teeba rashid - measurement of the top anti-top quark pair ...when a person starts a work by reciting...
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MEASUREMENT OF THE TOP ANTI-TOP QUARK PAIR
PRODUCTION CROSS-SECTION IN THE τ + JETS CHANNEL
AT√S = 7 TEV USING ATLAS DETECTOR.
by
Teeba Rashid
A Dissertation
Submitted to the University at Albany, State University of New York
in Partial Fulfillment of
the Requirements for the Degree of
Doctor of Philosophy
Arts & Sciences
Department of Physics
2013
ABSTRACT
The Large Hadron Collider (LHC) is a factory for top quarks, which are the heav-
iest elementary particle discovered so far. Due to its small life time a top quark
decays before hadronization, and hence most of its properties are not washed out.
Top quark events are often a large background in many beyond-the-Standard Model
scenarios. For this reason, a deep knowledge of its properties and behaviour is of cru-
cial importance in searches for new physics at the LHC. This dissertation describes a
measurement of the top anti-top (tt) pair production cross-section in the tau + jets
channel. The measurement is obtained by using 4.7 fb−1 data collected in year 2011
by the ATLAS detector from proton-proton (pp) collisions at the center of mass en-
ergy√s = 7 TeV. Selected events are required to have one isolated tau with missing
transverse energy and hadronic jets, at least one of which must be originated from a
b quark. The measured cross section is 152 ± 12 (stat.) +28−30 (syst.) ± 1.8 (lumi.)pb,
which is in agreement with standard model predictions 167+17−18. Using a data sample
of 1.67 fb−1 ATLAS collaboration had obtained a cross-section value at√s = 7
TeV, σtt = 194 ± 18(stat.) ± 47(syst.) pb at center of mass energy equal to 7 TeV.
The result obtained by CMS collaboration at√s= 7 TeV, using a data sample of is
3.9 fb−1 is σtt = 152± 12(stat.)± 32(syst.)± 3(lumi.) pb.
ii
IN THE NAME OF GOD, MOST GRACIOUS, MOST MERCIFUL
When a person starts a work by reciting Bismillah ar-rahman ar-raheem he
acknowledges and thanks God the most high, for the blessings which He provided
merely out of the demands of His attribute of Graciousness(Rehman). On the one
hand man is asking God’s help for knowledge, provided due to the attribute
Gracoiusness, of the right path to achieve his objective and on the other hand he is
asking God’s help, provided through the attribute Merciful(Raheem), that the work he
carries out produce excellent results.
iii
DEDICATION
To my Loving Parents
RASHID HUSSAIN and SAJIDA RASHID
To my Caring Husband
SAAD ABDUS SALAM
iv
ACKNOWLEDGMENTS
All inspiration comes from Prophet Muhammad (peace be upon Him) to whom the
first revelation was about gaining knowledge.
“Read! in the name of your Lord and Cherisher, Who created. Created man, out of
a (mere) clot of congealed blood. Read! And your Lord is Most Bountiful. He Who
taught (the use of) the Pen. Taught man, that which he knew not.” [Quran 96:001-
005].
With all the depths of my heart I bow down my head for Almighty Allah, without
His will and blessings this dissertation was not possible. He provided me the strength
to keep on working, no matter the difficulty. He filled my heart with patience so that
I could persevere through this work.
Though I have written down this dissertation with love and care, there are many
people whom without their involvement, this dissertation was not possible.
First, I would like to convey thanks to my advisor Professor Sajjad Alam. Thank
you very much Professor Alam for your reference to talk to Professor Patrick Skubic
and his physics group. May God bless you good health. I will never forget my stay
at University of Oklahoma (OU) which left fond memories in my heart.
Second, I would like to thank to Professor Carolyn MacDonald, Chair of the Physics
v
Department, for her support towards this work.
Third, a very special thanks to Professor Patrick Skubic for his invitation to OU and
the time that he spent in evenings for physics discussions with me during my stay
at Oklahoma. Thank you very much Professor Patrick Skubic for the time that you
dedicated to me while in Oklahoma, and for finding time to read the first chapter of
my dissertation.
I have no words to express my feelings of gratitude towards Oklahoma high energy
Physics group for their support through tough times. A special thanks to Christopher
Arnold Walker for helping me in scripting and C++. He taught me to use computers
efficiently, and brought joy to the learning experience.
Fourth, I would like to thank Dr. Muhammad Saleem. Being a post doctoral fel-
low of Professor Skubic and former graduate student of Professor Alam he guided
me through Physics Analysis and helped me to improve the analysis chapter of my
dissertation. Also I want to thank Carolyn Bertsche for her friendship and her help
in completing some important checking for my analysis.
Fifth, I also owe thanks to Professor Brad Abbott for the suggestions and ideas to
improve this analysis and reading not only the particle identification chapter, but
looking carefully at all chapters of my dissertation and giving valuable suggestions. I
also like to thank Professor Serban Protopopescue from Brookhaven National Lab for
his important suggestions. I would like to thank Prof Dick Greenwood from Louisiana
Tech University for his interest in the physics of this dissertation and for reading the
vi
Atlas detector chapter of my thesis.
Sixth, Thank you very much Professor Oleg Lunin, for reading the Theoretical Back-
ground chapter of my dissertation, and making important comments and suggestions.
I wish our time at the university overlapped more so I could benefit more from his
teachings. Professor Lunin is a wonderful theorist and enjoys physics discussions very
much.
And finally I would like to say thanks to my family. I am proud that I am a daughter
of two wonderful people who are noble in their thoughts, well-behaved in their man-
ners, sincere in their actions and loving in their nature. Thank you Mummy and Abu
Jee for raising me with love, injecting good moral values and planting a seed in my
heart for higher education. I feel that if I could achieve so much in my life, it is due
to my parent’s hard work; and without it, I could not have gained so much on my
own. I also feel proud that I am a sister of an intelligent, well-behaved person who
also encouraged me during uncertain times.
Last but not least, how can I forget my caring and the most wonderful husband at
this important point in my life. He is very supportive of me. He motivated me to
start my Ph.D. in the very early days of our marriage when we were in Pakistan. I
used to think that he was just trying to be “very good”. But he really meant that.
Thank you very much Saad for remaining by my side during thick and thin. Also at
this important point in my life I cannot forget my parents in-law. Thank you Ammi
Jaan and Abu Jaan for your never ending prayers for me.
vii
When I look at all of the people mentioned above who contributed towards this
achievement, I feel humble and full of gratitude towards my Creator. Thank you
God for sending me among such nice, kind, loving and intelligent people
on earth. Thank you very much.
viii
CONTENTS
Contents ix
List of Figures x
List of Tables xi
1 Introduction 1
2 Theoretical Background 5
2.1 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . . . . . 9
2.2 Electroweak Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Quantum Chromodynamics (QCD) . . . . . . . . . . . . . . . . . . . 14
2.4 Renormalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Particle Physics Experiments . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Structure of the Proton . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 Top Quark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.9 Why study Top quark . . . . . . . . . . . . . . . . . . . . . . . . . . 30
ix
3 LHC and Atlas Detector 35
3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 The Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Particle Identification 69
4.1 Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 tau jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Missing Transverse Energy . . . . . . . . . . . . . . . . . . . . . . . . 109
5 Monte Carlo Generators 111
5.1 Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2 Simulation of Particle Decay and Interaction in ATLAS Detector . . . 113
5.3 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.4 Monte Carlo Generators . . . . . . . . . . . . . . . . . . . . . . . . . 114
x
6 Measurement of Top Anti-Top Quark Pair Production Cross-Section
in the tau plus jets Channel 116
6.1 Monte Carlo and Data Samples . . . . . . . . . . . . . . . . . . . . . 116
6.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4 Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.5 Template Method to determine Multi-jet QCD background . . . . . . 126
6.6 Fit to Missing Transverse Energy . . . . . . . . . . . . . . . . . . . . 129
6.7 Fit with Multivariables . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.8 Number of events surviving all the cuts . . . . . . . . . . . . . . . . . 137
6.9 Linearity and Ensemble Testing . . . . . . . . . . . . . . . . . . . . . 140
6.10 Data versus MC comparison . . . . . . . . . . . . . . . . . . . . . . . 143
6.11 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.12 Cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7 Conclusion 154
A Electron Energy Direction 156
A.1 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
A.2 DIRECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
A.3 Transverse Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B Muon inner detector track 157
xi
C Jet Algorithms 159
C.1 Cone Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
C.2 kt algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
C.3 Cambridge/Aachen algorithm . . . . . . . . . . . . . . . . . . . . . . 160
D Jet Vertex Fraction Algorithm 161
E Good Runs List 163
F Comparison of Results 164
G Data and Monte Carlo Samples 165
Bibliography 184
xii
LIST OF FIGURES
2.1 Spontaneous Symmetry breaking Potential . . . . . . . . . . . . . . . . . 10
2.2 Gluon Self Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 A loop diagram representing quark self energy term . . . . . . . . . . . 19
2.4 Structure function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5 The parton distribution function . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Quark and gluon Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Feynman diagrams for tt Production . . . . . . . . . . . . . . . . . . . . 24
2.8 Feynman diagrams for Single Top Quark Production . . . . . . . . . . . 25
2.9 Illustration of momentum fraction carried by partons participating in hard
scattering and partonic cross-section in proton-proton collisions. . . . . . 26
2.10 tt Production in LO and NLO. . . . . . . . . . . . . . . . . . . . . . . . 26
2.11 Top Quark weak interaction. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.12 Top Quark Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.13 Top Quark Branching Ratios. . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 Schematic overview of LHC and ad-joint injection complex . . . . . . . . 35
3.2 A Toroidal LHC ApparatuS(ATLAS) Detector . . . . . . . . . . . . . . . 38
xiii
3.3 Inner Detector end-caps . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Structural elements of the inner detector in the central barrel . . . . . . 47
3.5 Amount of material in terms of interaction length, as a function of |η| for
ATLAS calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Cut-away view of Atlas Calorimeters. . . . . . . . . . . . . . . . . . . . . 51
3.7 Liquid Argon Electromagnetic calorimeter module. . . . . . . . . . . . . 53
3.8 Tile Calorimeter module. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.9 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.10 Overview of Atlas trigger system . . . . . . . . . . . . . . . . . . . . . . 66
3.11 Schematic sketch of Atlas trigger chain . . . . . . . . . . . . . . . . . . . 68
4.1 Perigee parameters of a track . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Schematic sketch of Jet Reconstruction at ATLAS. . . . . . . . . . . . . 83
4.3 Average jet energy scale correction and average simulated jet response . 88
4.4 Displaced vertex and Impact Parameter of B Quark . . . . . . . . . . . . 91
4.5 Feynman Diagram for τ decays. . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Tau decay Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.7 Illustrating the difference between a tau jet and hadronic jet . . . . . . . 93
4.8 The log-likelihood ratio for 1-prong and 3-prong τ candidates. . . . . . . 102
4.9 A simple example of a decision tree training process. . . . . . . . . . . . 103
4.10 The jet BDT score for 1-prong and 3-prong τ candidates. . . . . . . . . . 104
4.11 Efficiency of tau Identification Methods. . . . . . . . . . . . . . . . . . . 105
xiv
4.12 Score of the BDT-based electron veto for MC simulated hadronic tau de-
cays and electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.13 Inverse background efficiency as a function of signal efficiency for τ can-
didates with pT > 20 in four regions of |η|, for both electron discriminants. 109
5.1 Schematic illustration of a proton-proton collision event involving a gluon-
gluon scattering that leads to tt→ τ + jets. . . . . . . . . . . . . . . . 112
6.1 Feynman Diagram for tt→ τ + jets . . . . . . . . . . . . . . . . . . . . . 117
6.2 Number of Interactions per Crossing . . . . . . . . . . . . . . . . . . . . 118
6.3 Feynman diagram for W + jets production . . . . . . . . . . . . . . . . . 124
6.4 Representative Feynman diagram for Z + jets production . . . . . . . . 124
6.5 Feynman diagrams for Single Top Quark Production . . . . . . . . . . . 125
6.6 Feynman diagrams for diboson production (WW , WZ, ZZ), which pro-
vides a small background . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.7 MET Shape distribution after tau cut . . . . . . . . . . . . . . . . . . . . 128
6.8 Fit to Emisst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.9 Redefining Inverted Selection . . . . . . . . . . . . . . . . . . . . . . . . 134
6.10 Data fitted on all backgrounds, Signal, and QCD multi-jet for a histogram
obtained from four variables Emisst , di-jet mass mass, tri-jet mass(b1jj),
tri-jet mass (b2jj) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.11 Fractions of QCD multi-jet, signal and all backgrounds in Data obtained
from fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
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6.12 Fits of Emisst and di-jet mass distributions. . . . . . . . . . . . . . . . . . 138
6.13 Fits of tri-jet mass(b1jj) and tri-jet mass (b2jj) distributions. . . . . . . 139
6.14 Ensemble test for signal fractions ranging from 0.2 to 0.4 in steps of 0.1 . 141
6.15 Ensemble test for signal fractions ranging from 0.5 to 0.7 in steps of 0.1 . 142
6.16 Linearity fit for Signal Fractions . . . . . . . . . . . . . . . . . . . . . . . 143
6.17 Data vs MC comparison for pτt and Emisst . . . . . . . . . . . . . . . . . . 144
D.1 Schematic Representation of JVF . . . . . . . . . . . . . . . . . . . . . . 162
xvi
LIST OF TABLES
2.1 Elementary Spin-1/2 Fermions of the Standard Model . . . . . . . . . . . 6
2.2 Gauge Bosons in the Standard Model [5] . . . . . . . . . . . . . . . . . . 6
2.3 Chiral multiples in the Minimal Super Symmetric Standard Model . . . . 33
2.4 Gauge super multiplets in the Minimal Super Symmetric Standard Model 33
3.1 Configuration of the Pixel Barrel . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Configuration of the SCT Barrel . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Configuration of the SCT end-caps . . . . . . . . . . . . . . . . . . . . . 44
3.4 Radiation lengths for various materials [4]. Often the radiation length is
expressed in gcm− 2. The result in cm can be obtained by dividing the
density of material [39]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Parameters of the ATLAS Electromagnetic Calorimeter System . . . . . 56
3.6 Parameters of the ATLAS Hadronic Calorimeter System . . . . . . . . . 60
3.7 Parameters of ATLAS Muon Spectrometer . . . . . . . . . . . . . . . . . 64
4.1 Definition of variables used for loose and medium electron identification
cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 Definition of variables used for tight electron identification cuts . . . . . 75
xvii
4.3 The various categories for PDFs for likelihood discriminant . . . . . . . . 101
4.4 The loose, Medium and tight cut-based electron veto selection . . . . . . 107
4.5 The loose, Medium and tight BDTe cut values . . . . . . . . . . . . . . . 108
6.1 ATLAS Data Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 Number of events at an early stage of event selection after a τ selection
for inverted selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3 Number of events at an early stage of event selection after a τ selection
for baseline selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.4 Number of events surviving after applying all selection cuts . . . . . . . . 137
6.5 Relative systematic uncertainties (%) for the measured inclusive tt cross
section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
F.1 Number of events surviving after applying all selection cuts obtained for
tau + jets analysis by ATLAS collaboration from previous work [86]. . . 164
F.2 Number of events surviving after applying all selection cuts obtained for
tau + jets analysis by CMS collaboration [87] . . . . . . . . . . . . . . . 164
G.1 Cross-section and data set ID numbers for SM MC samples. . . . . . . . 165
.
xviii
chapter 1
INTRODUCTION
Particle physics is the study of fundamental constituent of matter and the interac-
tions between them.
In the early 1960’s particle physicists described nature in terms of four distinct forces,
characterized by widely different ranges and strengths. The strong nuclear force has
a range of about 1 fm or 10−15 m. The weak force which is responsible for radioactive
decay, with a range of 10−17 m. The electromagnetic force, which governs much of
macroscopic physics, has an infinite range. The fourth force, gravity, also has infinite
range and its coupling too weak to be observable in laboratory experiments. Standard
model (SM) is the theoretical framework which gives the description of strong, weak
and electromagnetic forces of nature.
The SM is tested by particle colliders.
The Large Hadron Collider at CERN is a 27 kilometer ring buried deep below the
countryside on the outskirts of Geneva, Switzerland. The LHC is the world’s most
powerful particle accelerator. The LHC experiments is designed to reveal the origins
of mass, to shed light on dark matter, to uncover hidden symmetries of the universe,
and possibly to find extra dimensions of space. Billions of protons in the LHC’s two
counter-rotating particle beams smash together at very high energy , and are collided
at four points, in the hearts of the main experiments, named ALICE, ATLAS, CMS
1
and LHCb.
ATLAS is one of two general-purpose experiments (the other is CMS) designed to
cover the entire range of LHC physics. The largest-volume detector ever constructed,
ATLAS is cylindrical in shape which is 44 meters long, 25 meters high, and weighs
about 7,000 tons. The ATLAS detector contains a series of concentric cylinders
around the central interaction point where the LHC’s proton beams collide. Its four
complementary components include the inner detector, the calorimeters, the spec-
trometer and the magnet systems. Together, these specialized components provide
detailed and comprehensive information about the particles emerging from proton-
proton collisions. From the millions of collisions occurring each second, a sophisti-
cated trigger system selects some hundreds of events for analysis by ATLAS scientists
around the world.
The ATLAS detector, records energy deposits and charged particle tracks. This in-
formation must be interpreted in order to identify what particles were created inside
the detector. ATLAS uses many algorithms which identify different particles passing
through the detector based on behavior of each particle as it passes through the com-
bined ATLAS detector. The performance of these algorithms is characterized by two
properties the efficiency and fake rate. Efficiency of an algorithm is the probability to
identify a particle. Fake rate is the probability to incorrectly identify another particle
instead of the particle for which search was initially started.
In order to be able to extract results from what is observed in real data collected in
2
proton proton collisions, it is needed to compare the observed results with the ex-
pected results determined from a model. Simulated samples are used for this purpose.
ATLAS uses different Monte Carlo generators to obtain the simulated samples. The
process of obtaining the simulated samples and different Monte Carlo generators are
described in chapter 5.
Top quark is the heaviest particle discovered so far. Due to its small life time, it
decays before hadronization and hence its properties are not washed out. There are
several theoretical predictions that new physics could appear in both production and
decay process of the top quark such as decay through a charged Higgs boson. These
new effect can be searched based on our good knowledge of top quark production and
the decay process. And this knowledge can be achieved by measuring top antitop
pair production cross-section at Large hadron Collider.
This thesis describes the measurement of the top antitop quark pair production cross
section at a center of mass energy√s = 7 TeV in the tau plus jets channel using
Atlas detector which is installed at one out of four interaction points in Large hadron
collider ring. The data collected in year 2011 which corresponds to 4.7 fb−1 is used
for this study. The measured cross-section is
σtt = 152± 12(stat.) +28−30(syst.)± 1.8(luminosity) pb (1.0.1)
which is in agreement with the prediction made by Standard Model. Chapter 2 of
thesis starts with overview of standard model and then the top quark production and
decay mechanisms are discussed. Chapter 3 deals with the experimental apparatus
3
used for this study in which Large Hadron Collider and ATLAS detector are described
detail. Chapter 4 focuses on the definitions of physics objects used in the ATLAS
experiment and the reconstruction algorithms. Chapter 5 devotes to the Monte Carlo
generators. Chapter 6 describes the measurement of cross-section of top anti top
quark pair production in tau plus jets channel. Concluding remarks are discussed in
Chapter 7.
4
chapter 2
THEORETICAL BACKGROUND
Particle physics is the study of the fundamental constituents of matter and the forces
of nature. In current understanding, particles are excitations of quantum fields. The
current set of fundamental fields and their dynamics are summarized in a theory
called the Standard Model [1].
The Standard Model (SM) is the theory of particle physics that describes in a sin-
gle theoretical frame-work the electromagnetic, weak, and strong interactions among
elementary particles. The elementary particles are divided into two types
• matter particles
• force carrying particles
The matter particles are spin 1/2 fermions and are naturally separated into quarks
and leptons according to their interaction with the strong force. Quarks carry colour
charge, while leptons carry no colour charge. Of the leptons, three carry electro-
magnetic charge (e, µ, τ), and three are electrically neutral, the neutrinos (νe, νµ,
ντ ). Unlike the matter particles, the force carrying particles of the SM are elemen-
tary spin-1 vector bosons. These vector bosons mediate the action of the following
three fundamental forces [1] [2] [3]: the electromagnetic, the weak and the strong
interaction. The particles of the SM are listed in Table 2.1 and 2.2. The experimen-
5
tally measured mass values are taken from [4]. Each of the fundamental forces is
Leptons QuarksFlavour Charge(e) Mass Flavour Charge(e) Massνe 0 0 u 2/3 2.3 MeVe -1 0.511 MeV d - 1/3 4.8 MeVνµ 0 0 c 2/3 1.5 GeVµ -1 105.6 MeV s -1/3 95 MeVντ 0 0 t 2/3 173.5 GeVτ -1 1.776 GeV b -1/3 4.18 GeV
Table 2.1:
Elementary Spin-1/2 Fermions of the Standard Model. For each fermion there existsa corresponding antiparticle with the same mass and quantum number but withopposite charge. Quarks are further characterized by a colour quantum number
which has three possible values: Red, Green, Blue.
Interaction Boson Charge Mass Range [m]Electromagnetic γ 0 0 ∞
Weak W± ±1 80.3 GeV, 10−18
Z0 0 91.18 GeVStrong 8 gluons 0 0 10−15
Table 2.2: Gauge Bosons in the Standard Model [5]
described by a gauge theory, i.e.; a theory that demands invariance under a local
transformation.
The electromagnetic force between two distinct electrons can be described by us-
ing gauge field theories [6] [7]. In its lowest order interaction, one electron emits
a photon, the spin-1 force carrying particle of the electromagnetic field, and recoils
while the second electron absorbs the emitted photon changing its motion. Within
the gauge theory framework, the electromagnetic interaction arises through the re-
quirement that the Lagrangian density is invariant under the action of a local gauge
transformation on the fermion field, ψ(x). The term local has the precise meaning
6
that the parameter α(x) of the transformation is dependent on the space-time point,
with the transformation taking the form
ψ(x)→ eiα(x)ψ(x), (2.0.1)
ψ(x)→ e−iα(x)ψ(x), (2.0.2)
where
ψ ≡ ψ†γ0, (2.0.3)
Such a transformation defines a U(1) symmetry and represents a building block of
quantum electrodynamics (QED). The local gauge invariance of the theory requires
the introduction of a new field describing a massless, spin 1 boson which, in case of
quantum electrodynamics, describes the photon.
In formulae, the Dirac free Lagrangian density for a massive fermion of mass m is
given by [8]
L = ψ(x)(iγµ∂µ −m)ψ, (2.0.4)
is clearly invariant under U(1) transformation, if the parameter α is not dependent
on the space-time point x = (t,−→x ). Where
∂µ = (∂
∂t,∇) and γµ ≡ (γ0, γk) = (β, βα) where k = 1, 2, 3 (2.0.5)
Note that γµ is set of 4 × 4 matrices, which is defined as
α =
0 σ
σ 0
and β =
I 0
0 I
(2.0.6)
7
where I denotes the unit 2 × 2 matrix and σ are the Pauli matrices:
σ1 =
0 1
1 0
σ2 =
0 −i
i 0
σ3 =
1 0
0 −1
(2.0.7)
If the global symmetry is switched to a local one in equation 2.0.4, the derivative term
is no more invariant and some modifications to the Lagrangian density are needed,
since
ψ∂µψ → e−iα(x)ψ∂µ(eiα(x)ψ) = ψ∂µψ + iψ(∂µα(x))ψ, (2.0.8)
The ordinary derivative is replaced by a covariant derivative,
Dµ = ∂µ − ieAµ, (2.0.9)
where Aµ is a real vector field. To preserve gauge invariance, the transformation
property of Aµ is fixed to be
Dµψ = eieαDµψ, (2.0.10)
which implies
Aµ = Aµ +1
e∂µα, (2.0.11)
The Lagrangian density
ψ(iγµDµ −m)ψ, (2.0.12)
is now invariant under a local U(1) gauge transformation.
Hence the requirement of a local gauge invariance implies the replacement of
ordinary derivatives with covariant ones, resulting in a new term proportional to
ψAµψ, which represents the coupling between the fermions and the photon. The
8
fermions now are predicted to interact via photon exchange by the theory.
If we are to regard this new field as the photon field, a term corresponding to its kinetic
energy must be added. Since the kinetic term must be invariant under equation 2.0.11,
it can only involve the gauge invariant field strength tensor
Fµν = ∂µAν − ∂νAµ, (2.0.13)
Thus the Lagrangian of QED is
L = ψ(iγµ∂µ −m)ψ + eψγµAµψ −1
4FµνF
µν , (2.0.14)
The addition of a mass term1
2m2AµA
µ is prohibited by gauge invariance. The gauge
particle, the photon, must therfore be massless.
While the photon and gluons are massless, the W± and Z bosons are not. So the
question arises: How can we modify gauge theory in such a way as to accommodate
massive gauge fields. The answer is by Spontaneous Symmetry breaking and Higg’s
mechanism which is explained in next section.
2.1 Spontaneous Symmetry Breaking
Consider a physical complex scalar field φ(x) =1√2
(φ1 + iφ2) transforming into a
φ′(x) field under a global gauge transformation such that φ
′(x) = eiθφ(x) where θ is
a constant parameter in space-time. The Lagrangian of the scalar spinless field φ(x)
is [8]
L. = (∂µφ)†(∂µφ)− V (φ†φ), (2.1.1)
9
where the first term is the kinetic energy density and the second term is the effective
potential energy density. Consider the potential energy density of the form
V (φ†φ) = µ2φ†φ+ λ(φ†φ)2, (2.1.2)
The Lagrangian is invariant under the global gauge transformation. For a bounded
potential µ2 > 0, equation 2.1.1 describes a scalar field φ with mass µ and the minima
of the potential occurs when φ1 = 0 and φ2 = 0. The (φ†φ)2 term shows that the
four-particle vertex exists with coupling λ. We say that φ is self interacting field. For
µ2 < 0 the ground state becomes unstable and a minima occurs at ν = ±√−µ2
λ. The
potential energy density no longer remains symmetric around the minima ±ν. By
choosing one of the two possibilities for the ground states either ν or −ν in this case,
we break the global symmetry of the Lagrangian. Expanding the potential around
Figure 2.1: The potential for the Lagrangian given in Equation 2.1.1. left: for thecase of µ2 > 0. The minimum is at |φ| = 0. right: when µ2 < 0. The minimum is at
ν = ±√−µ2
λ.
one of the ground state, say ν as φ =1√2
(ν + ξ + iζ) the Lagrangian becomes [8]
L =1
2(∂µξ)2 +
1
2(∂µζ)2 +(µξ)2 +
1
2µ2(ν)2 +
1
4λ(ν)4 +λνξζ2 +
1
2ξζ4 +
1
4λ(ζ)4 +
1
4λ(ξ)4,
(2.1.3)
10
The real field ξ in the Lagrangian appears to have mass√
2µ, while there is no
mass term for the field ζ. Such a massless field that appears after breaking of the
ground state is known as the Goldstone boson.
Under the local gauge transformation of U(1), the field φ(x) transforms as φ′(x) =
eiθ(x)φ(x), where θ(x) is the space-time dependent gauge parameter. For a Lagrangian
to be local gauge invariant, ∂µ is replaced by Dµ = ∂µ − iqAµ where the gauge field
transforms as Aµ → Aµ +1
q∂µθ . The Lagrangian then becomes
L. = (Dµφ)†(Dµφ)− 1
4F µνFµν − V (φ†φ), (2.1.4)
where the kinetic energy term for the gauge field Aµ is −1
4F µνFµν and Fµν = ∂µAν −
∂νAµ. The local gauge invariance of the Lagrangian requires the gauge boson field
Aµ to be massless, therefore no mass term for Aµ can be added by hand. The local
symmetry breaking of the ground state is introduced by expanding around one of the
new ground states and inserting into the Lagrangian in Eq 2.1.4 as [8]
L =1
2(∂µξ)2 +
1
2(∂µζ)2 − 1
4FµνF
µν + (µξ)2 + q2ν2A2 + 2qνAν(∂νξ)
+1
2(µν)2 +
1
4λ(ν)4
+1
4λ(ζ)4+
1
4λ(ξ)4+
1
2λ2ξ2ζ2+λνξζ2+q2A2(ξ2+ζ2)+2q2νξA2+2qAµ(ξ(∂µζ)−ζ(∂µξ)),
(2.1.5)
We see that real scalar ξ field and the gauge field Aµ are massive in the local gauge
invariant Lagrangian while the scalar field ζ is massless. The unphysical terms can
be made to disappear by redefining the real scalar fields h(x), θ(x) and Aµ such that
φ(x) =1√2
(ν + h(x))eθ(x)/ν , (2.1.6)
11
and by making a new choice of the gauge field Aµ → Aµ +1
qν∂θ(x). Substituting the
expression for φ(x) and the new choice of gauge field Aµ in to Equation 2.1.4, one
obtains
L =1
2(∂µh)2−λ2ν2h2 +
1
2(qνA)2− 1
4FµνF
µν − 1
4λ(h)4 +
1
2q2A2h2 + q2νA2h, (2.1.7)
The Lagrangian is free of Goldstone bosons, but it does contain a massive scalar
field h(x) and a massive gauge boson Aµ. The Goldstone boson is said to be eaten
by the massless gauge boson. By breaking the local gauge symmetry of the ground
state, the gauge invariance of the Lagrangian is preserved for a massive gauge field
by introducing a massive scalar field known as the Higgs boson. It can also be shown
that the fermions couple with the Higgs boson and gain masses depending on their
Yukawa coupling with the Higgs [8].
2.2 Electroweak Interactions
In 1967-68, Glashow, Weinberg and Salam proposed a gauge theory unifying weak and
electromagnetic [3] interactions. In the gauge field theory, the Lagrangian is invariant
under local gauge transformations provided that all gauge fields involved are massless.
In the renormalizable theories (physical quantities are calculable and finite), the non-
physical divergent terms that exist in quantum field theories must be cancelled to
describe an observable physical process. The electroweak unification is a counter
part of QED, where the U(1) symmetry group is replaced by SU(2) ⊗ U(1). The
Lagrangian of QED is invariant under both global and local phase transformation.
12
The fact that the symmetry of a U(1) phase transformation is unbroken requires
electric charge to be conserved in all interactions.
The Glashow-Weinberg-Salam theory used a weak isospin, I, SU(2) group and a
weak hyper charge Y, U(1) group where Y = 2(Q−I3)1, thus forming a non-Abelian2
SU(2) ⊗ U(1) gauge symmetry group to describe the electroweak gauge field. The
combination reveals the symmetry between the lepton and quark families, plus the
similarities between electromagnetic and weak interactions.
A Dirac field ψ representing a fermion, can be expressed as the sum of a left-handed
component, ψL and a right handed one ψR.
ψ = ψL + ψR, (2.2.1)
where, ψR and ψL of a fermion field ψ are obtained by applying the projection oper-
ators ψR =1
2(1 + γ5)ψ and ψL =
1
2(1− γ5)ψ.
also
γ5 ≡ iγ0γ1γ2γ3, (2.2.2)
where γ matrices were defined in equation 2.0.6. The left handed fermions field
transfer as doublets under SU(2) rotations, and the right handed fields transform as
singlets. This is a consequence of the fact that weak interactions violate parity. In the
Standard Model fermions are grouped into three generators of left-handed doublets
1Q is charge and I3 is the third component of isospin I.2The vector gauge boson of EM interactions does not contain any charge or mass and hence
does not conduct any self coupling, in contrast to the vector gauge bosons of weak interactions thatcarry the flavour charge as well as the mass under Higgs mechanism. For the weak interaction sucha field theory is often referred to as non-Abelian gauge theory, which involves the self coupling ofthe boson fields that in terms of group theory are expressed as the non-commuting generators.
13
and right-handed singlets of weak isospin given as, νe
e
L
νµ
µ
L
ντ
τ
L
eR, µR, τR,
u
d
L
c
s
L
t
b
L
uR, cR, tR, dR, sR, bR,
Only the left-handed doublets participate in the weak interactions. The weak isospin
doublets serve as the bases of the SU(2) group, while the iso-singlets form the bases
of the U(1) group.
A Lagrangian which is invariant with respect to the weak isospin SU(2) and with
respect to rotations in weak hyper-charge space, is needed. There are four electroweak
bosons, the weak isospin triplet W iµ with i = 1, 2, 3 and the singlet Bµ relating to
the SU(2) and the U(1) groups, respectively. The two charged bosons, W 1µ and W 2
µ ,
couple with a scalar Higgs field via a spontaneous symmetry breaking mechanism [11]
to become the massive W+ and W−. The linear combination of the neutrals W 3µ and
Bµ couple with the Higgs to form a massive neutral vector boson Zo and the massless
photon. The presence of the Higgs field is necessary for the renormalizability of the
theory.
2.3 Quantum Chromodynamics (QCD)
Quantum chromodynamics (QCD) is a quantum field theory that describes the color
interactions between fundamental particles such as quarks and gluons. Quarks come
14
in three colors, red, green or blue, with the corresponding anti-colors: anti-red, anti-
blue and anti-green. Gluons are bi-coloured objects, they carry a color and anti-color
such that net color is not white.
The strong force is held responsible for keeping the quarks and gluons together in
bound states known as hadrons (further sub-grouped into baryons and mesons de-
pending on their spins.)
All hadrons have a net strong charge (color) of zero, and their net quark content
has zero strong charge even though the quark content of the hadron is continuously
changing. In QCD, there are simple zero-color combinations of a hadron; (a) quark-
anti-quark (Mesons) (b) three quarks (Baryons) (c) three anti-quarks (anti-baryons).
The color transformations of quarks follow the algebra of the fundamental SU(3)
group representation that has eight generators corresponding to eight bi-coloured
gluon states. Like the weak interaction, QCD is a non-Abelian gauge theory.
QCD is developed as a gauge theory requiring the invariance principle like QED. The
color transformation of quarks follow the algebra of the fundamental SU(3) group rep-
resentation that has eight generators corresponding to eight bi-colored gluon states.
The covariant derivative acting on the quark field due to strong force is [8]
Dq. = (∂µ − iαsλaGaµ)q, (2.3.1)
15
where
q. =
qr
qb
qg
, (2.3.2)
represents the quark fields, αs is the strong coupling constant, λa = SU(3) generators;
a=1,2,...,8 and Gaµ = gluon fields.
The Lagrangian term for the gauge field for QCD is
F aµνF
µνa , (2.3.3)
where F aµν is the gluon field strength which is given as
F aµν = ∂µG
aν − ∂νGa
µ + αsfabcGµbGνc, (2.3.4)
and fabc are the structure constants of the SU(3) group.
From 2.3.4 it is evident that the kinetic energy term is not purely kinetic, but instead
include the self interaction between gluons. When expanded, the gauge field term
contains a three gluon term and a four gluon term [8]. These self interaction gluon
terms depicted in Figure 2.2 are characteristic of a non-abelian theory. Under a local
gauge transformation of
q(x)→ eiθa(x)λaq(x), (2.3.5)
the non-Abelian field Gaµ must transform as
Gaµ → Ga
µ +1
αs∂µθ
a(x) + fabcθb(x)Gµc, (2.3.6)
16
Figure 2.2: (a) Emission of gluon (b) Splitting of gluon into quark pairs (c) Selfcoupling of three gluons (d) Self coupling of four gluons [8].
where αs is the strong coupling constant. Under the transformation given in equation
2.3.5 and 2.3.6 the Lagrangian
L =∑
flavour
q(x)(iγµDµ −m)q(x)− 1
4F aµνF
µνa , (2.3.7)
remains invariant.
There are two distinctive features in QCD called asymptotic freedom and confinement
that explain why quarks appear to be free particles when hadrons are struck by
highly energetic particles and why quarks and gluons cannot exist is free states at
low energies or at higher distances than fermi distance which is of the order of 1 fm.
2.3.1 Asymptotic Freedom
One central property of QCD that has been verified by experiment is the property
known as asymptotic freedom. Asymptotic freedom refers to the fact that while quarks
are permanently bound into hadrons, at shorter distances they do behave more and
more as free particles. The strength of the interaction αs, that specifies the quark-
17
quark coupling strength, decreases at shorter distances. In other words the strong
coupling constant decreases with the increasing momentum transfer of the event (Q),
due to the antiscreening effect of the strong interaction. Thus, αs is often referred to
as a running constant.
2.3.2 Quark Confinement
From the running of the coupling constant αs, the interaction between the quarks and
gluons become stronger at low energy scales or large distances. Therefore quarks and
gluons cannot exist in a free state. The bound state of quarks and gluons is known as
a hadron, which is a colourless object. The momentum scale at which αs(Q2) diverges
is usually known as the ΛQCD parameter.
In terms of ΛQCD the strong coupling is given by the following equation:
αs(Q2) =
12π
(33− 2nf )ln(Q2
Λ2QCD
)
, (2.3.8)
An experimentally known fact is that ΛQCD is around 217 MeV. The value of αs at a
given energy depends on the number of quark flavours nf that can participate in the
binding process through their coupling to gluons.
2.4 Renormalization
The renormalization problem arises in the context of perturbation theory. In funda-
mental physics, quantities of interest such as scattering amplitudeM is calculated as
18
Figure 2.3: This loop diagram represents the quark self energy term which is of orderα2s. The scattering amplitude becomes undefined due to this divergent term. The
strategy is to absorb the infinities in into ’renormalized’ quantities such as couplingconstants [6].
expansions in order of coupling constants
M =∞∑i=o
giMi (2.4.1)
where Mi is the contribution to M bearing i vertices. Individual contributions can
diverge. For example in Figure 2.3 the momentum k is not bounded and must there-
fore be integrated over from 0 to infinity which ultimately results in divergence of a
function. The solution is to rewrite M in terms of renormalized parameters at the
specific scale µr instead of the bare non-renormalized scale.
2.5 Particle Physics Experiments
In particle physics one typically gains the knowledge about elementary particles by
accelerating particles to very high kinetic energy and letting them impact on other
particles. A collider is a type of particle accelerator involving directed beams of
particles. Colliders may either be ring accelerators or linear accelerators and may
collide a single beam of particles against a stationary target or two beams head ons.
Several examples of particle collider are given below:
The Stanford Linear Collider was a linear accelerator that collided electrons and
19
protons at SLAC. The up, down, charm and strange quarks were discovered at SLAC.
The Tevatron was a circular particle accelerator that collided proton anti-proton
beams at the Fermi National Lab. The bottom quark and top quark were discovered
at Fermi Lab.
The Super Proton Synchrotron was a particle accelerator that collided protons and
anti-protons at CERN, where the W and Z bosons were discovered.
The LHC is the highest energy particle accelerator that is colliding proton proton
beams successfully since November 2009 at CERN. The Higgs boson existence was
confirmed by LHC data.
This thesis utilizes the LHC data, obtained from proton proton collisions, for a top
anti-top cross-section measurement in decay channel τ + jets, that is why the next
part of this chapter deals with theoretical aspects of proton structure and top quark
production and decay mechanism.
2.6 Structure of the Proton
The proton is composed of several quarks and gluons, which are collectively referred
to as partons. The partons can be categorized into valence quarks, sea quarks and
gluons. The valence quark denotes the quark or anti quark which gives rise to quantum
numbers e.g uud for a proton. The sea quark denotes the quark-anti-quark pair
arising from a gluon splitting. The sea quarks are much less stable than the valence
quarks, and they annihilate with each other within a hadron. Each parton carries a
20
Figure 2.4: (a) Structure functions of a point like particle (b) Structure function ofparticle consisting of three point like constituents (c) Structure function of particleconsisting of three bound quarks (d) Structure function of the proton consisting ofthree valence quarks (uud), sea quarks, and gluons. The variable x denotes thefraction of the proton’s momentum, carried by partons [8].
fraction of the total momentum fraction among the total momentum of the parent
proton. The probability density for finding a parton with a momentum fraction x at
a given Q2 is known as the parton distribution function (PDF) fi(x). PDF have been
measured experimentally using a deep inelastic scattering process with an electron
and a proton. The gluon distribution grows rapidly at small x, as shown in Figure
2.5. The contribution from the sea quarks become much more visible in high Q2
as the process probes more deeply inside a proton. The collision of two protons at
LHC is thus the interaction of the parton constituents of the protons. The total
interaction is very complicated process. The hard scattering takes place when the
energy exchange between two partons from the two protons is high enough to kick
out of their confinement in the protons.
21
Figure 2.5: Parton distribution functions at Q2 = 10 GeV 2 and Q2 = 104 GeV 2 [9].
2.7 Factorization
Figure 2.6: Quark and gluon scattering
Figure 2.6a shows the scattering of gluon and a quark. Figure 2.6b shows the same
scattering including the radiation of gluon. It can be shown that the probability for
the emission of collinear gluon grows as the momentum k drops. With momentum
k approaching to zero, the probability goes to infinity. This infinity is dealt in a
way similar to renormalization problem. A factorization scale µf is defined in a way
such that the expression for probability is split into two parts one finite and the other
infinite. The infinite part is absorbed and one is left with finite expression of fi(x, µf ).
22
2.8 Top Quark
The top quark was discovered in 1995 at the Fermi Lab Tevatron collider by the CDF
and D0 collaborations [12], [13]. The Tevatron is a hadron collider, accelerating and
colliding protons with anti-protons. The two experiments associated with it, CDF
and D0, are the experiments where top quarks had been initially observed.
The top quark is a third generation up-type quark with electric charge +2/3. It
is the heaviest of all known elementary particles, with measured mass of 172.9± 1.5
GeV [4].
Studying top quarks is important for several reasons. With its large mass, the
top quark is the only fermion at the electroweak scale [16]. It is therefore of great
interest for the studies of electroweak symmetry breaking. Additionally, top quarks
will constitute a significant background process to many Beyond the Standard Model
searches, such as super-symmetry searches.
2.8.1 Top Quark Production Mechanism
In, pp collisions at the LHC, top quarks are mainly produced in pairs of one top
quark and one anti-top quark tt. The top quark pair production occurs through two
channels: Quark anti-quark annihilation qq → tt and gluon fusion gg → tt, both
mediated by the strong interaction [14].
At the LHC gluon gluon fusion gg → tt is the dominating process of tt production.
Leading order diagrams are shown in Figure 2.7 .
23
Figure 2.7: Feynman diagrams for tt production. From left to right: Quark-antiquark annihilation; gluon gluon fusion
2.8.2 Single Top Production
In addition to being produced in pairs through the strong interaction, top quarks
can also be produced in single top channels via the weak interactions. Single top
production can occur through three sub-processes [17].
• t-channel: The t-channel refers to the process where a space-like W-boson is
exchanged. It is also known as W-gluon fusion since the final state b quark
results from a gluon splitting to a bb pair. The t-channel is the largest source
of single top production.
• s-channel: In the s-channel, a time like W-boson is produced and decays to a t
and a b-quark. This process has the lowest cross-section of the three single top
channels.
• Wt : In the Wt process, a real W-boson is produced together with the top
quark.
Feynman diagrams for the three sub-processes can be seen in Figure 6.5.
24
Figure 2.8: Feynman diagrams for single top quark production. From left to right: tchannel production through flavour excitation and through W-gluon fusion; s-channelproduction; Wt-channel production
The production of tt is the result of an interaction between quarks and gluons
which are the constituents of the incoming protons. The partons possess varying frac-
tions x1 and x2 of the four momenta of their parent protons p1 and p2. The production
cross-section of top anti-top quark pair in proton proton collision, σ(√s,mt)pp→tt, is
given by [18]
σ(√s,mt)pp→tt =
∑i,j=g,q,q
1∫0
fi(x1, µ2f , )dx1
1∫0
fj(x2, µ2f )dx2×σij→tt(
√s,mt, x1, x2, µf , , αs(µr)),
(2.8.1)
where σij→tt(√s,mt, x1, x2, µf , , αs(µr)) is the short-distance cross-section between
parton i and j and fi(x1, µf ) is the parton distribution function (PDF) for the par-
ton type i(i = g, q, q) where q = u, d, c, s, b. µf and µr are the factorization and
renormalization scales. Factorization scale can be thought of as the scale that sepa-
rates the long- and short-distance physics, The top mass mt also depends on µr. The
dependence of the partonic cross section and the PDF on µf arises from absorbing
uncancelled initial state singularities into the PDF. The renormalization and factor-
ization scales are typically set to a hard scale of the process, and one often identifies
µ = µr = µf . In the case of the total cross section, one usually sets µ = mt. The
25
strong coupling constant is a function of the momentum transfer. It decreases with
increasing momentum transfer due to anti-screening effects of the strong interaction.
In the case of tt, it becomes on the order of ≈ 0.1, which is small enough to calculate
the partonic cross-section as a perturbation series in the strong coupling constant.
Leading order (LO), Next to Leading Order (NLO) and Next to Next to Leading
Order (NNLO) partonic cross-sections are calculated as a perturbation series in αs
σpp→tt(αs) = σ1(x1p1, x2p2)αs + σ2(x1p1, x2p2)α2s + σ3(x1p1, x2p2)α3
s + ....., (2.8.2)
where σ1, σ3 and σ2 are the calculated cross-sections based on LO, NLO and NNLO
respectively and so on. The LO and NLO diagrams are shown in figure 2.10
Figure 2.9: Illustration of momentum fraction carried by partons participating inhard scattering and partonic cross-section in proton-proton collisions.
Figure 2.10: tt production in leading order (LO) and next to leading order (NLO)
26
2.8.3 Top quark decay
A top quark decays predominantly into a W boson and a b-quark, regardless of
whether it was produced through QCD tt process or through an electro-weak single
top channel. The reason why almost all top quarks decay as t → Wb is that the
other decay modes t→ Ws and t→ Wd are heavily suppressed in the CKM matrix
[15]. According to the SM, quark masses and mixing of quarks are related. They
originate from interactions between the quarks and the Higgs field. The mixing
between the three quark generations are parametrized by the Cabibbo-Kobayashi-
Maskawa (CKM) matrix [19], [20]. The CKM matrix elements determine the coupling
constants of W-bosons to quarks and relate the initial and final state flavours. The
CKM-matrix is given in Eq 2.8.3
|Vud| |Vus| |Vub|
|Vcd| |Vcs| |Vcb|
|Vtd| |Vts| |Vtb|
∼
0.974 0.226 0.004
0.266 0.973 0.041
0.009 0.041 0.999
(2.8.3)
For this analysis all top quarks are assumed to decay via the t→ Wb process.
Figure 2.11: Top Quark weak interaction. According to the CKM matrix, the tWbvertex is dominant against tWd and tWs.
27
In the leading order approximation, the partial decay width of the t-quark via the
weak interaction can be calculated as, [21]
Γ(t± → W±b) =GFm
3t |V 2
tb|8π√
2= 1.68 GeV, (2.8.4)
where GF = 1.16639× 10−5 GeV −2 is the Fermi coupling constant, mt = 172.5 GeV
is the top quark mass and the Vtb is the coupling strength of the left handed Wtb
coupling in the CKM matrix. The partial decay width of 1.68 GeV corresponds to
the lifetime of τ =1
Γ= 4×10−25s. According to relativity, a hadron of typical radius
∼ 1fm cannot form in less than 10−22s, so this explains why a hadron containing a
top quark has never been observed. Thus the top quark is the only quark that can
be observed bare due to its high value of mass. The top quark decay width is much
larger than the QCD scale ΛQCD = 217MeV , so it decays before hadronization and
thus forms no bound states.
The W boson originating from each top quark can decay in two different ways. It
can either decay leptonically to a lepton and neutrino, or hadronically to a quark-anti
quark pair. The final states of a leptonically decaying W are eνe, µνe, τντ . The final
states are equally probable and hence have equal branching ratios. A W-boson can
decay hadronically to the two lightest generations of quarks (W → ud, W → cs),
where W → tb is not allowed kinematically. Since the quarks carry the colour charge,
a hadronic final state has three times the branching ratio than a leptonic final state
: BR(W → qq′=
3
9) and BR: (W → lνl =
1
9) For a given tt decay two W-bosons are
produced. There are three possible final states for the tt decay, depending on how
28
Figure 2.12: Top Quark Decay.
the W bosons decay [22]
• Fully Hadronic
In a fully hadronic decay mode both W bosons decay to a quark anti-quark
pairs. The final state of this mode consists of six jets of which two are b-
jets originating from the top decay and the other four are from the decaying
Ws. The Branching ratio for the fully hadronic mode is calculated as BR(all
jets):(2 ∗ 3
9) ∗ (2 ∗ 3
9) =
4
9. The multiplicative factor “2” stands for either ud or
cs quark anti-quark pairs. Quark anti-quark pairs such as us or cd are cabibbo
suppressed.
• Di leptonic
In Di leptonic mode both W-bosons decay to a lepton and neutrino. The final
state thus contains two high pT leptons, two neutrinos and two b-jets. The
branching ratios are given as BR(W → ee/µµ/ττ) =1
9∗ 1
9=
1
81and BR(W →
e±µ∓/e±τ∓/µ±τ∓) =1
9∗ 1
9∗ 2 =
2
81thus
1
9of tt pairs have both W-bosons
decaying leptonically. The multiplicative factor “2” corresponds to two sets of
combination e.g. W+W− can decay to either e+νeµ−νµ or µ+νµe
−νe.
29
• Semi leptonic
In the semi leptonic mode, one of the W- bosons decay leptonically while the
other decays hadronically. The final state is distinguished by one high pT lepton,
one neutrino, and four jets (of which two are b-jets from the top decay and the
other two originate from the hadronically decaying W). The branching ratio
is calculated using the branching ratios for the W decay above: BR(e/µ/τ +
jets) = (1
9∗ 3
9∗ 2) ∗ 2 =
4
27. (The first multiplicative factor “2” corresponds
to two types of qq pairs ud or cs. The second multiplicative factor corresponds
to two sets of combination i.e.; tt → W+b + W−b = l+νl + qq and tt →
W+b+W−b = qq+ l−νl. ) The branching ratio for each channel ( e+ jets, µ+
jets, τ + jets) is thus4
27resulting in a total branching ratio of
4
9for the semi
leptonic mode.
Figure 2.13: Top Quark Branching Ratios.
2.9 Why study Top quark
Although the Standard Model is a successful theory there are some weak points
and unanswered questions that different Beyond the Standard Model theories try to
30
answer, such as
• Hierarchy Problem
The hierarchy problem [23] [24] is one of the most serious drawbacks of the
SM and appears when one tries to extend the validity of the SM to describe
physics at energies higher than the electroweak scale MW , near the Planck scale,
MP =√
8πGnewton = 1.22 × 1019GeV , where quantum gravitational effects
becomes important. The fact that the ratioMP
MW
is so huge forms the basis of
hierarchy problem. The large disparity between the scale of quantum gravity,
i.e., the Planck scale, and the electroweak scale , of the order of 1 TeV, is known
in the standard model (SM) as the hierarchy problem. In the presence of this
hierarchy of scales it is not possible to stabilize the Higgs boson mass at the low
values required by experimental data, unless by using an unlikely large amount
of fine-tuning.
• Missing Dark Matter
Standard Model only accounts for 4% of the energy density of the universe.
Several observed phenomenon confirmed the presence of dark matter such as
rotational speed of galaxies, orbital velocities of galaxies in clusters, gravita-
tional lensing of background objects galaxy clusters, etc. The Standard Model
is quiet about the source of missing dark matter that would account for the vast
majority of the mass in the observable universe.
• Cosmological Constant Problem
31
The cosmological constant is the value of the energy density of the vacuum of
space. A major outstanding problem is that most quantum field theories pre-
dict a huge value for the quantum vacuum. A common assumption is that the
quantum vacuum is equivalent to the cosmological constant. If the universe is
described by Standard Model down to the Planck scale, then a cosmological
constant of the order of M4P is expected. The measured cosmological constant
is smaller than M4P by a factor of 10−120. This discrepancy is known as cosmo-
logical constant problem.
• CP Problem
Theoretically it can be argued that the standard model should contain a term
that breaks CP symmetry relating matter to antimatter in the strong interaction
sector. Experimentally, however, no such violation has been found, implying
that the coefficient of this term is very close to zero.
Super-symmetry [25] [26] [27] is a theory beyond the Standard Model that ad-
dresses the hierarchy problem (one of the unanswered questions). In the super-
symmetric extension of the Standard Model, each of the known fundamental particles
must have a super partner with spin differing by 1/2 unit. The spin-0 super part-
ners of leptons and quarks are generally called sleptons and squarks. For example,
the super-partners of the left and right handed electron are called the left and right
handed selectron and denoted as eL and eR.
32
All the super multiplets of the minimal extension to the Standard Model, the
Minimal Super-Symmetric Model [28] are summarized in Table 2.3 and Table 2.4.
Super-field Spin-0 Spin-1/2squarks, quarks
(uL dL
) (uL dL
)(× 3 families) u∗R u†R
d∗R d†Rsleptons, leptons
(ν eL
) (ν eL
)(× 3 families) e∗R e†R
Higgs, higgsinos(H+u Ho
u
) (H+u Ho
u
)(Hod Hd−
) (Hod Hd−
)Table 2.3: Chiral multiples in the Minimal Super Symmetric Standard Model
Super field Spin-1/2 Spin-1gluino,gluon g g
winos, W boson W± , W o W± , W o
bino, B boson Bo Bo
Table 2.4: Gauge super multiplets in the Minimal Super Symmetric Standard Model
If super-symmetry were unbroken then there would have to be super partners
with masses exactly equal to the Standard Model particles, and therefore extremely
easy to detect. As none of super-partners have been discovered, Super-symmetry is
a broken symmetry in a vacuum state.
According to this theory it is expected that masses of at least the lightest few
super partners should be 1 TeV and hence super-symmetry could be discovered at
the Large Hadron Collider.
Any discovery of new physics beyond the Standard Model can only be claimed
when the standard model processes are understood. In that sense the tt production
is the dominant background for the signatures produced by a large class of super-
33
symmetry models, as it provides a similar environment with large jet multiplicity and
missing energy.
While the semi-leptonic (where the lepton, is an electron, muon or a tau that
decays leptonically) channels of the tt production
tt→ W (→ lν)bW (→ qq)b (2.9.1)
are an important background to super-symmetry events with a hard lepton in the
final state, the semi leptonic channel with a tau that decays hadronically
tt→ W (→ τ [→ hadronsντ ]ν)bW (→ qq)b (2.9.2)
is an important background to super-symmetry events with no hard leptons in the
final state. It is therefore vital these processes be accurately measured at the LHC.
34
chapter 3
LHC AND ATLAS DETECTOR
3.1 The Large Hadron Collider
The Large Hadron Collider [29] [30] is a proton synchrotron accelerator and proton-
proton collider. It is installed in the 27 km long former LEP tunnel located in CERN,
Geneva, Switzerland. The LHC was designed to accelerate and collide two beams of
protons at 14 TeV with a peak luminosity of L = 1034 cm−2s−1. The protons are
accelerated in 5 steps using the accelerator chain (see Fig 3.1). A small linear acceler-
ator (LINAC2) gives each proton beam an initial energy of 50 MeV. Then the beam is
boosted to 1.4 GeV by the BOOSTER. The Proton Synchrotron (PS) accelerates the
Figure 3.1: Schematic overview of LHC and adjoint injection complex.
35
beam up to 26 GeV. The Super Proton Synchrotron (SPS) brings it to 450 GeV, the
so-called “injection energy”. Finally, the protons from SPS are injected into the LHC
ring and are accelerated to the collision energy. Superconducting magnets generate a
field of 8.33 T which keeps the proton beams on the orbits.
Luminosity is a measure of the number of particles colliding per second and per
effective unit area of overlapping beams. If two beams containing k bunches and
n1 and n2 particles collide with a revolutionary frequency f , then the luminosity is
defined as
L =n1n2kf
4πσ, (3.1.1)
where σ is the beam cross-sectional area.
In one year running at nominal high luminosity the LHC provides an integrated
luminosity of
L =
∫ 107s
0
Ldt = 100fb−1, (3.1.2)
The luminosity represents the constant of proportionality between event rate and
the cross-section for a given process to occur. At high luminosity, the two beams each
have 2808 bunches and every bunch contains about 1011 protons. The expected event
rate R is
R = σtotpp × L = 109s−1, (3.1.3)
where σtotpp is the total inelastic pp cross-section and its value at a center of mass energy
of 14 TeV is about 80 mb. A single set of particle interactions resulting from a proton-
proton collision is known as an event. The proton collisions are parton interactions
36
described by quantum chromodynamics. If the transverse momenta involved in the
scattering cross-section process are ≥O (10 GeV), the parton interaction is referred to
as “hard”, possibly representing interesting physics events. If the transverse momenta
are low, the parton interaction is “soft” and no new physics is expected. The soft
elastic collisions dominate at the TeV scale. These so-called minimum bias events
are usually discarded by the detector trigger system (discussed in section 3.6) as non
interesting events.
A signal rate of 109 Hz corresponds to 22 events occurring per bunch crossing on
average. These events are often referred to as pile-up and must be disentangled from
the main hard-scatter interaction that typically triggered an event of interest.
The hard scattering of protons actually involves the interaction of its gluon and
quark constituents. The remnants of the two protons fragment and hadronize result-
ing in more scattering products in the detector. These so-called underlying events
are also rejected by the detector trigger system.
The LHC provides rich physics potential, ranging from more precise measurements
of Standard Model parameters to the search for new physics phenomena. Further-
more, nucleus-nucleus collisions provide an unprecedented opportunity to study the
properties of strongly interacting matter at extreme energy density: the quark-gluon
plasma. Four major experiments are installed at different collision points around the
ring: ALICE (A Large Ion Collider Experiment), ATLAS (A Toroidal LHC Appara-
tuS), CMS (Compact Muon Solenoid), and LHCb.
37
Figure 3.2: Cut-away view of the ATLAS detector with labelled sub detectors. Theoverall weight of the detector is approximately 7000 tonnes.
3.2 ATLAS detector
ATLAS [31] is a general purpose detector built for probing proton proton collisions.
The overall detector layout is shown in Figure 3.2. ATLAS detector has a cylindrical
shape with sub-detectors arranged co-axially with respect to the beam axis in the
barrel region and perpendicularly to the beam-axis in the end-cap region.
The inner detector is immersed in a 2T solenoidal field. Pattern recognition,
momentum and vertex measurements, and electron identification are achieved with
a combination of discrete, high resolution semiconductor pixel detectors, and strip
detectors in the inner part of the tracking volume, and straw tube tracking detectors
with the capability to generate and detect transition radiation in its outer part.
High granularity liquid-argon electromagnetic sampling calorimeters, with excel-
lent performance in terms of energy and position resolution, cover the pseudo-rapidity
38
range |η| < 3.2. The symbol η is defined in section 3.2.1. The hadronic calorimetry
in the range |η| < 1.7 is provided by a scintillator tile calorimeter, which is separated
into a large barrel and two smaller extended barrel cylinders, one on each side of the
central barrel. Liquid Argon (LAr) technology is also used for the hadronic calorime-
ter in the end-cap region. The calorimeter is surrounded by the muon spectrometer.
The air-core toroid system, with long barrel and two inserted end-cap magnets, gen-
erates strong bending power in a large volume within a light and open structure.
Excellent muon momentum resolution is achieved with three layers of high precision
tracking chambers. The muon instrumentation also includes trigger chambers with a
timing resolution of 1.5-4 ns.
3.2.1 ATLAS coordinate system
The ATLAS experiment utilizes a right hand coordinate system. The nominal inter-
action point is defined as the origin of the coordinate system. The z-axis is parallel to
the beam and the x and y axes are perpendicular to the beam forming a right-handed
Cartesian coordinate system where x points towards the center of the LHC ring and
y points upward. The x-y plane is called the transverse plane. The azimuthal angle,
φ is measured around the z-axis and the polar angle, θ is measured from the z-axis.
Since the proton is a composite object, the colliding partons within each proton
carry some fraction of the proton momentum, and the partonic momenta are not
known a priori. At a hadron collider the laboratory frame and the partonic center of
mass frame do not coincide. Instead, the partonic center of mass frame is typically
39
boosted along the beam axis. This longitudinal boost is most easily taken into account
by describing four-momenta in terms of the rapidity y rather than the scattering angle.
The rapidity of an object in the detector is defined to be
y =1
2lnE + pzE − pz
, (3.2.1)
where E is the energy and pz is the component of momentum along beam axis.
Differences in rapidity remain invariant under an arbitrary boost along the z axis
[32]. The transverse momentum is also invariant under the Lorentz boost along the
z-axis. In situations where it is necessary to transform between various systems
which are boosted parallel to the z-axis, it is thus expedient to use rapidity y and
transverse momentum to describe the particle kinematics rather than the momentum
vector. Furthermore, in all hadronic collisions the distribution of final state particles
is uniform in rapidity. In the massless limit E ≈ |~p|
y ∼ 1
2ln
1 + cos θ
1− cos θ= ln[cot
θ
2] = −ln[tan
θ
2] ≡ η, (3.2.2)
The pseudo-rapidity η is equal to the rapidity y of the particle if its mass is equal
to zero. With the masses of most particles much smaller than their energies, the
pseudo-rapidity is often used, even for massive particles. However, the variable of
physical significance is the rapidity.
A distance ∆R in η − φ space is defined by
∆R =√
(∆η)2 + (∆φ)2, (3.2.3)
The separation ∆R between two objects is invariant under longitudinal boosts [33].
40
3.3 The Inner Detector
The Inner Detector [34] is designed to determine particle momenta to high precision
and reconstruct the primary and secondary vertices. It covers the region up to |η| <
2.5 and provides electron identification in a momentum region from 0.5 GeV up to
150 GeV with |η| < 2.0.
The Inner Detector itself is composed of three sub-detectors: the silicon pixel
detector, the semiconductor tracker and the Transition Radiation Tracker (TRT).
The first two are both based on semiconductor technology and have a high spatial
resolution, on the order of 10 µm. For the third sub-detector the choice was made
for a relatively lighter weight device. The TRT consists of gaseous straw tube ele-
ments and interleaved transition radiation material. Although it has a lower spatial
resolution than silicon detectors, it provides many space-points enhancing the track
reconstruction in the busy enviornments with up to ∼ 1000 particles expected. The
TRT is also suitable for electron identification.
The momentum resolution of the inner detector is
σpTpT
= 0.05%pT ⊕ 1%, (3.3.1)
3.3.1 Pixel Detector
The pixel detector [35] [36] consists of three cylindrical barrel layers and six end cap
disks, three on each side of the interaction point. The layers and six end caps are
41
Figure 3.3: Inner detector end-caps traversed by two charged tracks, at η = 1.4 andη = 2.2.
layer radius staves modules0 50.5 mm 22 2861 88.5 mm 38 4942 122.5 mm 52 676
Table 3.1: Configuration of the Pixel Barrel
mounted in one rigid frame which is 130 cm long and has an outer radius of 19 cm.
The first layer is very important for good vertex resolution and the performance of
b-quark identification algorithms (b tagging algorithms). The detector elements are
1744 flat silicon modules with identical design. Each module has a size of 19 x 63
mm2 and has 47132 readout pixels with a typical size of 50 x 400 µm2. 1152 of these
pixels do not have a separate readout channel but are ganged together with other
pixels. Consequently, each module has 46080 readout channels. 5284 readout pixels
are long pixels with a size of 50 x 600 µm2. The long pixels lie at the edges of the 16
bump-bonded read out chips of each module.
In the pixel barrel the modules are mounted on the layers in staves of 13 modules
42
layer radius modules tilt-angle0 284 mm 384 11o
1 355 mm 480 110
2 427 mm 576 11o
2 498 mm 672 11o
Table 3.2: Configuration of the SCT Barrel
each, along Z axis. The layer radii, the number of staves and the resulting number of
modules per layer are listed in Table 3.1. The staves are tilted by 20o with respect to
the radial direction from the beam line to overlap with each other (turbine arrange-
ment). In the end caps there are 48 modules mounted on each disk. The disks are at
the Z positions |Z| = 495 mm, 580 mm, and 650 mm.
The main task of the pixel detector is to accurately reconstruct the position of
primary and secondary vertices.
3.3.2 Semi Conductor Tracker
The Semi Conductor Tracker (SCT) contributes to the tracking of charged particles
by providing four space points in a range of |η| < 2.5. It consists of separate three
sub-parts: one barrel and two end caps. The barrel consists of four cylindrical layers
with its silicon modules mounted such that strips run parallel to beam axis. The
modules in the barrel have an angle of 11o with respect to the barrel’s tangent to
compensate for the Lorentz angle and to provide full coverage in the φ direction. The
radii, number of modules and tilt angles for each SCT barrel layer are listed in Table
3.2.
The two end caps each have nine disks with the modules oriented such that the
43
disk |Z| inner module middle modules outer modules total0 853.8 mm 40 52 921 934.0 mm 40 40 52 1322 1091.5 mm 40 40 52 1323 1299.9 mm 40 40 52 1324 1399.7 mm 40 40 52 1325 1771.4 mm 40 40 52 1326 2115.2 mm 40 52 927 2505.0 mm 40 52 928 2720.2 mm 52 52
Table 3.3: Configuration of the SCT end-caps
strips run radially. Each disk can have an inner and outer layer, mounted on the
side of disk facing the interaction point, plus a middle layer on the other side of the
disk. This setup ensures there are no gaps between the layers. The exact location of
the disks and their orientation in modules are chosen such that any charged particle
always hits at least four modules. The Z-positions, the number of various modules
types and the total number of modules for each SCT end-cap disk are listed in Table
3.3.
The SCT provides precision space-points for track reconstruction and momentum
measurement.
3.3.3 Transition Radiation Tracker
The transition radiation tracker is the outermost sub-detector in the ID. Its straws
(drift tubes) provide many extra space points for the track reconstruction, but with
a lower spatial resolution than the SCT or pixel detector. By detecting transition
radiation in the TRT, electrons can be identified in the large amount of charged
44
particles produced in the hard scattering.
The transition radiation tracker consists of cathode straws each with radius of 4
mm and length up to 144 cm. They are operated at -1530V and filled with a gas
mixture of 70% Xe, 27% CO2, 3% O2 with 5-10 mbar overpressure. The anodes are
31 µm diameter tungsten wires plated with 0.5-0.7 m gold and are kept at ground
potential. The wires are supported at the straw ends by end-plugs and are directly
connected to the front end electronics. For the barrel straws (with length of 144 cm)
the wire is supported near the center by the plastic insert glued to the inside of the
wall, isolating both parts and thus reducing the occupancy of each straw. For this,
each barrel straw is read out from both ends.
However each long barrel straw is therefore inefficient near its center over a length
of 2 cm. For some straws the wire is evenly divided into three segments, leaving the
middle segment inactive [31]. The straws are bundled in modules: the barrel consists
of three layers, each with 32 modules. Figure 3.4 is a schematic view of a part of the
ID barrel and depicts how the TRT straws are bundled in triangular shaped modules.
This provides full φ-coverage without any gaps. The end-caps straws are mounted
radially, starting at 63 cm and ending at 103 cm from the beam axis. The end caps
cover the range of 0.7 < |η| < 2.0, see Figure 3.3.
A charged particle crossing the TRT will ionize the gas inside the straws. The
released electrons drift to the anode wires; the drift time of these released charges in
the straw is used to determine the point of closest approach of the charged particle
45
to the wire with a spatial resolution of 170 µm. The TRT will provide typically 30
hits per track, with a maximum of 36, see Reference [37].
The straws are embedded in polypropylene fibers with different indices of refrac-
tion. A charged particle emits transition radiation in the X-Ray regime with energy
proportional to the Lorentz factor γ = E/m. The X-Rays are efficiently absorbed by
the xenon in the gas in the straws where energy deposits of several keV can easily be
distinguished from the energy deposits of ionized gas, which are of the order 200 eV.
The electronics discriminates the signal against the two thresholds and can handle
both energy deposits simultaneously. As the electron has a small mass, the amount of
radiation it emits is clearly larger than that of heavier particle with the same energy;
hence the TRT serves as electron identifiers.
To avoid pollution from permeation through the straw walls or through leaks, the
straws are operated in a CO2 envelope. A charged particle from the interaction point
hits on average 36 straw tubes and so the main task of the TRT is to provide an
accurate momentum measurement.
3.3.4 Inner Detector material distribution
The material distribution in a detector partly determines its performance. The dis-
tribution can be expressed with two important properties [38].
• Radiation Length (X0)
The radiation length is the mean distance over which a high energy electron
46
Figure 3.4: Cross section of Inner Detector. The drawing shows structural elementsof the Inner Detector in the central barrel. The red line simulates a charged trackwith pT of 10 GeV that traverses successively the beam pipe, three cylindrical pixel-layers, four cylindrical SCT barrel layers and 36 axial straws of the barrel transitionradiation tracker.
loses all but 1/e of its energy by bremsstrahlung. It is also 7/9 of the mean
free path for pair production by a high energy photon. The radiation length
depends on the material and can be approximated by
X0∼=
761.4A
Z(Z + 1)ln287√Z
(3.3.2)
where A and Z are the atomic weight and the atomic number of the propagation
medium respectively. The average absorption length of an electron of a given
47
Material Xo[g
cm2] Xo[cm]
Kapton 40.58 mm 28.6Liquid Argon 19.55 mm 14.0Aluminium 24.01 mm 8.89
Iron 13.84 mm 1.76Copper 12.86 mm 1.43Lead 6.37 mm 0.56
Table 3.4: Radiation lengths for various materials [4]. Often the radiation length isexpressed in gcm− 2. The result in cm can be obtained by dividing the density ofmaterial [39].
energy is independent of the material when expressed in radiation length. Table
3.4 gives the radiation length of some of the materials used in ATLAS detector.
• Nuclear Interaction Length (λ)
The nuclear interaction length is the mean free path between inelastic collisions.
For a hypothetical homogeneous material λ = A/Nρσ, where A is the atomic
weight, N is the Avogadro number, ρ is the density of the material and σ is the
cross-section of the incoming particle on the nucleus with weight A.
3.4 The Calorimeters
For the measurement of particle energy, two different types of calorimeter are em-
ployed [40]. The electromagnetic calorimeter is used for electrons and photons and
the hadronic calorimeter, for all strongly interacting particles. An electromagnetic
calorimeter must have a high enough Xo to stop the electrons and photons, yet a
low λ not to interfere too much with the hadrons; the EM energy does not depend
on λ. In contrast the hadronic calorimeter’s depth must be large enough to stop all
48
Figure 3.5: Amount of material in terms of interaction length, as a function of |η| forATLAS calorimeter in front of the electromagnetic calorimeter, in the electromagneticcalorimeter and in each hadronic layer. The last layer up to |η| < 3 corresponds tothe material in front of first layer of the muon spectrometer.
hadronic showers and prevent punch-throughs into the muon spectrometer. The total
thickness of the EM calorimeter is > 22 Xo in the barrel and > 2Xo in the end-cap.
The EM calorimeter amounts to a maximum of about 1.5 λ, compared to ∼ 7.5 λ
for the hadronic tile calorimeter, 10 λ for the hadronic end cap (HEC), and 10 λ
for the forward calorimeter (FCAL). Figure 3.5 shows the interaction lengths of all
calorimeters.
The calorimeters have been designed to cover the geometrical acceptance as her-
miticallly as possible. The only particle known so far, that can go undetected through
the whole of ATLAS is the neutrino. Its presence can however be deduced by ’miss-
ing energy’ in a certain direction. The longitudinal momenta of the colliding particle
is not known, but their transverse momentum is minimal. An unbalanced sum of
transverse energy in the event, called ETmiss, can thus be seen as the sum of the pT
49
of all neutrino’s in the event.
The principle of calorimetry is simple: in a dense absorber the incoming particle
interacts with the material, creating a shower of charged and neutral particles. The
charged particles are measured in the active medium. The number of particles counted
is ideally proportional to the energy of the original incoming particle. The active
material is made up of material that is sensitive to ionization caused by charged
particles. A sampling calorimeter is designed in such a way that interactions between
incoming particles and the absorbers produce particles that can be measured in the
active material. The total number of secondary particles produced by an interaction
with an absorber is proportional to the interacting particle’s energy. The amplitude
of the signal measured by the calorimeter in the active material is proportional to the
number of charged particles that traverse it. Therefore, the energy of the incoming
particle can be inferred from the signals originating in the active material. The
ATLAS calorimeter uses two different active materials and three different absorbers:
liquid argon (LAr) with lead/copper-tungsten and scintillation tiles with steel. The
sampling fraction of a calorimeter is the fraction of the energy measured in the active
medium to the total energy deposited in the module.
In the EM calorimeter, the showers are a cascade of mostly photons and electron-
positron pairs: photons interact with the nuclei resulting in the pair production of an
electron and a positron. The charged particle lose energy by ionizing the atoms or
by emitting bremsstrahlung; that is, the radiation as a consequence of acceleration in
50
Figure 3.6: Cut-away view of the ATLAS Calorimeters.
the EM field of the nuclei or the electrons. The hadrons scatter by strong interactions
with the nuclei into showers of lower energy hadrons. We note that in the hadronic
calorimeter a shower can be partially electromagnetic. This is mostly due to the pions
produced in the shower, of which πo decays to two photons.
3.4.1 Electromagnetic Calorimeter
The EM calorimeter is a liquid argon based detector and uses lead plus stainless
steel as the absorber. The lead gives the shower development with its short radiation
length and secondary electrons create ionization in the narrow gaps of liquid argon.
An inductive signal from the ionization electrons drifting in the electric field across
the gas-gap is registered by copper electrodes. The charged particle in the shower
ionize the argon; the free charges subsequently drift to electrodes under influence of
an electric field applied by high voltage electrodes. The calorimeters are housed in
51
three different cryostat environments cooling the argon down to a liquid state. One
cryostat keeps the barrel 88 K. To minimize the amount of material, the same cryostat
is used to cool the solenoidal magnet surrounding the ID to a temperature of 4.5 K.
Each end-cap has its own cryostat at a temperature of 88 K containing the entire
end-cap and the entire forward calorimeter.
The EM calorimeter is comprised of modules all built in a similar way, be it for
the barrel or the end-cap calorimeter. In the Forward Calorimeter (FCAL), however,
the modules are designed differently. Figure 3.7 shows the schematics of one barrel
module: 1.1-2.2 mm thick lead plates covered with stainless steel are folded in an
accordion shape.
The accordion shape makes it possible to have a full φ coverage without cracks
and a fast extraction of the signal at the outside of the detector. The orientation of
the module is not always the same: in the barrel the wave runs in the radial direction
and in the end-cap, parallel to the beam axis. In both cases the amplitude of the
wave is in the φ direction. The barrel covers the range of 0 < |η| < 1.475, and the
end-caps cover the range of 1.375 < |η| < 3.2. Between the barrel and each end-cap,
some space is reserved for cryostat services; electrons reconstructed at |η| ∼ 1.4 are
therefore treated with special care. In the FCAL the EM calorimeter is also a liquid
argon detector, but differently shaped. It covers the range of 3.1 < |η| < 4.9.
The readout of the EM Calorimeter is segmented with a decreasing granularity at
larger radius.
52
Figure 3.7: Sketch of accordion structure of EM calorimeter and barrel granularity.The pre-sampler is not shown here.
In the central rapidity region there are four samplings.
• Pre-sampler
A pre-sampler is a single thin layer of active liquid argon, with no lead absorber,
in front of the barrel and end-cap. The LAr layer is 1.1 cm (0.5 cm) thick in
the barrel (end-cap) region. The purpose is to correct for the energy loss in the
Inner Detector, solenoid and cryostat wall. The pre-sampler covers the range
of 0 < |η| < 1.8 and has a granularity of ∆η ×∆φ = 0.025× 0.1.
• First sampling
The first sampling has the depth of 4.3 radiation lengths (4.3Xo). The readout
is seen in Figure 3.7 in thin |η| stripes. i.e.; each strip has a size (∆η ×∆ϕ =
53
0.0031× 0.098). This provides an excellent resolution of in the η coordinate for
γ/πo and e/γ separation.
• Second sampling
The majority of energy is deposited in the 16 radiation lengths (16 X0) of the
second sampling. The clusters with energy below 50 GeV are fully contained
and the noise can be reduced by not adding the third sampling. For the position
measurement of the cluster, the two coordinates are equally important resulting
in square cells of size ∆η ×∆ϕ = 0.0245× 0.0245.
• Third Sampling
Only the highest energy electrons will reach this depth in the detector. Each
strip has the size ∆η×∆ϕ = 0.0245× 0.05. The clusters at this point are wide
and the cell size can be doubled in the η direction without loss of resolution.
This layer has the purpose of measuring the tail of high energy showers.
The resolution of the EM calorimeter is
∆E
E=
a√E⊕ b
E⊕ c, (3.4.1)
with energies measured in GeV.
The sampling term a is defined by the number of lead/argon interfaces and is
8− 11% depending on rapidity. Noise influences the resolution at the lowest energies
through the term b which is of the order of 400 MeV when running at high luminosity.
54
The constant term affects the resolution for high energy clusters and is limited by the
calibration and local variations (of less than 1%).
3.4.2 Hadronic Calorimeter
The ATLAS Hadronic Calorimeters [41] placed behind the EM Calorimeters cover
the pseudo-rapidity range |η| < 4.9. Three different technologies are used to meet
the physics requirements and to tolerate the different radiation levels. The region
|η| < 1.7 is covered by the Tile calorimeter while at larger pseudo-rapidities is used in
both the Hadronic End-Cap calorimeter (HEC) and the forward calorimeters (FCAL).
The hadronic calorimeters are designed to identify and measure the energy and
direction of jets ( jets will be defined in section 4.4 ). The required jet energy resolution
depends on the pseudo rapidity region and is given by the following:
σEE
=
50%√E⊕ 3% |η| < 3
50%√E⊕ 10% 3 < |η| < 4.9
(3.4.2)
The Hadronic Calorimeter must be thick enough to provide good containment for
hadronic showers and to keep punch through into the muon system to a minimum. A
thickness of about 10 (interactions lengths) provides good resolution for high energy
jets. Together with the large pseudo-rapidity coverage, this will also guarantee a good
EmissT measurement which is important for super symmetry particle searches.
55
Barr
el
End-C
ap
EM
Calo
rim
ete
rN
oof
laye
rsan
d|η|c
over
age
Pre
sam
ple
r1
|η|<
1.5
11.
5<|η|<
1.8
3|η|<
1.35
21.
375<|η|<
1.5
21.
35<|η|<
1.47
53
1.5<|η|<
2.5
Cal
orim
eter
22.
5<|η|<
3.2
Gra
nula
rity
∆η×φ
vers
usη
Pre
sam
ple
r0.
025×
0.1
|η|<
1.52
0.02
5×
0.1
1.5<|η|<
1.8
0.02
5×
0.1
|η|<
1.40
0.05
0×
0.1
1.37
5<|η|<
1.42
50.
025×
0.02
51.
40<|η|<
1.47
50.
025×
0.1
1.42
5<|η|<
1.5
0.02
5×
0.1
1.5<|η|<
1.8
0.02
5×
0.1
1.8<|η|<
2.0
0.02
5×
0.1
2.0<|η|<
2.4
0.02
5×
0.1
2.4<|η|<
2.5
Cal
orim
eter
1st
laye
r
0.1×
0.1
2.5<|η|<
3.2
0.02
5×
0.02
5|η|<
1.40
0.05
0×
0.02
51.
375<|η|<
1.42
50.
075×
0.02
51.
40<|η|<
1.47
50.
025×
0.02
51.
425<|η|<
2.5
Cal
orim
eter
2nd
laye
r
0.1×
0.1
2.5<|η|<
3.2
Cal
orim
eter
3rd
laye
r0.
050×
0.02
5|η|<
1.35
0.05
0×
0.02
51.
5<|η|<
2.5
Num
ber
ofR
eadou
tch
annel
sP
resa
mple
r78
0815
36(b
oth
sides
)C
alor
imet
er10
1760
6220
8(b
oth
sides
)
Tab
le3.
5:P
aram
eter
sof
the
AT
LA
SE
lect
rom
agnet
icC
alor
imet
erSyst
em
56
Hadronic Tile Calorimeter
The Tile Calorimeter is a sampling calorimeter that uses plastic scintillating tiles
as the active material and steel plates as the absorbers. The scintillating tiles are
oriented radially and perpendicular to the beam axis so that an almost seamless
azimuthal coverage is possible.
The tile calorimeter is segmented into one barrel and two extended barrels each
with 64 independent azimuthal modules divided into cells and towers. The barrel
tile calorimeter has a length of 5.8 m and two extended barrels have a length of 2.6
m and both have an inner radius of 2.28 m and an outer radius of 4.25 m. The
covering range of pseudo-rapidity are |η| < 1.0 in the barrel and 0.8 < |η| < 1.7 in
the extended barrels. The radial depth of the tile calorimeter is 7.4 λ. Thus a total
depth of 9.7 λ of active material is achieved in the barrel region when taken together
with the electromagnetic calorimeter. It is enough to achieve the required resolution
for high energy jets.
The tile calorimeter is required to identify and measure both the energy and
direction of jets with a relative energy resolution as given by equation 3.4.1, in addition
to providing a good measurement of EmissT .
Hadronic End-Cap Calorimeters
The Hadronic End-Cap Calorimeter (HEC) is a sampling calorimeter with copper
plate absorbers and LAr as an active material. It is designed to provide coverage
57
Figure 3.8: Sketch of Tile Calorimeter module
with hadronic showers in the range 1.5 < |η| < 3.2.
The HEC consists of two wheels, the front wheel and the rear wheel, each cylin-
drically shaped with an outer radius of 2.03 m. Each of four wheels is constructed of
32 identical wedge shaped modules.
The modules of the front wheel are made up of 24 copper plates, each 25 mm thick,
plus a 12.5 mm thick front plate. In the rear wheels, the sampling fraction is lower,
with modules made of 16 copper plates, each 50 mm thick, plus a 25 mm thick front
plate. The flat plates are stacked with honeycomb structure between them. The gaps
created this way all have a thickness of 8.5 mm and are filled with the liquid argon
and the electrodes. The readout is organised in cells with sizes of ∆η×∆φ = 0.1×0.1
in the region |η| < 2.5 and 0.2×0.2 for larger values of |η|. The readout is segmented
in 8 and 16 gaps for the front wheel, and 8 and 8 gaps for the rear wheel. These four
segments are named HEC0 to HEC3 and their contribution in material is shown in
58
Fig 3.5.
Forward Calorimeter (FCAL)
The Forward Calorimeter is a sampling calorimeter with LAr as the active material.
The FCAL covers a range of 3.1 < |η| < 4.9 and is located at approximately 4.7 m
from the interaction point. Due to its location, it is exposed to high level of radiation.
In order to sustain high particle flux, it is designed with very small liquid argon gaps,
which are obtained by using an electrode structure of small-diameter rods, centred
in tubes that are oriented parallel to the beam direction. Each of the two forward
Calorimeters consists of three wheels: FCAL1, FCAL2, FCAL3
The first layer (FCal1) is designed for electromagnetic measurements. It uses
copper as an absorber and comprises a total radiation length of 27.6Xo.
The Hadronic part (FCAL2 and FCAL3) uses Tungsten as the absorber and con-
sists of two wheels of radiation lengths of 91.3 and 89.2 Xo. The interaction lengths
of the three FCALs are respectively 2.7, 3.7 and 3.6 λ respectively.
3.5 Muon Spectrometer
The muon spectrometer [42] is the outermost part of the ATLAS detector. It measures
the charge and energy of the muons that escape from the hadronic calorimeter, based
on the deflection of the muon tracks traversing the large-air core toroid magnetic field.
Given the high background rates at the LHC, the muon drift chambers will have to
operate at high levels of occupancy. For this reason the muon system is instrumented
59
Barr
el
End-C
ap
LA
rhadro
nic
end-c
ap
|η|c
over
age
1.5<|η|<
3.2
Num
ber
ofla
yers
4G
ranula
rity
∆η×
∆φ
0.1×
0.1
1.5<|η|<
2.5
0.2×
0.2
2.5<|η|<
3.2
Rea
dou
tch
annel
s56
32(b
oth
sides
)L
Ar
forw
ard
Calo
rim
ete
r|η|c
over
age
3.1<|η|<
4.9
Num
ber
ofla
yers
3 FC
al1:
3.0×
2.6
3.15<|η|<
4.30
FC
al1:∼
four
tim
esfiner
3.10<|η|<
3.15
4.30<|η|<
4.83
FC
al2:
3.3×
4.2
3.24<|η|<
4.50
FC
al2:∼
four
tim
esfiner
3.20<|η|<
3.24
4.50<|η|<
4.81
FC
al3:
5.4×
4.7
3.32<|η|<
4.60
FC
al3:∼
four
tim
esfiner
3.29<|η|<
3.32
Gra
nula
rity
1st
laye
r
4.60<|η|<
4.75
Sci
nti
llato
rti
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mete
rB
arre
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xte
nded
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rel
|η|c
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1.7
Num
ber
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33
Gra
nula
rity
∆η×
∆φ
0.1×
0.1
0.1×
0.1
Las
tla
yer
0.2×
0.1
0.2×
0.1
Rea
dou
tch
annel
s57
6056
32(b
oth
sides
)
Tab
le3.
6:P
aram
eter
sof
the
AT
LA
SH
adro
nic
Cal
orim
eter
Syst
em
60
Figure 3.9: View of muon spectrometer.
separately with chambers for precision measurement and chambers for triggering.
The magnetic field provided by the ATLAS toroid system is mostly orthogonal to the
muon while the toroid magnet was designed trying to minimize the multiple scattering
effects on muon crossing the magnetic instruments.
In the barrel region, tracks are measured in chambers arranged in three cylindrical
layers around the beam axis containing chambers for tracking precision, Monitor Drift
Tubes (MDT) and chambers for trigger purposes, Resistive Plate Chambers (RPC).
In the transition and end-cap regions, the chambers are installed in three planes
perpendicular to the beam, containing MDTs and Cathode Stripe Chambers (CSC)
61
for precision tracking as well as Thin-gap Chambers (TGC) for trigger purposes.
MDTs are aluminium-walled 3 cm diameter gaseous drift chambers, with a central
wire of 50 µm diameter. The length of wire varies from ∼ 1 m up to ∼ 6 m depending
on the position of the chamber within the ATLAS detector. The tube is filled with
93% gas Ar and 7 % CO2.
A muon traversing the chambers ionises the gas under a high electric field. Ion-
isation electrons are drift to the sense wire inducing an electric charge that can be
measured. A typical track produces about 400 primary ion pairs. The maximum drift
time of ionised electrons is 800 ns and the typical drift velocity is ∼ 2 cm/µs. With
the timing measurements, the positional resolution that can be achieved is ∼ 1 mm.
RPCs are optimised to provide a good time resolution for triggering, meaning to
assign more than 99% of the triggered muons to the correct bunch crossing. In each
module of a RPC, a narrow gap is filled with gas. The RPC measures the ionisation
pulses in the gas at high voltage although it contains no wires and therefore the
spatial resolution is much coarser, while the time response is higher compared to the
MDT. The typical space-time resolution of the RPC is the order of 1 cm × 1 ns.
Although MDTs can cover the requirements for precious measurements of muons
in most of the coverage of the ATLAS detector, their rather large diameter and
high operating pressure make them unsuitable for use in areas where high ( > 200
Hz/cm2) counting rates are expected. In ATLAS such high background rates are
produced in the first muon measuring at 2.0 < |η| < 2.7. In this region (CSC) multi-
62
wire proportional chambers are used instead. They consist of an array of anode wires
in narrow gas enclosures with metal walls arranged in the form of stripes. Applying
the high voltage between wires and wall stripes, traversing muons produce signals.
They consist of an array of anode wires in narrow gas enclosures with metal walls
arranged in the form of stripes. Applying a high voltage between wires and small
strips, traversing muons produce signals on the strips that allow position resolution
better than 60 µm with a time resolution of the order of 7 ns.
For trigger muon measurements in the end-cap, TGCs are used instead of RPCs
which are used in the barrel. TGCs operate in the saturated mode and therefore
have a structure similar to multi wire proportional chambers. The high electric field
around the TGC wires and the small distance between wires strongly reduces the drift
component of isolation clusters, leading to a very good time resolution. Over most of
the |η| range, the precision measurement of the track is provided by MDT’s, while for
large pseudo-rapidities, 2 < |η| < 2.7, CSCs are used instead in the innermost plane.
The trigger system covers the |η| < 2.4. In the barrel region, the trigger chambers
are RPCs while in the end-cap regions, the TGCs are the chosen solution.
3.6 Trigger
The trigger system [43] [44] [45] of the ATLAS experiment has the challenging task to
select on the fly one out of 105 events and to ensure most physics processes of interest
are preserved for analysis.
63
Coverage |η| < 2.7(innermostlayer : |η| < 2.0)Number of Chambers 1150Number of Channels 354000
Monitored Drift tubes
Function precision tracking
Coverage 2.0 < |η| < 2.7Number of Chambers 32Number of Channels 31000
Cathode Stripe Chambers
Function precision tracking
Coverage |η| < 1.05Number of Chambers 606Number of Channels 373000
Resistive Plate Chambers
Function triggering
Coverage 1.05 < |η| < 2.7Number of Chambers 3588Number of Channels 318000
Thin gap Chambers
Function triggering
Table 3.7: Parameters of ATLAS Muon Spectrometer
The trigger and data acquisition system must work under the challenging envi-
ronment of around 109 proton-proton interactions per second (generating 1 PB/s of
data) and roughly 108 electronics channels of the ATLAS detector. This must be
reduced to 300 MB/s, the maximum sustained rate to mass storage, while efficiently
retaining rare physics signatures for off-line analysis. Interesting signals are very rare
at the LHC. To achieve the desired reduction rate, ATLAS has designed a three-level
trigger system depicted in Fig 3.10. Each step refines the previous decision by using
a larger fraction of the data and more advanced and time demanding algorithms.
Furthermore each trigger level must reach a decision quickly enough to handle the
output rate of the previous level.
64
First Level Trigger
The level 1 trigger is a hardware based trigger that is designed to reduce the 40
MHz bunch crossing rate to an event rate of about 75 kHz. The LVL1 trigger uses
information based on relatively coarse data from the calorimeters and total event
data. The event selection is based mainly on inclusive high-pT objects like muons,
electrons/photons, clusters τ -lepton decay, and missing and scalar transverse energy
sums with programmable thresholds.
During the LVL1 latency of 2.5 µs the data of all sub-detectors are buffered to
await the trigger decision. Then data for events passing the trigger selection at LVL1
are transferred to the next stage of detector specific electronics. For accepted events,
the geometrical location of the identified objects, Regions of Interest (ROI), and the
thresholds they passed, are sent to the second trigger level and the data are then
transformed from the pipeline memories to Read-out Drivers (RODs).
Second Level Trigger
The LVL2 trigger is a software based which uses the output of the LVL1 and reduces
the data rate from 75 kHz to 3 kHz. Algorithms running during the LVL2 processing
have access to the detector data with the full-spatial granularity, but only within RoIs
identified by LVL1, roughly corresponding to about 2 % of the total event data. This
approach reduces the data volume and processing time required for the selection and
makes it possible to handle the LVL2 input rate. The LVL2 trigger has a nominal
65
Figure 3.10: A schematic sketch of the ATLAS trigger, indicating the various stagesin which the data is processed and the event rates at the different trigger levels.
average processing time of 40 ms.
Event Filter
If LVL2 accepts an event, all the fragments from the RODs are combined and sent to
one EF processor for the final decision. The EF is the last trigger stage and is allowed
to take on average about 4s to make its decision. The EF makes decision whether the
event is recorded for off-line analysis or discarded. Using the complete event record,
it uses complex off-line algorithms such as track reconstruction, vertex finding, jet
finding, etc. The recorded data is reconstructed to produce quantities such as tracks,
energy clusters, jets, EmissT , secondary decay vertices, etc.
The maximum output of the event filter is ∼ 200Hz which corresponds to a data
rate of ∼ 300MB/s. All events that pass the event filter are written to mass storage
and are available for further analysis with the ATLAS off-line software.
66
3.6.1 Trigger menu and data streams
The complete configuration of the ATLAS trigger is called a menu. Here a menu
consists of different chains; one chain, also called a slice, can, for example, be the
sequence of the L1, L2 and EF trigger selecting two jets. An event is thus accepted
if at least one chain is satisfied.
At the end of the trigger chains the EF classifies the event into one or more
physics streams. Events with the same chains are thus grouped together, simplifying
further analysis. It also makes it possible to reprocess events separately for each
stream. An event however, can also end up in several streams, resulting in duplicate
events. The different streams therefore, are defined such as to have minimal amount
of overlap. There are four physics streams: electrons and photons (E gamma), muons,
jet/τ/EmissT and minimum bias triggers. With this definition, the overlap is less than
10%, [46]. The minimum bias trigger ensures that some of the minimum bias events
are saved. Their expected rate at the LHC have a large uncertainty. Minimum bias
events are saved to understand the background they form.
67
Figure 3.11: A schematic sketch of the ATLAS trigger chain for electrons and photonsof at least 60 GeV of transverse energy.
68
chapter 4
PARTICLE IDENTIFICATION
Different particles are produced from the proton-proton collision in the LHC. These
particles interact differently when passing through the material of the detector’s lay-
ers. Collecting information from the different parts of the detector, such as tracks and
energy depositions, makes it possible to identify particles passing through the detec-
tor and determine their properties like: energy, momentum and charge. The primary
physics objects that are reconstructed in events are tracks, vertices, calorimeter ob-
jects such as electrons, photons and jets, muons, and missing transverse energy.
4.1 Tracks
A track in ATLAS is parametrized at the point of closest approach with the global
z-axis using five perigee parameters.
• q
p: the charge of the particle divided by the momentum.
• φo: the angle with the x-axis in the x-y plane at the perigee point.
• θo: the angle with the z-axis in the R-z plane.
• do: the signed distance to the z-axis.
• zo: the z-coordinate of the track at the point of closest approach to the global
z-axis.
69
Figure 4.1: [Perigee parameters of a track (left): in transverse plane. (right): in R-zplane.
Track reconstruction in the inner detector uses the measurements of the pixel, SCT
and TRT detectors. The main track reconstruction strategy is the “inside-out” strat-
egy [47], which starts by finding a track candidate in the pixel and SCT detectors and
then extends the trajectories of successfully fitted tracks to the TRT to reconstruct a
full inner detector track. The track reconstruction sequence is complemented by an
‘outside-in’ strategy. The outside-in strategy starts from unassigned TRT segments
and looks for matching hits in the pixel and SCT detectors. The two track fitting tech-
niques which are widely using in high energy physics, the global least-squares fit [48]
and the Kalman filter [49] are both implemented in the ATLAS software framework.
4.2 Electron Identification
The ATLAS electromagnetic calorimeter is designed to identify electrons and photons
within an energy range of 5 GeV to 5 TeV [50]. A sliding window [51] algorithm is
used to identify and reconstruct electromagnetic clusters. Rectangular clusters with
70
a fixed size are formed and positioned to maximize the amount of energy within each
cluster. The optimal cluster size depends on the particle type being reconstructed.
Electrons need a larger cluster size than photons due to the electron’s larger interac-
tion probability and due to the fact that they bend in the magnetic field, radiating
soft photons in φ. Several different cluster sizes are then built by the reconstruction
software. These clusters are the starting point of the calibration and selection of
electron candidates. For each of the reconstructed clusters, the reconstruction algo-
rithm tries to find a matching track within a ∆η × ∆φ range of 0.05 × 0.10 with a
momentum p compatible with the cluster energy (E/p < 10 ). If a track match is
found, the reconstruction algorithm checks for the presence of an associated conver-
sion. An electron candidate is created if a matching track is found and no conversion
is flagged. Otherwise a candidate is classified as a photon. This early classification
allows different corrections to be applied to electron candidates and is the starting
point of a more refined identification based on shower shapes and on respective cuts.
Three levels of electron qualities are defined [52].
• Loose
This set of cuts performs a simple electron identification based only on limited
information from the calorimeters. Cuts are applied on the hadronic leakage
and on shower-shape variables, derived only from the middle layer of the EM
calorimeter (lateral shower shape and lateral shower width). This set of cuts
provides excellent identification efficiency, but low background rejection.
71
• Medium
This set of cuts improves the background rejection quality, by adding cuts on the
energy deposits in strips in the first layer of the electromagnetic calorimeter and
on the tracking variables. Strip based cuts are adequate for e− πo separation.
• Tight
This set of cuts makes use of all the particle-identification tools currently avail-
able for electrons. In addition to the cuts used in the medium set, the following
additional cuts are applied.
– The number of vertexing-layer hits (to reject electrons from conversions)
– The number of hits in the TRT
– The ratio of high-threshold hits to the number of hits in the TRT (to reject
the dominant background from charged hadrons)
– The difference between the cluster and the extrapolated track positions in
η and φ, and
– The ratio of cluster energy to track momentum.
Two different final selections are available within this tight category: they are
named
– tight (isol)
– tight (TRT)
72
and are optimised differently for isolated and non-isolated electrons. In the case
of tight (isol) cuts, an additional energy isolation cut is applied to the cluster,
using all cell energies within a cone of ∆R < 0.2 around the electron candidate.
This set of cuts provides, in general, the highest isolated electron identification
and the highest rejection against jets. The tight (TRT) cuts do not include the
additional explicit energy isolation cut, but instead apply tighter cuts on the
TRT information to further remove the background from charged hadrons.
To calibrate the electron signal, Monte Carlo based methods are used. They correct
for the energy deposited in the material, in front of the calorimeter, calibrate the
cluster energy deposited in the material, and correct for leakage outside the cluster
(lateral leakage) and beyond the calorimeter (longitudinal leakage). The four items
are parametrised as a function of the cluster measured signals in the pre-sampler and
in the longitudinal layers. The parameters are computed at each pseudorapidity value
corresponding to the centre of a middle cell [53].
In addition, electrons must have ET > 20 GeV where ET =Eclus
cosh(ηtrack). Elec-
tron candidates are selected with |ηcl| < 2.47 excluding the transition region between
the barrel and end-cap calorimeters, 1.37 < |ηcl| < 1.52. To reduce the QCD multi-
jet background (will be discussed in section 6.3.1) and to suppress the selection of
electron from the heavy flavour decay jets, tight isolation cuts are imposed on the
electron with cone size of ∆R = 0.2 and ∆R = 0.3 for calorimeter and track isolation,
respectively which leads to an efficiency of about 90% of true electrons.
73
Typ
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75
4.3 Muon
The ATLAS outer muon spectrometer is designed to detect and measure the momen-
tum of muons. Two families of algorithms are used for muon reconstruction. MuID
[54] and STACO [55]. The STACO family is implemented by an algorithm, that finds
the spectrometer tracks and extrapolates them back to the beam line. It assigns
energy loss based on the material crossed in the calorimeter. On the MuID side,
an algorithm finds the tracks and performs the inward extrapolation. Additionally it
makes use of the calorimeter energy measurements if they are significantly larger than
the most likely value and the muon appears to be isolated [56]. Muon identification
is performed in three complimentary ways.
Standalone
Standalone track reconstruction starts with a search pattern among hits in three
stations of the Muon Spectrometer (MS) that yields track segments. Standalone al-
gorithms extend out to |η| < 2.5. Muons produced in the calorimeter from the decay
of B hadrons, are likely to be found in the standalone reconstruction and represent a
background for most physics analysis.
Combined
A muon found in the spectrometer is matched to one track in the inner detector. The
match χ2 is defined as the difference between outer and inner track vectors weighted
by their combined covariance matrix:
χ2 = (TMS − TID)T (CID − CMS)−1(TMS − TID) (4.3.1)
76
where T is a vector of five track parameters expressed at the point of closest ap-
proach to the beam line, and C is its covariance matrix. STACO algorithm performs
a statistical combination of track vectors and covariance matrices from the tracks
extrapolated back to the beamline at vertex and inner detector tracks.
MuID standalone tracks require a global refit, using hits from both the ID and MS.
It starts from the inner track vector and covariance matrix and adds the measurements
from the outer track. The fit accounts for the material (multiple scattering and energy
loss) and magnetic field in the calorimeter and muon spectrometer.
For this analysis muons are required to have matching good quality tracks in the
inner detector and in the muon spectrometer. Muons having a PT > 15 GeV, along
with |η| < 2.5. are selected. Additional muon hit information from three individual
parts of Inner Detector is used in reconstruction of muons in a cone of radius ∆R = 0.2
are selected with ET < 4 GeV, where as for ∆R = 0.3, muons with PT < 4 GeV.
Furthermore as an isolation requirement, muon is rejected if found with in ∆R = 0.4
of jet with PT > 25 GeV. The event is rejected if an isolated muon with |η| < 2.5 and
PT > 15 GeV shares the same inner detector track as a selected electron.
4.4 Jets
A parton that has participated in a hard scattering hadronizes into a jet which can
contain many particles. A jet definition is a set of rules to cluster particles that
”belong together”, ideally originating from a single parton. So the question is which
77
particles get put together into a common jet? And how does one combine their
momenta?
A jet leaves tracks from its charged constituents in the Inner Detector and deposits
most of its energy in the calorimeter, where each incoming particle creates a shower of
charged and neutral particles. Most jet algorithms only use the information provided
by the calorimeters.
The major theoretical guidelines for jet reconstruction are:
Infra-red safety: The presence of additional soft particles between two particles
belonging to the same jet should not affect the recombination of these two particles
into a jet. In the same sense, the absence of additional particles between these two
particles should not disturb the correct reconstruction of the jet. Generally, any soft
particles not coming from the fragmentation of a hard scattered parton should not
effect the number of jets produced.
Collinear safety: A jet should be reconstructed independent of the fact that a cer-
tain amount of transverse momentum is carried by one particle, or if a particle is split
into two collinear particles.
Order independence: The same hard scattering should be reconstructed indepen-
dently at parton, particle or detector level.
The calorimeters in ATLAS have about 200,000 individual cells of various sizes and
with different readout systems. These cells provide: energy, time, quality and gain.
They are primarily set at the so called electromagnetic scale (EM). This energy scale
78
accounts correctly for the energy of electrons and photons. EM showers generate the
large signal than hadrons depositing the same energy, therefore a specific correction
for hadronic signals is needed.
Individual cells are hard to use for because they contain negative energy due to
noise effects and it is difficult to determine the source of noise without signals from
neighbouring calorimeter cells..
4.4.1 Jet Inputs
Two different object definitions are available in ATLAS, the calorimeter tower signals
and the topological cell clusters [57].
• Calorimeter tower
In the case of towers [58], the cells are projected onto a fixed grid in pseudora-
pidity (|η|) and azimuth (φ). The tower bin size is ∆η ×∆φ = 0.1× 0.1 in the
whole acceptance region of the calorimeters, i.e in |η| < 4.9 and −π < φ < π,
with 100 × 64 = 6, 400 towers in total. Projective calorimeters cells which
completely fit inside a tower contribute their total signal to the tower signal.
Non-projective cells and projective cells larger than the tower bin size contribute
a fraction of the cell area to the towers. Thus, the tower signal is the sum of
weighted cell signals. As the cell signals are on the basic electromagnetic energy
scale, the resulting tower signal is on the same scale. No further corrections and
calibrations are applied at this scale.
79
• Topological clusters
A topological cell cluster is a representation of the three-dimensional ”energy
blob” left by the shower of each particle entering the calorimeter [59]. Starting
with a seed cell with a high signal-to-noise ratio, or signal significance Γ =
E/σnoise,cell above a certain threshold Γ > 4. All directly neighbouring cells of
these seed cells, in all three dimensions are collected into the cluster. Neighbours
are considered for those cells which have Γ above a secondary threshold Γ > 2.
Finally a ring of guard cells with signal significances above a basic threshold is
added to the cluster. After the initial clusters are formed, they are analysed for
local significance maximums by a splitting algorithm, and split between those
maximums if they are found.
The tower signals and cell clusters are provided to the jet finding algorithms as
massless pseudo-particles. Their directions are fixed by the bin centre in the (η, φ)
grid for each tower, or they are reconstructed from the energy-weighted centre for the
cluster.
4.4.2 Jet algorithms
The most commonly used algorithms in ATLAS are a seeded fixed cone finder [60],
and the kt algorithm.
• Cone algorithm
See appendix C for details.
80
• Cluster Algorithm
Cluster algorithms are based upon pair-wise clustering of the initial constituents.
In general the algorithms define a distance measure between objects, and also
some condition upon which clustering should be terminated.
Two distances are introduced: dij (between entity i and j ) and diB (between
entity i and beam(B)). The clustering proceeds by identifying the smallest of
the distances. The quantities dij and diB are evaluated as follows:
dij = min(k2pti , k
2ptj )
(∆R)2ij
R2, (4.4.1)
diB = k2pti , (4.4.2)
∆R2ij = (yi − yj)2 + (φi − φj)2, (4.4.3)
where kti, yi, and φi are transverse momentum, rapidity and azimuth of particle
i. The parameter p governs the relative power of energy versus geometrical
(∆R)2ij scales.
A list of all the d values is compiled. If the smallest entry is a dij, objects i and
j are combined and the list is remade. If the smallest entry is a diB, this object
is considered a complete “jet” and is removed from the list. In the sense defined
by the algorithm, the dij is the distance between two objects, and diB is the
distance between the object and the beam. Thus the variable R is a parameter
of the algorithm setting the resolution at which jets are resolved from each other
81
as compared to the beam. For large values of R, the dij are smaller, and thus
more merging takes place before jets are complete; the reverse is of course also
true.
Three cluster algorithms are considered here. kT , Cambridge/Aachen, Anti−kT .
These differ for the value of the parameter p.
– kT Algorithm [61]
See See appendix C for details.
– Cambridge algorithm [62]
See appendix C for details.
– Anti-kT Algorithm [63]
p = −1 in equation 4.4.1. This means that in the vicinity ∆R < R of
a hard object, all softer objects will be merged with the harder object in
order of their closeness in ∆R. Thus the jet boundary is unaffected by
soft radiation. If two comparably hard objects are within R < ∆R < 2R
of each other, energy will be shared between them depending upon their
relative kT and distance. For hard objects within ∆R < R of each other, a
single jet will be formed containing both hard objects and the soft objects
within their vicinity. The ordering of the merging is not meaningful for
this algorithm. However, the constituents may be reclustered using one of
the other algorithms to recover subjet information.
82
Figure 4.2: A schematic sketch of Jet Reconstruction at ATLAS. From calorimetertowers (left), from topological calorimeter cell clusters (right) in ATLAS [37].
83
4.4.3 Jet Calibration
The jet calibration corrects for the following detector effects that affect the jet energy
measurement:
• Calorimeter non-compensation: partial measurement of the energy de-
posited by hadrons.
• Dead material: energy losses in inactive regions of the detector.
• Leakage: energy of particles reaching outside the calorimeters.
• Out of calorimeter jet cone: energy deposits of particles inside the truth jet
entering the detector that are not included in the reconstructed jet.
• Noise thresholds and particle reconstruction efficiency: signal losses in
the calorimeter clustering and jet reconstruction.
Reconstructed jets are calibrated based on the energy scale reconstructed by calorime-
ters, the EM1 scale. The goal of the jet energy scale calibration, called EM + JES is
to correct the energy and momentum of jets measured in the calorimeter, using as a
reference the kinematics of the corresponding Monte Carlo truth jets.
The jet pT response for a reconstructed jet is defined as the ratio between the trans-
verse momentum of the particle jet from the Monte Carlo event generator (pMCtruthjetT )
1The electromagnetic scale is the basic calorimeter signal scale for the ATLAS calorimeters. Itgives the correct response for the energy deposited in electromagnetic showers, while it does notcorrect for the lower hadron response
84
and the transverse momentum of the reconstructed calorimeter jet after the JES cal-
ibration (pjetT ) and it is denoted as R =pjetT
pMCtruthjetT
.
The EM + JES calibration scheme consists of three subsequent steps as outlined
below and detailed in the following subsections [64]:
• Pile-up correction
The average additional energy due to additional proton-proton interactions is
subtracted from the energy measured in the calorimeters using correction con-
stants obtained from in situ measurements
• Vertex correction
The direction of the jet is corrected such that the jet originates from the primary
vertex of the interaction instead of the geometrical centre of the detector.
• Jet energy and direction correction
The jet energy and direction as reconstructed in the calorimeters are corrected
using constants derived from the comparison of the kinematic observables of
reconstructed jets and those from truth jets in Monte Carlo simulation.
The calibration is derived using all isolated calorimeter jets that have a matching
isolated truth jet within ∆R = 0.3. Here, an isolated jet is defined as a jet having
no other jet with pT > 7 GeV within ∆R = 2.5R, where R is the distance parameter
of the jet algorithm. A jet is defined to be isolated, if it is isolated with respect to
the same jet type, i.e. either a calorimeter or a truth jet. The final jet energy scale
85
calibration is first parametrised as a function of uncalibrated jet energy and |η|. Here
the detector pseudo-rapidity is used rather than the physics η (used by default in
physics analyses), since it more directly corresponds to a region of the calorimeter.
Energy is used rather than pT , since the calorimeter responds to energy, and the
response curves can be directly compared to the expectation and between |η| bins.
The method to derive this calibration is detailed below.
The EM-scale jet energy response
RjetEM =
EEMjet
EMCtruthjet , (4.4.4)
for each pair of calorimeter and truth jets is measured in bins of the truth jet energy
Ejettruth and the calorimeter jet detector pseudorapidity |ηdet|.
For each (Ejettruth, |ηdet|) bin, the averaged jet-response < Rjet
EM > is defined as the peak
position of a Gaussian fit to theEEM
jet
EMCtruthjet distribution. In the same (Ejet
truth, |ηdet|)
-bin, the average jet energy response < EjetEM > is derived from the mean of the
distribution.
For a given |ηdet| bin k, the jet response calibration function Fcalib,k(EjetEM) is obtained
using a fit of the (< EEMjet >j, < Rjet
EM >j) values for each Etruthjet - bin j.
The fitting function is parametrized as :
Fcalib,k(EjetEM) =
Nmax∑i=0
ai(lnEjetEM)i, (4.4.5)
where ai are free parameters, and Nmax is chosen between 1 and 6 depending on the
goodness of fit.
86
The final jet energy correction that relates the measured calorimeter jet energy to the
true energy is then defined as1
Fcalib(EEMcalo)in the following:
EjetEM+JES =
EEMjet
Fcalib(EEMjet)|ηdet, (4.4.6)
where Fcalib(EEMjet)|ηdet is the jet response calibration function for the relevant |η|det
bin k.
The average jet energy scale correction1
Fcalib(EEMcalo)is shown as a function of
calibrated jet transverse momentum for three jet |η| intervals in Figure 4.3. The
calorimeter jet response RjetEM is shown for various energy and |ηdet| bins in Figure 4.3
Other calibration schemes use additional cluster-by-cluster and/or jet-by-jet in-
formation to reduce some of the sources of fluctuations in the jet energy response,
thereby improving the jet energy resolution. For these calibration schemes the same
jet calibration procedure is applied as the EM + JES calibration scheme, but the
energy corrections are numerically smaller.
The global calorimeter cell weighting (GCW) calibration exploits the observation
that electromagnetic showers in the calorimeter leave more compact energy deposi-
tions than hadronic showers with the same energy. Energy corrections are derived for
each calorimeter cell within a jet, with the constraint that the jet energy resolution
is minimised. The cell corrections account for all energy losses of a jet in the AT-
LAS detector. Since these corrections are only applicable to jets and not to energy
depositions in general, they are called “global” corrections.
87
Figure 4.3: (Top) Average jet energy scale correction as a function of the calibrated jettransverse momentum for three representative η intervals obtained from the nominalMonte Carlo simulation sample. (Bottom) Average simulated jet response Rjet
EM atthe electromagnetic scale in bins of EM + JES calibrated jet energy and as a functionof the detector pseudo rapidity |ηdet|.
88
The local cluster weighting (LCW) calibration method first clusters together topo-
logically connected calorimeter cells and classifies these clusters as either electromag-
netic or hadronic. Based on this classification energy corrections are derived from
single pion Monte Carlo simulations. Dedicated corrections are derived for the effects
of non-compensation, signal losses due to noise threshold effects, and energy lost in
non-instrumented regions. They are applied to calorimeter clusters and are defined
without reference to a jet definition. They are therefore called “local” corrections.
Jets are then built from these calibrated clusters using a jet algorithm.
For this analysis jets are reconstructed with the anti-kt algorithm with ∆R = 0.4
starting from topological clusters built from energy deposited in the calorimeter re-
constructed. Jet finding is performed on topological clusters at the electromagnetic
scale, which accounts for energy deposited by electrons or photons. A pile up subtrac-
tion scheme that accounts for the effect of both in-time (the number of interactions
in the SAME bunch crossing) and out-of-time (overlapping signals in the detector
from other neighbouring bunch crossings) pile-up is applied to jets at EM scale. This
correction is parametrized according to the number of primary vertices in an event
(NPV) and the number of interactions in a luminosity block Jets are then calibrated
to the hadronic scale using Monte Carlo-based pT and |η| dependent correction factors.
JVF is the fraction of each jet’s constituent transverse track-momentum con-
tributed by each vertex. More specifically, it is the sum pT of all matched-tracks from
89
a given vertex divided by the total jet-matched track pT . More details can be found
in Appendix D.
A cut on the Jet Vertex Fraction (JVF) is applied to further reduce the effect
of in-time pile up. This variable exploits the fraction of tracks coming from the
primary vertex that is associated to the jet to estimate the contribution of multiple
interactions, providing a discriminant for jets in form of a probability of the jet to
not have been generated by pile-up interactions if it has a sufficient fraction of tracks
from the primary vertex. Jets with |JV F | < 0.75 are rejected. For period E-H a jet
is rejected if it is found in LAr hole.( 0.1 < |η| < 1.5 and −0.5 < |φ| < −0.9 ).
4.4.4 b-jet
Using the precise track reconstruction of the ATLAS inner detector, it is possible to
identify jets arising from b quark hadronization by reconstructing the decay vertex of
long-lived B hadrons within the jet. The decay of a long-lived hadron produces several
charged particles emanating from a secondary vertex, displaced from the primary
interaction point. b-tagging plays a major role on top quark identification. For the
reconstructions of events with top quarks, a high-performance b-tagging algorithm
[66] is used. This tagger combines impact parameter information with the explicit
determination of inclusive secondary vertex. The cut point gives an efficiency of about
70% to select b tagged jets among all jets passing the reconstruction criteria.
90
Figure 4.4: Displaced vertex and Impact Parameter of B Quark. Lxy is the flightdistance and d0 is Impact Parameter.
4.5 tau jets
4.5.1 Hadronic tau decays in ATLAS
Having a mean lifetime of 2.9×10−13 seconds (cτ ≈ 87 µm), tau leptons decay before
leaving the ATLAS beam pipe. Tau leptons can decay [68]
Figure 4.5: Feynman Diagram for τ decays .
• leptonically (branching ratio = 35.3%)
– eνeντ (branching ratio = 17.9%)
91
– µνµντ (branching ratio = 17.4%)
• Hadronically (branching ratio = 64.7%)
– π± and π0
– rare decays involving kaons and others
Figure 4.6: Tau decay Modes
These hadronic states predominantly consist of 1 or 3 charged pions, along with
a neutrino, and possibly additional pions. There are also rare decays involving kaons
with a branching fraction of 2.9%. The hadronic decays of tau leptons are gener-
ally categorized by the number of charged decay products, that is the number of
tracks or prongs observable in the detector. Hadronic 1-prong decays are the most
common (branching ratio = 49.5%), followed by 3-prong decays (branching ratio =
15.2%). The challenge when identifying hadronic tau decays at high energy hadron
92
Figure 4.7: The basic principle for tau reconstruction is the observation that a tauin the detector is seen as a narrow jet. This translates into a requirement that anevent contains (a) a narrow energy deposition in the calorimeter (b) one or threetracks matching the calorimeter deposition (c) jet is required to be isolated. This isachieved by imposing the requirement that there be an area of inactivity (isolationcone) in the solid angle around the jet.
colliders is that the cross section for QCD production of quark or gluon initiated
jets, which can be falsely identified as tau decays, is many orders of magnitude above
the cross sections for weak interaction processes involving tau leptons1. The most
discriminating features for identifying taus among this multijet background are the
tau’s characteristic 1 or 3-prong signature, consequently low track multiplicity, and
relatively narrow clustering of tracks and depositions in the calorimeters.
4.5.2 Reconstruction and Identification of tau-leptons
The reconstruction and identification of hadronically decaying tau leptons can be
split into a number of steps [69].
1For example, the jet production cross section is approximately 4×103 nb for inclusive jets withpT > 60 GeV and |η| < 2.8 at
√s = 7 TeV [65]. On the other hand, the cross section for W → τhν
production is 6.5 nb at√s = 7 TeV [68].
93
1. The tau reconstruction is ’seeded’ from jet reconstruction by considering each
jet as tau candidate.
2. The list of calorimeter clusters associated to each tau candidate is refined to be
used to calculate kinematic quantities.
3. Tracks are associated to the candidates.
4. A list of identification variables is calculated from the tracking and calorimeter
information.
5. These variables are combined using multivariate discriminants to reject fake
candidate from QCD jets and electrons.
6. Selection on the output of the discriminants is used at the analysis level to select
a sample of tau candidates with the desired level of background rejection, or
signal efficiency.
4.5.3 Reconstruction seeds
Hadronically decaying tau leptons are reconstructed from calorimeter jets recon-
structed with the anti-kt algorithm, using a distance parameter, R = 0.4, from topo-
logical clusters of calorimeter cells. The clusters are calibrated using the local hadron
calibration (LC). Tau reconstruction is run on all seed jets with pT > 10 GeV within
|η| < 2.5.
94
4.5.4 Four-momentum
The reconstructed four momentum of the tau candidate is defined in terms of pT , η, φ.
The η and φ are taken from the seed jet, which are determined by calculating the
sum of the four-vectors of the constituent topological clusters, assuming zero mass for
each of the constituents. The mass of the tau candidates is defined to be identically
zero and therefore transverse momentum and transverse energy are identical.
4.5.5 Track association
Tracks are associated to each tau candidate if they are within the core cone, defined
as the region within ∆R < 0.2 of the axis of the seed jet and pass the following quality
criteria:
• pT > 1 GeV
• Number of pixel hits ≥ 2
• Number of pixel hits + number of SCT hits ≥ 7
• | do |< 1.0 mm
• | zo sin θ |< 1.5 mm
where do is the distance of closest approach of the track to the reconstructed primary
vertex in the transverse plane, while zo is longitudinal distance of closest approach.
Tau candidates are classified as single or multi-prong depending on the number of
tracks counted in the core cone. Tracks within the isolation annulus, defined by
95
0.2 < ∆R < 0.4 of the axis of seed jet, are also counted for variable calculations, and
are required to satisfy the same track quality criteria.
4.5.6 Reconstructed variables
The reconstructed variables are
• Electromagnetic radius(REM): Transverse energy weighted shower width in
the EM calorimeter
REM =
∑∆Ri<0.4i∈EM0−2E
EMT,i ∆Ri∑∆Ri<0.4
i∈EM0−2EEMT,i
, (4.5.1)
∆Ri is defined between a calorimeter cell and the tau jet seed axis. EEMT,i is the
cell transverse energy, calibrated at the EM scale. Where i runs over the cells
in the first three layers of the EM calorimeter (pre-sampler, layer 1, layer 2)
which are associated to the tau candidate. The calorimeter cells associated to
tau candidates are those which are clustered in the topological clusters that are
constituents of jet that seeded the tau reconstruction.
• Track Radius: pT weighted track width.
Rtrack =
∑∆Ri<0.4i pT,i∆Ri∑∆Ri<0.4i pT,i
, (4.5.2)
• Leading Track momentum fraction (ftrack),
ftrack =ptrackT,1
pτT, (4.5.3)
96
• Core energy fraction (fcore): Fraction of transverse energy in the core ∆R <
0.1 of the tau candidate.
fcore =
∑∆Ri<0.1i∈all EEM
T,i∑∆Ri<0.4j∈all EEM
T,j
, (4.5.4)
• Electromagnetic fraction (fEm): Fraction of transverse energy of the tau
candidate deposited in the EM calorimeter.
fcore =
∑∆Ri<0.4i∈EM0−2E
EMT,i∑∆Ri<0.4
j∈all EEMT,j
, (4.5.5)
• Cluster mass (mcluster): Invariant mass computed from the constituent clusters
of the seed, calibrated at the EM energy scale.
mclusters =
√ ∑clusters
(E)2 −∑
clusters
−→p 2, (4.5.6)
• Track mass (mtrack): Invariant mass of the track system, where the tracks used
for the invariant mass calculation use both core and isolation tracks.
mtrack =
√∑tracks
(E)2 −∑tracks
−→p 2, (4.5.7)
• Transverse flight path significance (SflightT ): The decay length significance of the
secondary vertex for multi-track tau candidates in the transverse plane:
S =LflightT
δLflightT
, (4.5.8)
where LflightT is the reconstructed signed decay length and δLflightT is the esti-
mated uncertainty of decay length.
97
• TRT HT fraction(fHT ): The ratio of high threshold to the low threshold hits
(including outlier2 hits), in the Transition Radiation Tracker (TRT), for the
leading pT core track. Since electrons are lighter than pions, and therefore
have higher γ factors, they are more likely to produce transition radiation that
causes high threshold hits in the TRT. This variable can be used to discriminate
hadronic 1-prong tau candidates from electrons.
fHT =NHThit
NLThit
, (4.5.9)
• Hadronic leak energy(EleakT,Had): the ratio of the hadronic transverse energy over
the transverse momentum of the leading track (ptrackT,1 ).
EleakT,Had =
ET,HadptrackT,1
(4.5.10)
4.5.7 Efficiency and rejection
For tau combined reconstruction and identification efficiencies derived from Monte
Carlo, true visible hadronic tau candidates are required to satisfy the fiducial re-
quirements: |η| < 2.5 and pvisT > 10 GeV. The visible four momentum is defined as
the four-vector sum of the generator level tau decays products excluding neutrinos.
Truth-matched tau candidates are those reconstructed candidates that are within
∆R < 0.2 of the simulated visible tau decays.
The signal and background efficiencies are defined as,
2An outlier is a hit that is not included in the final track parameter determination because itsχ contribution was too high.
98
Signal Efficiency:
ε1/3prongsig =
# of candidates with 1/3 reconstructed track(s),passing ID, and truth matched to a simulated 1/3 prong decay
# of simulated visible hadronic taus with 1/3 prong(s),
(4.5.11)
background Efficiency:
ε1/3prongbkg =
# of candidates with 1/3 reconstructed track(s),passing ID,
# of taus candidates with 1/3 prong(s), (4.5.12)
The above efficiencies are binned in kinematic quantities e.g (pT , η ) by requiring both
the numerator and denominator objects to be within the kinematic region of that bin.
4.5.8 Jet discrimination
ATLAS uses three methods for discriminating a tau from other QCD jets. The
methods are explained briefly.
Cut based Method
The cut-based tau identification uses cuts on only three variables: REM , Rtrack, ftrack
which are binned into one or three track bins. Two of the three variables, REM ,
and Rtrack rely on the narrowness of the width of hadronic shower in tau candidates
compared to QCD jets. While the tau can send its decay products in any direction
in the tau lepton’s rest frame, taus are not typically produced at rest in the ATLAS
detector. In the laboratory frame, the decay products will be collimated along the
momentum of the tau lepton. The Lorentz boost to the laboratory frame implies that
99
width-like variables should collimate as
R(pT ) ∝ 1
pT, (4.5.13)
hence making the optimal cuts on REM and Rtrack, pT dependent. This pT dependence
is partly removed by multiplying R by pT which flattens the pT dependence. The
remaining dependence is removed by fitting a second order polynomial to the means
of R× pT , binned in pT separately for both signal and background distributions.
Jet discrimination with a projective likelihood function
The likelihood function, LS(B), for signal (background) is defined as the product of
the one-dimensional probability density functions, pS(B)i of each identification variable
xi
LS(B) =N∏i=0
pS(B)i (xi), (4.5.14)
The discriminant (d) used by the tau likelihood based tau identification is defined as
the log-likelihood ratio between signals and background:
d = lnLSLB
=N∑i=1
ln
(pSi (xi)
pBi (xi)
), (4.5.15)
Each pS(B)i (xi) is calculated as the fraction of events per bin in a histogram of the
xi distribution. The histograms are produced from signal and background samples
and split into categories in order to maximize the method’s discrimination power.
This categorization is based on the properties of the τ jet (pT , number of prongs)
and of the event (number of vertices). For any give τ jet, the probability distribution
100
Bin Type categoriesjet number of reconstructed tracks 1-prong 3 - prong
τ pT 0-45 45 -100 100+Number of vertices 1-3 4 -7 8+
Table 4.3: The various categories for PDFs for likelihood discriminant
function (PDF) are obtained by the corresponding bin into which it falls. The PDF
are produced for three separate bins of pT : [< 45, 45 − 100, > 100] GeV. Further
separation between 1-prong and three prong is taken into account. To deal with
different pile-up conditions, three different sets of PDF have been produced for each
category depending on the number of vertices. The low pile-up PDF are applied to
events with at most 3 vertices, while the high pile-up PDFs are applied to events with
more than seven vertices. Tau-LLH discriminant carries the following variables
• 1-prong: REM , Rtrack, mclusters
• 3-prong: REM , ftrack, fEM , SflightT , mtracks
Distributions of the log-likelihood ratio are shown in Figure 4.8. Loose, medium and
tight selections on the log-likelihood score have been defined which yield an average
of 60%, 45%, and 30% signal efficiency.
Boosted Decision Trees
A decision tree makes a series of cuts on a set of identification variables. Compared to
cut based techniques, a decision tree is more powerful technique in a highly multivari-
ate environment. It does not immediately discard objects failing a cut, but continues
101
Figure 4.8: The log-likelihood score for 1-prong (left) and 3-prong (right) τ candi-dates [69].
by determining cuts on other variables to save signals which do not pass. Another
important difference is that a decision tree is not attempting to yield a certain level of
signal efficiency. Instead it produces a continuous score between 0 (background-like)
and 1(signal-like), on which a user may cut to yield a desired signal or background
[70].
Decision trees apply cuts on multiple variables in a recursive manner to classify
objects as signal or background. The algorithm begins with the entire training sam-
ple at the root node. The optimal cut, separating signal from background, is then
determined separately for each variable. The best of these optimal cuts is chosen and
two child nodes are constructed. All objects which fall below the cut are passed to
the left node, and all objects which fall above the cut are passed to the right node.
This cut improves the signal purity in one of the child nodes. The same algorithm
is then applied recursively on each child node until a stopping condition is satisfied
102
Figure 4.9: A simple example of a decision tree training process where we have twodistributions labelled signal (S) and background (B) over two variables X and Y. Theprocess begins at (1). by determining the best value of the best variable to cut on,which in this case is Y at a. All objects with Y > a are passed to the right node andall objects with Y ≤ a are passed to the left. This process continues recursively untila stopping condition is satisfied such as a minimum number of objects contained bya node [70].
(in our case, a minimum number of tau candidates contained within a node). This
leads to a binary tree structure. During classification, an object begins at the root
node and is passed down the tree according to the cut made by each node until a
leaf node is reached. The response of the decision tree is then the signal purity of
the leaf node. A boosted decision tree (BDT) takes advantage of multiple decision
trees in the form of a normalized weighted sum of their outputs. Each decision tree
is increasingly focused on correctly classifying objects misclassified by the previous
decision tree.
BDTs for jet rejection are trained separately on candidates with one track and
candidates with three tracks. Distribution of the jet BDT score is shown in Figure
103
Figure 4.10: The jet BDT score for 1-prong (left) and 3-prong (right) τ candidates.[69].
4.10
Performance of the jet discriminating Identification variables
Figure 4.11 shows plots of the tau signal and jet background efficiencies for each
identification method. The signal is a combination of Z → ττ and W → τν Monte
Carlo samples, with simulated hadronic tau decays. The background sample is taken
from a selection of dijet events in the ATLAS data taken in late 2010.
4.5.9 Electron Discrimination
The characteristic signature of hadronically decaying taus can be mimicked by elec-
trons. This is particularly true for 1-prong tau decays. Moreover the prompt electron
production, which is mainly due to vector boson decays, has a similar cross-section
to the tau production. Thus electrons contribute a significant part of background
after the jet related backgrounds are suppressed by kinematic, topological and tau
104
Figure 4.11: Inverse background efficiency as a function of signal efficiency for theBDT, Likelihood, and cut-based tau identification methods. Shown separately are1-prong (left) and 3-prong (right) tau leptons, for a pT region of 20-40 GeV (top) and40-100 GeV (bottom) [69].
identification criteria. Despite the similarities of tau lepton and electron signatures,
there are several properties that can be used to distinguish them. The most useful
examples are the emission of transition radiation of the electron track and the fact
that the shower produced by a tau lepton in the calorimeter tends to be longer and
wider than an electron-induced shower. These and other properties can be used to
define tau identification discriminants specialized in rejecting electrons misidentified
as tau leptons ATLAS uses two discriminants
• Cut based Method
105
• Boosted decision trees
Three working points loose, medium, and tight for both discriminants provide signal
efficiencies of both 95%, 85%, and 75% respectively.
Cut based Electron Veto
The cut-based electron veto is based on categorizing candidates by their direction
in |η| according to their leading track eta pseudorapidity |η|leadtrack . The tau lepton
candidates are first divided to barrel and endcap candidates according to their leading
track pseudorapidity |η|leadtrack . Barrel(encap) candidates are defined as τ leptons
wirh |η|leadtrack < 1.7 (> 1.7). Variables based on transition radiation tracker data are
used only for barrel candidates. Candidates are further categorized using two shower
shaped variables: hadronic leak energy EleakT,Had = ET,Had/p
trackT,1 and Es
T,maxtrip. and
in each category different cuts on TRT HT fraction (fHT ) and EleakT,EM are applied.
Loose, Medium, Tight cut-based electron veto
The cut values used in the definition of loose, medium and tight cut-based electron
veto selections is given in Table 4.4.
BDT based Electron Veto
Optimization of the BDT electron discriminant is performed in four regions of |η|:
barrel |η| < 1.37, crack 1.37 < |η| < 1.52, end-cap 1.52 < |η| < 2.0, and forward
end cap 2.0 < |η| < 2.3. A set of signal (τ) and background (e) was created for
106
Tightness ET,Had/ptrackT,1 Estrip
T,max EleakT,EM (fHT )
Loose Barrel 0.04 0.25 9.8 0.24/0.18/0.10Endcap 0.02 - 2.7 -
Medium Barrel 0.014 0.34 0.8 0.25/0.16/0.11Endcap 0.03 - 0.9 -
Tight Barrel 0.035 0.55 0.9 0.15/0.11/0.07Endcap 0.2 - 2.8 -
Table 4.4: The loose, Medium and tight cut-based electron veto selection
training the BDT. For the background , a Monte Carlo Z → ee sample was used.
To obtain a clean sample of background objects, the reconstructed τ candidates were
required to match to a truth-level electron within ∆R < 0.2, and an electron with
ET > 20 GeV was required in the event. For signal, a Monte Carlo Z → ττ sample
was used. To obtain a clean sample of signal objects, the reconstructed τ candidates
were required to have pT > 20 GeV, have only one associated track, and match to a
truth-level hadronically decaying τ within a ∆R < 0.2. Seven variables are used for
training purposes. The output score of the BDT electron discriminant for electrons
and hadronically decaying taus selected from MC simulated events is shown in 4.12.
The output demonstrates good separation between electron and hadronically decaying
taus.
Loose, Medium and Tight BDTe cuts
Loose, Medium and Tight BDTe cut values are shown in Table 4.5. The values of the
cuts on the BDTe score has been chosen to correspond to the cut-based veto signal
efficiencies.
107
Figure 4.12: Score of the BDT-based electron veto for MC simulated hadronic taudecays and electrons [69].
Cut Level Cut on BDTe score Signal EfficiencyLoose BDTe > 0.42 95%
Medium BDTe > 0.51 85%Tight BDTe > 0.56 75%
Table 4.5: The loose, Medium and tight BDTe cut values
Electron Veto Performance
The efficiency for MC simulated signal tau candidates versus the rejection of MC
simulated electrons is shown in Figure 4.13. The BDT-based electron discriminant
far out performs the cut based discriminant. The definition of the efficiencies used
for the performance evaluation given in Figure 4.13 is the same as defined in section
4.5.7.
4.5.10 Tau energy Calibration
The energy of hadronically decaying tau candidates, reconstructed from calorimeter
response, is calibrated by applying a correction to the reconstructed energy at the
electromagnetic (EM) energy scale. The EM scale energy is a sum over the energies
108
Figure 4.13: Inverse background efficiency as a function of signal efficiency for τcandidates with pT > 20 in four regions of |η|, for both electron discriminants [69].
of cells, within ∆R < 0.4 of the seed jet axis, that form the topo-clusters of the
jet. These correction factors are derived by determining response functions, R(pEMT ),
of the EM scale pT compared to the true generated pT of hadronic tau decays in
Monte-Carlo samples:
R(pEMT ) =pEMTpgenT
, (4.5.16)
With these response functions constructed, candidates are calibrated to the tau energy
scale by scaling the EM scale energy by the reciprocal of the response function:
pTEST =1
R(pEMT )pEMT , (4.5.17)
4.6 Missing Transverse Energy
The missing transverse momentum is used as the signature of an undetected neutrino.
The quantity is calculated based on the energy imbalance in a transverse plane, since
109
∑pT = 0 is satisfied at the beginning of the collision. All the detected particles such
as leptons, jets (including low pT jets, called soft-jet, with 5 ≤ pT ≤ 20 GeV), and
energy deposit not associated with any reconstructed objects (called cell out 3) are
all considered for the calculation. The definition is,
EmissT =
√(Emiss
x )2 + (Emissy )2, (4.6.1)
where
−Emissx,y =
∑electron
(Emissx,y ) +
∑muon
(Emissx,y ) +
∑jet
(Emissx,y ) +
∑softjet
(Emissx,y ) +
∑cellout
(Emissx,y ),
(4.6.2)
3Calorimeter cells that reside with in the topological cluster but do not contribute to any otherobject. This term is proven to give a better absolute Emiss
T value and a better resolution [71]
110
chapter 5
MONTE CARLO GENERATORS
Every experimental instrument has imperfections which can result in bias of obser-
vations. In order to be able to extract results from what is observed in real data
collected in pp collisions, it is necessary to compare the observed results with the
theoretical expectations. For this purpose Monte Carlo (MC) simulated samples are
used. The complete description of simulated events consist of following steps.
• Generation of collision events as produced in pp collisions
• Simulating particle decays and their interactions with the ATLAS detector
• Conversion of interaction in terms of electronic signals
The whole procedure is described in detail below
5.1 Event Generation
Event generation refers to the various sub-processes which take place during a proton-
proton collision. In this process particles emerge from pp collisions and decay before
their interaction begin with the atlas detector. Figure illustrates a pp collsion event
at the parton level.
Hard scattering describes the interaction between two incoming partons of the
colliding protons and the particles emerging from the interaction. This process occurs
111
Figure 5.1: Schematic illustration of a proton-proton collision event involving agluon-gluon scattering that leads to tt→ τ + jets.
at the high momentum transfer Q2 of simulation, where perturbation theory can be
applied and thus matrix elements of the scattering are calculated using Feynman
Diagrams.
Parton Shower is the process which describes the splitting of the partons, namely
Initial State Radiation (ISR) and Final State Radiation (FSR) effects. ISR means
that an energetic parton has a probability to radiate quark or gluon before undergoing
interaction while FSR means a parton in final state can also radiate a quark and
gluon giving rise to a shower of partons. These process occur at lower Q2 and hence
scattering matrix elements become infinite. These effects are handled by DGLAP [10]
splitting functions.
Hadronization is the process of the formation of hadrons out of quarks and gluons.
112
This process occurs below the cut off energy which is defined of the order of Λ2QCD
= 1 GeV2 where the QCD coupling constant approaches to unity. The hadronization
process are not yet fully understood, but are modelled and parametrized in a number
of phenomenological studies, including the Lund string model and in various long-
range QCD approximation schemes. The Lund string model [72] treats all but the
highest-energy gluons as field lines, which are attracted to each other due to the gluon
self-interaction and so form a narrow tube (or string) of strong color field, compared
to electric or magnetic field lines, which are spread out because the carrier of the
electromagnetic force, the photon, does not interact with itself.
5.2 Simulation of Particle Decay and Interaction in ATLAS Detector
After event generation, the next step is to simulation which means how these particles
interact with ATLAS detector before decaying. This process is handled by GEANT4,
which is a platform for the simulation of the passage of particles through matter,
using Monte Carlo methods. The whole process can be divided into four steps
1. Geometry analysis of the detectors
2. Tracking the passage of a particle through matter. This involves considering
possible interactions and decay processes.
3. Recording detector response when a particle passes through the volume of a
detector, and approximating how a real detector would respond.
113
5.3 Digitization
While traversing through the detector particles produce “hits”, which are the mea-
surements of points through which the charged particle has passed through. In other
words these are the records of energy deposition and with information of position and
time. The process of converting GEANT4 simulated hit information to Raw Data
Objects (RDOs), which act as an input to the reconstruction is known as digitiza-
tion. A digit is a signal produced when the voltage or current on a particular read
out channel rises above a threshold with in a particulat time-window. Digitization
algorithms exist for all ATLAS sub-detectors.
5.4 Monte Carlo Generators
There are different MC generators available which are discussed briefly below
• Pythia is a leading order generator. It uses a string model parton shower, how-
ever it provides reduced accuracy in multi-parton final states. It can generate
events in the high energy interaction of two partons producing two particles in
the final state. It is used for hadronisation and underlying event modelling.
• Herwig is also leading order generator. Unlike Pythia it uses a cluster based
parton shower model, to generate its underlying event. Like Pythia it provides
reduced accuracy in multi-parton final states. It is also used for hadronisation
and underlying event modelling.
114
• Alpgen is a leading order matrix element generator which provides more accu-
rate description for multi-parton final states (upto six partons) in association
with the W/Z production at high center-of-mass energy, using perturbation the-
ory on all the relevant tree Feynman diagram with a fixed number of outgoing
particles.
• Acer MC is a leading order generator. It can be used to study the process with
large number of partons in the final states.
• MC@NLO is a next to leading order generator. Its parton shower model is
implemented by Herwig with Jimmy modelling the underlying event. The
MC@NLO is used to generate the signal event for tt cross-section analysis. This
generator produces events that have weights of ± 1, where negative weights rep-
resent a subtraction of events that would otherwise be double counted in NLO
calculation of this algorithm.
• POWHEG is a NLO generator, which generates only positive weighted events.
It can be used to check and assign systematics to the MC@NLO samples.
115
chapter 6
MEASUREMENT OF TOP ANTI-TOP QUARK PAIRPRODUCTION CROSS-SECTION IN THE TAU PLUS JETS
CHANNEL
This chapter describes a measurement of the top anti-top (tt) pair production cross-
section in the tau (τ) + jets channel. The measurement is obtained by using 4.7 fb−1
data collected in the year 2011 by proton proton (pp) collisions at√s = 7 TeV. In this
physics channel top quark pairs are dominantly produced by gluon fusion. Each top
quark is assumed to decay to a W boson and a bottom quark. One of the W bosons
decays to a hadronically decaying τ and a neutrino, while the other W boson decays
to quarks (see Figure 6.1). These events will be referred as signal in this chapter.
The theoretical prediction of the tt cross section for pp collisions at a centre-of-mass
energy of√s = 7 TeV is 167+17
−18 pb [73]. This calculation assumes a top quark mass
of 172.5 GeV.
tt = [W+b][W−b] = [(τhad + EmissT b)][(jjb)], (6.0.1)
6.1 Monte Carlo and Data Samples
The SM background and signal samples used in this study are summarized in Table
G.1.
The purpose of Monte Carlo samples is to validate the analysis method, calculate
the signal selection efficiency and the evaluation of systematic errors.
116
Figure 6.1: Feynman Diagram for tt→ τ + jets.
The tt events are simulated using MC@NLO event generator [74] with next-to-
leading order (NLO) approximation. The background processes (explained in detail
in section 6.3) such as W+jet, Z+jet are modeled based on the Alpgen generator
[75] with leading order (LO) approximation. For the single-top events, the MC@NLO
event generator with a NLO approximation is used, except for the t-channel of the sin-
gle top quark production, which is modelled with AcerMC [76]. Smaller backgrounds,
arising from diboson events (WW, WZ, and ZZ) are generated and hadronized using
Herwig [77]. All the MC samples are processed by the standard ATLAS detector and
trigger simulation, GEANT4 [78].
The analysis exploits the pp collision data with a center-of-mass energy of√s = 7
TeV accumulated by the ATLAS detector from 13 March 2011 to 30 October 2011
[79].
In August 2011 the LHC started running with a higher number of protons in each
117
Figure 6.2: The luminosity-weighted distribution of the mean number of interactionsper crossing for 2011.
colliding bunch. While this increases the instantaneous luminosity, it also increases
the number of pp interactions in each bunch crossings. These additional interactions
are referred as pile-up.
ATLAS data is divided into periods. Each period represents a significant change
in the performance of either the LHC or ATLAS. The periods are given in Table 6.1
along with the amount of data recorded and instantaneous peak luminosity. The total
data recorded during 2011 is 4713.11 pb−1.
At the end of period D a significant number of LAr front end boards failed. These
electronic boards also known as front end boards (FEB) transmits data from the
calorimeter, and without them a region of the LAr calorimeter was unusable. Since
this problem existed with a substantial period of time, the affected region of the
calorimeter was excluded while the Front End Boards (FEBs) were not functioning.
118
Per
iod
Run
Num
ber
Dat
aR
ecor
ded
Pea
kL
um
inos
ity
feat
ure
pb−
1(cm−
2s−
1)
B17
7986
-17
8109
11.7
377
2.44×
1032
D17
9710
-18
0481
166.
6502
6.65×
1032
no
LA
rpro
ble
m
E18
0614
-18
0776
48.7
802
8.37×
1032
F18
2013
-18
2519
132.
4979
1.11×
1033
G18
2726
-18
3462
507.
9311
1.27×
1033
H18
3544
-18
4169
259.
4593
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1033
LA
rpro
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m
I18
5353
-18
6493
337.
5425
1.90×
1033
no
LA
rpro
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1867
5522
6.39
132.
02×
1033
no
LA
rpro
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mK
1868
73-
1878
1559
0.36
382.
35×
1033
no
LA
rpro
ble
m,
L18
8902
-19
0343
1404
.792
33.
28×
1033
M19
0503
-19
1933
1026
.944
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no
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gger
Up
dat
e
Tab
le6.
1:A
TL
AS
Dat
aP
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ds
119
This procedure was performed to both data and to an equivalent fraction of MC.
Besides the ATLAS detector problem, periods are also triggered by changes in
the ATLAS trigger menu (see section 3.6.1). The LHC continuously increased the
instantaneous luminosity throughout 2011. As the instantaneous luminosity increases
so does the rate of events that pass the trigger. Since ATLAS must maintain a
reasonable rate of physics events, this increase in trigger rate must be accounted for
by an adjustment in trigger algorithms to reject more events.
For this analysis two different algorithms are used for two different data periods.
For periods B-K (see Table 6.1) the trigger has a pT threshold at 29 GeV for the τ ob-
ject and an EmissT threshold of 30 GeV and a muon veto (Tau29-medium-xe35-noMu).
For the data period (L-M) the trigger has the same pT threshold, but additionally
requires three Level-1 jets with a minimum pT of 10 GeV (Tau29T-medium-xe35-
noMu-3L1J10).
In addition to increasing the trigger, changes in luminosity often come with in-
crease pile-up 1. To account for the differences between the recorded data and the
simulated MC, scale factors are applied to MC as a function of the number of expected
interactions [80]. When scale factors are applied on MC due to pile-up, it is called as
pile-up re-weighting. It is provided by pile-up re-weighting tools. A correction factor
is determined by dividing the average number of interactions µ in data to the average
number of interactions (µ) in MC. A pile-up weight is determined by applying a fit
1Pileup is distinct from underlying events in that it describes events coming from additionalproton-proton interaction, rather than additional interactions originating from the same protoncollision.
120
on this correction factor. This pile-up weight is then applied to every event in MC.
6.2 Event Selection
The event selection for tt→ τ + jets process is based on the following requirements.
• Event-level cleaning cuts, selecting the Good Run List2 and removing those
events which carry any noise burst or corrupt data at the event level.
• τ + EmissT trigger is selected
– Tau29-medium-xe35-noMu (for data period B-K)
– Tau29T-medium-xe35-noMu-3L1J10 ( for data period L-M)
• Events are selected for which primary vertex or pile up vertex with number of
tracks greater than four.
(The primary vertex is defined as the vertex with the highest associated sum
of squared track transverse momenta∑
(ptrackT )2 , where the sum runs over all
tracks used in the vertex. )
• A veto is applied on events if any electrons or jets are found in the region with
dead Liquid Argon FEB. i.e. in range 0.1 < |η| < 1.5 and −0.5 < |φ| < −0.9.
• No bad jets with pT > 20 GeV and E > 0 GeV. Bad jets are jets not associated
to real energy deposits in the calorimeters. They arise from various sources
2A Good Run List is an ATLAS standard XML file format which defines a list of runs andluminosity blocks to be considered. For more detail see Appendix E.
121
ranging from background effects, detector effects (hardware problems), LHC
beam conditions and cosmic ray showers.
• Events with at least 4 jets with pT > 20 GeV, |η| < 2.4 and |JV F |3 > 0.75.
For more detail see Appendix D.
• Events with exactly one tau with pT > 40 GeV. The selected τ , using selection
criterion explained in section 4.5.8, has to match the trigger tau object.
• Veto identified electrons and muons.
• Missing transverse energy (EmissT ) > 60 GeV
• Events with at least 1 b tagged jet (see section 4.4.4) are selected.
6.3 Backgrounds
Events coming from tt→ tau+ jets form the signal for this decay channel. There are
some other physics channels that can have the same final state but they do not arise
from a tt→ tau+ jets process (see section 6.3.2, 6.3.3, 6.3.4, 6.3.5). Another type of
events consist of fake taus and fake missing energy (see section 6.3.1). Such physics
channels constitute the background for this decay channel. These background events
are classified in five groups as discussed below.
3explained in section (4.4.3)
122
6.3.1 Multi Jet(QCD)
It is an important background because of the very large cross-section from hadronic
processes. This source of background comes from events where a jet is misidentified
as τhad−vis4 candidate in the event which arises either from gluon initiated or quark
initiated jets. So if one of the jets is mis-reconstructed as a tau lepton and there is
enough missing transverse energy, then QCD multi jet can pass the tt event selection.
Missing transverse energy in QCD can arise from instrumental sources such as limited
energy resolution of the detector. The method to estimate QCD multi-jet is discussed
in detail in section 6.5.
6.3.2 W + Jets
The production of a W boson via the weak interaction is shown in Figure 6.3. The W
boson decays leptonically and has at least four associated jets. Due to its large cross-
section, W + jets is a second major background process after QCD multi-jet because
the events have a similar final state i.e., one isolated tau, four jets and EmissT due
to neutrinos. Jets are produced through gluon bremsstrahlung and gluon splitting.
NLO calculation adds the effect of tree-level processes involving additional particles,
as well as the 1-loop effects, therefore NLO terms are also considered for this analysis.
4An anti-kT jet with in ∆R = 0.4 calculated from topological clusters, having a transverse energyET > 10GeV and with in |η| < 2.5
123
Figure 6.3: Feynman diagrams for W + jets production.
6.3.3 Z + Jets
Z bsoson can decay into two taus. If one of the two leptons is not detected then the
event can pass the selection criterion of tt → τ + jets. However this background
is suppressed by applying a cut on missing transverse energy because there is no
neutrino in the Z boson decay. The Feynman Diagram for Z + jets production is
shown in 6.4.
Figure 6.4: Representative Feynman diagrams for Z + jets production. When onetau is missed, the event can pass the selection criterion of tt events.
6.3.4 Single Top
Single top is produced via electroweak interaction t-channel, s-channel and Wt chan-
nel. In the t-channel a top quark is produced from an intermediate W boson decaying
124
into a b and t. This channel has at least three jets, two of which are b jets in the final
state plus a lepton and a neutrino from the W leptonic decay. In the s-channel, two
b quarks are in the final state plus the W boson decay products. In the Wt channel,
one of the W decays leptonically and the other hadronically, the final state signature
is a lepton, a neutrino, one b jet and two light jets.
Figure 6.5: Feynman diagrams for single top quark production. From left to right: tchannel production through flavour excitation and through W-gluon fusion; s-channelproduction; Wt-channel production
6.3.5 Diboson
Diboson process are interactions in which two bosons are produced and decay subse-
quently, the most important being WW, WZ, and ZZ. It is a small background for
Figure 6.6: Feynman diagrams for diboson production (WW , WZ, ZZ), which pro-vides a small background.
tt→ τ + jets events. If one vector boson e.g. in Figure 6.6(a) one W deacays to a τ
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and ντ and the other W boson decay to quark anti-quark pair, this lead to a similar
signature as tt events.
6.4 Reconstruction Efficiency
The reconstruction efficiency is defined as the ratio of number of events survived N surv
after applying all event selection cuts to the initial number of events N initial.
εreco =N surv
N initial(6.4.1)
6.5 Template Method to determine Multi-jet QCD background
The uncertainties in the contribution of multi-jet events in the simulation are large.
Multi-jet events can enter into the τ + jets selection through misreconstruction and
misidentification of final state objects. Therefore it is preferable to use data-driven
method to estimate this background.
Samples for data (2011), tt signal, W+Jets, Z+Jets, single top and diboson are ob-
tained by the following two (event) selection criterion.
• Baseline selection
• Inverted selection
Baseline selection uses the same set of event selection as explained in section 6.2,
except the τ candidate, which is required to pass a tight likelihood identification
(as explained in section 4.5.8). Samples obtained by applying baseline selection are
named as “baseline samples”.
126
Inverted selection uses the same set of event selection as explained in section 6.2,
where the τ candidate is required to pass a loose likelihood identification and not a
tight likelihood identification. This orthogonal selection enriches the data in QCD
background. Samples obtained by applying control selection are named as “control
samples”.
The contribution of the QCD jets background is estimated by developing a tem-
plate for the shape of the QCD from EmissT distributions from control samples and
fitting this template to the data in the baseline selection.
The following templates are obtained for EmissT distribution.
1. Signal matched template from tt −→ τ + jets
2. A Background template obtained from the sum of all background W + jets, Z
+ jets, diboson and single top.
3. QCD multi-jet template
The QCD multi-jet template for the EmissT distribution is obtained by subtracting
the shapes of tt, W+jets, Z+jets, single-top and diboson background using the MC
simulation from the control sample data .
In order for the EmissT shape in the control sample to be used as a template for the
QCD multi-jet distribution in the baseline sample, their shapes must be sufficiently
similar. These two distributions are compared at a very early stage of the event
selection, just after applying the event cleaning, trigger, and tau selection criteria.
127
The comparison for EmissT shapes in the baseline and inverted samples are given in
Figure 6.7: Distribution of EmissT after subtracting the expectation from tt, W +
jets, Z + jets, di-boson and single top simulations. Compared are the distributionsafter applying a tau cut as detailed in section 6.2, for both the baseline and invertedselection, with the exception that for the ”inverted” distribution, the τ selectionrequirements have been inverted.
Figure 6.7. These shapes for baseline and control samples agree sufficiently to perform
the fit.
The QCD accounts for 96.7 % ± 0.14 % of events in the control sample at this
early stage of selection, as shown in Table 6.2.
tt W + Jets Z + Jets Single Top Di-boson QCD Data6249 (15) 5060 (54) 856 (13) 501 (6) 51 (1) 383150 (540) 395868 (629)
Table 6.2: Number of events at an early stage of event selection after a τ selectionfor inverted selection
A complete set of event selection criteria is then applied to obtain the final control
sample. The QCD template is again obtained from data, with the contributions from
128
tt W + Jets Z + Jets Single Top Di-boson QCD Data1091 (6) 1073 (25) 261 (6) 92 (2) 5 (0.4) 20224 (91) 22751 (151)
Table 6.3: Number of events at an early stage of event selection after a τ selectionfor baseline selection
tt, single-top, di-boson, and W+jets, and Z+jets subtracted using the luminosity
normalized MC simulation.
6.6 Fit to Missing Transverse Energy
Figure 6.8: Fit to EmissT after all selection cuts.
The QCD template obtained using the procedure explained in the previous section
129
is now fitted to the EmissT distribution in the baseline sample. In addition to the QCD
template from the control sample, the shape of tt, single-top, di-boson, and W + jets
and Z + jets is also fit to the data. The result of fit is shown in Figure 6.8. The QCD
fraction is determined to be (60.9 ± 2.7)%, where the uncertainty is only statistical.
The fitting procedure is explained in detail in following paragraph.
The number of background events (W + jets, Z + jets, single top, diboson) were
subtracted from total number of data 2011 events. Then the fractions of tt → τ +
jets events and QCD multi-jet events were determined by feeding the tt signal MC
EmissT distribution and QCD multi-jet Emiss
T distribution (explained in section 6.5 ) in
Tfractionfitter [81] which is a C++ class provided by ROOT data analysis framework
[82]. Tfractionfitter fits MC fractions to data histograms [83]. The virtue of the fit is
that it takes into account both data and MC statistical uncertainties. The number
of QCD events were determined as given in equation 6.6.1
∫(Ndata − Nbackground)dn× fTFractionFit
QCD = NTFractionFitQCD (6.6.1)
where fTFractionFitQCD is the QCD multi-jet fraction obtained from TFractionFit. Since
originally our QCD template (which is fed into TFractionFitter) was obtained from
inverted selection (control samples) hence correction factor to the number of QCD
multi-jet events is applied to QCD multi-jet EmissT distribution at the fitting stage
of EmissT distribution shown in Figure 6.8. The correction factor is obtained in the
130
following way
Original number of QCD multi-jet events from Inverted Selection = NOriginalQCD
(6.6.2)
Number of QCD multi-jet events from TFractionFit = NTFractionFitQCD (6.6.3)
Correction Factor =NOriginal
QCD
NTFractionFitQCD
(6.6.4)
Similarly the number of tt→ τ + jets events were obtained in the following way∫(Ndata − Nbackground)dn× fTFractionFit
tt→τ+jets = NTFractionFittt→τ+jets (6.6.5)
where fTFractionFittt is the tt signal fraction obtained from TFractionFit. Originally our
tt template for EmissT distribution (which is fed into TFractionFitter) was obtained
from baseline selection (baseline samples) hence correction factor to the number of
Ntt→τ+jets events is applied to tt EmissT distribution at the fitting stage of Emiss
T dis-
tribution shown in Figure 6.8. The correction factor is obtained in the following way
Original number of signal events from baseline Selection = NOriginaltt Signal MC (6.6.6)
Number of signal events from TFractionFit = NTFractionFittt→τ+jets (6.6.7)
Correction Factor =NOriginal
tt Signal MC
NTFractionFittt→τ+jets
(6.6.8)
131
6.7 Fit with Multivariables
In order to reduce systematic uncertainties (discussed in section 6.11) and to show the
model which fits the data in more than one variable, additional distributions included
in the fit rather than just EmissT . For this purpose four distributions are picked. The
distributions are
1. EmissT
2. Di-jet mass
3. Tri-jet mass (b1jj)
4. Tri jet mass (b2jj)
Jets are arranged in descending order according to their transverse momentum pT .
There are two sets of jets. One set carries b-tagged jets, the second set carries all
other jets. In a given event if one jet is tagged as a b-jet, the highest pT jet belonging
to the other set is assumed to be a b-jet. The di-jet mass is reconstructed from the
second and third highest pT jet from a set of non b-tagged jets. When this di-jet
mass is combined with the original b tag jet, the tri-jet mass is defined as tri-jet mass
(b1jj). However when the di-jet mass is combined with the 2nd highest pT jet, the
tri-jet mass is named as tri-jet mass (b2jj). The situation is similar when two jets are
tagged as b jets. Due to the high correlation among these variables, these variables
are considered 100% correlated.
In order to estimate the QCD multijet in section 6.5, a QCD multi-jet template
132
was derived from control samples. These control samples were obtained by a loose
likelihood criteria for τ identification. Then the QCD multi-jet template was fitted
on baseline samples, which were obtained by applying tight likelihood criteria. The
difference between tight taus and loose taus is the ratio of fake5 to real taus. Therefore,
the real tau templates were separated from the fake tau templates. Electrons faking
taus contribute to tight taus, however an electron veto (BDTe discussed in section
4.5.9) makes that contribution negligible.
Again three types of templates are obtained from each distribution.
1. Signal matched template from tt −→ τ + jets
2. Background template obtained from the sum of all background W + jets, Z +
Jets, Di-boson, Single top.
3. QCD Multi-jet template
To eliminate any biases, the QCD-multi jet statistics were increased by redefining the
inverted tau selection criterion used to obtain the control sample. A cut is introduced
on the tau likelihood score (explained in section 4.5.8) to allow more QCD-multi jets
to be selected in the control samples. The taus selected using this method do not fulfill
the off-line tight cuts for tau identification. A tau that is selected by this inverted
selection is not tight but Event filter matched (see section 3.6). Event matched
taus means that at the event filter stage of the trigger system these candidates were
5fake tau is a misreconstructed jet, which is identified as τ object.
133
Figure 6.9: The loose and not tight selection eliminates many of QCD events. Usinga lowscore threshold more QCD events can be captured without adversely effectingthe template shape.
134
Figure 6.10: Data fitted on all backgrounds, Signal, and QCD multi-jet for anappended histogram obtained from four variables Emiss
t , di-jet mass mass, tri-jetmass(b1jj), tri-jet mass (b2jj).
identified as taus, but later can be recognized as fake taus when off-line tight cut
identification criterion is applied. This inverted selection is named as lowscore.
Figure 6.9 shows some representative plots from data for the selection of multi-jet
events.
The QCD multi-jet template is obtained by subtracting the lowscore signal
matched template tt −→ τ + jets and background template from lowscore data.
In order to perform a fit using four variables shown in figure 6.10, a one dimen-
sional template is produced using four variables. The fractions of QCD multi-jet and
135
Figure 6.11: Fractions of QCD multi-jet, signal and all backgrounds in Data.
tt→ τ+jets signal events are obtained again by feeding tt signal MC, QCD multi-jet
and background templates in TFraction fitter and the obtained fractions are shown in
figure 6.11. It is worth mentioning here that backgrounds are not kept fixed as were in
section 6.6, rather these backgrounds are allowed to float with in there uncertainties.
Also bins having less than ten events were combined in a single bin for each variable
for data 2011. The number of QCD and tt events are determined in the following
way ∫(Ndata)dn× fTFractionFit
QCD = NTFractionFitQCD (6.7.1)
∫(Ndata)dn× fTFractionFit
tt→τ+jets = NTFractionFittt→τ+jets (6.7.2)
Again originally our QCD template(tt signal MC) (which is fed into TFractionFitter)
was obtained from lowscore selection (baseline selection) hence correction factor to
136
the number of QCD multi-jet (tt signal MC) events is applied to QCD multi-jet (tt
signal MC) distributions at the fitting stage for each variable shown in Figure 6.12
and 6.13. The correction factor is obtained in the following way
Original number of QCD muti-jet( signal) events
from lowscore selection = NOriginalQCD(tt signal MC)
(6.7.3)
Number of QCD muti-jet(signal) events
from TFractionFit = NTFractionFitQCD(tt→τ+jets)
(6.7.4)
Correction Factor =NOriginal
QCD(ttSignal MC)
NTFractionFitQCD(tt→τ+jets)
(6.7.5)
The QCD template is then fit on baseline distributions for each variable i.e; Emisst ,
di-jet mass, tri-jet mass(b1jj), tri-jet mass(b2jj). In addition to the QCD template
from the inverted sample, the shape of tt, single-top, di-boson, W + jets and Z +
jets is also fitted to the data. The result of the fit is shown in Figure 6.12. The QCD
fraction is determined to be (54.88 ± 2.62)%, where the uncertainty is only statistical.
6.8 Number of events surviving all the cuts
The number of events surviving after applying all selection cuts for the baseline
samples and QCD multijet is given in Table 6.4.
tt Signal W + Jets Z + Jets Single Top Di-boson QCD total Data506 (5) 120 (8) 16 (1) 40 (2) 0.34 (0.1) 746 (19) 1428(21) 1362 (37)
Table 6.4: Number of events surviving after applying all selection cuts
137
Figure 6.12: Fits of Emisst and di-jet mass distributions.
138
Figure 6.13: Fits of tri-jet mass(b1jj) and tri-jet mass (b2jj) distributions.
139
6.9 Linearity and Ensemble Testing
The validation of the fitting method is done by pseudo data samples (ensemble test).
The purposes of validating the fit is to check
1. if there is any bias in the fractions obtained by fit.
2. the error in the uncertainty of the fractions.
3. the linearity for the fractions.
In order to perform an ensemble test, ten thousand pseudo experiments are performed.
The input templates are obtained from baseline and control samples. For each his-
togram the bin content was randomized. An arbitrary signal fraction is chosen and
QCD fraction of (1 − fsignal − fbackground) where the background fraction is fixed to
its original fraction of the data (2011). These histograms were added together to
produce pseudo data in shape and integral. This process is repeated ten thousand
times using different randomly generated pseudo data in place of the real data. A
histogram is then produced of the resulting fractions. For each ensemble histogram,
a Gaussian function is fitted and the mean and the sigma from the fit is extracted,
which is shown in Figures 6.14 and 6.15.
In order to perform a linearity test, pseudo data are generated as explained above
and a fraction fit is performed here for only one iteration. The process is repeated
using fictitious signal fractions ranging from 0.2 to 0.7 in steps of 0.1. A graph is
produced for a resulting fractions (obtained by fit) as a function of input fractions
140
Figure 6.14: Ensemble test for signal fractions ranging from 0.2 to 0.4 in steps of0.1. Right hand column shows histograms for the errors each respective fraction.
141
Figure 6.15: Ensemble test for signal fractions ranging from 0.4 to 0.7 in steps of0.1. Right hand column shows histograms for the errors for each respective fraction.
142
Figure 6.16: A linearity fit (red line) is performed for different signal fractionsranging from 0.2 to 0.7 in steps of 0.1. The horizontal axis represents fictitious signalfractions that were used as input whereas the vertical axis represent the signal fractionreturned by the fit. The black line (x = y), shows no bias in fitting procedure.
and with errors taken from the fraction fit. A line is fitted to the graph and the χ2 of
the fit is obtained. A good linearity is observed with its slope close to unity as shown
in Figure 6.16. In other words no deviation is seen in the input signal fraction and
fitted fraction. The intercept of the fitting line (red line) is almost zero, indicating
almost no bias of the method.
6.10 Data versus MC comparison
Figure 6.17 shows plots of pτt just before the τ selection cut and EmissT just before the
missing transverse energy cut during event selection 6.2. The disagreement, arising
143
Figure 6.17: The distribution of the pt of the highest pt τ candidate (left) and EmissT
(right) before cutting on these quantities.
144
from events with low missing transverse energy is due to QCD multi-jet which is
estimated from the template method.
6.11 Systematic Uncertainties
There are several sources of systematic uncertainties in this measurement. They can
be split into several subgroups. First subgroup includes all object related uncertainties
coming from the object reconstruction and its energy and momentum measurements.
Uncertainties due to signal modeling constitute the second subgroup, and uncertain-
ties from the background evaluation can be combined in the third subgroup. Object-
related uncertainties account for uncertainties in jet energy scale (JES), jet energy
resolution (JER), missing transverse energy, tau trigger, identification (ID) and re-
construction scale factors (SF) tau energy/momentum scales. Uncertainties related
to the signal modeling are due to ISR/FSR, PDF, MC event generator and parton
shower. Background modelling uncertainties include the W+jets modeling, shape
of the QCD multi-jet background modeling and normalization of small backgrounds
and QCD. The procedure of evaluation of various types of systematic uncertainties is
described below in more detail.
• Jet Energy Scale
Reconstructed jets are first calibrated to the electromagnetic (EM) scale. This
EM energy scale accounts correctly for the energy of photons and electrons, but
it does not correct for instrumental (detector) effects including calorimeter non-
145
compensation, energy losses in inactive regions of the detector (dead material),
particles which are not totally contained in the calorimeter (leakage), particles
that fall out of the reconstructed jet but are included in the truth jet, and
inefficiencies in calorimeter clustering and jet reconstruction. The goal of the
JES calibration is to correct the energy and momentum of the jets measured
in the calorimeter. The choice of JES calibration is a jet by jet correction
applied as a function of the pT and |η| (called simply JES). There is an error
associated with this jet’s energy which is determined through the application
of corrections. This error is typically referred to collectively as the jet energy
scale ( JES ) systematic error. The uncertainty on tt → τ + jet cross-section
due to jet energy scale is measured by varying the jet energy scale by ±1σ
(up and down) in MC. Applying such a setting causes the jets in an event to
get more/less energy than they otherwise might have had given the nominal
approach to jet reconstruction.
A jet energy correction is applied to all reconstructed jets. And then EmissT is
recalculated. A change in the number of selected tt events due to a variation of
the jet energy scale propagates as a systematic uncertainty to the cross-section.
• Jet Energy Resolution
The jet energy resolution (JER) is defined as
σET
ET=
S√ET
+N
ET+ C (6.11.1)
146
where S represents the statistical fluctuations in the amount of energy sampled
from the jet hadron shower.
N term is due to external noise contributions that are not dependent on jet pT
and include the electronics and detector noise.
C represents the fluctuations that are a constant fraction of energy.
The uncertainty due to different jet energy resolution is determined by smear-
ing the jet transverse momentum depending on pT and η. After smearing, all
selection cuts are applied and the number of tt events are calculated. The dif-
ference between the nominal and modified number of tt events is interpreted as
a change in the pre-selection efficiency due to JER. The variation in the num-
ber of tt events due to the modified selection efficiency is propagated to the tt
cross-section uncertainty.
• Jet Reconstruction Efficiency
The jet reconstruction efficiency is measured relative to track jets. JRE is
determined in the MC simulation by counting how many cases a calorimeter jet
can be matched to a truth(track) jet. Reconstructed jets are matched to truth
jets, if their jet axis are with in ∆R < 0.4. JRE is defined as
Efficiency =# matches of truth jets with reconstructed jets
# truth jets(6.11.2)
The uncertainty due to jet reconstruction efficiency is estimated by randomly
dropping a fraction of jets according to the difference in jet reconstruction ef-
ficiency on MC. Changes in the expected number of tt number of events is
147
calculated and propagated to the uncertainty to the measured cross-section.
• Monte-Carlo Generator
It is important to check how stable is the obtained result against the different
MC generators and parton shower schemes. In order to estimate the effects of
different tt kinematic simulation on the cross-section, the following comparisons
were made.
1. Event generator MC@NLO interfaced with Herwig for hadronization model
and event generator POWHEG interfaced with Pythia for hadronization
model.
2. Event generator Alpgen interfaced with Herwig for hadronization model
and event generator POWHEG interfaced with Pythia for hadronization
model.
3. Event generator Powheg interfaced with Herwig for hadronization model
and event generator POWHEG interfaced with Pythia for hadronization
model.
The largest difference in cross section occured from the comparison made at
number 2 in the above mentioned list.
• ISR-FSR
Processes that contain coloured or electrically charged objects or both in their
initial or final configurations can emit photon/gluon radiation. Initial State
148
Radiation (ISR) refers to radiation from any objects before the main hard scat-
tering event, while Final State Radiation (FSR) refers to any emissions added to
the collision products. Initial and final state radiation can change the number
of jets in the event. The addition(subtraction) of both ISR and FSR for the tt
is done by using MC samples. The ISR/FSR more sample is used to evaluate
an upper 1σ systematic. The ISR/FSR less sample is used to evaluate the lower
1σ shift of this systematic. The uncertainty is estimated as half of the difference
between results obtained with more and less samples.
• W + Jets normalization
W + jets is the next big background after QCD for tt → τ + jets. Since all
backgrounds were normalized against data, it is therefore necessary to find the
uncertainty in cross-section due to uncertainty in selected W + jets events. The
theory uncertainty for inclusive W production is 4%. The additional uncertainty
per additional jet is 24%, added in quadrature. For the signal 4-jet bin, this
corresponds therefore to 48%. The overall effect of this uncertainty on the
selected W + jets events contributing to this analysis is 5%. This is propagated
to the uncertainty on the measured tt cross-section.
• QCD
The uncertainty due to the fit range is estimated by varying the range of the fit
to 250 GeV and 350 GeV and taking the difference in the QCD fraction. This
gives an absolute uncertainty of +5.6−1.7
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The uncertainty due to binning of the fit is estimated by varying the size of bins
using 20, 30, and 40 GeV bin sizes. This gives an absolute uncertainty of +0.27−2.1
• pile-Up
The expected systematic uncertainty on the measured tt cross section due to
pile-up was evaluated using the pileup re-weighting tools recommended by the
TopReco group. Reweighted Monte Carlo samples were used to get new selection
efficiencies. The difference between nominal and recalculated cross-sections was
quoted as systematic uncertainty due to pile-up. This value is taken from the
charged Higgs boson search in τ + jets analysis [85], due to same final states.
Also τ + jets is the biggest background for charged higgs searches, and the
effect of pile-up systematic uncertainty was determined on tt background from
charged higgs analysers.
• τ Energy Scale, τ ID efficiency
The energy calibration of tau candidates differs in the final steps from the gen-
eral hadronic calibration. A correction is applied, derived from the simulation
of various physics processes with tau leptons, which restores the tau energy to
the true value as explained in section 4.5.10. There is an uncertainty associated
to tau energy scale. In order to determine the effect of this uncertainty on the
cross-section value for tt→ τ + jets the pt and |η| of tau should be varied with
in ±1σ.
• τ + EmissT Trigger efficiency
150
The triggers used in the analysis are mentioned in the event selection. The
systematic uncertainty for tt → τ + jets events is determined to be equal to
2.9−4.8% [85].
• Monte Carlo Parton Distribution Function (PDF)
Parton distribution function describes the probability to find a parton with a
momentum fraction x when a proton is probed at a factorization µF scale as ex-
plained in section 2.6 and 2.8.1. Parton distribution functions play a central role
in event generators, for the simulation of hard processes. The choice of PDF set
therefore influence the value of cross section. This uncertainty need to be eval-
uated with respect to three sets of PDF namely CTEQ6.6, MWST2008nlo68cl
and NNPDF20 which have 44, 42 and 100 parameters. These parameters are
varied with in ±1σ. An event by event re-weighting is applied for each set of
pdf to obtain a new set of MC samples. Each event obtains a new weight which
is calculated as
w =Pdfnew(x1, f1, Q)× Pdfnew(x2, f2, Q)
Pdforiginal(x1, f1, Q)× Pdforiginal(x2, f2, Q)(6.11.3)
where Pdforiginal(xi, fi, Q) is the original pdf and Pdfnew(xi, fi, Q) is the new
pdf, fi represents the flavor of parton and xi represents the momentum fraction
carried by parton. The analysis needs to be evaluated for each set of pdf. The
error in top cross-section is obtained by using symmetric Hessian formula given
in equation (6.11.4) for CTEQ6.6, asymmetric Hessian formula given by equa-
tion ( 6.11.5) for MWST2008nlo68cl, and by evaluating the standard deviations
151
for variations for NNPDF20. .
∆X =1
2
√√√√ n∑i=1
(Xi(up) −Xi(down))2, (6.11.4)
error up =
√√√√ n∑i=1
(Xi(new) −Xi(original))2 if (Xi(new) −Xi(original)) > 0
(6.11.5a)
error down =
√√√√ n∑i=1
(Xi(new) −Xi(original))2 if (Xi(new) −Xi(original)) < 0
(6.11.5b)
Source Error (in %)Jet Energy Scale UP,DOWN +12.6, -14.4Jet Energy Resolution 3.6, -3.6Jet Reconstruction Efficiency << 1 , << 1MET Cell out UP,DOWN < 1, < 1Pileup UP,DOWN < 1, < 1QCD due to binning,fit range of templates +5.1 , -5.1QCD template Shape < 1W+jets Normalization + 4.1, -4.1τ ID ± 4τ Energy Scale ± 2.1ISR-FSR ± 4MC Generator 8.5, -8.5MC PDF ± 2Total + 19 , − 20luminosity ±1.8Statistic ± 12
Table 6.5: Relative systematic uncertainties (%) for the measured inclusive tt crosssection.
152
6.12 Cross-section
The tt cross-section is obtained by performing the counting method.
σtt =Ntt→τ+jets
B.R×L× εreco(6.12.1)
Where Ntt−→τ+jets is the total number of tt −→ τ + jets observed events obtained by
multiplying tt signal fraction given by fit to the total number of observed data events.
The Ntt−→τ+jets is divided by the branching ratio of signal events. B.R = 0.544,
integrated luminosity L which is equal to 4713.11 pb−1 and the total reconstruction
efficiency εreco explained in section 6.4. The reconstruction efficiency is obtained from
tt signal MC. The tt cross-section is found to be equal to
σtt =1365× (0.3205± 0.0259)
0.544× 4713.11pb−1 × 1.124× 10−3(6.12.2)
σtt =437± 35
0.544× 4713.11pb−1 × 1.124× 10−3(6.12.3)
σtt = 152± 12 pb (6.12.4)
σtt = 152± 12(stat.) +28−30(syst.)± 1.8(luminosity) pb (6.12.5)
The SM calculation of the tt pair production cross section is predicted to be 167+17−18
at approximate NNLO [73].
153
chapter 7
CONCLUSION
To study τ lepton is not only crucial for precise measurements of SM but also nec-
essary for beyond SM searches. As mentioned in section 2.9, tt → τ + jets form
a background for new physics searches such as super-symmetry, and hence studying
τ lepton will eventually lead to better understanding of background of new particle
discoveries as predicted by many beyond SM theories.
This dissertation reports the top anti-top cross-section measurement in tt→ τ + jets
channel where on W boson decays to a hadronically decaying τ and ντ , whereas the
other W boson decays to quark anti-quark pairs forming jets see Figure 6.1.
To identify τ in the busy multi-jet environment of ATLAS is not an easy task, there-
fore likelihood method which is multivariate technique is utilized for τ identification
method. The obtained production cross-section is
σtt = 152± 12(stat.)± +28−30(syst.)± 1.8(luminosity) pb (7.0.1)
where the source of uncertainty comes from statistics, systematic errors and lumi-
nosity measurement. Both one and three prong τ decays were combined for this
measurement.
The cross-section value for tt→ τ+jets obtained previously by ATLAS collaboration
154
at center of mass energy equal to 7 TeV, using a data sample of 1.67 fb−1 is [86]
σtt = 194± 18(stat.)± 47(syst.) pb (7.0.2)
The cross-section value for tt→ τ+jets obtained by CMS collaboration [87] at centre
of mass energy equals to 7 TeV and using a data sample of is 3.9 fb−1
σtt = 152± 12(stat.)± 32(syst.)± 3(luminosity) pb (7.0.3)
The result obtained for cross-section measurement for top anti top pair production is
not only in agreement with the theoretical value predicted by standard model but is
also in good agreement obtained by previous ATLAS collaboration and CMS result.
Using more data this measurement is another effort to test the Standard Model
prediction and also to understand ATLAS detector at a better level. This result
will ultimately help to discover new particles predicted by beyond standard model
searches e.g.; tt→ τ + jets is major background for t → H+b → τντ process.
155
appendix a
ELECTRON ENERGY DIRECTION
A.1 Energy
Eclus = Energy from cluster
A.2 DIRECTION
• if track contains at least 4 silicon hits(this is always the case after medium/tight
cuts)
USE track(eta,phi)
• if track contains less than 4 silicon hits(basically TRT standalone tracks)
USE cluster(eta,phi)
A.3 Transverse Energy
if ((nST + nPix) > 4)ET =Eclus
cosh(ηtrack)
else ET =Eclus
cosh(ηcluster)
156
appendix b
MUON INNER DETECTOR TRACK
Combined and segment/calo tagged muons have associated inner detector tracks. The
following cuts on the associated inner detector tracks have to be applied.
• ( ! expectBLayerHit) OR (numberOfBLayerHits > 0)
• Number of pixel hits+number of crossed dead pixel sensors > 1
• Number of SCT hits+number of crossed dead SCT sensors > 5
• Number of pixel holes + 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. The technical recommendation is
therefore:
– Let nhitsTRT denote the number of TRT hits on the muon track, noutliersTRT the
number of TRT outliers on the muon track, and |η| := nhitsTRT + noutliersTRT
– Case 1: |η| < 1.9 Require nhitsTRT > 5 and noutliersTRT < 0.9nhitsTRT .
– Case 2: |η| ≥ 1.9 if nhitsTRT > 5 then require noutliersTRT < 0.9nhitsTRT .
157
An outlier is a hit that is not included in the final track parameter determination
because its χ2 contribution was too high. The outliers (attached to tracks) can be
written out separately for Pixel, SCT and TRT detectors (see flags). The variable
names contain the detector type, where XXX = Pixel, SCT or TRT.
158
appendix c
JET ALGORITHMS
In this section, some features of jet finder algorithm are given in more detail.
C.1 Cone Algorithms
The algorithm starts by ordering all input objects in decreasing order in transverse
momentum. The object with the highest pt serves as a seed if its transverse momen-
tum lies above a certain threshold (1 GeV in ATLAS). All objects which then lie
within a cone
Rcone =√
(∆η)2 + (∆φ)2 ,
are combined with the seed into a new object. Rcone is an indicative quantity for the
size of a formed jet. If the direction of the new object does not coincide with the
previous direction of the jet, objects are recollected in the new cone and the previous
steps are repeated. This stops when the direction of the four-momenta sum does not
change substantially and the jet is subsequently called stable. The following step is
to take the next seed from the input list, from which a new jet is formed with the
same procedure. This stops when no more seeds are available. At this point the
created jets can overlap, that is share constituents. This problem is solved by the
split-and-merge step: jets which share constituents with more than a certain fraction
f of the pT of the less energetic jet are merged. If they share less than the fraction
159
f they are split. The default values used in ATLAS are Rcone = 0.4 and Rcone = 0.6.
However cone algorithms are not infrared safe.
C.2 kt algorithm
For the kt algorithm, p = 1 in Equation 4.4.1. This means that objects with low
relative kT are merged first. In some sense this mimics and inverts the splitting
within a parton shower, which tend to be strongly ordered in kT . This also means
that within a jet, the final merge is the hardest, and this information can be exploited
to interrogate the substructure of the jets, looking for scales associated with the decays
of massive particles. Note that if the kT of an object with respect to the beam is
lower than its kT relative to anything else it will not be merged any further. Thus
soft objects are either merged with nearby hard objects, or left alone with low pT . In
the latter case, they will not be selected by a hard jet pT cut, and so are ignored.
C.3 Cambridge/Aachen algorithm
For the Cambridge/Aachen algorithm, p = 0 in Equation 4.4.1. This means that the
kT of the objects is irrelevant in the clustering, and objects near to each other in ∆R
are merged first. Thus within a jet the final merge is the most distant one, and this
information can be exploited to interrogate the substructure of the jets, removing
small and peripheral subjets to improve the single-jet mass resolution.
160
appendix d
JET VERTEX FRACTION ALGORITHM
The jet-vertex association algorithm requires the collections of reconstructed tracks,
jets and primary vertices in an event and is comprised of three distinct steps,
1. track and jet selection
2. calorimeter jet-to-track matching
3. jet-vertex association.
All tracks in the event must pass a set of quality criteria and are then matched to
cal-jets which lie within the fiducial tracking volume |η| < 2.5. Any track falling
within a δR cone of a jet axis is associated to that jet. Each track matched to a
jet is then required to have originated in a reconstructed primary vertex (PV) in the
event. Although no explicit secondary vertex (SV) finding is performed, all tracks
which pass the selection criteria, including SV tracks, are considered by the algorithm.
The combination of these steps results in the jet-vertex association. The resulting
discriminant is termed the jet-vertex fraction (JVF) and is defined for each jet with
respect to each PV. For a single jet jeti the JVF with respect to the vertex vtxi in
the event is written
JV F (jeti, vtxj) =
∑k pT (trkjetik , vtxj)∑
n
∑l pT (trkjetil , vtxn)
(D.0.1)
161
where, jet i has a fraction JVF(i,j) of it’s total matched-track momentum originating
in vertex j. Calorimeter jets which fall outside of the fiducial tracking region (see ref
for JVF paper) or which have not been matched to tracks are assigned a JVF=−1.
Figure D.1: Schematic Representation of JVF.
162
appendix e
GOOD RUNS LIST
To define a good dataset we need Data Quality (DQ) information. The approach to
using DQ information in a physics analysis is through the use of dedicated lists of
runs and luminosity blocks, known as “good run lists” (GRLs).
A luminosity block is the unit of time for data-taking, and lasts about two minutes.
A good run list is formed by applying DQ criteria, and possibly other criteria, to the
list of all valid physics runs and luminosity blocks.
DQ flags are simple indicators of data quality, and act much like a traffic light. They
are issued by each sub-detector, are set per luminosity block.
A tag is issued after each new reconstruction processing of the data, or when defining
a dataset epoch. A red status indicates the data taken by the relevant sub-system
has been declared bad, so recorded data should be excluded from physics analysis. To
form a GRL, a query of DQ flags is required to be green, i.e. indicating good data.
Most of the available DQ flags are set by detector sub-systems. Some combined per-
formance groups already fill flags as well, for example to qualify jet, missing energy,
and tau reconstruction.
In summary, good run lists are the way to select good data samples for physics anal-
ysis.
163
appendix f
COMPARISON OF RESULTS
The number of events surviving after full event selection obtained previously by AT-
LAS collaboration are given below
QCD multi jet W + Jets Single Top All tt tt with fid. τhad629 16 13.7 445 178
Table F.1: Number of events surviving after applying all selection cuts obtained fortau + jets analysis by ATLAS collaboration from previous work [86].
The number of events surviving after full event selection obtained previously by
CMS collaboration are given below
Source Eventstt→ τ + jets 383QCD multi jet 2392W + Jets 62Single Top 41Z + Jets 21other tt 151
total background 2667Data 3050
Table F.2: Number of events surviving after applying all selection cuts obtained fortau + jets analysis by CMS collaboration [87] .
164
appendix g
DATA AND MONTE CARLO SAMPLES
Proccess Event Generator approximation Sample(s) Cross-Sectionpb−1
tt with MC@NLO NLO 105200 90.6at least 1 leptonSingle top quark Acer MC 117360-2 20.92t-channel(with l)Single top quark MC@NLO NLO 108343-5 1.5s-channel(with l)Single top quark MC@NLO NLO 108346 15.74
WtLO 107680-5(eν)LO 107690-5 (µν)W( lν) + jets Alpgen
LO 107700-5(τν)
3.1× 104
Wbb + jets Alpgen LO 107280-3 128107650-5 (ee)107660-5 (µµ)Z(ll) + jets Alpgen LO
107670-5 (ττ) 1.5× 104
WW Herwig LO 105985 17.0ZZ Herwig LO 105986 1.26WZ Herwig LO 105987 5.5
Table G.1: Cross-section and data set ID numbers for SM MC samples.
MonteCarlo Samples
Signal
mc11 7TeV.105200.T1 McAtNlo Jimmy.merge.NTUP
TOP.e835 s1272 s1274 r2920 r2900 p834
W + Jets
165
mc11 7TeV.107680.AlpgenJimmyWenuNp0 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107681.AlpgenJimmyWenuNp1 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107682.AlpgenJimmyWenuNp2 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107683.AlpgenJimmyWenuNp3 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107684.AlpgenJimmyWenuNp4 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107685.AlpgenJimmyWenuNp5 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107690.AlpgenJimmyWmunuNp0 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107691.AlpgenJimmyWmunuNp1 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107692.AlpgenJimmyWmunuNp2 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107693.AlpgenJimmyWmunuNp3 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
166
mc11 7TeV.107694.AlpgenJimmyWmunuNp4 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107695.AlpgenJimmyWmunuNp5 pt20.merge.NTUP
TOP.e825 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107700.AlpgenJimmyWtaunuNp0 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107701.AlpgenJimmyWtaunuNp1 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107702.AlpgenJimmyWtaunuNp2 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107703.AlpgenJimmyWtaunuNp3 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107704.AlpgenJimmyWtaunuNp4 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107705.AlpgenJimmyWtaunuNp5 pt20.merge.NTUP
TOP.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107280.AlpgenJimmyWbbFullNp0 pt20.merge.NTUP TOP
.e887 s1310 s1300 r2920 r2900 p834
mc11 7TeV.107281.AlpgenJimmyWbbFullNp1 pt20.merge.NTUP TOP
.e887 s1310 s1300 r2920 r2900 p834
167
mc11 7TeV.107282.AlpgenJimmyWbbFullNp2 pt20.merge.NTUP TOP
.e887 s1310 s1300 r2920 r2900 p834
mc11 7TeV.107283.AlpgenJimmyWbbFullNp3 pt20.merge.NTUP TOP
.e887 s1310 s1300 r2920 r2900 p834
Z + Jets
mc11 7TeV.107650.AlpgenJimmyZeeNp0 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107651.AlpgenJimmyZeeNp1 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107652.AlpgenJimmyZeeNp2 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107653.AlpgenJimmyZeeNp3 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107654.AlpgenJimmyZeeNp4 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107655.AlpgenJimmyZeeNp5 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107660.AlpgenJimmyZmumuNp0 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107661.AlpgenJimmyZmumuNp1 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
168
mc11 7TeV.107662.AlpgenJimmyZmumuNp2 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107663.AlpgenJimmyZmumuNp3 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107664.AlpgenJimmyZmumuNp4 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107665.AlpgenJimmyZmumuNp5 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107670.AlpgenJimmyZtautauNp0 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107671.AlpgenJimmyZtautauNp1 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107672.AlpgenJimmyZtautauNp2 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107672.AlpgenJimmyZtautauNp2 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107673.AlpgenJimmyZtautauNp3 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
mc11 7TeV.107674.AlpgenJimmyZtautauNp4 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
169
mc11 7TeV.107675.AlpgenJimmyZtautauNp5 pt20.merge.NTUP TOP
.e835 s1299 s1300 r2920 r2900 p834
Single Top
mc11 7TeV.108343.st schan enu McAtNlo Jimmy.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
mc11 7TeV.108344.st schan munu McAtNlo Jimmy.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
mc11 7TeV.108345.st schan taunu McAtNlo Jimmy.merge.NTUP TOP
.e835 s1310 s1300 r2920 r2900 p834
mc11 7TeV.108346.st Wt McAtNlo Jimmy.merge.NTUP TOP
.e835 s1310 s1300 r2920 r2900 p834
mc11 7TeV.117360.st tchan enu AcerMC.merge.NTUP TOP
.e835 s1310 s1300 r2920 r2900 p834
mc11 7TeV.117361.st tchan munu AcerMC.merge.NTUP TOP
.e835 s1310 s1300 r2920 r2900 p834
mc11 7TeV.117362.st tchan taunu AcerMC.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
Diboson
mc11 7TeV.105985.WW Herwig.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
170
mc11 7TeV.105986.ZZ Herwig.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
mc11 7TeV.105987.WZ Herwig.merge.NTUP TOP
.e825 s1310 s1300 r2920 r2900 p834
DATA-2011
data11 7TeV.00178044.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00178047.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00178109.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179725.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179739.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179771.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179804.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179938.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179939.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00179940.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180122.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180124.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180139.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180144.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180149.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180153.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
171
data11 7TeV.00180164.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180212.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180225.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180241.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180242.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180309.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180400.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180448.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180481.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180614.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180636.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180664.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180710.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00180776.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182013.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182161.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182284.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182346.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182372.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182424.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182449.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
172
data11 7TeV.00182450.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182454.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182455.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182456.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182486.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182516.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182518.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182519.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182726.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182747.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182766.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182787.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182796.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182879.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182886.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00182997.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183003.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00183021.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183038.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183045.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183054.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
173
data11 7TeV.00183078.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183079.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183081.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183127.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183129.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183130.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183216.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183272.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183286.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183347.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183391.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183407.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183412.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183426.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183462.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183544.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00183580.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183581.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183602.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00183963.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184022.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
174
data11 7TeV.00184066.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184072.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184074.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184088.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184130.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00184169.physics JetTauEtmiss.merge.NTUP TOPJET.r2603 p659 p694 p822
data11 7TeV.00185353.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185518.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185649.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185731.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185761.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185823.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185856.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185976.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00185998.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186049.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186156.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186169.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186178.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186179.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186180.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
175
data11 7TeV.00186182.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186216.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186217.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186275.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186361.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186399.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186456.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186493.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186516.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186532.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186533.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186669.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186673.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186721.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186729.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186753.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186755.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186873.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186877.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186878.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186923.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
176
data11 7TeV.00186933.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186934.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00186965.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187014.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187196.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187219.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187457.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00187552.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187763.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187811.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187812.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00187815.physics JetTauEtmiss.merge.NTUP TOPJET.r2713 p705 p694 p822
data11 7TeV.00188921.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00188951.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m980 p694 p822
data11 7TeV.00189027.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m975 p694 p822
data11 7TeV.00189028.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m975 p694 p822
data11 7TeV.00189049.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m975 p694 p822
data11 7TeV.00189079.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00189090.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m975 p694 p822
data11 7TeV.00189184.physics JetTauEtmiss.merge.NTUP TOPJET.f403 m980 p694 p822
data11 7TeV.00189207.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
177
data11 7TeV.00189242.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189280.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189288.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189372.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189421.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189425.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m980 p694 p822
data11 7TeV.00189481.physics JetTauEtmiss.merge.NTUP TOPJET.f404 m985 p694 p822
data11 7TeV.00189483.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189530.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189536.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189561.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189598.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189602.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189610.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189639.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189660.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189693.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189719.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189751.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m985 p694 p822
data11 7TeV.00189813.physics JetTauEtmiss.merge.NTUP TOPJET.f405 m991 p694 p822
data11 7TeV.00189822.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
178
data11 7TeV.00189836.physics JetTauEtmiss.merge.NTUP TOPJET.f406 m991 p694 p822
data11 7TeV.00189845.physics JetTauEtmiss.merge.NTUP TOPJET.f406 m991 p694 p822
data11 7TeV.00189875.physics JetTauEtmiss.merge.NTUP TOPJET.f406 m991 p694 p822
data11 7TeV.00189963.physics JetTauEtmiss.merge.NTUP TOPJET.f406 m997 p694 p822
data11 7TeV.00189965.physics JetTauEtmiss.merge.NTUP TOPJET.f406 m991 p694 p822
data11 7TeV.00190046.physics JetTauEtmiss.merge.NTUP TOPJET.f407 m997 p694 p822
data11 7TeV.00190116.physics JetTauEtmiss.merge.NTUP TOPJET.f407 m997 p694 p822
data11 7TeV.00190119.physics JetTauEtmiss.merge.NTUP TOPJET.f407 m997 p694 p822
data11 7TeV.00190120.physics JetTauEtmiss.merge.NTUP TOPJET.f407 m997 p694 p822
data11 7TeV.00190236.physics JetTauEtmiss.merge.NTUP TOPJET.f408 m1007 p694 p822
data11 7TeV.00190256.physics JetTauEtmiss.merge.NTUP TOPJET.f408 m1007 p694 p822
data11 7TeV.00190297.physics JetTauEtmiss.merge.NTUP TOPJET.f408 m1007 p694 p822
data11 7TeV.00190300.physics JetTauEtmiss.merge.NTUP TOPJET.f409 m1007 p694 p822
data11 7TeV.00190343.physics JetTauEtmiss.merge.NTUP TOPJET.f409 m1007 p694 p822
data11 7TeV.00190608.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190611.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190618.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190643.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190644.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190661.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190689.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
179
data11 7TeV.00190872.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00190878.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00190933.physics JetTauEtmiss.merge.NTUP TOPJET.f412 m1007 p694 p822
data11 7TeV.00190934.physics JetTauEtmiss.merge.NTUP TOPJET.f412 m1007 p694 p822
data11 7TeV.00190975.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00191138.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1007 p694 p822
data11 7TeV.00191139.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
data11 7TeV.00191149.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1019 p694 p822
data11 7TeV.00191150.physics JetTauEtmiss.merge.NTUP TOPJET.f411 m1019 p694 p822
data11 7TeV.00191190.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191217.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191218.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191235.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191239.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191425.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1019 p694 p822
data11 7TeV.00191426.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1025 p694 p822
data11 7TeV.00191513.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1025 p694 p822
data11 7TeV.00191517.physics JetTauEtmiss.merge.NTUP TOPJET.f413 m1025 p694 p822
data11 7TeV.00191635.physics JetTauEtmiss.merge.NTUP TOPJET.f414 m1025 p694 p822
data11 7TeV.00191676.physics JetTauEtmiss.merge.NTUP TOPJET.f414 m1025 p694 p822
data11 7TeV.00191715.physics JetTauEtmiss.merge.NTUP TOPJET.f414 m1025 p694 p822
180
data11 7TeV.00191920.physics JetTauEtmiss.merge.NTUP TOPJET.f414 m1025 p694 p822
data11 7TeV.00191933.physics JetTauEtmiss.merge.NTUP TOPJET.f415 m1025 p694 p822
Samples for Systematics
MC- Generator
mc11 7TeV.105894.AlpgenJimmyttbarlnqqNp0 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105894.AlpgenJimmyttbarlnqqNp0 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105894.AlpgenJimmyttbarlnqqNp0 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105895.AlpgenJimmyttbarlnqqNp1 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105895.AlpgenJimmyttbarlnqqNp1 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105895.AlpgenJimmyttbarlnqqNp1 baseline.merge.NTUP TOP
.e891 s1372 s1370 r3043 r2993 p937
mc11 7TeV.105896.AlpgenJimmyttbarlnqqNp2 baseline.merge.NTUP TOP
.e887 s1372 s1370 r3043 r2993 p937
181
ISR-FSR ACER Samples
mc11 7TeV.117862.AcerMCttbar Perugia2011C MorePS.merge.NTUP TOP
.e1449 a131 s1353 a145 r2993 p937
mc11 7TeV.117863.AcerMCttbar Perugia2011C LessPS.merge.NTUP TOP
.e1449 a131 s1353 a145 r2993 p937
ISR-FSR ALPGEN Samples
mc11 7TeV.117520.AlpGenPythia P2011radHi KTFac05CTEQ5L ttbarlnqqNp0
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117521.AlpGenPythia P2011radHi KTFac05CTEQ5L ttbarlnqqNp1
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117522.AlpGenPythia P2011radHi KTFac05CTEQ5L ttbarlnqqNp2
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117523.AlpGenPythia P2011radHi KTFac05CTEQ5L ttbarlnqqNp3
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117524.AlpGenPythia P2011radHi KTFac05CTEQ5L ttbarlnqqNp4INC
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117530.AlpGenPythia P2011radLo KTFac2CTEQ5L ttbarlnqqNp0
.merge.NTUP TOP.e1608 a131 s1353 a14 993 p937
mc11 7TeV.117531.AlpGenPythia P2011radLo KTFac2CTEQ5L ttbarlnqqNp1
182
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117532.AlpGenPythia P2011radLo KTFac2CTEQ5L ttbarlnqqNp2
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117533.AlpGenPythia P2011radLo KTFac2CTEQ5L ttbarlnqqNp3
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
mc11 7TeV.117534.AlpGenPythia P2011radLo KTFac2CTEQ5L ttbarlnqqNp4INC
.merge.NTUP TOP.e1608 a131 s1353 a145 r2993 p937
183
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