
Last layer
0.2 × 0.1
0.2 × 0.1
The HEC consists of two wheels in each end-cap: a front wheel (HEC1) and a rear wheel(HEC2). The wheels are cylindrical with an outer radius of 2030 mm. Each of four HEC wheels
consists of 32 identical modules. Figure 2.26 shows the schematic view of a module of the LAr
hadronic end-cap calorimeter. The modules of the front wheels are made of 24 copper plates of
25 mm thick. In the rear wheels, module consists of 16 copper plates of 50 mm thick. The gap
between the the plates is 8.5 mm thickness. The size of the readout cells is ∆η × ∆φ = 0.1 × 0.1

Figure 2.25: Photograph of the assembled LAr Figure 2.26: Schematic view of the LAr
hadronic end-cap calorimeter. A cutaway shows
hadronic end-cap calorimeter.
the readout and active pad.
for |η| < 2.5 and ∆η × ∆φ = 0.2 × 0.2 for |η| ≥ 2.5. The main parameters of HEC is summarized
in the Table 2.10.
Table 2.10: The main parameters of LAr hadronic calorimeter of the ATLAS.
LAr hadronic end-cap calorimeterη coverage
1.5 < |η| < 3.2
Number of layers
4
Granularity ∆η × ∆φ 0.1×0.1
1.5 < |η| < 2.5
0.2×0.2
2.5 < |η| < 3.2

52

CHAPTER 2. EXPERIMENTAL APPARATUS
Forward Calorimeter
The forward calorimeter (FCal) covers over 3.1 < |η| < 4.9. The forward calorimeter consistsof three modules. One is the electromagnetic module (FCal1) and the other modules are thehadronic modules (FCal2 and FCal3). Figure 2.27 shows the schematic view of the forward
calorimeter.
It has a design with very small liquid-argon gaps, which have been obtained by employing anelectrode structure of small-diameter rods. These rods are centered in tubes which are oriented
parallel to the beam. The liquid-argon gaps are smaller than 2 mm. The FCal1 layer consistsof copper plates stacked one behind the other. An electrode consists of a co-axial copper rod
and the copper tube separated by a precision, radiation-hard plastic fiber wound around therod. Figure 2.28 shows the arrangement of electrodes and the effective Moliére radius for themodules.
The hadronic modules FCal2 and FCal3 is employing tungsten as a absorption material. The
modules consists of two copper end-plates, each 2.35 cm thick, which are spanned by electrodestructures. The main parameter is shown in the Table 2.11.

Figure 2.27: Schematic view of the LAr hadronic end-cap calorimeter. A cutaway shows thereadout and active pad.

Figure 2.28: The structure of the electrode of FCal1. The Moliére radius which is represented
R M is shown with magenta disk.

53

CHAPTER 2. EXPERIMENTAL APPARATUS

Table 2.11: The main parameters of forward calorimeter of the ATLAS.
LAr forward calorimeterη coverage
3.1 < |η| < 4.9
Number of layers
3
Granularity ∆x(cm) × ∆y(cm) FCal1
0.1×0.1 3.15 < |η| < 4.30
∼ four times finer 3.10 < |η| < 3.15,
4.30 < |η| < 4.83
FCal2
3.3×4.2 3.24 < |η| < 4.50
∼ four times finer 3.20 < |η| < 3.24,
4.50 < |η| < 4.81
FCal3
5.4×4.7 3.32 < |η| < 4.60
∼ four times finer 3.29 < |η| < 3.32,
4.60 < |η| < 4.75

2.2.5 Muon Spectrometer
Muon spectrometer is the outermost part of the ATLAS detector. Muon spectrometer is designed to detect the charged particle which penetrates calorimeter of the ATLAS, especiallymuon. Figure 2.29 shows the whole Muon Spectrometer of ATLAS. It consists of four parts

Figure 2.29: The overview of Muon Spectrometer of ATLAS.
of sub-detector which are Resistive Plate Chamber(RPC), Monitored Drift Tube(MDT), Thin
Gap Chamber(TGC) and Cathode Strip Chamber(CSC). It plays a roll to trigger on the outgoing charged particle and to give precise position and momentum of that. This system covers
the pseudorapidity range |η| < 2.7 to measure the momentum of particle and covers the range,|η| < 2.4 to measure the position Tracking chambers are located between and on the eight-coil
54

CHAPTER 2. EXPERIMENTAL APPARATUS
superconducting toroid magnet for barrel and in front of and behind the end-cap toroid magnet
for end-cap.
For end-cap region, there are three types of wheels. The inner wheel is refereed as the small
wheel. TGC and CSC are mounted on the small wheel. The middle wheel is called the big
wheel or EM-wheel . TGC and MDT are mounted on it. The outer wheel is refereed as EO.
Only MDT is mounted on EO.

Figure 2.30: The cross section of Muon Spectrometer on r-z plane.

Table 2.12: Parameters of the four sub-detector of muon spectrometer.
Resolution (RMS) in
Hits per track
Numbers ofDetector Main Function
z or rφtbarrel end-cap chambers channels
RPC
Trigger
10mm (z) 10mm 1.5ns
6—544
359000MDT
Tracking
35µm (z)
—
—
20
20
1088
339000TGC
Trigger
2-6mm (r) 3-7mm 4ns—
93588
318000CSC
Tracking
40µm (r)
5mm
7ns
—
4
32
30700

Resistive Plate Chamber
Resistive Plate Chamber (RPC) is the muon trigger system in the barrel. Figure 2.31 shows aphotograph of RPC.
RPC has good space resolution and time resolution.
RPC is a no wire chamber and a gaseous parallel electrode-plate detector. There are tworesistive plates which are kept 2mm apart with insulating spacer. The electric field between theplates is about 4.9 kV/mm. Due to the electric field, the avalanche occurs along the track ofparticle towards anode.
There is gas in the gap of plates. The gas mixture is C2 H2 F4 /Iso − C4 H10 /SF6 (94.7/5/0.3).
A chamber of RPC consists of two rectangle detector which are called units. Each unit
consists of two detector layer and these are called gas volume. Gas volume has two type of
strips and signals are read out from these strips. The two types of strips are the φ-strips and the55

CHAPTER 2. EXPERIMENTAL APPARATUS
η-strips. As these name suggest, The φ-strips and the η-strips measure the φ-coordinate and theη-coordinate, respectively.

Figure 2.31: Photograph of the RPC.

Figure 2.32: Cut-away view of the barrel
muon system. RPC is marked with color.

Monitored Drift Tube
Monitored Drift Tube (MDT) consists of many layers of drift tubes and serves as a muon tracker.
MDT covers |η| < 2.7 except for the inner most layer. MDT is replaced for Cathode Strip
Chamber in 2 < |η| < 2.7.
A diameter of a drift tube constituting MDT is 29.970 mm. Tube is made from aluminum.
Wall thickness is 0.4 mm. Wire diameter is 50 µm. Material of wire is gold-plated tungsten andrhenium. Gas mixture is Ar/CO2 /H2 O(93/7/≤1000pm). Gas pressure is 3 bar and gas gain is
2 × 104 . Wire potential is 3080 V. Maximum drift time is about 700 ns and average resolution
per tube is about 80 µm.
Chamber is rectangular for the barrel and is trapezoidal for the end-cap. The length of tube
in the barrel chamber is identical while the length in the end-cap varies radially.MDT chambers
consists of two collections of drift tubes. This collection is called multi-layer. Two multi-layers
are separated by mechanical spacers.
Alignment of tubes is needed to maintain a good precision in order to achieve its inherent
resolution. For that, drift tubes are mounted on the support frame made from aluminum. Additionally, internal chamber alignment is also monitored with four alignment rays. Two alignment
rays are parallel to tubes. The other two rays are diagonal. By using this, deformation of a fewµm can be measured. This system works in production, installation and operation of ATLAS.
Thin Gap ChamberThin Gap Chamber (TGC) is a multi wire proportional chamber. The photograph of TGC
mounted on the big wheel of the muon spectrometer is shown in Figure 2.34. TGC serves twofunctionality in the end-cap muon detector. One is working as a detector for muon trigger andthe other one is giving the information of φ-direction in order to complement the informationof muon position obtained from MDT.
56

CHAPTER 2. EXPERIMENTAL APPARATUS

Figure 2.33: The photograph of drift tubes of MDT.

Figure 2.34: The photograph of the big wheels of the muon spectrometer.

57

CHAPTER 2. EXPERIMENTAL APPARATUS
The character of TGC structure is that the distance from wire to cathode is smaller than thatfrom wire to wire. The distance from wire to cathode is 1.4 mm while the distance from wire to
wire is 1.8 mm.
The gas mixture is CO2 /n-C5 H12 (n-pentane). CO2 is 55% and n-pentane is 45%. A gas
gain is about 3 × 105 .
TGC has good time resolution for most of muons because electric field around wire is highand the distance from wire to wire is small. However, for muons incidenting normally to detectors and passing halfway between wires, the drift time becomes longer due to vanishing a drift
fields.
TGC is mounted on two concentric discs. Outer disc (end-cap one, the big wheel) covers
1.05 ≤ |η| ≤ 2.4. TGC consists of seven layers in the big wheels, that is, one triplet and two
doublets. On the other hand, inner disc (forward one, the small wheel) covers 1.92 ≤ |η| ≤ 2.4.
On the small wheel, there are two TGC layers.
The structure of TGC detector is shown in Figure 2.35. The TGC consists of wire plane,cathode plane, strip plane, shields and honeycomb support structures. The cathode plane is
1.6mm thick plate. It is coated with graphite and facing to wire and copper cladding is outside.
The gas volume including wire plane and two cathode is called chamber. A collection of
Two (three) chamber for doublet (triplet) is called a unit. TGC on the Big Wheel is divided
into twelve sectors for φ-direction. Furthermore, a sector in the outer ring is separated into
four module. A sector in the inner ring is separated into two module. They are referred as EI(end-cap region) and FI (forward region).

Figure 2.35: The structure of TGC.

Cathode Strip Chamber
Cathode Strip Camber(CSC) is multi wire proportional chamber.
The limitation of the safe operation for MDT is 150 Hz/cm2 . MDT is replaced for CSC
in |η| > 2 for this reason. The distance from interaction point to CSC is about 7 m. Inner
radius is 881 mm and outer radius is 2081 mm. This corresponds to the coverage of rapidity,
2 < |η| < 2.7. CSC has high spacial and time resolution. CSC has also high-rate capability
which is up to 1000 Hz/cm2 .
CSC system is divided into large and small chambers in φ-direction. CSC consists of two
discs. One is made of eight large chambers while the other one is made of eight small chambers.
58

CHAPTER 2. EXPERIMENTAL APPARATUS
A chamber consists of four plane. Therefore, four dependent measurements in η and φ can beobtained.
Wires are along radial direction. Two cathodes are segmented to strips. Direction of one
cathode strips is orthogonal to wires and direction of the other one is parallel to the wire. Operating voltage is 1900V. Anode wire diameter is 30 µm. Gas gain is 6 × 104 . Gas mixture is
Ar/CO2 (80/20). Total ionization for nominal track is 90 ion pairs. A distance from anode towire is 2.5mm. Anode wire pitch is 2.5mm. The position of a track is determined by interpolating the induced charge of neighboring strips. Position resolution is about 60 µm/plane.

Figure 2.36: A small wheel of the muon spectrometer. The inner and outer detector mounted
on the small wheel are the CSC and the MDT, respectively.

59

CHAPTER 2. EXPERIMENTAL APPARATUS

2.2.6 Forward Detector
Three sub-detectors are located in the very forward region in addition to the main ATLAS
detector. These are LUCID, ZDC and ALFA. These detectors are located for providing goodcoverage.
LUCID (Luminosity measurement using Čerenkov Integrating Detector) is the main relative
luminosity monitor. It is located at a distance of 17 m from the interaction point.
ZDC (Zero-Degree Calorimeter) is 140 m away from the interaction point. This location is
the point where the LHC beam-pipe separates to two pipes. The main purpose of ZDC is for
detecting forward neutron in heavy-ion collision.
ALFA (Absolute Luminosity For ATLAS) consists of scintillating-fiber trackers in Roman
pots. The distance between ALFA and the interaction point is 240 m. ALFA is the absolute
luminosity detector.
The LUCID detector
LUCID (Luminosity measurement using Čerenkov Integrating Detector) is used for online luminosity monitoring. This detector serves as a relative luminosity detector. LUCID measuresinelastic pp scattering in forward region and monitors instantaneous luminosity and beam conditions.
Multiple pp interactions occur in bunch-crossing at LHC design luminosity. In order tomeasure luminosity, the number of interaction per bunch-crossing must be known. LUCID
is based on that the number of interaction in bunch-crossing is proportional to the number ofcharged particle. LUCID is required for good-acceptance for minimum-bias, sufficient time
resolution to measure individual bunch-crossing, tolerance for very-high radiation and ability
to measure each charged particle from the interaction point. There are two LUCID detector
for each end-cap. These are located at ±17 m from the interaction point. The radial distanceis about 10 cm from beam-pipe and it corresponds to |η| ≈ 5.8. LUCID consists of twenty
aluminum tubes surrounding beam-pipe. These tubes are 1.5 m long. The diameter of the tube
is 15 mm. These tubes are in gas vessel. C4 F10 gas is filled in the vessel with 1.2-1.4 bar.
Čerenkov light is emitted when charged particles traverse the tube. Čerencov light is detected with photomultiplier tubes. The signal amplitude from photomultiplier tubes is used for
identification for the number of charged particles per tube.
Furthermore, for the studies for upgrade the detector after several years of LHC operation,a different readout scheme is used. A winstone cone, which is parabolic shape and designed tomaximize incoming rays, is attached to the end of Čerenkov tube and the light is collected toa bundle of 37 fused silica fibers with 0.8 mm diameter. In this manner, four of twenty tube isreadout with fibers.
The Zero-Degree Calorimeter
The main purpose of Zero-Degree Calorimeter(ZDC) is to measure the forward neutron inheavy-ion collision. It locates at ±140 m from the interaction point. There are four modules per arm; one module is the electromagnetic module and the other modules are the hadronic
module. The electromagnetic module has 29 radiation length. The hadronic modules has 1.14
interaction length per module.
60CHAPTER 2. EXPERIMENTAL APPARATUS
There are eleven tungsten plates in the electromagnetic module. These plates are perpendicular to beam. These tungsten plates are extended with steel plates of 290mm long. 95 quartz
rods of 1.0 mm diameter penetrate the tungsten plates parallel to beam. These rods are bent
upward and viewed by the multi-anode phototube’s. Čerenkov light emitted from the shower ofincident particles are measured. The position of the rod corresponds the position of the incident
particle. The intensity of the light reflects the energy of the incident particle.
There are quartz strips between plates. These strips are viewed by photomultiplier tubes
from above via air light-guide. These strips are actually rows of quartz rods. In order to distinguish from rods for position-measurement, they are called strips. The purpose of strips is forthe improved measurement of the energy of the incidenting particle.
The structure of hadronic module is similar to that of electromagnetic module. But there areseveral differences. The electromagnetic module maps each position-measuring rods onto one
pixel of the multi-anode phototube. On the other hand, the hadronic module maps a group offour rods onto the individual phototube. Furthermore, not all hadronic module have positionsensing rods. There are one module having position-sensing rods per arm.
The ALFA Detector
ALFA (Absolute Luminosity For ATLAS) is a detector for measuring the absolute luminosity.
The absolute luminosity at hadron collider has been measured by using elastic scattering at
small angles. ALFA is also based on this method. Optical theorem says that the total crosssection is obtained from the amplitude of inelastic scattering in the forward region. The absolute
luminosity can be obtained by using this theorem.
A detector must be placed far from the interaction point and as nearest to beam as possible
for that. The Roman pots techniques are used in the past experiments. Also ATLAS experiment
adopt this method. Roman pots are located ±240 m away from the interaction point. There
are two Roman pots on each side separated by 4 m. There is a scintillating-fiber tracker in the
Roman pot.

2.2.7 Trigger and Data Acquisition
Overview of Trigger System
The ATLAS trigger consists of three level triggers; Level-1 (L1), Level-2 (L2) and Event Filter(EF).Level-2 trigger and event filter is also called the high level trigger (HLT). Level-1 trigger
is implemented in the detector and works with the hard-ware. The high level trigger is using
computer and network hardware.
Event rate is extremely high at the bunch-crossing with designed parameter of LHC. In
order to trigger event to see, multi-stage triggers are used. Figure 2.37 show the diagram of dataacquisition of the ATLAS.
The L1 trigger is required to make a decision in less than 2.2 µs and to lessen the trigger rate
to about 75 kHz. Then, the L2 trigger uses the L1 seed, which is defined as Region of Interest(RoI) defined by the L1 trigger. The L2 trigger is required to reduce the trigger rate to 3.5 kHz.
Finally, the information is passed to EF trigger. The EF uses the whole detector informationand is required to reduce the rate up to 200 Hz.

61

CHAPTER 2. EXPERIMENTAL APPARATUS

Figure 2.37: The diagram of data acquisition system.

62

CHAPTER 2. EXPERIMENTAL APPARATUS
Level-1 Trigger
The L1 trigger looks for high transverse-momentum (pT ) muons, photons, electrons, jets, taus
decaying into hadrons, large missing transverse energy (ETmiss ) and large total transverse energy.
The diagram of L1 trigger scheme is shown in the Figure 2.38. L1 trigger selects events initiallyand this is performed by using the information from the detectors. For the trigger decision,
calorimeter and muon chamber are used. All L1 trigger is made a decision at Central Trigger
Processor(CTP). When a event is passed in L1 trigger, the information for the positions oftrigger objects are sent to L2 trigger as RoI. An important role of L1 is to identify a bunchcrossing of interest.
Calorimeters

Muon detectors

L1 trigger
Calorimeter triggers

EM



Jet

Muon trigger

Emiss
T

µ

ET

Central trigger
processor

Timing, trigger andcontrol distribution

Regionsof-Interest

Detector front-ends

L2 trigger

DAQ

Figure 2.38: The diagram of L1 trigger flow.
The interval of bunch-crossing is very short and it makes challenging to make a L1 decision.
For calorimeter triggers, the signals of calorimeter are long and over times for some bunchcrossing. For muon triggers, time of flight of muons exceeds the time for the interval of bunchcrossing due to the location of the muon spectrometer. Therefore, the L1 latency, which is thetime between pp-collision and L1 trigger decision, needs to be short as possible. The L1 latency
is designed to be less than 2.5µs.
The L1 calorimeter trigger The L1 calorimeter trigger is called L1Calo. L1Calo is based on
the information from the all calorimeters. This trigger is used to identify high-ET objects suchas jets, photons, electrons, taus and large ETmiss and large ET events. Furthermore, the triggers
on the events with large sum-ET of jets is available.
63

CHAPTER 2. EXPERIMENTAL APPARATUS
The L1Calo uses the information of 7000 analogue trigger tower. The granularity of this is
0.1 × 0.1 in ∆φ × ∆η in most region and larger in the other higher |η| region. In order to makea L1 trigger decision, both electromagnetic calorimeter and hadron calorimeter are used. These
information are sent to CTP within 1.5 µs after an event occurred. The total latency is about
2.1 µs.
The L1Calo system is located at off-detector. The Pre Processor digitizes analogue signal
and associate to bunch-crossing of interest. The trigger algorithm uses the look-up table forcalculation of calorimeter ET . Data are sent to the Cluster Processor and the Jet/Energy-sum
Processor in parallel. The Cluster Processor identifies electron, γ and τ by requiring certain ET
threshold and isolation criteria.The Jet/Energy-sum Processor uses jet trigger elements, whose
granularity is 0.2×0.2 in ∆φ×∆η and identifies jets. It also calculates the sum of ET and missing
transverse energy. Once L1 Accept (L1A) decision is made, data are sent to the data acquisition
system. These data, calculation and trigger results are also used for monitoring or verificationof trigger. The information of Jets, τ, and EM cluster is sent to RoI builder.

The L1 muon trigger The L1 muon trigger is performed with the information from muonchambers. RPC is used for muon in the barrel region, while TGC is used for end-cap region. The
timing accuracy is required for muon detector to identify a bunch-crossing which has muons.
The principle for finding muons is performed by requiring coincident hits in different trigger
station in the road, that is,searching for tracks originating from the interaction point penetrates
a detector.
RPC is used for the muon barrel trigger. RPC covers the range of |η| < 1.05. If there are hits
in the second RPC doublet (the pivot plane), the trigger algorithm searches for the hits in thefirst RPC doublet by requiring that there are hits in the road made by drawing a line from theinteraction point to the hit in the pivot plane. The center of the road is the hit in the pivot plane
and the width depends on the transverse momentum of muon. The higher the pT of muon is,
the narrower the width of road become. A 3-out-of-4 coincidence hits are required for trigger
decision. This suppresses the fake tracks which is made from noise hits. For high-pT muons,
RPC3 is also used with the trigger information of RPC1 and RPC2. The algorithm works as well
as low-pT muons and the center of the road is determined. After that, a 1-out-of-2 coincident
hits in RPC3 is required in addition to trigger pattern for low-pT muons. The latency is about
2.1 µs.
TGC is used for the muon end-cap trigger. The coverage is 1.05 < |η| < 2.4 except for
the innermost layer on the small wheel, which covers the range 1.05 < |η| < 1.92. Eachtrigger chamber plane consists of a wheel of eight octets of chambers symmetric in φ. Eachoctant is divided radially into ’end-cap region’ and ’forward region’. The algorithm works byextrapolating hits in the pivot plane to the interaction point. The road is made by a track ofinfinite momentum muon. Coincidence signals are generated separately in R and φ. A 3-outof-4 coincidence hit is required for the two doublet planes on the big wheel for both wires andstrips. A 2-out-of-3 coincidence hit is required for triplet wire plane and 1-out-of-2 coincidence
hit is required for triplet strip plane. In order to make final decision R and φ coincidence signals
are merged and the information of EI/FI chambers are also used. The latency is 2.1µs.

64CHAPTER 2. EXPERIMENTAL APPARATUS
Level-2 Trigger
Events passed for L1 trigger is transferred to the Level-2 (L2) trigger. The RoI builder receive
the RoI information from the different sources within the L1 trigger and merges them into thesingle data structure. It is at the boundary between the L1 and the L2 trigger systems andoperated at the L1 trigger rate.
The principle component of the L2 trigger is the L2 processing farm. The L2 processing
farm executes event selection. This system is designed to perform to execute event selection
with an average throughput per farm node of about 200 Hz. The HLT starts from the RoIs
delivered by the L1 trigger and applies trigger decisions. A list of physics signatures whichis called trigger chains, implemented event reconstruction (feature extraction) and selection
algorithms are used to build signature for all HLT steps. Feature extraction uses detector dataof RoI in order to identify the features of events such as tracks, calorimeter cluster, and so on.
Then, this feature is checked to meet the criteria e.g. shower shape, ET threshold, et cetra.
Whether the event is rejected or not is decided by the validity of signature considering pre-scale
and pass-through factor. The full data set and RoI information are kept if the event fulfill the L2
trigger selection.
Event Filter
Event filter (EF) reconstructs and analyzes events of ATLAS unlike the L2 trigger. The EF has
the processing farm. The processing farm is a collection of processing nodes which receive
tasks and process events. The steering of the event selection is the same as the L2. For those
events passing the selection criteria, a subset of the data generated during the event analysis isadded to the event data structure. An integral part of the selection process is the classificationof the events according to the ATLAS physics streams. Finally, the tags are append to events
which fulfill the selection criteria of EF trigger. These tags enables to classify physics streams.
The main functionality of the EF output nodes, which is called SFO’s, is to receive events
which have passed the selection criteria of the EF. The SFO maintains a set of files into which
the SFO records events at a peak event rate of up to 400 Hz. In the case of a prolonged failurein the transmission of data to the CERN’s central data storage, there is sufficient local storage
capacity to buffer all events locally for up to one day. The set of files maps to the ATLASdefined data steams: electrons, muons, jets, photons, ETmiss , τ and B-physics. Each event isrecorded in one or more files according to the stream classification made by the EF processing
task. In the addition to the streams mentioned above, a subset of the events is also written
to the calibration and express stream. The calibration stream provides the minimum amountof information needed for detector calibration. The express stream is a subset of the events
selected by the event filter and fulfill additional criteria for monitoring the quality of the data
and the detector.

65

CHAPTER 3. PERFORMANCE OF TRT DETECTOR

Chapter 3
Performance of TRT Detector
3.1 Performance of TRT with Cosmic Data
The performance of TRT detector with cosmic runs in 2008 is summarized. Figure 3.1 showsthe event displays of a cosmic event in the commissioning runs. Green disk shows the TRT
detector region and red or white points on the disk represent the high or low threshold hits in
the TRT detector. The yellow strips in the inner region correspond to the SCT hits. The orange
line shows a cosmic muons traversing the Inner Detector.

Figure 3.1: Event display of the cosmic ray obtained in the commissioning runs.

66CHAPTER 3. PERFORMANCE OF TRT DETECTOR

3.1.1 Occupancy Study
Some of occupancy studies are performed using cosmic data. The studies of occupancy is doneby using the TRT barrel modules. The occupancy for each drift tube in this study is defined as,
Occupancy ≡The number of hits in a tube.
The number of all events.

(3.1)

4

10

occupancy [%]Figure 3.2 shows the occupancy distributions in different runs. Occupancy of most of drift tube
is around 2%. Figure 3.3 the average occupancy of whole drift tubes. The average occupancy
is about 2.2%.

run 91361
run 91391
run 91400

103

run 91464
run 91636
run 91639

102

2.3
2.25
2.2
2.15
2.1

run 91800

2.05
10

2
1.95

1
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.9

1

91400

91500

91600

91700

occupancy

91800

run number

Figure 3.2: Occupancy distributions in cosmic
runs.

Figure 3.3: The average occupancy of the barrel
module in cosmic runs.

The average occupancies for different phi-module on both side are shown in Figure 3.4.
The TRT barrel module can be divided into 32 modules in φ direction. There are totally 96
phi-modules in each side. The average occupancy in most of phi-module results in about 2.2%.
The average occupancy of TRT barrel detector is nearly 2.2%. The noise level of TRT detector
0.05

0.05
run 91361

0.045

run 91400

0.04

run 91636
run 91800

run 91464
run 91636
run 91639
run 91800

0.03
0.025

0.025
0.02

0.02

0.015

0.015

0.01
0

run 91400

0.035

run 91639

0.03

run 91391

0.04

run 91464

0.035

run 91361

0.045

run 91391

10

20

30

40

50

60

70

80

0.01
0

90

10

20

30

40

50

60

70

80

90

C-side Type-1 (0-31) Type-2 (32-63) Type-3 (64-95)

A-side Type-1 (0-31) Type-2 (32-63) Type-3 (64-95)(a) A-side(b) C-side

Figure 3.4: The average occupancy in each straw layers. (a) and (b) shows the average numbersof the module of A-side and C-side, respectively.
is stable at cosmic runs.

67

CHAPTER 3. PERFORMANCE OF TRT DETECTOR

3.1.2 Efficiency Study
Efficiency studies are also performed with cosmic data. Similarly to the occupancy study, thisstudies done for the barrel module. The reconstructed tracks are employed in order to estimate
the efficiency of the TRT drift tubes. Using the reconstructed tracks of cosmic rays, hit efficiency
as a function of the distance from track to drift wire is defined as,ε(d) ≡

Nhits,
Ntubes(3.2)

where d is the track distance to the drift wire, Nhits is the number of hits in tube whose track
distance is d and Ntubes is the number of tubes whose track distance is d.
For the efficiency study, these track selection criteria are required:• pT > 1 GeV.
• Npixel ≥ 1.
• NSCT ≥ 6.
• Quality selection for the SCT only track. Using the SCT information of the cosmic track,
the SCT only track is reconstructed. Good quality for the SCT only track is required.
χ2 /n.d.o. f < 5(3.3)• The residual cut for the last TRT hit. The selection requirements for the last hit of the
track of cosmic ray traversing the whole of the Inner Detector. Using a drift radius and a
track distance as shown in Figure 3.5, the residual is defined as
residual ≡ drift radius − track distance.

(3.4)

As a selection criterion, |residual| < 0.3mm is required. This selection removes the effectof multiple scattering. Figure 3.6 shows the efficiency distributions of the TRT drift tubes.
The black line shows the efficiency without the residual selection. On the other hand, thered line shows the efficiency with the residual selection. The efficiency with residual
selection falls steeply around d ∼ 2mm which is corresponding to the radius of the drift
tubes due to the removal of the multiple scattering effects.
Figure 3.7 shows the efficiency for different types of modules as a function of a track distance.
The efficiency in the plateau region that the track distance is less than 2mm is above 90%.
The efficiency for the type-2 module is given by about 93%. The method of the estimation for
the efficiency is affected by the precision of tracking or the alignment of the detectors. The
efficiency of the TRT detector in this study results in above 90%.

3.2 Performance of TRT with pp Collision data of
The performance of TRT detector in 2011 runs [45] is summarized here.

68√

s = 7 TeVefficiency

CHAPTER 3. PERFORMANCE OF TRT DETECTOR

1
without residual cut
with residual cut

10-1

10-20

2

4

6

8

10

12

14

16

18

20

track distance [mm]efficiency

Figure 3.5: The residual of the track position.

Figure 3.6: TRT hits efficiency with or without
residual selections.

1
Barrel Type-1
Barrel Type-2
Barrel Type-3

10-1

10-20

2

4

6

8

10

12

14

16

18

20

track distance [mm]Figure 3.7: TRT hits efficiency for different barrel modules.

69

CHAPTER 3. PERFORMANCE OF TRT DETECTOR

3.2.1 Occupancy Study

Occupancy

Figure 3.8 shows average number of hit occupancy as a function of straw layer in the barrel
module. Occupancies are shown for different number of the reconstructed vertices. The firstnine layers are the innermost layers. They are shorten in order to keep the occupancy low as
described in Section 2.2.3.
ATLAS Preliminary# vertices=0# vertices=1# vertices=2# vertices=3# vertices=4# vertices=5# vertices=6# vertices=7# vertices=8# vertices=9# vertices=10# vertices=11

0.3
0.25
0.2

Data

0.15
0.1
0.05
0

10

20

30

40

50

60

70

Barrel straw layer

Figure 3.8: Average number of hit occupancy in each straw layer of the barrel module.

3.2.2 Efficiency Study
Figure 3.9 shows the TRT hit efficiency as a function of the distance from track to the straw
center. Only straws between the first and the last layers with a hit on the track is considered forthe estimation of the efficiency. The corresponding the first and the last layer is removed forthe calculation. The tracks are required to have at least one pixel hit and six SCT hit and fifteen
TRT hits. Furthermore, pT > 1 GeV, |d0 | < 10mm and |z0 | < 300mm are also required. The
efficiency for data and MC are about 94% and 95% respectively in the plateau region which isdefined by the solid lines. The√ threshold simulated in the Monte Calro is tuned to the data withthe center-of-mass energy s = 900 GeV.

70

Efficiency

CHAPTER 3. PERFORMANCE OF TRT DETECTOR

1
0.95
0.9
0.85
TRT barrel
0.8
Data 2010
0.75
Monte Carlo
0.7
Fit to data, ε = 0.944
0.65
Fit to Monte Carlo, ε = 0.951
0.6
0.55 ATLAS Preliminarys = 7 TeV
0.5
-2 -1.5 -1 -0.5 0
0.5
1
1.5
2
Distance from track to straw centre [mm]Figure 3.9: TRT efficiency as a function of a distance from track to the wire.

71

CHAPTER 4. ANALYSIS OVERVIEW

Chapter 4
Analysis Overview
4.1 Event Topologies of the AMSB Model
4.1.1 Production Processes
Two types of production processes of the AMSB models could occur in pp collisions at the
LHC.
• Pair production of colored sparticles via strong interaction.
A pair of colored sparticles such as gluinos are produced via strong interactions. Colored
sparticles have heavier masses than those of gauginos, therefore, the cross section of thisprocess is small. However, the high momentum jets are emitted from the cascade decayof these colored sparticles and the signal events in pp collisions are effectively triggered.
• Pair production of gauginos via electroweak interactions.
±
Charginos could be directly produced via electroweak interactions. The χ̃1 has a lighter
mass than that of colored sparticle, which leads to a larger production cross section. While
this process has larger cross section, triggering signal events with this process is challenging because objects such as jets in this events are soft or absent.
This analysis is dedicated to the colored sparticle pair production process. The colored
sparticles produced in pp collision decay to lighter sparticles, leading to the final state withmultiple jets. Furthermore, these jets become energetic due to the heavy mass of the colored
sparticle.
The lightest chargino could be emitted in the cascade decay of the colored sparticles. When
lifetime of the long-lived chargino is long enough to decay inside the tracking volume of the
ATLAS detector, a signal of the chargino is expected to be fully detected. Characteristics ofchargino signals in the ATLAS experiment is summarized in the following section. The lightest neutralino (as the LSP) from chargino is energetic and escapes detection, therefore, large
missing transverse momentum is expected to be observed when the signal is produced.

4.1.2 Characteristics of the Chargino Signal in the ATLAS Experiment
Expected signatures of the chargino signals depend on the lifetime, namely the position whereχ̃±1 decays in the ATLAS detector.
72

CHAPTER 4. ANALYSIS OVERVIEW• Decaying before entering the inner tracking volumes. (Decay length is ∼ O(1) mm)±±
In the case that χ̃1 decays promptly, the χ̃1 does not leave any hits in the detector. The large
missing transverse momentum is expected but the detection of the chargino is impossible.
• Decaying in the silicon detectors.(Decay length is O(1) ∼ O(10) mm)
If the lightest chargino decays in the silicon detectors, an associated short track is expected be detected. This short track has large dE/dx hits due to its heavy mass. However,the large number of hits from underlying low momentum particles such as pions makes it
hard to reconstruct the short track.
• Decaying in the TRT detector.(Decay length is O(10) ∼ O(100) mm)±
The χ̃1 decaying in the TRT detector is fully reconstructed with the standard track reconstruction employed in the ATLAS experiment, as stated in Section 5.2.1. The TRT
detector consists of a large number of drift tubes, then charged particle makes numerous
hits in the detector, which results in a visible trajectory along the path of charged track.
Such a signal is observed as a track breaking up in the TRT detector.

reconstruction efficiency

In the AMSB models, the decay length of the lightest charginos are preferred to be O(1) ∼ O(10)cm and a fraction of the charginos could decay inside the tracking volume.
Figure 4.1 shows the track reconstruction efficiency for the decaying charginos as a functionof the transverse distance R of the decay point. The reconstruction efficiency reaches nearly
100% for the charginos decaying after the fourth SCT layer which is located at R = 514 mm.

1
0.8
0.6
0.4
0.2
0
0

200

400

600

800

1000 1200 1400
R [mm]

Figure 4.1: The track reconstruction efficiency for the decaying charginos as a function of theradial distance of the decay point.
The chargino track has high pT and is well isolated from the other tracks. Figures 4.2 (a)and (b) show distributions of the chargino track pT and the minimum distance in the η-φ space∆R between the chargino track and other tracks in various AMSB models. The parametersof these AMSB models used in these figures are described in Section 5.3.2. The difference
between colored sparticles and chargino masses is so large that produced charginos have large
momentum.
The number of TRT hits along the chargino track is employed in order to identify decaying
chargino. A Chargino decays to a neutralino, which escapes from detection, and a soft charged73CHAPTER 4. ANALYSIS OVERVIEW∼±) = 90.236 GeV
AMSB: m(χ1∼±) = 117.769 GeV
AMSB: m(χ1∼±) = 147.714 GeV
AMSB: m(χ

102

102

1

10

10

∼ ) = 90.236 GeV
AMSB: m(χ1±∼±) = 117.769 GeV
AMSB: m(χ1∼±) = 147.714 GeV
AMSB: m(χ1

1
0

100 200 300 400 500 600 700 800 900 1000

0pT [GeV](a) pT of chargino tracks

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1±
minimum ∆ R(∼
χ ,track)
1(b) Minimum ∆R between chargino track and other track

Figure 4.2: Distribution of the chargino track pT and the minimum ∆R between the chargino
and other tracks in various AMSB models. The normalization of AMSB signals is not taken
into account.
particle which is hard to be reconstructed. Chargino makes many hits in the TRT before its
decay. The track break up at decay point and there is expected to be few hits arising from noiseor other particles on the trajectory of reconstructed track of chargino, as illustrated in Figure
4.3. Therefore, chargino is expected to be determined by counting the number of TRT hits on
the track. The distribution of the number of TRT hits on chargino track is shown in Figure 4.4.
It is proportional to the decay radius of chargino and provide discrimination from backgroundtracks originating from stable charged particles. TRT consists of three modules in depth as
described in Section 2.2.3. The inner, middle, and outer is called Type-1, Type-2, and Type-3,
respectively. When a chargino decays in the TRT Type-1 or Type-2, nearly zero hit is expectedin the Type-3 while, the average number of hits on a ordinary track is about 34 in the whole TRT
detector. In the Type-3 module, the average number of hits is about fifteen. Figure 4.5 shows
the number of TRT Type-3 hits distribution of the reconstructed chargino tracks penetrating theouter
TRT barrel module (|η| < 0.63). NTRTis expected to give nearly zero when chargino decaysouter
before the TRT Type-3 module. On the other hand, NTRTis expected to be about fifteen if a
track penetrates the TRT detector.

74

CHAPTER 4. ANALYSIS OVERVIEW

A small number of hits is expectedon the trajectory of neutralino

Actual trajectory of chargino
Actual trajectory of neutralino
Actual trajectory of a soft pion
Reconstructed track
TRT drift tube
TRT hits or noise

Figure 4.3: Decaying chargino in the TRT detector.

75

NTRT

CHAPTER 4. ANALYSIS OVERVIEW

50
45
40
35
30
25
20
15
10
5
0
400

500

600

700

800

900

1000 1100
R [mm]

Figure 4.4: The number of TRT hits of reconstructed chargino tracks with |η| < 0.63 as afunction of its decay R. TRT is instrumented between R = 563 mm and 1066 mm.

350
300
reconstructed track, |η| < 0.63

250

R < 863 mm
R > 1066 mm

200
150
100
50
0
0

10

20

30

40

50
NTRT3

outer
Figure 4.5: The NTRT
distribution of reconstructed chargino tracks with |η| < 0.63. Black line
shows all the reconstructed chargino track.Magenta shaded and blue shaded histograms are thetracks which decay before the TRT Type-3 module and the tracks which penetrates the whole
TRT detector, respectively.When charginos decay before reaching (after penetrating) the TRT
outertype-3 module, NTRT
gives nearly zero (fifteen).

76

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

Chapter 5
Dataset and Monte Carlo Simulation
5.1 Data Preparation
5.1.1 Analysis Framework
Most of studies on performance or physics are performed via a common analysis framework,
which is called ATHENA [46]. ATHENA software framework is an enhanced version of theC++ based software framework GAUDI [47] which is initially developed by the LHC-b collaboration. ATHENA enables a user to implement an algorithms easily for studies using data
or Monte Carlo simulation of ATLAS. In order to run ATHENA, scripts written in Python areused. Detector description, software setup, etc are specified in these scripts.

5.1.2 Software Chain in the Data Preparation
Simulated and experimental data are prepared through a series of software chain.
Event Generation
This is the first step of generation of Monte Carlo simulations. Simulation of event generationis also performed via ATHENA. ATHENA uses external softwares like PYTHIA, MC@NLO,
and so on. Event of proton-proton collision is simulated by these softwares. Decays of particles
before incidenting to the detector are also simulated in this step.
Simulation
This step is the simulations of particle in the detector materials. ATHENA uses the GEANT4[48] for the simulation. GEANT4 provides physics models in the detector. The geometry description of the ATLAS detector is written in the GEANT4 format. This description is provided
by ATHENA. The deposited energy of particles in the active volume of the detector is calculated in GEANT4. Furthermore, decays of particles including the late-decay particle such as
long-lived chargino in the detector are also calculated by GEANT4. After this step, the files
containing data of energies deposited in the detector are generated.

77

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION
Digitization
In this stage, the hits information generated by simulation is converted into detector responses.
Detector responses are called “digits”. A digit is produced if the voltage or current exceed athreshold of a readout channel within a time-window. The features of charge collection suchas cross-talk and electric noise in each detector are also simulated in this step. In addition to
the hard scattering, other proton-proton interaction must be considered. The response of theseinteractions in the detector are also simulated. Many inelastic proton-proton interaction may
appear at bunch crossing. The effects of beam gas and beam halo are also incorporated in thisstep. Furthermore, the detector response to long-lived particles is also calculated. After thedigitization step, the files containing the digits of each sub-detector. This data format is called
Raw Data Object, or RDO for short.
Reconstruction
This is the last step of ATLAS software chain. In this stage, the event reconstruction is performed using experimental or simulated data of the detector. Reconstruction algorithms forphysics object such as track, jet, muon, electron and ETmiss are deployed from detector data. After this step, two types of data format are provided. One is Analysis Object Data (AOD), whichcontains physics object data for analysis. The other is Event Summary Data (ESD), which holds
not only physics objects but also the detector information.
Data Formats for Analysis
In the series of software chain, many of data formats are produced such as RDO, AOD and
ESD. However, the access of this data is restricted due to the problem of the huge amount of thefile size. There are some of data formats for physics analysis or performance study. The data
formats mentioned below has small size of data for easy access.
Derived ESD (DESD) DESD is small ESD by removing unnecessary data. ESD contains
full detector information and its file size is huge. Therefore, it is necessary to lessen file sizefor study using ESD data. There are some operations for data reduction: Skimming, Slimming
and Thinning. Skimming is removing uninteresting events. Slimming is removing details ofobjects. Thinning is removing unnecessary objects.
Derived Physics Data (DPD) DPD is also data whose file size is reduced. There are different
kinds of DPD. The different kinds are D1PD, D2PD and D3PD. D1PD has the same format as
AOD. D1PD is provided by the GRID production system. D1PD is not very specific to analysis.
D2PD also has the same format as AOD. D2PD is more analysis-specific than D1PD. D1PD
and D2PD can be read with ATHENA. D3PD is different from the other DPD and it contains
flat ntuples. Many analyzers in ATLAS use D3PD data.

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CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

5.2 Object Reconstruction
At the reconstruction stage of the software chain, many of physics objects are reconstructed.
These objects are used for physics analysis or the performance study. The detail of reconstruction algorithm for each object is explained here.

5.2.1 Track Reconstruction
The reconstruction algorithm of the inner track [49, 50] employs the data of the Inner Detector.
The tracking algorithm of ATLAS is called New Tracking or NEWT for short. The NEWT
covers two reconstruction algorithm: the main algorithm is inside-out track reconstruction andthe consecutive algorithm is outside-in tracking.
Track Parametrization
Track is described with the parameters at Perigee, which is the closest point to the beam-pipe (zaxis). Parameters at perigee, P(xP , yP , zP ) for track with momentum p = (px , py , pz ) and charge
Q is summarized in the Table 5.1.

d0
z0
φ0
θ
q
p

Table 5.1: Track parameters at perigeeq: Transverse impact parameterd0 = ± xP2 + y2P: Longitudinal impact parameter z0 = zPp
: Azimuthal angle at perigee
φ0 = arctan( pxy ): Polar angle at perigee
θ = arccot( √ p2z 2 )
q
Q
= |p|
p

: Q over Ppx +pyThe convention of the sign of d0 is following: May φ denote the azimuthal angle of theperigee, i.e. φ = arctan( yxPP ). The sign of d0 is defined as positive if φ = φ0 + π2 + 2nπ where n is
an integer.
Inside-Out Track Reconstruction
The first step of the inside-out track reconstruction is the formation of the three-dimensional
information using the silicon detector measurements, which is called SpacePoint. The formation of the SpacePoint objects with the pixel detector is performed by the simple way. The
measurements on the pixel module has two-dimensional information and the three-dimensional
representation is obtained by using the constraint of the information for detector element whichis called the Surface. On the other hand, the SpacePoint objects cannot be formed from thesingle SCT measurements because the SCT is the strip sensor detector. However, a module of
the SCT detector is built with two sensor rotated with each other. Therefore, three-dimensional
information is obtained by using two strip measurements. The pixel detector can give directly
the SpacePoint but the formation of SpacePoint with the SCT detector needs two measurements. That leads an intrinsic noise suppression in the SCT SpacePoint formation at the very
first pattern recognition.
79

CHAPTER 5. DATASET AND MONTE CARLO SIMULATIONThe SpacePoint objects formed with the silicon detector are collected for seeding the track
candidate. This procedure has two different tasks which are the track seed finding and the track
candidate creation.. There are two different seed finding algorithm:• Seed search with z vertex constraint: SpacePoint pairs of the pixel detector are employed and z vertices are created. The vertices are filled in histograms and the seeds are
selected if they are in the tolerance region for predicted vertices.
• Unconstrained seed search: The seed search without z vertex constraint is also prepared.
This procedure leads to be more time consuming but the more efficient to find tracks inevents.
After the SpacePoint seeds are obtained, the “road ” building process is started. The seeds
provide directional information to build roads and enables to associate hits in the detector toa track candidate. In this stage, a Kalman fitter-smoother formalism is employed to follow
the trajectory and include successive hits in the track fit simultaneously. The Kalman filter
progressively updates the track information and predicts precisely the track representation on
the next detector measurement.
The seeded track finding leads to a large numbers of track candidates. Many of these track
candidates share hits with other candidates. These candidates are incomplete tracks or faketracks whose hits are not originate from a single particle. Therefore these track candidates
are ordered by the likelihood to describe the real trajectories of particles. This procedure iscalled Ambiguity Solving. The first step is refitting the track using the refined reconstruction
geometry. Nevertheless, the track fit only gives reduced chi-square and this parameter does
not discriminates a good track from a fake track. Then, the track scoring strategy is developed
for the classification of tracks. This strategy uses the different characteristics of tracks whichis represented by a beneficial or penalty score. For the scoring, the associating hits on the
track is employed. The measurements of different sub-detectors are weighted and the precision
measurements such as the pixel detector has preferred.
Table 5.2: Track characteristics in the track scoring.
Track characteristics Detector
Track scoring
B-layer holepixel
strong penalty
Layer hole
pixel
penaltyOverlap hit
pixel,SCT strong benefit
Sensor hole
SCT
weak penalty
Layer hole (module) pixel
strong penalty
The silicon track obtained from these procedures are extended into the TRT detector. The
tracks determined by the silicon seeds are used as an input for finding TRT measurements
corresponding to the tracks. These TRT measurements are further processed for extension of
tracks. After the association of TRT hits to the track, comparisons of the refitted combined
track and the silicon seeded track are performed based on the track scoring. In case that the
track score of the silicon seeded track is higher than the combined track, the silicon track is kept
and the TRT measurements are categorized as outlier on the track.

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CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

Figure 5.1: Illustration of the ambiguity solving in the SCT module.Tracks a,b and c are foundby the seeded track finding. Module hit of the SCT detector is scored relatively higher. Hits ina overlap region for track b are high scored.On the other hand, holes where hits are expected
results in a penalty.
Outside-In Track Reconstruction
In the inside-out track reconstruction process, some of initial track may not be found. For
example, tracks originating from secondary decay vertices such as K s decays inside the Inner
Detector or tracks from photon conversions may not make sufficient hits in the silicon detector.
Accordingly, the outside-in track reconstruction algorithm is developed.
The fist stage of the outside-in reconstruction is TRT segment finding. This algorithm follows the two-step procedure, which is starting with global pattern recognition and a subsequentlocal pattern recognition. The TRT measurements can not provide the information about thecoordinate along to the straw direction. The SpacePoint objects are not formed by the TRT
measurements. Therefore, the global pattern recognition is performed in the projective plane:r-φ plane is adopted for the TRT in the barrel region and r-z plane is employed for the TRT in
the end-cap region. The Hough transform technique, which is a very common technique in highenergy physics, is adopted for The global pattern recognition. After the TRT track segments
are obtained by the global pattern recognition, these segments are further processed in a second
step of the TRT segment finding. The local pattern recognition algorithm uses the informationof drift time while the global pattern recognition employs only the straw center. Eventually,
the track segments are obtained via a Kalman filter-smoothing formalism. In the second stage,
the track segments are extended towards the silicon detector. If the track extension towards thesilicon detector is failed, this track is categorized as the TRT-standalone tracks.
Common Tools Using Tracking Software• ATLAS Extrapolator[51]The estimation of track parameters on a given detector surface and their associated covariances is a important process in track reconstruction. Track fitting techniques such as the81CHAPTER 5. DATASET AND MONTE CARLO SIMULATION
Kalman Filter formalism relies on the prediction of the track information on successive
surface.
The ATLAS extrapolator mainly consists of three different tasks: propagation, navigation and integration of material effects. In the task of propagation, track parameters on
a destination surface are estimated by the initial parameters and the traversed magnetic
field. The various techniques are implemented for propagation of tracks. The propagation with a straight line model or a helical track model is assuming no magnetic field ora homogeneous magnetic field. These method are employed for the runs using cosmic
rays or test beam. The propagation with the Runge-Kutta-Nyström integration technique
is mainly used in a inhomogeneous magnetic field. In the navigation task, the information about the traversed detectors are gathered. In the task of material effects integration,
the material effects for a particle is estimated. A particle traversing material is affected
the energy loss and scattering. Multiple scattering is a stochastic process with zero mean
deflection. This effect is regarded as Gaussian or multi-Gaussian process noise addition
to the track covariance. Energy loss effects changes the trajectory of a particle and theuncertainties on the track of the particle because of the loss of the momentum. These
effects are taken into account by a deterministic mean value.
The ATLAS Extrapolator is employed for the TRT association to the track for thischargino track search.
• TrackToCalo tool
TrackToCalo is the tool for track extrapolation in the calorimeters. TrackToCalo tool
employs the ATLAS Extrapolator. When the track information and the depth of thecalorimeter are fed into the tool, TrackToCalo tool calculates the track position in thecalorimeter. For propagation, Runge-Kutta technique is used similarly to the ATLAS
Extrapolator. This tool is also used in this analysis in order to associate calorimeter clusters to track.

5.2.2 Vertex Reconstruction
The iterative vertex finding approach is used for vertex reconstruction [52, 53]. Reconstructed
tracks originating from the interaction region are employed for vertex reconstruction. The procedures of primary vertices reconstruction have two steps. The first step is the primary vertex
finding algorithm, which is dedicated for the association the reconstructed tracks to the vertex
candidates. The second step is the vertex fitting algorithm, which is dedicated for the reconstruction of vertex position and the error matrix of it.
The seed of the vertex is obtained by looking for the global maximum of z-coordinationof the tracks at the point of the closest approach to the beam spot. The vertex position isdetermined by the adaptive vertex fitting [54] algorithm, which makes use of the seed position
and the tracks. The adaptive vertex fitter is a robust χ2 based fitting algorithm which deals with
outlying tracks by down-weighting their contribution to the overall. The weight wi depends onthe compatibility of the i-th track with the vertex, which is measured as χ2 ,exp(−χ2i /2T )wi (χi ) =exp(−χ2i /2T ) + exp(−χ2c /2T )
82

(5.1)

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION
where χ2c defines the threshold that the weight is equal to 12 and the temperature T is a parameter
which defines the functional shape of weights. The shape of the weight results in the step
function when T approaches to zero.
Tracks displaced by more than 7σ are removed from the vertex and used to make a newvertex candidate. A vertex is required that more than two tracks must be associating to thevertex. The compatibility of the track to the vertex is expressed by χ2 . The default selection isχ2 > 49. This procedure of the vertex finding algorithm is repeated until new additional vertices
are no longer found.

5.2.3 Calorimeter Cluster Reconstruction
Calorimeter cluster is reconstructed as inputs for jet-finding in ATLAS. There are various algorithms for clustering the calorimeter energy.
• Tower algorithm
The calorimeter cells segmented into bins of a ∆η × ∆φ = 0.1 × 0.1 grid. The towers areformed by collecting the cells and summing up their signals. When the information of
the cells are summed up, all calorimeter cells are merged. Towers with negative energy isdominated by noise; therefore, these towers are not used when jet-finding algorithms areapplied.
• Topological clustering algorithm
Topological clustering algorithm attempts to reconstruct three-dimensional energy depositions using the calorimeter cells. At first, the nearest neighboring cells which absoluteenergy exceeds the major seed threshold, i.e. |Ecell | > 4σcell where the total noise is represented as σcell are collected and the seed of the calorimeter cluster is formed. Then, if theneighboring cells whose absolute energy is above a secondary seed threshold, typically
2σcell , these cells are merged to the primary seeds. Finally, all the surrounding cells areadded when the energy of the cell exceeds the 0σcell .
Topological clustering algorithm suppress the actual noise contrary to the tower algorithm. In this algorithm, the cells with no signal are not likely to be include in the cluster.
• Sliding window algorithm
The sliding window algorithm also makes use of cells segmented into ∆η×∆φ = 0.1×0.1.
This algorithm uses the sliding window with programmable size.

5.2.4 Jet Reconstruction
The jet reconstruction employs “anti-kt ”algorithm [55]. This algorithm makes use of the reconstructed cluster of calorimeter. In this algorithm, di j is defined as,−2
di j ≡ min(p−2T i , pT j )

∆2i j
R2

(i , j, R = 0.4 or 0.6),

dii ≡ p−2
Ti ,

83

(5.2)
(5.3)

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION
where ∆2i j = (yi − y j )2 + (φi − φ j )2 and pT i , yi andφi are transverse momentum, rapidity andazimuthal angle of the cluster i. All of the clusters are ordered by p−1
T and dmin for the i-thcluster is defined asdmin ≡ min(dii , di j ).
(5.4)
The cluster i is considered as a jet when dmin is equal to dii . If dmin is not dii , the i-th cluster ismerged with the j-th cluster by calculating vector sum of four-momenta of clusters. Then dminof the new cluster object is evaluate for all the remaining clusters. This procedure is repeateduntil the all of the jet candidates are not remained.

5.2.5 Electron Reconstruction
Electron reconstruction [56, 57] in the region of |η| < 2.47 starts from searching for clusters in
the EM calorimeter which are then associating to a reconstructed track in the Inner Detector. In
order to reconstruct the EM clusters, seeds of cluster which transverse energy ET > 2.5 GeVare
searched for by sliding window algorithm. The window size is 3 × 5 in units of 0.025 × 0.025
in η × φ space. Reconstructed tracks in the tracking volume of |η| < 2.5 are extrapolated to the
middle layer of the calorimeter and loosely matched to seeds. The distance between the track
position at the middle layer and the cluster position is required to satisfy ∆η < 0.05. In orderto take into account for bremsstrahlung losses, ∆φ < 0.1 is required on the side where the track
bends in the solenoid field and ∆φ < 0.05 on the other side. An electron is reconstructed if
at least one track is matched to the seed. In the case that more than one tracks are matchedto the seed, a track with the silicon hits is preferred and the one with the smallest ∆R is tothe seed is selected. The electron cluster is rebuild by using 3 × 7 (5 × 5) longitudinal towerof calorimeter cells in the barrel (end-caps). The cluster energy is determined employing four
different contributions: the estimated energy deposit in the materials in front of EM calorimeter,
the measured energy deposition in the cluster, the estimated external energy deposition outside
the cluster (lateral leakage) and the estimated external energy deposition beyond the EM cluster(longitudinal leakage). The four-momentum of electron is calculated using information of boththe track and the calorimeter cluster. The electron energy is given by the calorimeter cluster.
The η and φ directions are determined by using the track information.
In the forward region of 2.5 < |η| < 4.9, where there are no trackers, electrons are reconstructed by employing only deposited energy in the calorimeters. The topological clustering
algorithm is used for reconstruction of forward electrons. The direction of the electron is determined by the barycenter of the cells associating to the cluster. The energy of the electronis calculated by summing up the energies in the cluster of the cells and is corrected for energy
loss in the passive material before calorimeter. The candidate of electron is required that it has
a small hadronic energy component and a transverse energy ET > 5 GeV.

5.2.6 Muon Reconstruction
Two independent muon reconstruction algorithms are implemented in the ATLAS:STACO (Statistical Combined) [58, 59] and MUID (Muon Identification) [60, 61]. In order to identify
muons, the tracks which are reconstructed in the Inner Detector and the Muon Spectrometer are
combined. STACO is based on the statistical combination of two independent measurements of84

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION
track parameters and the covariance matrices. On the other hand, MUID is based on the fitting
the global muon track using hits in the Inner Detector and the Muon Spectrometer.
STACO
In the STACO algorithm, the standalone muon tracking package is called Muonboy. The strategy of the muon tracking in Muonboy consists of the main four steps:
1. Identification of Regions of Activity (ROA) in the muon system with trigger chambers.
2. Reconstruction of local straight track segments in each muon station of these ROA.
3. Combination of track segments in different muon station.
4. Global track fit of the muon track.
Furthermore, the back-tracking of the muon candidates to the beam region is performed toobtain the track parameters at the perigee. When the back-tracking is performed, the energy
loss and the scattering in the calorimeter are also taken into account.
The match chi-square is used in order to combine the standalone muon track and the trackreconstructed in the Inner Detector,
χ2match = (ξMS − ξID )T (ΣMS + ΣID )−1 (ξMS − ξID ),(5.5)

where ξ are the track parameters and Σ are the covariance matrix of the track parameters. After matching the tracks reconstructed in the Inner Detector and the Muon Spectrometer, theparameters of the combined track is obtained as,
−1
−1 −1
−1
−1
ξSTACO
match = (ΣMS + ΣID ) (ΣMS ξ MS + ΣID ξ ID ).

(5.6)

MUID
MUID also has the standalone muon tracking package which is called MOORE (Muon Object
Oriented Reconstruction). The strategy of tracking in the muon spectrometer in the MOORE
is,
1. A global pattern recognition with Hough transformation using hits in the Muon Spectrometer.
2. Straight MDT segments and straight CSC segments are formed with hits obtained by thepattern recognition.
3. The track segment are refitted and the track are built.
After building tracks, the refitted muon tracks are extrapolated to the beam region. Then tracks
are matched by forming a χ2 . A combined fit requires that χ2 probability is above 0.001. If
this criterion is not satisfied, the fitting attempts for the best match using the measurements
within a road of a muon track. Eventually, all matches to the Inner Detector which fulfill therequirements of the combined fit are identified as combined muons.
85CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

5.2.7 Missing Transverse Energy Reconstruction
The missing transverse energy ETmiss includes contributions from energy deposits in calorimetersand muons reconstructed in the muon spectrometer [62]. The missing energy in x(y)-direction
is defined as,
XX
calorimeter
E miss=−E−
E muon
(5.7)
x(y)
x(y)
x(y) .
where E calorimeterand E muonx(y)x(y) are each component of deposited energies in calorimeter and reconstructed muons. The values of ETmiss and its azimuthal angle (φmiss ) is calculated as,
ETmiss =
miss

φ

q
2
miss 2(E missx ) + (E y ) ,= arctan(

Eymiss
E miss
x

).

(5.8)
(5.9)

ETmiss definition depends on what term is employed in calculation. The various term is describedin the following:
miss,µmiss,τ
• E miss,ex(y) , E x(y) and E x(y)Reconstructed missing energy from cells in clusters associated to electrons, muons, andτ-jets from hadronically decay, respectively.

• E miss,jetsx(y)Reconstructed from cells in clusters associated to jets with calibrated pT >20 GeV.
• E miss,softjets
x(y)Reconstructed from cells in clusters associated to jets with 7 GeV< pT <20 GeV.
• E miss,calo,µx(y)The contribution to ETmiss originating from the energy lost by muons in the calorimeter.
• E miss,CellOutx(y)Calculated from the cells in topoclusters which are not included in the reconstructed objects.

5.3 Collision Data and Monte Carlo Simulation
Collision data and Monte Carlo simulation samples concerning this analysis are described here.

5.3.1 Collision Data√
This analysis used the data of pp collisions at s = 7 TeVwith collected at the ATLAS detector
in 2011. Figure 5.2 shows the evolution of cumulative luminosity in 2011. The green filled
histogram shows the luminosity delivered by the LHC while the yellow histograms show theluminosity recorded by the ATLAS detector. The delivered luminosity accounts for the luminosity from the start of the stable beams until the LHC requests the ATLAS to be off for a beam
dump or beam studies. In the AMSB model with colored sparticle pair production process,86Total Integrated Luminosity [fb -1]

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

7
6
5

ATLAS Online Luminositys = 7 TeV

LHC Delivered
ATLAS Recorded
Total Delivered: 5.61 fb-1
Total Recorded: 5.25 fb-1

4
3
2
1
0
28/02

30/04

30/06

30/08
31/10
Day in 2011

Figure 5.2: Cumulative luminosity delivered from the LHC (green) and recorded by the ATLAS
detector (yellow) during stable beam.
gluinos and squarks are expected to be produced via the strong interaction in pp collisions. As±
0mentioned in Section 4.1, the cascade decay of sparticles to the χ̃1 and χ̃1 produces multiple jets
0with high momentum. The large missing transverse energy of χ̃1 also expected due to escapefrom detection. Therefore, events are selected at the trigger level by requiring at least one jetwith a transverse momentum, measured at the electromagnetic scale, above 75 GeV, and a missing transverse momentum above at 55 GeV. The total integrated luminosity after the applicationof the beam, detector and data quality requirements is estimated to be 4.71fb−1 .
In addition to the data for the search for charginos, the data obtained with the pre-scaled jet
trigger is employed for the studies of the tracking or the control samples for the backgroundestimation.

5.3.2 Signal Simulation
Three benchmark points of AMSB models are used for this analysis. The mass spectrum ofsparticles, the branching ratios and decay width are calculated using the ISASUSY .7.78.
The MC signal samples are produced using HERWIG++[63] with MRST2007 LO*[64] parton
distribution functions. The proper lifetime of chargino is set to 1 ns and its decay is simulated
by GEANT4. The chargino lifetime follows the exponential decay with 1 ns in the rest frame.
The samples with different lifetimes are also obtained by applying event weights so that the
distribution of the proper lifetime follows that for a given lifetime value. All the parametersof these signal samples are summarized in Table 5.3. Parameters of these points are chosen bytaking account of values of chargino masses excluded by LEP2 search. The cross sections arecalculated at next-to-leading order (NLO) including next-to-leading-logarithmic (NLL) softgluon re-summation by using NLL-FAST[65, 66, 67, 68, 69]. Mass spectrum of sparticles foreach signal point is also summarized in Table 5.4. Furthermore, the signal samples generated by87

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

Table 5.3: Parameters of signal Monte Carlo samples.The NLO+NLL cross sections include
only g̃g̃, q̃g̃ and q̃q̃ production process.
Sample m0 [ GeV] m3/2 [ TeV] tan β sgn(µ) τχ̃±1 [ns] mχ̃±1 [ GeV] Cross section[pb]
LL01
1500
32
5.0
+1
1
90.2
6.79 × 10−2
LL02
1800
41
5.0
+1
1
117.8
8.66 × 10−3
LL03
2000
51
5.0
+1
1
147.6
1.16 × 10−3

Table 5.4: Mass spectrum for each benchmark point of AMSB signal. The values are in the unitof GeV.
LL01
LL02
LL03
g̃
801.32 997.87 1026.39
ũL 1620.68 1961.31 2221.59
ũR 1628.73 1970.59 2232.28
d̃L 1622.54 1962.84 2222.95
d̃R 1632.26 1974.94 2237.44
b̃1 1341.76 1627.44 1850.43
b̃2 1624.37 1965.61 2226.43
t˜1
991.24 1206.88 1386.47
t˜2 1354.36 1640.07 1863.78
χ̃01
90.036 117.585 147.536
χ̃02 291.385 375.181 468.173
χ̃03 658.077 806.529 958.832
χ̃04 666.196 813.295 964.627
χ̃±1
90.236 117.769 147.714±
χ̃2 665.803 813.248 964.871
ν̃e 1489.70 1787.58 1984.52
ẽL 1491.42 1788.87 1985.63
ẽR 1492.21 1789.37 1985.56
ν̃τ 1488.03 1785.59 1982.32
τ̃1 1487.22 1783.86 1979.69
τ̃2 1491.03 1787.98 1984.42
h108.45 109.87
110.72H 1662.69 2002.52 2251.00
A 1651.38 1989.06 2235.96
H ± 1664.15 2003.73 2252.07

88CHAPTER 5. DATASET AND MONTE CARLO SIMULATIONATLFAST II are employed in addition to these samples. Figure 5.3 show the various parametersof the minimal AMSB on the m0 -m 23 plane. Figure 5.3 (a) shows mχ̃±1 . The chargino mass ismostly defined by the m 32 , therefore, the chargino mass is mostly constant for m0 . The constraint
obtained by the LEP2 experiments (mχ̃±1 > 92 GeV) is corresponding to m 32 ∼ 32 TeV. Figure
5.3 (b) shows ∆m ≡ mχ̃±1 − mχ̃01 . The mass difference ∆m used in this study is more than pionχ̃±1 decays to a soft pion and χ̃01 in the signal samples. Figure 5.3 (c) showsmass, therefore, √cross-section at s = 7 TeV. The region where m0 is too small is prohibited theoretically due
to the generation of tachyonic particles. Furthermore, the region where m0 is small (600 < m0 <1000 GeV) has slightly larger cross-section because the masses of squarks become small andsquarks are generated by the pp collisions.

5.3.3 Background simulation√
The signal and background events are generated at s = 7 TeV. The background events are
generated with P [70], A [71] and M@ [72, 73]. For the events generated withA and M@, parton showers and hadronization are simulated with H [74], andthe underlying activity with J [75]. These simulated events are finally reconstructed withthe same algorithms used for the data.
Following processes are backgrounds for the long-lived chargino search and considered inthis analysis.
QCD Jet production: Even though the analysis requires the events to have large ETmiss , due
to the large cross sections of the inclusive two or multi-jet processes, this is still an importantbackground. The events are generated with P. The samples are generated separately for
different slices of the hard process momentum, to ensure enough statistics in the large jet pT
region.
tt¯ production: Due to the large missing transverse energy and the hard jets in the final state,
this process can survive the event selection. The M@ generator has been used to simulate
the process. The CTEQ6.6 [76] next-to-leading-order (NLO) PDFs are used.
Boson+Jets production: The production of W ± and Z bosons in association with jets arealso considered as the backgrounds. Since the event selection requires multiple jets in the final
state, A generator is used. The generator is interfaced to H for parton shower andfragmentation, and also to J for the underlying event. The CTEQ6L1 [77] PDFs are used.
The decay channels, W → `ν, Z → `+ `− , Z → νν (` = e, µ, τ), are all used in this analysis. The
processes including the genuine ETmiss , W → `ν, Z → νν are especially expected to remain after
the event selection. The background samples are summarized in Table 5.5.

89

300

200 GeV

70

250

60

1

mAMSB: tanβ=5, µ >0mχ∼± [GeV]

m3/2 [TeV]CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

200
150 GeV

50

150

40

100

100 GeV

30

50

20
500

1000

1500

2000

2500
3000
m0 [GeV]0mAMSB: tanβ=5, µ >0

0.3

0.25

60
∆m =
0

50

.18 G
eV

1

1

70

∆m ≡ mχ∼±-mχ∼0[GeV]

m3/2 [TeV](a) mχ̃±1

0.2

40
∆m =

30
20
500

∆m =

∆m =

0.22

0.24
GeV

1000

0.20

0.15

GeV

GeV

1500

2000

2500
3000
m0 [GeV]

0.1

mAMSB: tanβ=5, µ >0

s = 7 TeV

70
60

10

1

50

Cross section [pb]m3/2 [TeV](b) mχ̃±1 − mχ̃01

10-1
40
10-2

30
20
0

500

1000

1500

2000

-3
2500
3000 10m0 [GeV](c) cross-section

Figure 5.3: Various parameters of the AMSB models on the m0 -m 23 plane. (a), (b) and (c) show√
the mχ̃±1 ,mχ̃±1 − mχ̃01 and cross-section at s = 7 TeV, respectively.

90

CHAPTER 5. DATASET AND MONTE CARLO SIMULATION

Table 5.5: Standard Model background Monte Carlo samples. The cross sections of LO values
are shown for QCD jets, while NLO with NLL and NNLO values are given for tt¯ and boson
production processes respectively. p̂T represents the transverse momentum of the two partons in
the hard scattering process used in P.
Physics process
Cross section × BR [pb] MC generator
QCD Jets 8 ≤ p̂T < 17 GeV
9.75 × 109
PQCD Jets 17 ≤ p̂T < 35 GeV
6.73 × 108
P7
QCD Jets 35 ≤ p̂T < 70 GeV
4.12 × 10
PQCD Jets 70 ≤ p̂T < 140 GeV
2.19 × 106
P4
QCD Jets 140 ≤ p̂T < 280 GeV
8.78 × 10
P3
QCD Jets 280 ≤ p̂T < 560 GeV
2.33 × 10
PQCD Jets 560 ≤ p̂T < 1120 GeV
33.8
PQCD Jets 1120 ≤ p̂T < 2240 GeV
0.137
PQCD Jets 2240 ≤ p̂T GeV
6.28 × 10−6P
tt¯
160.8
M@
4
W → eν + N jets (N = 0 − 5)
1.04 × 10
A
W → µν + N jets (N = 0 − 5)
1.04 × 104
A
4
W → τν + N jets (N = 0 − 5)
1.04 × 10
A
3
Z → νν + N jets (N = 0 − 5)5.82 × 10
A
Z → ee + N jets (N = 0 − 5)
1.07 × 103
A
3
Z → µµ + N jets (N = 0 − 5)
1.07 × 10
A
Z → ττ + N jets (N = 0 − 5)
1.07 × 103
A

91

CHAPTER 6. EVENT SELECTION

Chapter 6
Event Selection
6.1 Object Definition
The objects used in this analysis are defined as below:• Track
The tracks reconstructed in the inner detector used in this analysis are required to fulfill
the following criteria:– ptrack> 0.4 GeV,T
– |d0 | <1.5mm,– |z0 sin(θ)| < 1.5mm,– Number of pixel hits (NPixel ) ≥ 1,
– Number of SCT hits (NSCT ) ≥ 6.
The definition of track parameters are described in Section 5.2.1. Figure 6.1 shows the
distributions of track parameters after the application of these requirements. The chargino
search relies on the reconstructed tracks in the inner detector; therefore, the reproducibility of the track qualities in the MC simulation is of importance to this analysis. The
b-layer referred in Figure 6.1 is the innermost layer of the pixel detector. The details
are mentioned in Section 2.2.3. The dataset obtained with jet triggers is compared to the
QCD MC samples. They show the reasonable agreements.
• Jet
Jets are reconstructed using anti-kt algorithm with the distance parameter of R = 0.4 in
Equation 5.2. The measurement of jet transverse momentum at the electromagnetic scale(pjet,EM) underestimates that of hadron-level jets due to the nature of the non compensatingT
calorimeters and the dead material. Thus, an average correction is applied to obtain thecorrect transverse momentum depending on η and pjet,EM. The details of the jet calibration
Tprocedure is given in Ref. [78]. The acceptance cuts of pT > 20 GeVand |η| < 2.8 areapplied in this analysis.
• Electron
Electrons are identified with medium selection criteria as described in Ref. [57]. The
92

Tracks

TracksCHAPTER 6. EVENT SELECTION

data

106

SM BG

106

data
SM BG

5

10

105
104

104

103

103
102
-1.5

102
-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1.5

(b) z0 sin θ

107

Tracks(a) d0Tracks1z0sin(θ) [mm]d0 [mm]

data

6

SM BG

10

107
data

106
SM BG

105

105

104
103

104

102
103

10

102
0

1
1

2

3

4

5

6

0

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2

3

4

Nb-layer

6

7

8

9
NPixel(c) Nb-layer
Tracks5(d) NPixel
107

data

106

SM BG

105
104
103
102
10
1
0

5

10

15

20

25
NSCT

(e) NSCT

Figure 6.1: The distributions of track parameters. The black point show the data obtained with
jet triggers while the red lines show the MC expectation with P QCD samples.

93

CHAPTER 6. EVENT SELECTION
variables used for the identification are summarized in Table 6.1. Electrons are required
to fulfill the requirements of ET > 10 GeV and |η| < 2.47.
Table 6.1: The definition of variables used in medium selection for electrons.
Acceptance|η| < 2.47
Hadronic leakage
Ratio of ET in the first layer of the hadronic calorimeter to ET of
the EM cluster
Ratio of ET in the hadronic calorimeter to ET of the EM cluster
Middle layer ofRatio of the energy in 3 × 7 cells over the energy in 7 × 7 cells
EM calorimeter
centered at the electronqcluster position
P
P
PP
Lateral shower width, ( Ei η2i )/( Ei ) − (( Ei η)/( Ei ))2 , where
Ei is the energy and ηi is the pseudorapidity of cell i and the sum is
calculated within a window 3 × 5 cells.
√P
P
Strip layer ofShower width is defined as ( Ei (i − imax ))( Ei ), where i runs
EM calorimeterover all strips in a window of ∆η × ∆φ ∼ 0.0625 × 0.2,
corresponding typically to twenty strips in η, and imax is the index of
the highest-energy strip.
Ratio of the energy difference between the largest and the second
largest energy deposits in the cluster over the sum of these energies
Track quality
Number of hits in the pixel detector (≥ 1)
Number of hits in the pixel and SCT detectors (≥ 7)
Transverse impact parameter (|d0 | < 5mm)
Track-cluster matching ∆η between the cluster position in the strip layer and the extrapolated
track (|∆η| < 0.01)• MuonMuons reconstructed with STACO algorithm are used in this analysis. Muons are required
to be Combined muons or Segment tagged muons:Combined muons are muon candidates
with a full track in the muon spectrometer and Segment tagged muons are reconstructedwith a specific algorithm in order to recover efficiency in poorly covered regions and at
low-transverse momenta. In addition, the selections requirements on the qualities of the
ID tracks are also applied.
– Number of b-layer hits > 0 if b-layer hits are expected.
– Number of pixel hits plus number of crossed dead pixel sensors > 1.
– Number of SCT hits plus number of crossed dead SCT sensors ≥ 6.
– Number of pixel holes plus number of SCT holes < 3.
– A successful TRT extension where expected (i.e. in the eta acceptance of the TRT).
An unsuccessful extension corresponds to either no TRT hit associated, or a set of
TRT hits associated as outliers:
hits
outliers
outliers
hitsoutliers
1. Require NTRT+ NTRT> 5 and NTRT
< 0.9(NTRT+ NTRT) for |η| < 1.9
hitsoutliers
outliers
hitsoutliers
2. If NTRT + NTRT > 5, then require NTRT < 0.9(NTRT + NTRT ) for |η| ≥ 1.9.

94

CHAPTER 6. EVENT SELECTION
hits
outliers
and NTRT
denote the number of TRT hits and the number of TRT, where NTRT
outliers on the muon track, respectively.

Finally, the selection requirements of pT > 10 GeV and |η| < 2.4 are applied.
• Missing transverse energy
The missing transverse energy is calculated based on the transverse momenta of selectedjets and lepton candidates described above, and all calorimeter clusters not associated tosuch objects.

6.1.1 Criteria for Resolving Object Overlapping
The defined physics objects overlap with each other, one o the overlapping objects is removed
based on the following order:
1. If an electron and a jet are found within ∆R < 0.2, both are classified as one electron andthe jet is ignored.
2. If a muon and a jet are found within ∆R < 0.4, both are classified as one jet and the muon
is ignored.
3. If an electron and a jet are found within 0.2 ≤ ∆R < 0.4, both are classified as one jet andthe electron is ignored.

6.2 TRT Hits Association to a Trackouter
As described in Section 4.1.2, the number of TRT hits in the outer modules (NTRT) in barrel region is used in order to identify charginos decaying in the TRT detector. The ATLAS
outer
Extrapolator tool is employed for the association of NTRT
to the track. The procedure of thisassociation is visually explained in Figure 6.2.
The information of a track and the TRT hits are fed into the ATLAS extrapolator. The
detector information is expressed as a Surface, which is each TRT layer. If the extrapolation
succeeds, the ATLAS Extrapolator returns an expected track position on the Surface. Using
the expected position , the distance between the track and the center of the drift tube (dtrack,tube )is calculated. If dtrack,tube is less than the radius of drift tube (rtube ), the hits of the TRT drift tube
is associated to the track.

6.3 Kinematic Selection Criteria
A small fraction of jets are reconstructed from the calorimeter noise or cosmic rays. All jets are
required to pass the loose criteria of jet quality described in Ref.[78]. After the trigger decisionand the jet cleaning, the selection requirements are applied on the event kinematics in order tosuppress the SM background events. Selection criteria for the event kinematics are as follows:
1. Non-collision background rejection,95

CHAPTER 6. EVENT SELECTION

track position
on detector surface
detector
surfacetrack distance froma wire of drift tube

track

Figure 6.2: A sketch of the TRT hits association to track. The track position on a detector
surface is calculated by the ATLAS extrapolator. If the track distance from a wire of drift
tube is less than the radius of drift tube, the TRT hits is associated to the track.
2. Lepton veto: If there are one or more identified leptons (electrons or muons), the eventsis rejected,
3. ETmiss > 130 GeV,
4. The leading jet pT is larger than 130 GeV,
5. The second and third jet pT are larger than 60 GeV.
Figure 6.3 shows the distributions of ETmiss and pT of three highest-pT jets. The distributionsof the AMSB signal are also shown, and one can see that these kinematic selection requirements
are reasonably suppress the background process and enhance the signal events. The event selection criteria and the data reductions are summarized in Table 6.2. The selection efficienciesof the AMSB signals are also given in the Table.
Table 6.2: Summary of kinematic selection cuts and data reduction. The selection efficiencies
for each AMSB signal model are also shown.
Selection cut
Observed events Signal efficiency [%]LL01 LL02 LL03
Trigger
8855753 94.9 96.8 97.8
Jet cleaning
7141026 87.3 89.1 90.1
Lepton veto6644394 72.8 72.5 72.6
Missing transverse momentum > 130 GeV
321412 66.5 68.2 69.6
First leading jet pT > 130 GeV
276311 66.2 68.1 69.6
Second and third leading jet pT > 60 GeV
73433 64.9 67.4 69.0

6.4 Selection Criteria for Chargino Candidate Track
Chargino tracks are expected to have high-pT and well-isolated. In addition to the track definition described in Section 6.1, tighter selection requirements are applied on the tracks as follows:96Events

EventsCHAPTER 6. EVENT SELECTION

106
data

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AMSB LL01

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103∫ Ldt = 4.71 fb

-1

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AMSB LL02

103∫ Ldt = 4.71 fb

10

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100 200 300 400 500 600 700 800 900 1000AMSB LL01

104

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-1

100 200 300 400 500 600 700 800 900 1000

Emiss
[GeV]
T

pT [GeV](b) First leading pT jet
EventsEvents(a) ETmiss
106
5

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∫ Ldt = 4.71 fb

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100 200 300 400 500 600 700 800 900 1000

data
AMSB LL01
AMSB LL02∫ Ldt = 4.71 fb-1

100 200 300 400 500 600 700 800 900 1000

pT [GeV]pT [GeV](c) Second leading pT jet(d) Third leading pT jet

Figure 6.3: The ETmiss and jet pT distributions after the lepton veto. The selection boundaries areindicated by arrows.

97

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105
104

data
Background MC±
Signal events (LL01,τ(∼χ )=1ns)
1
Charginos in signal events (decay radius<863mm)

103
102

∫ Ldt = 4.7 fb

10

s = 7TeV

-1

1
10-10

5

10

15

20

25

30

35
NouterTRT

outer
Figure 6.4: The NTRT
distributions for data and signal events (LL01, τχ̃±1 = 1 ns). The signal
events are shown by the hatched histogram with the high-pT isolated track selection. In thesignal events, the contribution of chargino tracks decayed before the TRT outer module (r <outer863 mm) is indicated by the filled histogram. For these tracks, NTRTis expected to have aoutervalue near zero. On the other hand, charged particles traversing the TRT typically have NTRT'
15. The selection boundary is indicated by the arrow. The expectation from QCD multi-jet
background MC events, normalized to the number of observed events, is also shown.

1. NPixel ≥ 1 and the numbers of the b-layer hits Nb−layer ≥ 1 if b-layer hits are expected,
2. NSCT ≥ 6,
3. There are no tracks as defined in Section 6.1 within ∆R < 0.1,
4. The track is pointing to the TRT barrel layers and expected not to pass the inactive regions
around η = 0,
5. A candidate track should have ptrack> 10 GeV and the highest among isolated tracks inTthe event,outer
6. The number of the TRT hits in the outer module NTRTis less than five.

The first three criteria are applied for ensuring good qualities of the reconstructed tracks. The
fourth criterion selects tracks which go through all 73 layers of TRT detector in order to avoid
outer
misidentifying a track with a small NTRT
due to not penetrating all active layers. Figure 6.5
shows the sketch of acceptance selection. The red tracks are removed for not penetrating all
active layers and the blue track are chosen by this criterion. The sixth criterion is the selection
outerfor the decaying track before the TRT outer module. NTRTof the traversing the TRT gives aboutouter
fifteen while NTRTof decay before reaching the TRT outer module is expected to be nearly zero.
outer< 5 is required.
As indicated in the arrow of Figure 6.4, NTRT
A summary of track selection and data reduction is given in Table 6.3.

98

CHAPTER 6. EVENT SELECTION

Track which pass through thecentral inactive region

Track which is passing the
all active layers

Track which does not

TRT（Barrel）

penetrate the all layersrzFigure 6.5: Acceptance cut for chargino track candidates. Only the tracks expected to penetrate
the all active layers of the TRT detector are selected. Tracks which is passing inactive region at
the center of the TRT or is not penetrating the all layers are rejected.

Table 6.3: Summary of selection requirements, the data reduction and the selection efficienciesof the AMSB signals. The purities of chargino tracks are also shown in parentheses.
Requirement Observed events
Signal efficiency [%]
LL01
LL02
LL03
Kinematic selection (Section 6.3)
73433
64.9
67.4
69.0
High-pT isolated track selection
8458 24.8 (67.6) 26.2 (66.8) 27.2 (66.7)(Section 6.4, 1∼5)Disappearing track selection
304
6.1 (94.6)
6.6 (94.5)
7.3 (94.7)(Section 6.4, 6)99

CHAPTER 6. EVENT SELECTION

6.5 Monte Calro Expectation
The expected breakdown of the background processes after all the high-pT selection criteria is
in Table 6.4. Most of events originate from high-pT charged hadrons in jets and tau hadronic
decays. Muons and electrons have a negligible contribution by applying the lepton veto andthe disappearing track selection. The studies on the charged hadrons in jets or from hadronic
decays of tau are investigated in the following section.
Table 6.4: The breakdown of the SM background process after applying the high-pT isolated
track selection criteria.
MC process fraction (%)
QCD
66.3
W+Njets
10.7
Z+Njets
6.4
tt¯
16.6

100

CHAPTER 7. BACKGROUNDS

Chapter 7
Backgrounds
7.1 Category of Background Tracks
The selection criteria described in Section 6.3 are applied for the search for Long-lived charginos.
There are two main background sources contributing to the events containing isolated high-pT
tracks after these selection requirements. Figure 7.1 shows origins of disappearing tracks.
1. High-pT hadrons interacting with the materials of TRT detector.
2. Low-pT charged particles whose pT is badly reconstructed as high-pT tracks due to scattering in the silicon detector.
The former and the latter are categorized as interacting hadron track and badly reconstructed
track, respectively. High-pT hadrons may cause interactions with the detector materials. The

Figure 7.1: Origins of disappearing tracks.
corresponding particle can give a good track qualities but small number of hits in the TRT Type3 module on the extrapolated track when an hadron interaction takes place in the TRT modules,
especially in Type-1 or Type-2 modules.

101CHAPTER 7. BACKGROUNDS
A small fraction of low-pT charged particles may be scattered with the detector materials ofsilicon detector. This particles may be reconstructed as nearly straight tracks which are high-pT
tracks. The badly reconstructed tracks can contribute to the background for disappearing tracks.
The detail properties of badly reconstructed tracks are also given in Section 7.1.1.
The rate for the events containing these backgrounds are small, thus the background estimation using the Monte Carlo simulation may have the difficulty for the understandings ofthe background tracks. Therefore, this analysis adopts a fully data-driven techniques using the
track pT spectra of backgrounds in the control samples for the extraction of signal yield and thebackground estimation.
This chapter is dedicated for the studies on properties of these backgrounds.

7.1.1 Studies on Background Tracks
The studies on the properties of background tracks in this analysis is performed with Monte
Carlo samples and real data of pp collisions.
Properties of Interacting Hadron Track
Figure7.2 shows the display of a interacting hadron track. Many secondary particle can be seenfrom the point of the interaction with the TRT detector. In order to investigate the properties of

Figure 7.2: Example of a interacting hadron track. A high-pT momentum track makes interaction with TRT detector material. From the point of the interaction in the detector, many ofsecondary particles is generated.
interacting hadron tracks, the single pion MC is employed. Figure 7.3 shows the breakdown of102

CHAPTER 7. BACKGROUNDS
pion tracks. Figure 7.3 (a) and (b) are the truth and the reconstructed pT distributions, respectively. The inelastic interaction track is dominant and its rate has nearly no pT -dependence inthe pT range above 10 GeV. The pT spectrum of interacting hadron tracks is supported to be thesame as that of non-interacting hadron tracks in this analysis. The pT of charged particles are
determined by the silicon detectors. Hence, pT of the reconstructed track is not affected by the
position of hadron interaction in the TRT detector. The reconstructed pT spectrum of interacting
hadron tracks is also supported to be the same as that of non-interacting hadron tracks.
105

105
No interaction
Inelastic interaction
Elastic interaction
Decay in flight

104
103

103

102

102

10

10

1

1

10

20

30

40

50

60

70

80

90

100

10

10-1

10-1

-2

-2

10

10

10-3

10-3

-4

10 10

20

30

40

50

60

70

80

90

No interaction
Inelastic interaction
Elastic interaction
Decay in flight104

10-410

100

20

30

40

50

60

70

80

90

100

20

30

40

50

60

70

80

90

100

Prec
T [GeV]

Ptruth[GeV]T(a) Truth pT(b) Reconstructed pT

Figure 7.3: The breakdown of the interacting hadron tracks in the TRT detector. (a) and (b)show the truth and the reconstructed pT distributions, respectively. The top figure shows pT
spectra of non-interacting charged pions, interacting elastically and inelastically, and decaying
into µ + ν in single charged pion MC events of a flat pT distribution. The bottom figure shows
the ratios with respect to the non-interacting.
P
Figure 7.4 shows the calorimeter activity ∆R<0.1 ETclus /ptrack
T , which is the sum of calorimetercluster ET fulfilling within ∆R < 0.1 around the track over the pT of the track. TrackToCalo
tool is used for the calculation of ∆R. The interacting hadron track cluster around one, i.e. there
are activities on calorimeter originating from actual hadrons. On the other hand, chargino gives
values of nearly zero because neutralino from chargino decay does not make the activities on
calorimeters and there is no actual particle.
From these studies, selection criteria listed below are required for extraction of the control
sample of the interacting hadron tracks.
• Interacting hadron tracks depends on the kinematics, hence, the same kinematic selection
criteria need to be required.
• The pT spectra of interacting hadron tracks expected to be same as that of tracks withno interaction. For the extraction of the pT spectrum of interacting hadron track, thenon-interaction track is chosen by requiring many hits in the TRT Type-3 module.
• There are activities on calorimeter originating from actual hadrons on interacting hadron
track; therefore, the calorimeter activities are required for extracting the the control sample of the interacting hadron track.
103

Arbitrary Units

CHAPTER 7. BACKGROUNDS

1
chargino track (AMSB LL01)
interacting hadron track

10-1

bad track

10-2

10-3

10-4

10-2

10-1

1

10
track
Σ∆ R<0.1 Eclus
T /pTP
Figure 7.4: The ∆R<0.1 ETclus /ptrack
distributions for chargino (solid line), high-pT interactingT
hadron (dashed line) and bad tracks (dotted line) derived from MC events.
Properties of Badly Reconstructed Track
Figure 7.5 shows the pT distribution of reconstructed tracks as a function of pT of truth particle.
Track pT of particle with high momentum is reconstructed properly. However, some of particles
with low momentum, typically less than a few GeV, are reconstructed as a high pT track. Whena low-pT particle is reconstructed as a high-pT track, the trajectory of the track does not reflects
the true particle properly. Figure 7.6 shows the display of the badly reconstructed track. The
corresponding track is shown as a red line. However, there are few corresponding TRT hits tothe track because its track does not originate from a true particle. Thus, the badly reconstructed
tracks could contribute to the background for the chargino search.
Isolated tracks in QCD MC events are used in order to investigate the properties of badly
reconstructed track. Figure 7.7 shows the reconstructed momentum distributions for charged
pions in the range of 0 < ptrue
T < 5 GeVwith a variety of classifications for badly reconstructed
track. The badly reconstructed track is here defined as that a track has no corresponding trueprec −ptrue
charged particle, that is, large σ(pT ), where σ(pT ) ≡ T ptrueT and prec(true)is the reconstructedTT(true) transverse momentum. Actually, σ(pT ) > 5 is required for tracks as the definition of
badly reconstructed track.
• σ(pT ) > 5 (No selection).
• σ(pT ) > 5, |d0 | < 1.5mm and |z0 sin(θ)| < 1.5mm.
• σ(pT ) > 5 and |NSCT | ≥ 6.
• σ(pT ) > 5 and |NPixel | ≥ 1.
When applying the cuts on the impact parameter, the distributions slightly differ from eachother.
104

PT [GeV]

CHAPTER 7. BACKGROUNDS

500
400
300
200
100
0
0

10 20 30 40 50 60 70 80 90 100
Ptrue
[GeV]
T

Figure 7.5: the pT distribution of reconstructed tracks as a function of ptrue
T .

Figure 7.6: Event display of the badly reconstructed track candidate. The corresponding trackis shown as a red line. There is continuous TRT hits of a low momentum particle near to thebadly reconstructed track.

105

CHAPTER 7. BACKGROUNDS

no selection|d |<1.5mm && |z sin(θ)|<1.5mm
00NSCT ≥ 6
NPixel ≥ 1

10-2

no selection|d |<1.5mm && |z sin(θ)|<1.5mm
00NSCT ≥ 6
NPixel ≥ 1

10-1

10-2
10-3

-3

10
3

3

2

2

1
0

1
0

3

2

10

T

(a) 0 < ptrue
T < 1 GeV(b) 1 < ptrue
T < 2 GeV

no selection|d |<1.5mm && |z sin(θ)|<1.5mm
00NSCT ≥ 6
NPixel ≥ 1

10-1

no selection|d |<1.5mm && |z sin(θ)|<1.5mm
00NSCT ≥ 6
NPixel ≥ 1

10-1

10-2

10-2

3

3

2

2

1
0

103
prec [GeV]

102

10
prec
[GeV]
T

1
0

3

2

10

102

10
[GeV]
prec
T

(c) 2 < ptrue
T < 3 GeV

103
[GeV]
prec
T

(d) 3 < ptrue
T < 4 GeV
no selection|d |<1.5mm && |z sin(θ)|<1.5mm
00NSCT ≥ 6
NPixel ≥ 1

10-1

10-2

3
2
1
0

102

103
[GeV]
prec
T

(e) 4 < ptrue
T < 5 GeV

< 1 GeV , (b)Figure 7.7: The pT distribution of badly reconstructed tracks for (a) 0 < ptrue
T
true
true
true
1 < pT < 2 GeV, (c) 2 < pT < 3 GeV, (d) 3 < pT < 4 GeV and (e) 4 < ptrue< 5 GeV.
T
Each distribution is normalized to unity. The ratio of the distribution of each selection (see thetext) to that of no selection is also shown at the bottom of each figure.

106

CHAPTER 7. BACKGROUNDS
Figure 7.8 show the pT distributions of badly reconstructed tracks for each ptrue
T range. Theyshow reasonable agreement in high-pT region. The distributions of badly reconstructed track
does not depend on the momenta of the truth particles. Therefore, the pT distribution of badly
reconstructed track does not depend on the kinematics.

0 < ptrue < 1 GeVT
1 < ptrue < 2 GeVT
2 < ptrue < 3 GeVT
3 < ptrue < 4 GeVT
4 < ptrue < 5 GeV

1

T

10-1

10-2
102

103
prec
[GeV]
T

Figure 7.8: The pT distribution of badly reconstructed tracks. The distributions are normalized
by the number of tracks with pT above 50 GeV.
Furthermore, the number of pixel hits NPixel of the badly reconstructed track is investigated.
Figure 7.9 shows the NPixel distributions of correctly and badly reconstructed tracks. Correctly
reconstructed track is defined as |σ(pT )| < 0.5 while badly reconstructed track is defined asσ(pT ) > 5 or σ(pT ) > 3. The number of NPixel gives around three for correctly reconstructed
tracks. On the other hand, a number of the badly reconstructed track is enhanced by requiring
the small number of the NPixel . Moreover, the calorimeter activity of the badly reconstructed
track is also investigated in Figure7.4. The calorimeter activity of the badly reconstructed track
gives nearly zero similarly to chargino tracks.
From the studies on the badly reconstructed track, the properties of the badly reconstructed
tracks are;
• The pT distribution of the badly reconstructed track does not depend on the kinematics.
• By requiring the small number of Pixel hits, the number of badly reconstructed tracks isenhanced.
• There are no associating calorimeter activity of the badly reconstructed track.
The selection criteria for extraction of two backgrounds from these studies are shown in thefollowing section.

7.2 Control Regions for Background Tracks
The resulting selection criteria for high-pT interacting hadron track and badly reconstructed
track is summarized in Table 7.1.
107

CHAPTER 7. BACKGROUNDS|σ(p )| < 0.5Tσ(p )>3
T
σ(p )>5

104

T

3

10

102

10
0

1

2

3

4

5

6

7

8

9

10

NPixelFigure 7.9: The NPixel distributions of correctly and badly reconstructed tracks in QCD MC
events. Correctly reconstructed track is defined as |σ(pT )| < 0.5 while badly reconstructed trackis defined as σ(pT ) > 3 or σ(pT ) > 5.

Table 7.1: Selection criteria for the control samples of interacting hadron track and badly reconstructed track.
Kinematic selection
Interacting hadron track
Badly reconstructed trackjet
missTrigger
ET > 75 GeV& pT > 55 GeV
pre-scaled jet trigger
jet
Leading pT> 130 GeV——
jet
Leading second and third pT> 60 GeV——
Missing transverse energy> 130 GeV
< 100 GeV
Track quality
Number of pixel hits
Npixel ≥ 1
Npixel = 0
outer
outer
Number of Type-3 hits
NTRT > 10
NTRT3
<5
P
P
clus
track
clus
track
E
/p
< 0.3
E
/p
≥
0.3
Calorimeter Activity∆R<0.1 T∆R<0.1 T
T
T

108

CHAPTER 7. BACKGROUNDS

7.3 Extraction of Background Track Shapes
Figure 7.10 shows the pT distributions in the control samples of interacting hadron tracks andthe shape of the function derived by a maximum likelihood fit. The track pT distribution falls
steeply and has a long tail, which is “power low with exponential tail cutoff” like. This track pT
distribution is fitted by using a function,(1 + x)a0,(7.1)
xa1 +a2 ln(x)where x is pT of tracks in the control samples of interacting hadron and ai (i = 0, 1, 2) are fit
parameters. The fitted results and the covariance matrix results in: 27.5 ± 0.314 ai =  26.5 ± 0.274 
(7.2)


0.401 ± 0.0226
f (x) =



0
1
2 



0 0.09853
0.074220.003009 

cov(ai , a j ) = .
0.07498 −0.0005225  1 0.07422

2 0.003009 −0.0005225
0.00051
The values of the correlation coefficient between parameters, ρi j are also given as


0
1
2 



0
1
0.864
0.424 
ρi j = .
1 −0.0845  1 0.864

2 0.424 −0.0845
1

(7.3)

(7.4)

ρi j is defined as cov(ai , a j )/σi σ j , where σi is the error on ai .
The distribution of badly reconstructed tracks are shown in Figure 7.11. For the badly
reconstructed tracks, the similar functional form is applied but an constant term is appended to
the function in order to reproduce the long high-pT tail as in Equation 7.5.
g(x) =(1 + x)b0+ b3 ,
xb1 +b2 ln(x)(7.5)

where x ≡ ptrack
and bi (i = 0, 1, 2, 3) are fit parameters. The obtained function by the fittingTis also shown in Figure 7.11. The fitted parameters, the covariance matrix and the correlation
coefficient are given as: 83.2 ± 0.356  79.5 ± 0.325  ,bi = 
(7.6)

0.487
±
0.0352
0.0336 ±
3.21


0
1
2
3 


 0
0.12670.08116 0.005561
0.02414 

cov(bi , b j ) =  1 0.08116
0.1054 −0.003554 −0.008744  , 2 0.005561 −0.003554 0.001239 0.004255 
3 0.02414 −0.008744 0.004255
10.29
109

(7.7)

Tracks / 1GeV

CHAPTER 7. BACKGROUNDS

103
s=7TeV,102∫ Ldt = 4.71 fb

-1

10
1
10-1
10-2

∑ E /pSignificance∆R<0.1

clus
T

track
T

≥ 0.3, Nouter
>10
TRT

100

1000

2
1
0
-1
-2

10

20

50

100

200

500 1000
track pT [GeV]

Figure 7.10: The top figure shows pT distribution of interacting hadron track in the control
sample. The data and the fitted line are shown by solid circles and a line, respectively. The
bottom figure is the significance of the data-model difference on a bin-by-bin.

110CHAPTER 7. BACKGROUNDS

Tracks / 1GeV



0
1
2
3 


 0
1
0.702 0.444
0.0211 

ρi j =  1 0.702
1 −0.311 −0.00840  .
−0.31110.0377  2 0.444

3 0.0211 −0.00840 0.0377
1102
s=7TeV,(7.8)∫ Ldt = 4.71fb

-1

10
1
10-1
10-2

∑ E /pSignificance∆R<0.1

clus
T

track
T

< 0.3, NPixel=0

100

1000

2
1
0
-1
-2

10

20

50

100

200

500 1000
track pT [GeV]

Figure 7.11: The top figure shows pT distribution of badly reconstructed track control sample.
The data and the fitted line are shown by solid circles and a line, respectively. The significanceof the data-model difference on a bin-by-bin are also shown in the bottom.
Figure 7.12 shows the pT distributions of badly reconstructed tracks with different numberof the primary vertices NPV . The significant difference cannot be seen with each other.

111

Arbitrary Units

CHAPTER 7. BACKGROUNDSNPV ≤ 45 ≤ NPV ≤ 6
7 ≤ NPV

10-1

10-2

10-3

Ratio to NPV ≤ 4

10-4
2.5
2
1.5
1
0.5
0

3
102

3

10
ptrack [GeV]T

Figure 7.12: The pT distributions of badly reconstructed tracks in events with various NPV .

112

CHAPTER 8. SYSTEMATIC UNCERTAINTIES

Chapter 8
Systematic Uncertainties
8.1 Systematic Uncertainties on Backgrounds
The normalizations for the two background components are free parameter in the fitting forsignal extraction. The uncertainties on the background shapes are incorporated as nuisance parameters in the fitting. The covariance matrices in Section 7.3 are incorporated as uncertainties
on the background shapes.

8.2 Systematic Uncertainties on Signal Normalization
The following items are the systematic uncertainties on the signal normalization to be considered in the fitting.

8.2.1 Uncertainty on the Theoretical Cross Section
Theoretical uncertainties on the signal cross section are evaluated by computing the changes
in the cross section when the renormalization and factorization scales. For the estimation of
uncertainty of the signal cross section, the uncertainties listed below are taken into account.
• Choice of parton distribution function (PDF).
For the calculation, CTEQ6.6 [76] and MSTW2008 NLO [79] PDFs are employed.
• PDF errors.
The uncertainty originating from PDF is evaluated by error sets of the PDF set.
• Uncertainty on strong coupling constant (αs ).
The uncertainty of αs arising from the scale of the strong coupling constant.
• Uncertainty on renormalization/factorization scale.
The renormalization scale is the the scale which determines the strong coupling constantby the renormalization theory. The factorization scale is the scale which determines thestrong coupling constant of short-distance interaction of partons.

113

CHAPTER 8. SYSTEMATIC UNCERTAINTIESThe uncertainty on the cross section arising from the renormalization/factorization scale (µ)of
the strong coupling constant αs (µ) is estimated by varying the scale µ with factors of 0.5 or 2.
A total uncertainty on the cross section for LL01 model results in 27.2% by taking the
maximum difference between 68% confidence level upper and lower limits on the cross sections
calculated using CTEQ6.6 and MSTW2008 NLO PDFs. The resulting uncertainties on the crosssection for the other models are also summarized in the Table 8.2.1. The dominant component of
the uncertainty comes from PDF errors. The second component originates from the uncertainty
on the renormalization/factorization scale.
Table 8.1: The uncertainties on the theoretical cross section of the AMSB signals.
Signal
LL01
LL02
LL03
Uncertainty ±27.2 % ±36.7 % ±47.1 %

8.2.2 Uncertainty on the Jet Energy Scale
Jets are reconstructed at the electromagnetic scale, which is the basic signal scale for calorimeters. This energy scale is established using test-beam measurements. The jet energy is scaled inorder to correct the energy and momentum of the jets measured in the calorimeter to those of thejet at the hadronic scale. this uncertainty is estimated according to Ref.[80]. The contributions
to the jet energy scale systematics are following.
• Uncertainty from the jet energy scale calibration method
There are any deviation in transverse momentum and energy response after calibrationof the jet energy scale to the nominal MC. This is due to the assumption that every constituent needs the same average compensation when deriving the calibration constants or
the same correction factor used for transverse momentum and energy of jets.
• Uncertainty from the calorimeter response
The response of single particles interacting in calorimeters is used to derive the uncertainty on jet energy scale. The uncertainty of the calorimeter response to a jet is obtained
from the uncertainty of the individual particles constituting the jet.
• Uncertainty from the detector simulation
The uncertainty is arising from thresholds of calorimeter cell noise or the additional detector material.
• Uncertainty from the the physics model and parameters employed in the MC
The contributions from the modeling of the fragmentation and underlying event of the
MC are obtained by comparison of the several MC.
For each pT , η bin, the contributions from these uncertainties are added in quadrature. The
uncertainty arising from jet energy scale affects the overall normalization. The uncertainty on
missing transverse energy due to the jet energy scale is also taken into account. Figure 8.1
shows the distributions of ETmiss and the first leading jet pT distributions of signal sample after
kinematic selections with the nominal value and ±σ variations. The resulting uncertainty is
estimated to be 2.8%.
114

CHAPTER 8. SYSTEMATIC UNCERTAINTIES

103
nominal2

nominal

+1 σ

+1 σ

-1 σ

-1 σ

10

102

10
10

1
0

100 200 300 400 500 600 700 800 900 1000

0100 200 300 400 500 600 700 800 900 1000

Emiss
[GeV]
T

PT [GeV](a) ETmiss(b) the first leading jet pT

Figure 8.1: The distributions of ETmiss and the first leading jet pT distributions of signal sample
after kinematic selections with the nominal value and ±σ variations. The black, red and blueshows the nominal value, +1σ and −1σ variations, respectively.

8.2.3 Uncertainty on the Track Reconstruction Efficiency
The modeling of the Inner Detector materials changes reconstruction efficiency of tracks. The
uncertainty on reconstruction efficiency is arising from the modeling of materials. The uncertainty is estimated in the Ref.[81, 82].
The overwhelming majority of particles used for the estimation is hadrons. A good description of the materials in the detector is needed for determining the reconstruction efficiency. In
order to estimate the uncertainty of the reconstruction efficiency, two different data-driven methods are used. The first method reconstructs the invariant mass of KS0 mesons decaying into two
charged pions. The second method compares the track lengths in the data and simulation. The
first method studies the mass as a function of the decay radius of the KS0 meson. This method has
sensitivity to small radii. The second method probes the material description in the simulationin terms of the interaction length in the SCT. The combination of both methods provides goodsensitivity throughout the silicon detectors. The uncertainty on the reconstruction efficiency inthe barrel region is estimated to be 2.0% in the barrel region.

8.2.4 Uncertainty on the Integrated Luminosity
The uncertainty on the integrated luminosity is investigated in Ref.[83, 84]. There are some ofuncertainties on the integrated luminosity.
• vdM Scan Calibration
As mentioned in Appendix A, the vdM scan is employed for the luminosity determination.
The uncertainty of the vdM Scan is the dominant uncertainty in the luminosity calibration.
• Afterglow Correction
The luminosity detectors observe some small activities in the BCISs immediately following a collision. With a 2011 bunch spacing of 50ns and a relatively large number ofbunches, this afterglow tends to reach a stable equilibrium after the first few bunches in115

CHAPTER 8. SYSTEMATIC UNCERTAINTIESa train, and is observed to scale the instantaneous luminosity. The effect of the afterglow
is taken into account for the luminosity determination. The uncertainty of the afterglow
correction is also considered.
• Long-term Stability
One source of potential uncertainty is the assumption that σvis determined by the vdMscans is stable in the entire 2011 runs. Several effects could degrade the long-term stability of a detector.
• µ Dependence
The dependency of the average numbers of interactions per bunch crossing µ is also assessed.
The uncertainty on the integrated luminosity is estimated by employing the data with low µ.
The uncertainty is larger for the last part of the 2011 data due to the increasing pile-up. The
resulting uncertainty is estimated to be ±3.9%.

8.2.5 Uncertainty on the Pile-up Modeling
The uncertainty arising from the pile-up modeling in the simulation is evaluated by comparing
the difference of acceptance of the signal sample with the nominal value of average number ofpile-up interaction hµi to one with the different value of hµi. The sample with a different hµi are
obtained by re-weighting a factor of 0.9 on hµi.

8.2.6 Uncertainty on the Trigger Efficiency
The measured trigger efficiencies for data and MC events as a function of ETmiss are shown in
Figure 8.2. Their turn-on curves are parametrized by the fit with a function,!!
ETmiss − t1
missε(ET ) =,(8.1)
1 + erf√2
2σwhere t and σ are the threshold and resolution parameters. By varying t and σ within their
fit uncertainties and taking the difference between data and MC events, the uncertainty on thetrigger efficiency is evaluated. The resulting uncertainty is quoted as ±2.3%.
Summary
Contributions of each systematic uncertainty in signal expectations are summarized in Table 8.2.6. In total, an uncertainty of ±27.8% is quoted on the signal normalization.

116

efficiency

CHAPTER 8. SYSTEMATIC UNCERTAINTIES

1
0.8
0.6
0.4
data

0.2
SM BG

0

50

100

150

200

250

offline Emiss[GeV]
T

Figure 8.2: Trigger efficiencies for data and MC events as a function of ETmiss

Table 8.2: Summary of systematic uncertainties in the signal normalization.
SourceUncertainty
Theoretical cross section±27.2 %
Jet energy scale±2.8 %
Track reconstruction efficiency±2.0 %
Luminosity±3.9 %
Pile-up modeling±0.5 %
Trigger efficiency±2.3 %
Total±27.8 %

117

CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION

Chapter 9
Background Estimation and Signal
Extraction
9.1 Estimation of Background and Signal Yields
For the estimation of background and the extraction of signal yield, a simultaneous fit on the
track pT is performed. The pT shapes of the two background components derived using theircontrol samples, as described in Section 7.1 are used in the fit. The pT shape of the signal isfully based on the MC prediction with the application of all the selection requirements. The
following sections describe the details of the fit procedure.

9.1.1 Unbinned Maximum Likelihood Fit
A statistical test is performed in order to evaluate how well the observed data agree with a given
signal model. A likelihood function is employed as the estimator for the statistical test and theunbinned maximum likelihood is performed. In this analysis, pT spectra of the signal and thebackground tracks are used; they give a discrimination of signal events to the background, as
shown in Figure 9.1. The effects of systematic uncertainties are incorporated via constraint terns
on nuisance parameters; the overall normalization of the signal and the parameters describing
the background track pT shapes are set as nuisance parameters.
Using track pT spectra, the resulting likelihood function, L, is given as
L=
L(pT ; µ, nb , α, ~β) =nobs
YL(pT ; µ, nb , α, ~β),

µnexp
nb
s
Lb (pT ; ~βbad , ~βhad ),exp L s (pT ; µ, α) +nb + µn s
nb + µnexp
s

(9.1)
(9.2)

= Lσ s ε s (1 + α),
nexp
s

(9.3)

Lb (pT ; ~βbad , ~βhad ) = fbad Lbad (pT ; ~βbad ) + (1 − fbad )Lhad (pT ; ~βhad ),

(9.4)

where

118

CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION
µ
nobs
nexp
s
nb
L
σs
s
fbad
α
~βbad
~βhad

:
:
:
:
:
:
:
:
:

signal strength,
the observed number of events,
the expected number of signal events for a given signal model,
the number of background events,
the integrated luminosity,
the signal cross section,
the signal selection efficiency,
the fraction of badly reconstructed tracks in the background,the nuisance parameter representing the overall normalization of
the signal yield,: the nuisance parameters representing the pT spectrum of the badly
reconstructed tracks,: the nuisance parameters representing the pT spectrum of the interacted hadron tracks.

The likelihood functions of L s ,Lbad and Lhad in Equations 9.1 and 9.4 are given by incorporating
the effects of the systematic uncertainties as
L s (pT ; α) = F s (pT )N(α; ∆norm ),(9.5)

Lbad (pT ; ~βbad ) = Fbad (pT ; ~βbad )M(~βbad ; C~bad ),(9.6)

Lhad (pT ; ~βhad ) = Fhad (pT ; ~βhad )M(~βhad ; C~had ),

(9.7)

where
Fs
∆norm
N
Fbad
Fhad
Mhad
Cbad
Chad

: the normalized probability density function derived from signal
Monte Carlo samples,: the systematic uncertainty of the signal normalization,: the normal distribution,: the normalized probability density function derived from the control samples of badly reconstructed tracks,: the normalized probability density function derived from the control samples of interacting hadron tracks,: the multivariate normal distribution,: the covariance matrix of the normalized probability density function of badly reconstructed tracks,: the covariance matrix of the normalized probability density function of interacting hadron tracks.

The hypothesis test uses the profile likelihood ratio [85] to compare two hypothesis of ’backgroundonly’ and ’signal+background’ models.

9.2 Fit results
Figures 9.2 (a) and (b) show the pT distributions of candidate tracks with the best-fit spectra
derived by the ’signal + background’ and ’background only’ fits, respectively. By the ’signal+ background’ fitting, the signal strength of LL01 model results in less than 0.048 at 68%CL,119

Probability density

CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION

1∼± ) = 1ns)
Signal events (LL01, τ(χ1Charginos in signal events
Hadron track background
Bad track background

-1

10

10-2
10-3
10-4
10-5
10

20

100

50

200

1000
500
track pT [GeV]

Figure 9.1: Probability density functions employed for the background estimation and the signal
extraction. The dotted line is the shape of the pT distribution in the control sample of theinteracting hadron tracks. The dashed line is the shape of the badly reconstructed tracks. The
hatched histogram is the pT distribution of the signal Monte Carlo (LL01).
i.e. no excess of data observed and expected number of background events is 303.9 ± 16.7.
The observed pT spectra is consistent with the background-only hypothesis. fbad is nearly zeroas expected. Furthermore, the results with ’background only’ fits are also consistent with thatof the ’signal + background’ fits. The resulting values of the fit parameters are summarized inTable 9.1.
Table 9.1: Summary of the fit
signal(LL01)+background
Signal strength<0.048 (68% CL)
Number of background events
303.9 ± 16.7
Fraction of bad tracks
1.5 × 10−6 ± 1.7 × 10−1p-value of null hypothesis—

background only—
304.0 ± 16.9
2.2 × 10−8 ± 1.4 × 10−1
0.50

9.3 Validation
Various of validations for the fitting and the background estimation are performed.

120

102

Tracks / 1GeV

Tracks / 1GeV

CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION

Data
Hadron track background10

Bad track backgroundTotal background + signal

1
s=7TeV,102
Data

Total background∫ Ldt = 4.7 fb-1

s=7TeV,

10-1

10-2

10-2
20

50

100

200

Bad track background

1

10-1

10

Hadron track background

10

1000
500
track pT [GeV](a) signal+background fit

102∫ Ldt = 4.7 fb-1

103
track pT [GeV](b) background-only fit

Figure 9.2: The pT distribution of candidate tracks with the best-fit shape of the ’signal +background’ and ’background only’ model. The signal point of LL01 and τχ̃±1 = 1 ns are used,
but the best-fit signal contribution is found to be zero.

9.3.1 The Background Shape with Alternative Functions
In order to assess any possible biases on the fit result due to the choice of the functional form
especially for the hadron background tracks, the fit results with alternative functions are compared. The shapes of interacting hadron tracks are derived by adopting the following functional
forms that are expected to reasonably describe the data:f (x) =

a0 (1 + x)a1,
xa2 +a3 ln x

a0 (a1 + x)a2,
xa3 +a4 ln(x)a0f2 (x) =,(a1 + a2 x + a3 x2 )a0
f3 (x) =,(a1 + a2 x + a3 x2 )a4
a0
f4 (x) =,(a1 + a2 x + a3 x2 + a4 x3 )a5
a0 exp(−x/a1 )f5 (x) =.
(a2 + x)a3
f1 (x) =

(9.8)
(9.9)
(9.10)(9.11)(9.12)(9.13)The best-fit shapes of each functional form and the resulting χ2 values of the fit are shown in
Figure 9.3 and Table 9.2. In the figure, the distributions are normalized to unity. They shows anagreement comparatively with each other down to the fourth order of magnitude. The choice ofthe functional form for the background tracks has a negligible impact on the final results.

9.3.2 Validation of the Signal Extraction Method
A closure test is performed based on an ensemble of pseudo-experiments of observing threehundred and four events with various values of fit parameters. This pseudo-experiments are121CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION

Function
χ2
f (x)
47.00
f1 (x)
44.41
f2 (x)
89.54
f3 (x)
67.08
f4 (x)
67.08
f5 (x)
66.04
Table 9.2: Corresponding χ2 values for the interacting hadron track.

1aa +a log(x)a0(1+x) 1/x 2 3
a +a log(x)aa0(a +x) 2/x 3 4
1a0/(a +a2x+a3x2)
1
aa0/(a +a2x+a3x2) 41
a5a0/(a +a2x+a3x2+a4x3)
1
a3
a0exp(-x/a )/(a +x)

10-1

10-2

1

2

-3

10

10-4

-5

10

102

3

10
track pT [GeV]

Figure 9.3: Best-fit form of alternative functions for interacting hadron track shape.

122

CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION
performed on the assumption of the appearance of signal events. Figures 9.4 and 9.5 show
(true)
fitted values of fbad and µ as a function of the value used as input ( fbad). In addition, Figures( f itted)(true)
9.4 (c) and 9.5 (c) show fbad − fbad distributions with the pseudo-experiments without andwith signals, respectively.
The signal strength obtained by the pseudo-experiments injecting the LL01 signal results in( f itted)(true)(true)
around one for difference fbad
. The fitted value fbad
is also correctly estimated for fbad
with the deviation σ( fbad ) ∼ 0.2. Hence, if the signals are in the observed data, this datadriven method works properly. On the other hand, the signal strength obtained by the pseudo( f itted)(true)
experiments without signals results in around zero for any fbad
. The fitted value fbad
obtained by the pseudo-experiments is also correctly estimated. Therefore, even if the signal isabsent in the observed data, this method estimates the number of signals and the fraction of thebadly reconstructed tracks.

9.3.3 Distributions of Candidate Tracks
After all the selection cuts are applied, 304 events containing a high-pT isolated track candidates
are remained in the entire data. Figures 9.6 (a) and (b) are the distributions of the number ofhits in the TRT inner and middle modules for candidate tracks. The background expectations ofinteracting hadron tracks and badly reconstructed tracks are derived from control samples andinnermiddlenormalized to the observed number of candidate tracks. NTRT
and NTRTof badly reconstructed
tracks is small because this track does not originate from a actual particle. On the other hand,innermiddleNTRTand NTRTof interacting hadron tracks, which are associates to true charged particle,
becomes large.
The observed tracks follows the distributions of the interacting hadron tracks. This is consistent with the result of the estimation that the interacting hadron tracks are dominant backgroundas expected.

123

f bad(fitted)CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION1
0.9

nobs=304, BG +Signal(LL01)

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.2

0.4

0.6

0.8

1
(true)f badµ(fitted)

fittedtrue(a) fbadvs. fbad5
nobs=304, BG +Signal(LL01)
4
3
2
1
0

0

0.2

0.4

0.6

0.8

1
(true)f badtrue(b) µfitted vs. fbad

103

nobs=304, BG +Signal(LL01)

102

f bad(true)=0.00
f bad(true)=0.25
f bad(true)=0.50
f bad(true)=0.75
f bad(true)=1.00

10

1-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

1(fitted)(true)
f bad - f bad

true
fitted− fbad(c) fbad

Figure 9.4: The fitted parameters of fbad (a) and µ (b) as a function of true fbad derived frompseudo-experiments observing 304 events including signals (LL01). The pull distributions offbad (c) for various true values are also shown.
124

f bad(fitted)CHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION1
0.9

nobs=304, BG only

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.2

0.4

0.6

0.8

1
(true)f badµ(fitted)

fittedtrue(a) fbadvs. fbad5
nobs=304, BG only
4
3
2
1
0

0

0.2

0.4

0.6

0.8

1
(true)f badtrue(b) µfitted vs. fbad

103

nobs=304, BG only

f bad(true)=0.00
f bad(true)=0.25
f bad(true)=0.50
f bad(true)=0.75
f bad(true)=1.00

102

10

1
-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

1(fitted)(true)
f bad - f bad

true
fitted− fbad(c) fbad

Figure 9.5: The fitted parameters of fbad (a) and µ (b) as a function of true fbad derived frompseudo-experiments observing 304 events with the only backgrounds. The pull distributions offbad (c) for various true values are also shown.
125

102

EventsEventsCHAPTER 9. BACKGROUND ESTIMATION AND SIGNAL EXTRACTION

data
interacting hadron tracks

102

data
interacting hadron tracks

bad tracks

bad tracks

1010∫ Ldt = 4.7 fb∫ Ldt = 4.7 fb

-1

-1

1

10-10

1

2

4

6

8

10 12 14 16 18

10-10

20 22

5

10

15

20

25

NinnerTRT

30
NmiddleTRT(a) The TRT inner module(b) The TRT middle module

Figure 9.6: The distributions of the number of hits in the TRT module. The backgroundexpectations are derived from the control samples and normalized to the observed number oftracks. (a) and (b) show the distributions of hits in the inner module and the middle module,
respectively.

126

CHAPTER 10. RESULTS AND DISCUSSION

Chapter 10
Results and Discussion
10.1 Results
Following the absence of an excess of data in the pT spectrum of the high-pT isolated disappearing tracks, the constraint on the isolated disappearing tracks is set.

10.1.1 Model Independent Limits
Model-independent upper limits on the cross-section times the acceptance for the non-SM processes with the final state satisfying the kinematic and track selection criteria are calculated.
Figure 10.1 shows the upper limit at 95% CL on a cross section times acceptance from a counting of candidate tracks fulfilling that pT > p0T as a function of p0T , where p0T is the thresholdon the track pT . The expected pT spectrum of background tracks is derived by the backgroundonly fit in the region 10 < pT ≤ 50 GeV. A limit of less than 10−3 pb for p0T > 100GeVon the
cross-section times the acceptance is set at 95% CL.

10.1.2 Constraints on the Production Cross Section and the Properties ofχ̃±1
The upper limits on the production cress section for a given model at 95% confidence level isset by a point where the confidence level ’signal+background’ hypothesis falls behind 5% when
scanning a confidence level along various values of signal strength µs . Figure10.2, 10.3 and10.4 show the upper limits on the cross section of LL01, LL02 and LL03 models at 95% CL
as a function of the proper lifetime of the chargino. The interval 0.2< τχ̃±1 <90 ns is excluded
for the LL01 model. A limit on the production cross section for chargino having a lifetime
1 < τχ̃±1 < 2 ns is set to be less than 8.7 × 10−3 pb. With the given dataset, the sensitivity is notenough to constrain the LL03 model at any value of τχ̃±1 .
Figure 10.5 shows the constraint on the chargino mass and lifetime.The constraint on chargino
mass up to nearly 118 GeV with the lifetime of 1 ∼ 2 ns is set at 95% CL. This constraint isobtained by interpreting the cross section limits for the LL01, LL02 and LL03 models describedabove. Using the upper limits of µ s of the given models for each lifetime, the point at which theµ s gives a value below one is calculated by using the linear interpolation. Figure 10.6 shows127σ( pT > p0T ) × A [pb]CHAPTER 10. RESULTS AND DISCUSSION

10-1
Observed 95% CL limit
Expected 95% CL limits = 7 TeV
-2

10

∫

Expected (±1σ)-1Expected (±2σ)

Ldt = 4.7 fb

10-3

50

100

150
p0
T

200
[GeV]

Cross section [pb]Figure 10.1: Model-independent upper limits on the cross section times the acceptance for an
non-SM physics production with an isolated disappearing track with pT > p0T as a function of
p0T . The observed bound at 95% CL and the expected bound with an integrated luminosity of
4.71 fb−1 are shown. The background estimate is derived from the background-only fit in theregion 10 < pT ≤ 50 GeV.

mAMSB ( LL01: m =32TeV, m0=1.5TeV, tanβ=5, µ >0 )3/2

Observed 95% CL limit

1

Expected 95% CL limit
Expected ( ±1σ )Expected ( ±2σ )

10-1
LL01

10-2
s=7TeV,

-3

10

10-1

1

10

∫ Ldt=4.7 fb-1102τχ∼± [ns]1

Figure 10.2: The observed and expected upper limits on the signal cross section as a function of
chargino lifetime at 95% CL for mχ̃±1 = 90.2 GeV. The band and dotted line indicate the range
where the limit is expected to lie, assuming no signal. The line of 6.79 × 10−2 pb corresponds
to the theoretical cross section of the LL01 model.
128

Cross section [pb]CHAPTER 10. RESULTS AND DISCUSSION

10-2
LL02
mAMSB ( LL02: m =41TeV, m =1.8TeV, tanβ=5, µ >0 )3/2

0Observed 95% CL limit
Expected 95% CL limit
Expected ( ±1σ )s=7TeV,

Expected ( ±2σ )

10-4

10-1

1

10

∫ Ldt=4.7 fb-1102τχ∼± [ns]1

Cross section [pb]Figure 10.3: The observed and expected upper limits on the cross section as a function of thechargino lifetime at 95% CL for mχ̃±1 = 117.8 GeV. The line of 8.66 × 10−3 pb corresponds tothe theoretical cross section of the LL02 model.

10-2

LL03
mAMSB ( LL03: m =51TeV, m 0=2TeV, tanβ=5, µ>0 )3/2-4Observed 95% CL limit
Expected 95% CL limit

10

Expected ( ± 1σ )Expected ( ± 2σ )

10-1

1

s=7TeV,10∫ Ldt=4.7 fb-1102τχ∼± [ns]1

Figure 10.4: The observed and expected upper limits on the cross section as a function of thechargino lifetime at 95% CL for mχ̃±1 = 147.7 GeV. The line of 1.16 × 10−3 pb corresponds tothe theoretical cross section of the LL03 model.

129

140

(mAMSB: m <32TeV, m0<1.5TeV, tanβ=5, µ>0)
3/2

Observed 95% CL limit
Expected 95% CL limit
Expected (±1σ)

1mχ∼± [GeV]

CHAPTER 10. RESULTS AND DISCUSSION

130

s=7TeV,∫ Ldt = 4.7 fb

-1

120
110
100
90
10-2

10-1

1

10

102
τχ∼± [ns]1

Figure 10.5: The constraint on the chargino mass and lifetime with 4.7fb−1 data. The observed
bound is set at 95% CL. The black line shows the observed bound and the dashed blue line
shows the expected bound. The constraint on chargino mass up to nearly 118 GeV with the
lifetime of 1 ∼ 2 ns is set.
the constraint on the AMSB models in the m0 -m 32 plane. The constraint is calculated by interpreting the results on the assumption of τχ̃±1 = 0.3(1.0) ns. In the region of m0 > 2000 GeV, theconstraint of m 32 < 34(38) TeV is set. The constraint on a chargino with τχ̃±1 = 1 ns is set to
be around 120 GeVin the region that m0 > 2000 GeV while the constraint on a chargino withτχ̃±1 = 0.3 ns is set to be around 100 GeVin the same m 32 region. In the small m0 region, more
stringent limits are set: m 32 < 38(48) TeV for m0 = 1000 GeV at 95% CL.

10.2 Discussion
The direct search for decaying chargino is performed in this analysis. The method for theidentification of the disappearing tracks is established in order to distinguish the exotic signalsof the high-pT tracks disappearing in the detector. For this search, the TRT detector is essential
because it has a large number of drift tubes and provide continuous hits for charged particles.
The analysis techniques newly developed in this dissertation make it possible to explore newlong-lived particles expected to appear in many SUSY scenarios, even in pp collisions where
huge background particles prevent finding such signatures.
Moreover , a search for the AMSB with the direct chargino pair production is promising as±
an extension of this analysis. The χ̃1 has a lighter mass than that of colored sparticle, whichleads to a larger production cross section as mentioned in Section 4.1.1. The production of the
AMSB events via electroweak process in pp collisions is as following:
± 0

+ −

pp → χ̃1 χ̃1 j, pp → χ̃1 χ̃1 j,
130(10.1)

m3/2 [TeV]CHAPTER 10. RESULTS AND DISCUSSION

80mAMSB: tanβ=5, µ>070±
Observed 95% CL limit :τ(∼χ )=1ns1±
Expected 95% CL limit :τ(∼χ )=1ns1±
Expected (± 1σ) : τ(∼χ )=1ns1±
Observed 95% CL limit :τ(∼χ )=0.3ns
1±
Expected 95% CL limit :τ(∼χ )=0.3ns
1±
Expected (± 1σ) : τ(∼χ )=0.3ns
1±
Excluded by LEP2: m(∼χ )<92GeV

s=7TeV60∫ Ldt = 4.7 fb

-1

50

1

Tachyonic Particle
NO EW Symmetry Breaking

40
30
20
1000

2000

3000

4000

5000

6000

m0 [GeV]m3/2 [TeV](a) with expected band

80
mAMSB: tanβ=5, µ>070

Observed 95% CL limit : τ(∼χ )=1ns±1

s=7TeV

60∫±
Observed 95% CL limit : τ(∼χ )=0.3ns
1-1±
Excluded by LEP2: m(∼χ )<92GeV

Ldt = 4.7 fb

150

Tachyonic Particle
NO EW Symmetry Breaking

40
30
20
1000

2000

3000

4000

5000

6000

m0 [GeV](b) without expected band

Figure 10.6: The constraint on the AMSB models in the m0 -m 23 plane. (a) shows the observed
and expected upper limits. (b) shows the only observed excluded region. The black line andthe dashed blue line show the observed and the expected upper limits for chargino having alifetime τχ̃±1 = 1 ns at 95% CL, respectively. The red line and the dashed orange line show theobserbed and the expected upper limits for chargino having a lifetime τχ̃±1 = 0.3 ns at 95% CL,
respectively. The red region is theoretically excluded because the sfermion becomes a tachyon
due to a small m0 . The green region is also theoletically excluded due to no electroweak symmetry breaking. The mass of chargino in the gray region is below 92 GeVand is experimentally
excluded by the LEP2.
131

CHAPTER 10. RESULTS AND DISCUSSION
where j denotes an energetic jet from initial-state radiation used to trigger the signal event.
However, these jets in these events are soft or absent, therefore, the dedicated trigger for the
events must be thought out well.
In addition, the use of pixel-seeded tracks may help to improve the sensitivity. This analysis
is based on well-reconstructed tracks. Hence, it is impossible to detect charginos decaying before the TRT detector as mentioned in Section 4.1. The number of chargino falls exponentiallyas a function of the decay length. The charge of the hits in the pixel detector is read out, andexpected to be also useful for the search for the short track with large dE/dx originating fromcharginos decaying in the SCT detector. However, the underlying hits from hadrons such aspions is enormous at pp collisions. These extended searches require dedicated studies on the
track reconstruction and its performance.
There are many ideas for improving the sensitivities of the search for long-lived charginos.
It may be challenging to develop the trigger dedicated for the direct chargino pair production
and the method for the detection of the short track with large dE/dx. However, they must bevery interesting and attracting studies and lead further understandings of the physics on the
supersymmetry.

132

CHAPTER 11. SUMMARY

Chapter 11
Summary
The search for long-lived
charginos inspired by the AMSB models is performed using 4.7 fb−1 data√of pp collisions at s = 7 TeV with the ATLAS detector.
The AMSB model is a very attractive SUSY model for a simple mechanism of the SUSY
mediation. In the AMSB model, the wino is the lightest gaugino. The dominant component±
0of the lightest chargino χ̃1 and the lightest neutralino χ̃1 are charged and neutral wino respec±0
tively. The mass of χ̃1 and χ̃1 are degenerated and the difference of masses are nearly a few
hundred MeV. Due to the mass degeneracy, the lifetime of the lightest chargino becomes long.
The lightest chargino produced in LHC decays to energetic neutralino and a soft charged pion.
When the charginos decay in the inner detector of the ATLAS, the exotic signal of the chargino
is expected. The lightest chargino having a long lifetime is reconstructed as a high-pT trackwith the detector. Neutralino escapes detection and a soft charged particle is hard to be reconstructed in the detector. Therefore, the chargino decaying in the tracking volume is expected tobe reconstructed as “disappearing ”track.
In this dissertation, a method for detecting such chargino tracks is newly developed. The
TRT detector is suitable for detecting the long-lived chargino signals. The TRT detector consistsof a large number of the drift tubes and the number of hits are proportional to the decay point ofouter
a particle. In this analysis, the number of TRT hits in the outer module (NTRT) is employed for
identification of the decaying track in the inner detector. The high-pT isolated tracks is required
outerthat NTRTis less than five as a chargino track selection
In this search, the data of pp collisions collected with the ATLAS detector is corresponding
to 4.7fb−1 . The analysis is focused on the colored sparticle pair production process. As event
selection criteria, large missing ET and multiple energetic jets are required. The chargino track
selections are required for the events fulfilling these event selection.
After the selection requirements are applied, the major backgrounds are Interacting hadron
track and Badly reconstructed track. Interacting hadron track is a dominant source of the background for this analysis. This track originates from jets or taus and makes hadron interaction
with the TRT detector material. The second source of the background is badly reconstructed
tracks. This is a high-pT mis-reconstructed track of the low-momentum particle which is scattered in the silicon detector materials.
In order to estimate backgrounds and extract the signal yields, the data-driven method is
employed by using the unbinned maximum likelihood techniques. The pT spectra of the signal and two backgrounds are used for the estimation. The pT spectra of two background are
133

CHAPTER 11. SUMMARY
extracted from these control samples of each backgrounds. The pT spectrum of the candidate
tracks is consistent with the background-only hypothesis and no excess of data is found.
New constraints on the chargino properties and the AMSB model parameters are then set.
The constraint on a chargino with τχ̃±1 = 1 ns is set up to around 120 GeV in the region thatm0 > 2000 GeV while the constraint on a chargino with τχ̃±1 = 0.3 ns is set up to around
100 GeVin the same m 32 region. In the small m0 region (m0 < 2000 GeV), the constraint on achargino with τχ̃±1 = 0.3 ns having a mass mχ̃±1 ∼ 150 GeV is set at 95%CL.

134

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141

APPENDIX A. LUMINOSITY DETERMINATION

Appendix A
Luminosity Determination
A.1 Luminosity
The instantaneous luminosity [84] at pp collider is expressed as,
L=

Rinel
σinel

(A.1)

where Rinel is the rate of inelastic collisions and σinel is the pp inelastic cross section. This
expression is also described asµnb fr
L=
(A.2)
σinel
where µ, nb and fr are the average number of inelastic interaction per bunch crossing, the numberof bunch crossing and a revolution frequency, respectively. The instantaneous luminosity also
can be rewritten asµvis nb fr µvis nb fr
L=
=
(A.3)
εσinelσviswhere ε is the efficiency for an inelastic pp collision to satisfy the event selection, and µvis isdefined as εµ, which is the average number of visible inelastic interaction per bunch crossing.
The visible cross section σvis is defined as εσinel , which is the calibration constant that relatesµvis to L. µvis is measured by using several sub-detectors in the ATLAS.
In terms of the beam parameters, the absolute luminosity is expressed as,
Z
L = nb fr n1 n2 ρ1 (x, y)ρ2 (x, y)dxdy,(A.4)
where n1 and n2 are the numbers of particles in the two colliding bunches and ρ1 (x, y) andρ2 (x, y) are two transverse beam distributions[86, 87, 88]. For equal Gaussian beams,
"
#
1
x2
y2
ρ1 (x, y) = ρ2 (x, y) = √exp − 2 − 2 .
(A.5)
2Σ x 2Σy
2πΣ x Σy142

APPENDIX A. LUMINOSITY DETERMINATION
where Σ x and Σy characterize the widths of the horizontal and vertical beam profiles.
" 2
#
Z
1
x
y2
L = nb fr n1 n2
exp − 2 − 2 dxdy
2πΣ2x Σ2y
Σ x Σy1
Σ x Σy= nb fr n1 n22πΣ2x Σ2ynb f r n1 n2=2πΣ x Σy(A.6)

For determination of Σ x and Σy , van der Meer (vdM) Scan is employed. The observed event
rate is recorded when scanning the two beams across each other in x-direction and y-direction.
This measurements gives two bell-shaped curves, with the maximum rate at zero separation. Σ xand Σy can be extracted from these curves. Using Σ x and Σy determined by the vdM scan, theluminosity L is calculated by Equation A.6. σvis is also extracted from A.3 using the measured
value of L.
The vdM technique allows the determination of σvis without a priori knowledge of theinelastic pp cross section. The ATLAS uses the vdM technique for the determination of theabsolute luminosity. The basic time unit for storing luminosity information is referred as the
Luminosity Block (LB) which is set by the ATLAS DAQ system. The duration of a LB is about
two minutes. All data quality information are stored for each LB.

A.2 Luminosity Detector
Several detectors such as the Inner Detector or the Forward Detector are employed for the luminosity determination. In the several sub-detectors of the ATLAS, the Beam Conditions Monitor(BCM) is mainly used for the luminosity calculation. The primary purpose of BCM is monitoring beam loses and providing fast feedback to the accelerator operation. The BCM consists of
two arms of diamond sensors located at Z = ±184 cm and r = 5.5 cm. It uses programmablefront-end electronics to histogram the single-sided and coincidence rates as function of Bunch
Crossing Identifier (BCID). These histograms are read out by a software and made available
to other online applications. The BCM has a excellent timing (0.7ns) which allows for therejection of backgrounds from beam-halo.

A.3 Luminosity Calculation
The calculation of instantaneous luminosity is performed by the Online Luminosity Calculator(OLC). The task of OLC is retrieving the raw luminosity information such as hit counts or
number of colliding bunches nb and using these data to determine µ. There are several algorithm
for calculation and the OLC outputs the instantaneous luminosity, which is averaged over all
colliding BCIDs for each algorithm.
Main algorithm using the BCM detector counts the number of events per bunch crossings(BC) in which at least one hit above threshold occurs on either the A-side, the C-side or both.
The value of µvis
i used to determine the bunch luminosity Li in BCID i is obtained from the raw
number of counts Ni and the number of bunch crossings NBC . The algorithm is assuming that:143

APPENDIX A. LUMINOSITY DETERMINATION• the number of pp interactions occurring in any BC obeys a Poisson distribution.
• the efficiency to detect a single inelastic pp interaction is constant.
The bunch luminosity is given by

µvis
i fr
.
(A.7)
σvis
using the value of σvis measured during the vdM scans for the algorithm considered. The Poisvis
son probability for observing zero events in a given bunch crossing is P0 (µvis ) = e−µ . Then, byusing the raw number of counts N, the probability of observing at least one event is
Li =

N
NBC
= 1 − P0 (µvis )vis= 1 − e−µ .

P(µvis ) =(A.8)

In terms of µvis , the event counting rate is given as
vis

µ

!
N
= −ln 1 −
.
NBC

(A.9)

By using the µvis determined by the detector and the σvis measured by vdM scans, the bunch
luminosity is obtained.

144

APPENDIX B. DETAILS OF CONCEPTS FOR TRACKINGAppendix B
Details of Concepts for Tracking
B.1 Pattern Recognition
B.1.1 Histogramming
Histogramming methods is widely uses as a common technique for a pattern recognition. Track
momentum p as expressed by using a curvature ρ as
p = 0.3Bρ,(B.1)

where B is a magnetic field. A radius of a curvature is proportional to the momentum of a
track. Therefore, the higher momentum track has, the nearer to a line the trajectory of the track
becomes. By assuming tracks come from a origin of the coordinate, the point corresponding to a
track make a peak in the histogram filled the φ information of hits in the detector. This technique
is for high momentum tracks originating from the origin of the coordinate. Therefore, it isn’t
suitable for tracks with low momentum or not from the collision.

B.1.2 Hough Transform
Hough transform technique is also commonly used in tracking. This technique is a transformation from hits information in detector to the parameter space. For example, (x, y) informationof hits is transformed to parameters by assuming a lined = x cos θ + y sin θ,(B.2)

where, d is a distance from the origin to a track and θ is a azimuthal angle of a normal line to
the track. Each hits are transformed to d by scanning values of θ and filled in a histogram. A
peak in the histogram corresponds to a track.

B.2 Track Fitting
After the pattern recognition, track fitting is performed. In this section, some of major methods
in tracking is explained.
145

APPENDIX B. DETAILS OF CONCEPTS FOR TRACKING

B.2.1 Global χ2 Fit
The measurement in a Surface, i.e. information of a hit is employed for track fitting.
 m1 
c =  ...  = f (x) + ,


mn

(B.3)

where  is a random noise and hi = 0. The covariance matrix V is defined as
V = h(c − hci)(c − hci)T i= h(c − h f (x)i)(c − h f (x)i)T i.

(B.4)
(B.5)
(B.6)

Global χ2 fit calculates χ2 by using the track information and the detector measurements.
f (x) = f (x0 ) + A(x − x0 ),where A is defined asA=∂ f (x).
∂x x=x0

(B.7)
(B.8)

χ2 is defined as
χ2 = (c − f (x))T V −1 (c − f (x)),

(B.9)

2

and the track fitting is performed as χ is minimized.

B.2.2 Kalman Filter
The global χ2 fit is the method which employs all the measurements for track fitting comprehensively while Kalman Filter is the method that repeats fitting a tracks state with the neighboringmeasurement recursively.[89, 90] Kalman Filter is a technique for filtering discrete data anddevised by S.E. Kalman in 1960. This filtering technique is used in high energy physics for
tracking.
Kalman Filter mainly consists of three steps: Prediction, Filtering and Smoothing. Discrete
states of a track and the corresponding measurements of a detector are expressed as xk andmk (k = 1, . . . , N). The relation of xk and mk is
mk = Hk xk +  k ,(B.10)

where  k is errors of measurements and in ideal case,h k i = 0.

(B.11)

The covariance matrix of  k is expressed ascov[ k ] ≡ V k .

(B.12)

Moreover, the transition of (k-1)-th state of a track to the k-th state is expressed as
xk = Fk xk−1 + ωk ,146

(B.13)

APPENDIX B. DETAILS OF CONCEPTS FOR TRACKING
where ωk is a process noise through the transition. ωk fulfills thathωk i = 0.

(B.14)

The covariance matrix of ωk is expressed ascov[ωk ] ≡ Qk .

(B.15)

x̃k| j denotes the predicted state estimate using the 0, · · · , j states and the covariance matrix ofxk − x̃k| j is expressed as Ck| j .
rk| j = mk − Hk x̃k| j = Hk (xk − x̃k| j ) +  k .

(B.16)

cov[rk| j ] ≡ Rk| j .

(B.17)

B.2.3 Prediction
Prediction is the estimation of the state at a future time. Extrapolation of the state vector isexpressed asx̃k|k−1 = Fk−1 x̃k−1|k−1 .
(B.18)
Extrapolation of the covariance matrix is expressed as
Ck|k−1 ====cov[xk − x̃k−1|k−1 ]cov[xk − Fk−1 x̃k−1|k−1 ]cov[Fk−1 (xk − x̃k−1|k−1 ) + ωk−1 ]Fk−1 Ck−1|k−1 FTk−1 + Qk−1 .

(B.19)

Residuals of the prediction is given byrk|k−1 = mk − Hk x̃k|k−1 .

(B.20)

Covariance of the predicted residuals is expressed as
Rk|k−1 ====cov[mk + Hk x̃k|k−1 ]cov[Hk xk − Hk x̃k|k−1 +  k ]cov[Hk (xk − x̃k|k−1 ) +  k ]Hk Ck|k−1 HTk + V k .

(B.21)

B.2.4 Filtering
Filtering is the estimation of the present state based on all past measurements. Using the residualrk|k−1 , the track state is updated asx̃k|k = x̃k|k−1 + K k r̃k|k−1= x̃k|k−1 + K k (mk − Hk x̃k|k−1 ).
147(B.22)

APPENDIX B. DETAILS OF CONCEPTS FOR TRACKING
Here, the matrix K k is required to be∂(TrCk|k )
= 0,
∂K k

(B.23)

where Ck|k is a covariance matrix of xk − x̃k|kThen, K k satisfies

Ck|k = cov[xk − x̃k|k ].

(B.24)

K k = Ck|k−1 HTk R−1
k|k−1 .

(B.25)

K k is called a Kalman gain matrix.

B.2.5 Smoothing
Smoothing is the estimation of the state at some time in past based on the all measurements. By
repeating prediction and smoothing, x̃k|k is obtained. This procedure is called forward filtering.
However, only x̃N|N contains the all measurements and x̃k|k (k < N) has information of i =0, · · · , k. In order to evaluate track state x̃k|k using the all measurements, the prediction and thefiltering are performed from N-th state backwardly. This procedure is called backward filtering.
By using the covariance matrix of prediction with backward filtering Cbk|k+1 , the covariancematrix of k-th state is written as
−1
b
−1
C−1
k|n = Ck|k + (Ck|k+1 ) .

(B.26)The prediction with all the measurements x̃k|n is expressed asb−1 bx̃k|n = Ck|n (C−1
k|k x̃k|k + (Ck|k+1 ) x̃k|k+1 ).

148(B.27)

APPENDIX C. HYPOTHESIS TESTAppendix C
Hypothesis Test
A hypothesis test is performed by using the unbinned maximum likelihood estimator in orderto evaluate how well the observed data agree with the signal model. In this section, the theoryof the estimation [91] is reviewed briefly.

C.1 Maximum Likelihood Method
Estimation can be considered as the measurement of parameters by making use of the limited
number of observations. A function of the observations which is called the estimator is employed for the estimation of parameters. The values yielded by using the estimator for a set ofobservation is called the estimate.
In the maximum likelihood method, the likelihood function of N observations X = (X1 , X2 , · · · , XN )is defined as,NY
f (Xi , θ),(C.1)
L(X|θ) =i=1

where f (Xi , θ) is the probability density function of observation X. The maximum likelihood
estimation of the parameter θ is the estimation of the value θ̂ for which L(X|θ) has the maximum
value. It is more convenient for the estimation by using log-likelihood,lnL(X|θ) =NX

ln f (Xi , θ).

(C.2)

i=1

Then the likelihood equation,N∂ X∂
lnL(X|θ) =ln f (Xi , θ) = 0,∂θ∂θ i=1(C.3)

is a necessary condition for the existence of a maximum in likelihood estimator. It is assumedthatZ
f (Xi , θ) = 1.
(C.4)
For r parameters θ = (θ1 , θ2 , · · · , θr ), a set of r likelihood equations are given as∂lnL(X|θ) = 0, j = 1, 2, · · · , r.
∂θ j
149

(C.5)

APPENDIX C. HYPOTHESIS TEST

C.2 P-value
The goodness-of-fit tests compare the experimental data with their probability density function
under the null hypothesis H0 , leading the statement that if H0 were true and the experiments are
performed many times, the data would obtained as the observed data from H0 with a probability
P. This probability is called p-value. A small value of p-value means a bad fit. In order to theconstruct a test for the goodness-of-fit, (1)a test statistic, which is a function of the data and H0and (2) a way to calculate the probability of exceeding the observed value of the test statisticfor H0 are needed.
If a test statistic is expressed as t = t(X) with data X, the p-value is given by
Z
P=
P(X|H0 ),(C.6)
X:t>t0where t0 = t(X0 ) and P(X|H0 ) is a probability with X under H0 .

C.3 The Profile Likelihood Ratio
For the estimation of background and signal yields, the profile likelihood ratio is used for the
hypothesis test. In this section, the profile likelihood ratio is summarized briefly.
In order to test a hypothesized value of µ, the profile likelihood ratio using likelihood function L is given byˆL(µ, θ̂)λ(µ) =.
(C.7)
L(µ̂, θ̂)θ represents the parameters characterizing the shape of the probability density function. The
quantity θ̂ˆ denotes the value of θ that maximizes L for specified µ. L(µ̂, θ̂) is the maximized
likelihood function with µ̂ and θ̂.
From Equation C.7, λ satisfies 0 ≤ λ ≤ 1. When λ is near to one, the data and the hypothesized value of µ have good agreement. As a test statistic,tµ = −2lnλ(µ)(C.8)

is often employed. Then, in order to quantify the goodness-of-fit, the p-value is defined as,
Z inf
P=f (tµ |µ)dtµ ,
(C.9)
tµobs

where tµobs is the value of the statistic tµ observed from the data and f (tµ |µ) denotes the probability density function of tµ . When µ̂ is Gaussian distributed, tµ follows a chi-square distribution.

150