Measurement of the Weak Boson Production Cross Sectionin the Events with Muons√
in Proton-Proton Collisions at s = 7 TeVwith the ATLAS Detector

Takashi Kubota
A dissertation submitted to the Department of Physics
for the degree of Doctor of Philosophy
The University of Tokyo
February 2011

Abstract
The Large Hadron Collider (LHC) – a proton-proton collider with the highest center-of-massenergy which surpasses the previous energy frontier – was built at CERN to investigate the TeV
energy region where the existence of undiscovered physics such as the origin of the electroweak
symmetry breaking and the Supersymmetry is expected. The LHC started operation on 30
March, 2010, then has been delivering proton-proton collision events.
The ATLAS (A Toroidal LHC ApparatuS) experiment is held using one of the two general purpose detectors placed at the LHC. The detector is designed to exploit the full physics
potential of the LHC.
In this thesis, a measurementof the W and Z-boson production cross sections in proton√
proton collisions at s = 7 TeV are presented in the W → µν and Z → µµ processes using
the data collected with the ATLAS detector. The integrated luminosity used in the W → µν
analysis is 310 nb−1 and in the Z → µµ analysis is 331 nb−1 .
This production cross sections measurement is particularly significant in two aspects. One
is to provide√the first test of QCD prediction on the distribution of partons in proton-proton
collisions at s = 7 TeV. This will constitute a solid basis for every physics analysis performedin the ATLAS experiment. The other is to establish an event selection criterion for Z → µµ
process. This process plays a central role in the precise calibrations of detectors and algorithms
for its ease of identification and the precise knowledge of the Z-boson mass and width.
The muon detection efficiency of the ATLAS detector is estimated using experimental data.
The muon trigger efficiency is estimated by counting the number of muon trigger signatureson the path of a given reconstructed muon track. The data taken by triggers based on thecalorimeter information are used to avoid trigger biases. The muon reconstruction efficiency isestimated with respect to a track reconstructed in the inner tracking detector. In the estimation,
about half the number of the layers in the muon spectrometer are required to be fired on theextrapolated path of a given inner detector track to reject non-muon backgrounds.
The results of both efficiency estimations are confirmed by other independent estimation
using muons in Z → µµ process. This estimation provides the first trial of the detector performance measurement utilizing Z → µµ process in the ATLAS experiment.
The results of the cross sections measurement are as follows.
σW × BR (W → µν)σW + × BR (W + → µ+ ν)
σW − × BR (W − → µ− ν)
σZ × BR(Z → µµ)

=
=
=
=

9.57 ± 0.31 (stat) ± 1.15 (syst) nb.
5.69 ± 0.23 (stat) ± 0.69 (syst) nb.
3.87 ± 0.20 (stat) ± 0.47 (syst) nb.
0.87 ± 0.08 (stat) ± 0.12 (syst) nb.

1181 W-bosons and 109 Z-bosons are observed in data. The σW × BR (W → µν) is measured
with a transverse mass cut of MT > 40 GeV and σZ × BR (Z → µµ) is measured within an
invariant mass window of 66 < mµµ < 116 GeV. All the results are in agreements with thetheoretical prediction including next-to-next-to leading order QCD corrections.
This measurement is the W and Z-boson production cross sections measurement performedat the highest center-of-mass energy ever.

Contents
1

Introduction

2

2

Physics Background
2.1 The Standard Model of the Elementary Particle Physics . . . . . . . . . . . . .
2.1.1 The Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . .
2.1.2 The Grashow-Weinberg-Salam Theory . . . . . . . . . . . . . . . . .
2.1.3 The Quantum Chromodynamics and the Parton Model . . . . . . . . .
2.2 Precise Electroweak Measurements at the LHC . . . . . . . . . . . . . . . . .
2.2.1 W-boson Mass Measurement . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Z-boson Rapidity Measurement . . . . . . . . . . . . . . . . . . . . .
2.2.3 Z-boson Transverse Momentum Measurement . . . . . . . . . . . . .
2.3 The Motivation and Significance of This Study . . . . . . . . . . . . . . . . .

7
7
9
10
17
22
24
27
28
29

3

The Large Hadron Collider
3.1 The Injector Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The LHC Main Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30
31
33

4

The ATLAS Detector
4.1 Magnet System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Solenoid Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Toroid Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Pixel Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Semiconductor Trackers . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Transition Radiation Trackers . . . . . . . . . . . . . . . . . . . . . .
4.3 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 LAr Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . .
4.3.2 Hadronic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 The Detector Layout . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Monitored Drift Tubes . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Cathode Strip Chambers . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.4 Thin Gap Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.5 Resistive Plate Chambers . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Forward Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37
40
40
41
42
44
45
46
47
50
52
57
58
61
63
64
67
68

CONTENTS

4.6

4.7

4.5.1 Luminosity Measurement Using Cherenkov Integrating Detector . . . .
4.5.2 Absolute Luminosity For ATLAS . . . . . . . . . . . . . . . . . . . .
4.5.3 Minimum Bias Trigger Scintillator . . . . . . . . . . . . . . . . . . . .
Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Level-1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Level-2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Event Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis Platform and Monte Carlo Samples . . . . . . . . . . . . . . . . . . .
4.7.1 The Data Preparation Chain in the ATHENA Framework . . . . . . . .
4.7.2 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . .

iii
68
69
71
72
73
74
74
75
75
77

5 The Muon Trigger at the ATLAS Experiment79
5.1 Muon Identification and Transverse Momentum Measurement . . . . . . . . . 79
5.1.1 Energy Loss of Charged Particles in Matter . . . . . . . . . . . . . . . 80
5.1.2 Muon Transverse Momentum Measurement . . . . . . . . . . . . . . . 84
5.2 Level-1 Muon Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.1 Level-1 Endcap Muon Trigger . . . . . . . . . . . . . . . . . . . . . . 87
5.2.2 Level-1 Barrel Muon Trigger . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.3 Muon to Central Trigger Processor Interface . . . . . . . . . . . . . . 98
5.3 Level-2 Muon Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4 Muon Event Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 The Muon Reconstruction at the ATLAS Experiment101
6.1 The ATLAS Tracking Event Data Model . . . . . . . . . . . . . . . . . . . . . 101
6.1.1 The Concept of a Track . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1.2 The Track Parametrization . . . . . . . . . . . . . . . . . . . . . . . . 102
6.1.3 The Expression of Detector Measurements . . . . . . . . . . . . . . . 102
6.2 The Hough Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.3 Tracking in the Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.3.1 Inside-Out Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.3.2 Outside-In Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.4 Tracking in the Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . 107
6.4.1 Tracking in the STACO Algorithm . . . . . . . . . . . . . . . . . . . . 107
6.4.2 Tracking in MuId Algorithm . . . . . . . . . . . . . . . . . . . . . . . 109
6.5 Combined Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7 Experimental Conditions and the Datasets
111
7.1 Good Quality Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.2 Operation of the LHC and the Experiment . . . . . . . . . . . . . . . . . . . . 112
7.3 Trigger Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 W / Z Boson Event Reconstruction and Selection
116
8.1 Cross Section Measurement Overview . . . . . . . . . . . . . . . . . . . . . . 116
8.2 Luminosity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.2.1 van der Meer (vdM) scan . . . . . . . . . . . . . . . . . . . . . . . . . 118

iv

CONTENTS
8.3

8.4

9

W / Z Event Reconstruction and Selection . . . . . . . . . . . . . . . . . . . . 119
8.3.1 High Quality Muon Selection . . . . . . . . . . . . . . . . . . . . . . 119
8.3.2 Missing Transverse Energy Reconstruction . . . . . . . . . . . . . . . 122
8.3.3 Primary Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . 123
8.3.4 Jet Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Common Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 128
8.4.1 Muon Momentum Resolution and Scale . . . . . . . . . . . . . . . . . 128
8.4.2 Muon Isolation Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 129
8.4.3 Theoretical Uncertainty on Acceptance . . . . . . . . . . . . . . . . . 131

Muon Trigger Efficiency Estimation using Collision Data132
9.1 Level-1 Muon Trigger Configuration . . . . . . . . . . . . . . . . . . . . . . . 132
9.1.1 Timing Acceptance Stretch for Muon Level-1 Trigger Commissioning . 135
9.2 Trigger Efficiency Estimation by the Single Combined Track Method . . . . . . 136
9.2.1 The Combined Track Selection . . . . . . . . . . . . . . . . . . . . . . 136
9.2.2 Track Extrapolation and Search Range Definition . . . . . . . . . . . . 137
9.2.3 RoI Finding in a Search Range . . . . . . . . . . . . . . . . . . . . . . 140
9.2.4 Estimated Efficiency and Scale Factor . . . . . . . . . . . . . . . . . . 142
9.2.5 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.2.6 Trigger Efficiency Stability . . . . . . . . . . . . . . . . . . . . . . . . 153
9.3 Trigger Efficiency Estimation by Z → µµ Tag-and-Probe Method . . . . . . . . 154
9.3.1 Tag and Probe Method . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.3.2 Event Selection and Muon Distribution . . . . . . . . . . . . . . . . . 154
9.3.3 Estimated Efficiency and Scale Factor . . . . . . . . . . . . . . . . . . 154
9.4 Single Muon Trigger Efficiency Scale Factor . . . . . . . . . . . . . . . . . . . 156

10 Muon Reconstruction Efficiency Estimation using Collision Data
158
10.1 MS Hit Tagging Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.1.1 MDT Hits – ID Track Association . . . . . . . . . . . . . . . . . . . . 158
10.1.2 Event Selection and Muon Distribution . . . . . . . . . . . . . . . . . 160
10.1.3 Decay in Flight Background Subtraction . . . . . . . . . . . . . . . . . 162
10.1.4 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 165
10.2 Z → µµ Tag-and-Probe Method . . . . . . . . . . . . . . . . . . . . . . . . . 166
10.2.1 Event Selection and Muon Distribution . . . . . . . . . . . . . . . . . 166
10.2.2 Efficiency and Scale Factor . . . . . . . . . . . . . . . . . . . . . . . . 168
10.2.3 ID Track Reconstruction Efficiency . . . . . . . . . . . . . . . . . . . 169
10.3 Single Muon Reconstruction Efficiency Scale Factor . . . . . . . . . . . . . . 170
11 Measurement of W Boson Cross Section
171
11.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
11.2 Signal Acceptance and Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . 173
11.2.1 Overall Acceptance of W → µν Selection . . . . . . . . . . . . . . . . 173
11.2.2 Efficiency Scale Factors . . . . . . . . . . . . . . . . . . . . . . . . . 174
11.2.3 Acceptance Decomposition . . . . . . . . . . . . . . . . . . . . . . . 175
11.2.4 Summary of Acceptance and Efficiency . . . . . . . . . . . . . . . . . 175

CONTENTSv

11.3 Systematic Uncertainty on Acceptance . . . . . . . . . . . . . . . . . . . . . . 176
11.4 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
11.4.1 QCD Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
11.4.2 Electroweak and tt¯ Backgrounds . . . . . . . . . . . . . . . . . . . . . 179
11.4.3 Cosmic Ray Background . . . . . . . . . . . . . . . . . . . . . . . . . 180
11.4.4 Background Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 181
11.5 Results for W-Boson Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 182
11.5.1 Event Cut Flow in the W → µν Selection . . . . . . . . . . . . . . . . 182
11.5.2 Kinematics of Pre-Selected Samples . . . . . . . . . . . . . . . . . . . 182
11.5.3 Kinematics of the W → µν Candidate Events . . . . . . . . . . . . . . 186
11.5.4 Cross Section Measurement . . . . . . . . . . . . . . . . . . . . . . . 189
12 Measurement of Z Boson Cross Section
192
12.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
12.2 Signal Acceptance and Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . 193
12.2.1 Overall Acceptance of Z → µµ Selection . . . . . . . . . . . . . . . . 193
12.2.2 Efficiency Scale Factors . . . . . . . . . . . . . . . . . . . . . . . . . 194
12.2.3 Acceptance Decomposition . . . . . . . . . . . . . . . . . . . . . . . 195
12.2.4 Summary of Acceptance and Efficiency . . . . . . . . . . . . . . . . . 195
12.3 Systematic Uncertainty on Acceptance . . . . . . . . . . . . . . . . . . . . . . 196
12.4 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.4.1 QCD Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.4.2 Electroweak and tt¯ Backgrounds . . . . . . . . . . . . . . . . . . . . . 198
12.4.3 Cosmic Ray Background . . . . . . . . . . . . . . . . . . . . . . . . . 198
12.4.4 Background Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 199
12.5 Results of Z-Boson Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
12.5.1 Event Cut Flow in the Z → µµ Selection . . . . . . . . . . . . . . . . . 200
12.5.2 Kinematics of Pre-Selected Samples . . . . . . . . . . . . . . . . . . . 200
12.5.3 Kinematics of Z → µµ Candidate Events . . . . . . . . . . . . . . . . 203
12.5.4 Cross Section Measurement . . . . . . . . . . . . . . . . . . . . . . . 208
13 Discussion and Conclusions

211

Bibliography

219

List of Figures
1.1
1.2
1.3

Observed and expected exclusion limits for the SM Higgs boson at the 95 %C.L. for the combined CDF and D0 experiments at the Tevatron. . . . . . . . .
Prediction for the W-boson mass in the MSSM and the SM as a function of the
top quark mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cumulative luminosity in the ATLAS experiment versus day. . . . . . . . . . .

3
4
5

2.1
2.2
2.3
2.4

Tree level Feynmann diagram of the W → f f vertex. . . . . . . . . . . . . . . 13
Tree level Feynmann diagram of the Z → µµ vertex. . . . . . . . . . . . . . . . 15
The kinematics in deep inelastic lepton-nucleon scattering. . . . . . . . . . . . 18(a) The form factors measured by the ZEUS experiment at the HERA accelerator, DESY. (b) The parton distribution function measured at the ZEUS experiment (Q2 = 10GeV2 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Cross sections for various physics processes in proton-(anti)proton collisions
calculated by MSTW team. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 A transverse view of a Z → µµ event. u represents the combined transverse
momentum of the recoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7 A transverse view of a W → µν event. u represents the combined transverse
momentum of the recoil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8 Calculated results of (a) dσ/d pT and (b) dσ/dMT showing sharp Jacobian peaks. 25
2.9 Measurement of the W-boson mass by the LEP and the Tevatron experiments. . 26
2.10 The allowed parton kinematic region for the LHC and the Tevatron. . . . . . . 27
3.1
3.2
3.3
3.4

A schematic view of the LHC complex . . . . . . . . . . . . . . . . . . . . . .
A schematic view of the LHC main ring. . . . . . . . . . . . . . . . . . . . . .
A schematic view of the LHC arc corrector magnets. . . . . . . . . . . . . . .
Standard cross section of the LHC two-in-one dipole magnet. . . . . . . . . . .

32
34
35
35

4.1
4.2
4.3
4.4

A cutaway view of the ATLAS detector. . . . . . . . . . . . . . . . . . . . . .
Particle detection in the ATLAS detector. . . . . . . . . . . . . . . . . . . . .
A cutaway view of the ATLAS superconducting magnetic system. . . . . . . .
Bending power of the toroidal magnets in terms of η. The black and red lines
show the bending power sliced at different φ positions in an octant. . . . . . . .
A cutaway view of the ATLAS Inner detector (ID). . . . . . . . . . . . . . . .
A detailed configuration of the ATLAS Inner Detectors. . . . . . . . . . . . . .
Material distribution in the inner detector as a function of |η|. . . . . . . . . . .

37
38
40

4.5
4.6
4.7

41
42
43
43

LIST OF FIGURES

vii

4.8 A schematic view and a picture of a PIXEL Modules. . . . . . . . . . . . . . . 44
4.9 A schematic view and a picture of a SCT barrel modules. . . . . . . . . . . . . 45
4.10 Pictures of the barrel and endcap TRT. . . . . . . . . . . . . . . . . . . . . . . 46
4.11 A cutaway view of the ATLAS Calorimeters. . . . . . . . . . . . . . . . . . . 47
4.12 Cumulative amounts of material in units of X0 (radiation length) and as a function of |η| in front of and in the EM calorimeters. (a) The total amount ofmaterial in front of the presampler layer and in front of the first layer of the EM
calorimeters over the full η range. (b) The thickness of each layer as well as thematerial in front of the first layer in the barrel. (c) The thickness of each layer
as well as the material in front of the first layer in the endcap. . . . . . . . . . . 48
4.13 Cumulative amount of material in units of λ (interaction length) as a functionof |η| in front of and in the EM calorimeters, in each hadronic layer, the total
amount at the end of the active calorimetry and the total amount of material infront of the first active layer of the muon spectrometer. . . . . . . . . . . . . . 50
4.14 Sketch of a barrel LAr Calorimeter module. . . . . . . . . . . . . . . . . . . . 51
4.15 The layout of the signal layers in the EM calorimeters in r − z plane. The figures
on top are for the barrel and the extended endcap. The figure on bottom-left is
for the endcap inner and bottom-right is for the endcap outer wheels. . . . . . 51
4.16 Scintillator tile calorimeter segmentation in the radial direction. . . . . . . . . . 52
4.17 A schematic view of a scintillator tile calorimeter module. . . . . . . . . . . . 53
4.18 The layout of the calorimeters in the endcap and forward region. All the calorimeters are housed in the same cryostat. . . . . . . . . . . . . . . . . . . . . . . . 54
4.19 A schematic view of the HEC segmentation (Dimensions are in mm). . . . . . 55
4.20 (a) A schematic view of a HEC1 module. (b) A schematic view of the arrangement of the HEC readout structure. . . . . . . . . . . . . . . . . . . . . . . . . 55
4.21 (a) A schematic view of a FCal1 copper electrode wound by a rad-hard plastic
fiber. (b) The layout of the electrodes of FCal1. RM represents the Moliere
radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.22 A schematic R-Z view of the ATLAS muon spectrometer. . . . . . . . . . . . . 57
4.23 A calculated typical momentum resolution for muons reconstructed in the muon
spectrometer. The alignment curve is for an uncertainty of 30 µm in the chamber
positions. (a) is for |η| < 1.5 and (b) is for |η| > 1.5. . . . . . . . . . . . . . . . 58
4.24 3-D view of the ATLAS detector in the underground hall. The muon chambers(partly removed to show the inner structures) are arranged in three layers aroundthe inner detector and the calorimeter in the space between 5 and 10 m in radius
and 7 and 23 m distance from the interaction point. . . . . . . . . . . . . . . . 59
4.25 A schematic R - φ view of the ATLAS muon spectrometer. . . . . . . . . . . . 60
4.26 A schematic view of a barrel MDT chamber. . . . . . . . . . . . . . . . . . . . 62
4.27 A schematic view of an endcap MDT chamber with the optical alignment system. 62
4.28 (a) The CSCs mounted on a rigid wheel inclined by 11.59◦ . (b) A cutout viewof a single CSC layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.29 (a) A schematic illustration of a TGC chamber. (b) TGC structure showing
anode wires, graphite cathodes, G-10 layers, and a read-out strip orthogonal to
the wire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

viii

LIST OF FIGURES
4.30 The cross section of five detector layers of the middle station of the TGC. . . .
4.31 Time jitter of the TGC chamber for the various incident angles. . . . . . . . . .
4.32 The cross section of a RPC chamber. . . . . . . . . . . . . . . . . . . . . . . .
4.33 (a) The configuration of the LUCID in a side of the ATLAS detector around thebeam-pipe. (b) A schematic view of a LUCID detector and its readout structure.
4.34 A schematic view of the ALFA detector in the Roman Pot. . . . . . . . . . . .
4.35 A simulated and fitted dN/dt spectrum by PYTHIA. . . . . . . . . . . . . . .
4.36 A picture of the MBTS mounted on endcap calorimeter cryostat. . . . . . . . .
4.37 Schematic vies of the ATLAS TDAQ system. . . . . . . . . . . . . . . . . . .
4.38 Block diagram of the L1 trigger. . . . . . . . . . . . . . . . . . . . . . . . . .
4.39 A schematic view of the data preparation chain in the ATHENA. . . . . . . . .
4.40 The MSTW 2008 NNLO PDFs (68 % C.L.). . . . . . . . . . . . . . . . . . . .

66
66
67

5.1
5.2

80

−dE/dx for positive muons in copper as a function of βγ (solid curve). . . . . .
(a) Fractional energy loss per radiation length in lead as a function of electron
or positron energy (b) Photon total cross section in lead as a function of energy
5.3 Energy deposition of hadrons in a matter [1]. . . . . . . . . . . . . . . . . . .
5.4 Motion of a negative charged particle in a homogeneous magnetic field. . . . .
5.5 Sagitta measurement in a magnetic field. . . . . . . . . . . . . . . . . . . . . .
5.6 A schematic drawing of the ATLAS L1 muon trigger. . . . . . . . . . . . . . .
5.7 The cross section in R − Z plane of the TGC system. . . . . . . . . . . . . . .
5.8 The pT decision scheme in the TGC. . . . . . . . . . . . . . . . . . . . . . . .
5.9 A schematic view of the segmentation of a TGC octant. . . . . . . . . . . . . .
5.10 A schematic view of the TGC electronics system. . . . . . . . . . . . . . . . .
5.11 A block diagram of the Patch-Panel. . . . . . . . . . . . . . . . . . . . . . . .
5.12 A block diagram of the variable delay logic in the Patch-Panel ASIC. . . . . . .
5.13 A schematic of the BCID circuit on the Patch-Panel ASIC. . . . . . . . . . . .
5.14 A block diagram in the SLB ASIC. . . . . . . . . . . . . . . . . . . . . . . . .
5.15 A schematic illustration of the wire doublet coincidence matrix in SLB ASIC. .
5.16 A schematic illustration of the functionalities in a wire high-pT ASIC. . . . . .
5.17 A coincidence matrix configured in the SL. . . . . . . . . . . . . . . . . . . .
5.18 A schematic view of the trigger principle in the RPC. . . . . . . . . . . . . . .
5.19 The RPC trigger segmentation. . . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 A schematic view of the RPC trigger slice. . . . . . . . . . . . . . . . . . . . .

68
69
70
71
72
73
76
77

81
83
84
85
86
87
88
89
90
91
91
92
93
94
94
95
96
97
98

6.1
6.2
6.3
6.4
6.5

An image of a reconstructed track in the ATLAS Event Data Model. . . . . . . 102
A simplified UML diagram showing the extended class of the MeasurementBase. 103
A schematic view of a segment in the MDT. . . . . . . . . . . . . . . . . . . . 104
Set of points (a) and their representation in the Hough Space (b). . . . . . . . . 105
A Hough histogram for the curves in Figure 6.4 (b). . . . . . . . . . . . . . . . 106

7.1

A schematic diagram of the L1 jet algorithm showing a window of 2 × 2, 3 × 3
and 4 × 4 jet trigger elements spanning the EM and hadronic calorimeter. . . . 115

LIST OF FIGURES
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9

9.1
9.2
9.3
9.4

9.5

9.6

ix

pTID − pTMS distribution for combined tracks with pT > 20 GeV and |η| < 1.05 forthe events which passed the Z → µµ pre-selection . . . . . . . . . . . . . . . . 120
z0 − zvtx distributions for combined tracks with pT > 20 GeV in the events which
passed the (a) W → µν pre-selection (b) all W → µν selection. . . . . . . . . . 121
Relative track isolation distributions for combined tracks with pT > 20 GeV in
the events which passed the (a) W → µν pre-selection (b) all W → µν selection. 121
Two dimensional distribution of reconstructed primary vertices in 6 nb−1 of 7
TeV data taken by MBTS trigger in x − y plane [2]. . . . . . . . . . . . . . . . 124
Two dimensional distribution of reconstructed primary vertices in 6 nb−1 of 7
TeV data taken by MBTS trigger in the x − z (a) and the y − z (b) [2]. . . . . . . 124
The mean position and RMS of primary vertices in (a) x, (b) y and (c) z coordinate in each run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125(a) The number of good vertices in an event in data and W → µν MC. (b)z-position of primary vertices reconstructed with three of more tracks. . . . . . 126
Jet cleaning variables: (a) n90, (b) fHEC , (c) fQLAr , (d) fEM , (e) Jet timing. . . . 127
The calculated distributions of ∆χ2 between the di-muon invariant mass distribution in data and MC in C1 − C2 plane ((a), (b), (c)). (a) is for all Z → µµ
events, (c) is for events in which both muons are generated into the endcap and(e) is for events in which both muons are generated into the barrel. The yellow
contour lines indicate where ∆χ2 = 1, 4, 9.... The di-muon invariant mass distributions in data and MC with C1 and C2 which reports the minimum χ2 are also
shown ((b), (d), (f)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Simulated TGC L1MU6 trigger efficiency for muons with pT of 20 GeV generated in 1.05 < |η| < 2.4 in the r − φ plane. . . . . . . . . . . . . . . . . . . . . 133
A map of the RPC trigger coverage in η − φ plane. . . . . . . . . . . . . . . . 134
Distribution of the trigger time difference in units of bunch crossing (BC) withrespect to the L1 MBTS for the TGC (a) and the RPC (b) triggers. . . . . . . . 135
Event displays of the events used in the efficiency estimation. Red lines aremuons, yellow lines are tracks reconstructed in the inner detector, purple cones
are jets and yellow blocks are clusters in the calorimeter. Most of muons are
immersed in a jet. All events are taken from RunNumber = 159224, LumiBlock = 260 and (a) EventNumber = 4628851 (b) EventNumber = 4634992 (c)EventNumber = 4636444 (d) EventNumber = 4659650 and (d) EventNumber= 4665286. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
η, φ and pT distributions of muons which passed all the selections listed inTable 9.1 except for the pT distributions (the cut of pT > 20 GeV is not appliedon these distributions). Positive and negative muons are shown separately andboth are stacked. The φ and pT distributions are shown for the endcap ((b), (d))
and the barrel ((c), (e)) separately. . . . . . . . . . . . . . . . . . . . . . . . . 139
Estimated trigger efficiency for L1 MU6 in data in the η−φ. The track selection
is based on Table 9.1 but pT cut value is relaxed to 15 GeV. . . . . . . . . . . . 142

x

LIST OF FIGURES
9.7

Estimated L1 MU6 trigger efficiency as a function of η, φ and pT for muons
which passed all the selections listed in Table 9.1 except for the cut of pT > 20
GeV in pT distributions. Efficiencies for positive, negative and all muons areshown separately. The φ and pT distributions are shown for the endcap ((b), (d))
and the barrel ((c), (e)) separately. . . . . . . . . . . . . . . . . . . . . . . . . 143
9.8 Isolation dependence of L1 MU6 efficiency in the endcap (a) and the barrel (b). 144
9.9 Relative pT and ET isolation variables for denominator muons in endcap ((a),(c)) and barrel ((b), (d)) with various cone sizes. . . . . . . . . . . . . . . . . 145
9.10 L1 MU6 trigger efficiencies estimated in data and MC in the endcap ((a)) andthe barrel ((b)). Muons are selected by the selection in Table 9.3 except for pT
cut of 20 GeV. In the scale factor calculation, the average efficiency in the pT >20 GeV is used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.11 Fluctuation of averaged L1 MU6 efficiency for muons with pT > 20 GeV andscale factor with shifting pT cut. . . . . . . . . . . . . . . . . . . . . . . . . . 149
9.12 Fluctuation of L1 MU6 efficiency and scale factor with shifting |pTID − pTMS |cut. The maximum shift of the central value between 10 GeV and 20 GeV arecounted as a systematic component. . . . . . . . . . . . . . . . . . . . . . . . 150
9.13 Fluctuation of L1 MU6 efficiency and scale factor against the change of matching tolerance. The maximum shift of the central value between 2 σ and 4 σ arecounted as a systematic component. . . . . . . . . . . . . . . . . . . . . . . . 151
9.14 η distribution of muons in data, Z → µµ and W → µν MC. . . . . . . . . . . . 152
9.15 L1 MU6 trigger efficiency stability over the data taking period in the endcap (a)and barrel (b). The dotted line shows the overall average, the light blue bandshows the statistical error and the yellow band shows the total uncertainty. The
error bars on the black square points shows the statistical error only. . . . . . . 153
9.16 (a): Invariant mass distribution of tag and probe muons. (b) (c) (d) (e) (f): η, φand pT distribution for probe muons. . . . . . . . . . . . . . . . . . . . . . . . 155
9.17 Estimated L1 MU6 trigger efficiency by tag-and-probe and single combined
track methods as a function of η, φ and pT for probe muons. . . . . . . . . . . 157
10.1 A schematic illustration of the MDT Hits – ID track association. . . . . . . . . 159
10.2 (a) η (b) φ and (c) pT distribution of selected ID tracks for the muon reconstruction efficiency estimation by the MS hit tagging method. . . . . . . . . . . . . 161
10.3 Matching ∆R between ID tracks and standalone tracks (black) and ID tracks
and combined tracks (blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.4 (a) ∆R between the selected ID tracks and their nearest standalone tracks (b)difference in pT between the selected ID tracks and their nearest standalone
tracks (c) two dimensional histogram of (a) and (b). . . . . . . . . . . . . . . . 163
10.5 Fitting result for MDT hit residuals of tagged ID tracks in data and MC. . . . . 164
10.6 (a) Invariant mass of tag and probe tracks. (b) pT (c) η and (d) φ distributionsof the probe tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
10.7 (a) pT (b) η and (c) φ distribution of the measured muon reconstruction efficiency by the Z → µµ tag-and-probe method. . . . . . . . . . . . . . . . . . . 168
10.8 (a) pT (b) η and (c) φ distributions of the measured ID tracking efficiency by the
Z → µµ tag-and-probe method. . . . . . . . . . . . . . . . . . . . . . . . . . . 170

LIST OF FIGURES

xi

11.1 Shape comparison between di-jet MC and data for pT > 20 GeV. . . . . . . . . 179
11.2 A cut flow of the W → µν event selection with backgrounds. . . . . . . . . . . 183
11.3 Distributions of the highest-pT muons in events after pre-selection. Histograms
are scaled by the cross section and normalized to the number of events in data.
The number of vertices, trigger and muon reconstruction efficiency scale factors
are applied as well as the QCD scaling factor. . . . . . . . . . . . . . . . . . . 184
11.4 ETmiss and MT distributions of the events after pre-selection. The muon which
gives the MT nearest to mW is selected. Histograms are scaled by the crosssection and normalized to the number of events in data. The number of vertices,
trigger and muon reconstruction efficiency scale factors are applied as well as
the QCD scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
11.5 Distributions of the muons used in MT calculation after all the W → µν selection. Histograms are scaled by the cross section and normalized to the numberof events in data. The number of vertices, trigger and muon reconstruction efficiency scale factors are applied as well as the QCD scaling factor. . . . . . . . 187
11.6 ETmiss and MT distributions of the events after all the W → µν selection. The
muon which gives the MT nearest to mW GeV is selected. Histograms are scaledby the cross section and normalized to the number of events in data. The numberof vertices, trigger and muon reconstruction efficiency scale factors are applied
as well as the QCD scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . 188
11.7 Muon charge, ETmiss and MT distributions of the events after all the W → µν
selection. The muon which gives the MT nearest to mW GeV is selected. MC
predictions are given as an integrated histogram with 11 % of the luminosity
uncertainty as the error. MC predictions are scaled by the cross section andnormalized to integrated luminosity of 310 nb−1 . The number of vertices, trigger
and muon reconstruction efficiency scale factors are applied as well as the QCD
scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
11.8 η, φ and pT distributions of muons after all the W → µν selection. The muons
which give the MT nearest to mW GeV are selected. MC predictions are given
as an integrated histogram with 11 % of the luminosity uncertainty as the error.
MC predictions are scaled by the cross section and normalized to integrated luminosity of 310 nb−1 . The number of vertices, trigger and muon reconstruction
efficiency scale factors are applied as well as the QCD scaling factor. . . . . . . 191
12.1 Dimuon invariant mass distributions for isolated and non-isolated muons. . . . 198
12.2 Distributions of the highest-pT muons after pre-selection. Histograms are scaledby the cross section and normalized to the number of events in data. The numberof vertices, trigger and muon reconstruction efficiency scale factors are applied
as well as the 0.61 of QCD scaling factor. . . . . . . . . . . . . . . . . . . . . 201
12.3 Mµµ distributions of the muons after the pre-selection. Histograms are scaled by
the cross section and normalized to the number of events in data. The numberof vertices, trigger and muon reconstruction efficiency scale factors are applied
as well as the 0.61 of QCD scaling factor. . . . . . . . . . . . . . . . . . . . . 202
12.4 A cut flow of the Z → µµ event selection with backgrounds. . . . . . . . . . . 204

xii

LIST OF FIGURES
12.5 Distributions of the muons making up Z candidates after all Z → µµ selection.
Histograms are scaled by the cross section and normalized to the number of
events in data. The number of vertices, trigger and muon reconstruction efficiency scale factors are applied as well as the 0.61 of QCD scaling factor. . . . 205
12.6 Mµµ distributions of the muons after all cuts. Histograms are scaled by the crosssection and normalized to the number of events in data. The number of vertices,
trigger and muon reconstruction efficiency scale factors are applied as well as
the 0.61 of QCD scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . 206
12.7 pT and rapidity distribution of the Z-bosons after all selections. Histograms are
scaled by the cross section and normalized to the number of events in data. The
number of vertices, trigger and muon reconstruction efficiency scale factors areapplied as well as the 0.61 of QCD scaling factor. . . . . . . . . . . . . . . . . 207
12.8 Mµµ and Z-boson pT and rapidity distributions after all Z → µµ selection. The
muon pair with Mµµ which is the nearest to mZ is selected. MC prediction is
also given as integrated in one histogram with the error of 11 % of luminosity
uncertainty. MC prediction is scaled by the cross section and normalized to
331 nb−1 of integrated luminosity. The number of vertices, trigger and muonreconstruction efficiency scale factors are applied as well as the QCD scaling
factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
12.9 η, φ and pT distributions of the muons which make up Z-boson candidate after
all Z → µµ selection. The muon pair with Mµµ which is the nearest to mZ GeV
is selected. MC prediction is also given as integrated in one histogram with theerror of 11 % of luminosity uncertainty. MC prediction is scaled by the crosssection and normalized to 331 nb−1 of integrated luminosity. The number ofvertices, trigger and muon reconstruction efficiency scale factors are applied aswell as the QCD scaling factor. . . . . . . . . . . . . . . . . . . . . . . . . . . 210
13.1 (a) Parton x distribution in Z-boson candidate events obtained from Figure 12.7(c). The invariant mass of di-muon is used as Q. The Monte Calro prediction
is normalized to the number of events in data and background components are
assumed negligible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
13.2 η distribution of muons in Z-boson candidate events which have a partons withx < 0.0038. The Monte Calro prediction is normalized to the number of eventsin data and background components are assumed negligible. . . . . . . . . . . 212
13.3 Comparisons between the measured cross section times branching ratios andtheoretical predictions in (a) W → µν (b) Z → µµ processes. . . . . . . . . . . 213
13.4 Comparison between the measured production cross section times branchingratios for W → µν channels in this thesis with MT > 40 GeV and theoretical predictions including next-to-next-to-leading order QCD corrections. The
results of the previous experiments are also shown. . . . . . . . . . . . . . . . 215
13.5 Comparison between the measured production cross section times branchingratios for Z → µµ channel in this thesis with 66 < mµµ < 116 GeV and theoretical predictions including next-to-next-to-leading order QCD corrections. The
results of the previous experiments are also shown. . . . . . . . . . . . . . . . 215

List of Tables
2.1
2.2
2.3

Fermion constituents in the standard model. . . . . . . . . . . . . . . . . . . .
Calculated decay width and branching ratio of W-boson (αS (mZ ) = 0.1200). . .
Calculated decay width and branching ratio of Z-boson after QCD and QEDcorrections assuming αS (mZ ) = 0.1200. xW represents the sin2 θW . . . . . . . . .

8
14

3.1

LHC design beam parameters. . . . . . . . . . . . . . . . . . . . . . . . . . .

36

4.1
4.2
4.3
4.4
4.5
4.6

Coverage in η, granularity and segmentation in depth of the ATLAS calorimeters. 49
The MDT tube main parameters . . . . . . . . . . . . . . . . . . . . . . . . . 61
The CSC chamber main parameters . . . . . . . . . . . . . . . . . . . . . . . 64
The TGC chamber main parameters . . . . . . . . . . . . . . . . . . . . . . . 65
The RPC chamber main parameters . . . . . . . . . . . . . . . . . . . . . . . 67
Summary of the Monte Calro samples used in this study. The cross-sections are
the ones used to normalize number of events except for QCD di-jet samples.
For QCD samples, a data driven scale factor is used for a normalization. . . . . 78

7.1
7.2
7.3
7.4

DQ flags selected for the W / Z analysis . . . . . . . . . . . . . . . . . . . . . 112
A summary of data taking periods . . . . . . . . . . . . . . . . . . . . . . . . 112
Luminosity weighted relative detector uptime and good quality. . . . . . . . . . 113
L1 single muon trigger items for ItemStreamer chain in run 159224, LB 746 –
813. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
A summary of the Level-1 jet trigger items. . . . . . . . . . . . . . . . . . . . 115

7.5
8.1
8.2
8.3
9.1
9.2
9.3
9.4
9.5

16

Event reweighing factors in terms of number of good vertices in an event. . . . 126
The determined C1 and C2 parameters by di-muon invariant mass distribution
fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
The determined C1 and C2 parameters with calculated χ2 value by Chi-square
test on the di-muon invariant mass distributions. . . . . . . . . . . . . . . . . . 129
Event and muon selection for trigger efficiency measurement. . . . . . . . . . . 136
Region dependence of RoI size. . . . . . . . . . . . . . . . . . . . . . . . . . 140
A summary of the L1 single muon trigger efficiencies. Assigned errors contain
only statistical components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Relative systematics for the L1 MU6 trigger efficiencies and scale factors. . . . 148
A summary of the L1 MU6 trigger efficiencies and scale factors with respect tomuons reconstructed in MuId algorithm. . . . . . . . . . . . . . . . . . . . . . 148

xiv

LIST OF TABLES
9.6

9.7
9.8

A summary of the derived L1 MU6 efficiencies in the endcap and the barrel
after reweighed by the η distributions of muons obtained in Z → µµ and W →µν MC. The assigned errors are statistical only. . . . . . . . . . . . . . . . . . 151
Estimated L1 MU6 trigger efficiencies and scale factors with tag-and-probe
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
A summary of the L1 MU6 trigger efficiency and scale factor . . . . . . . . . . 156

10.1 The event and track selections for muon reconstruction efficiency estimation
using MS hit tagging method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.2 Measured muon reconstruction efficiency by the MS hit tagging method withoutbackground subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.3 The breakdown of the measured muon reconstruction efficiency drop in the MS
hit tagging method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10.4 Derived prompt muon fractions by the MDT hit residual template fits. . . . . . 164
10.5 Muon reconstruction efficiency for prompt muons with the MDT hits residual
template fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
10.6 Systematics for the muon reconstruction efficiency by the MS hit tagging method.165
10.7 Event and muon selection for muon reconstruction efficiency estimation by the
Z → µµ tag-and-probe method. . . . . . . . . . . . . . . . . . . . . . . . . . . 166
10.8 Measured reconstruction efficiency by the Z → µµ tag-and-probe method. . . . 168
10.9 standalone probe track selection for ID reconstruction efficiency estimation. . . 169
10.10Measured ID track reconstruction efficiency by the Z → µµ tag-and-probe method.169
11.1 A summary of the requirements for the W → µν candidate event selection. . . . 171
11.2 Effect of the W → µν selection criteria on simulated W → µν events. . . . . . . 173
11.3 A summary of the acceptance and scale factors for the W → µν events. . . . . . 175
11.4 A summary of the systematic uncertainty on the W → µν acceptance. . . . . . 176
11.5 QCD scaling factor derived with events with non-isolated muons with pT > 20
GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
11.6 The predicted number of electroweak, QCD and cosmic ray background events
after corrections of number of vertices, trigger and muon reconstruction efficiency scale factors. The predicted number of events are normalized to 310
nb−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
11.7 Event cut flow of the W → µν selection on data. . . . . . . . . . . . . . . . . . 182
11.8 The number of events which passed the W → µν selection in data and MC
with its error. The error does not contain contributions coming from luminosity
uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
11.9 Results for the W → µν total cross section measurements. . . . . . . . . . . . . 189
12.1 A summary of the requirements for the Z → µµ candidate event selection. . . . 192
12.2 Effect of the Z → µµ selection criteria on simulated Z → µµ events. . . . . . . 193
12.3 A summary of the acceptance and scale factors for the Z → µµ events. . . . . . 195
12.4 A summary of the systematic uncertainty on the Z → µµ acceptance. . . . . . . 196
12.5 The background contributions predicted by MC. Predictions are normalized to
331 nb−1 and vertex, trigger and muon reconstruction scale factors are applied. . 199

LIST OF TABLES

1

12.6 Event cut flow of the Z → µµ selection on data. . . . . . . . . . . . . . . . . . 200
12.7 The number of events which passed the Z → µµ selection in data and MC
with its error. The error does not contain contributions coming from luminosity
uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
12.8 Z → µµ total and fiducial cross-section measurement. . . . . . . . . . . . . . . 208

Chapter 1
Introduction
On the ground of relativistic quantum field theory, the Standard Model (SM) of the elementary
particle physics has been developed so far. This model incorporates Glashow-Weinberg-Saslam(GWS) theory [3, 4] of the electroweak interaction and the Quantum Chromo Dynamics (QCD)of strong interaction, and both have shown excellent agreements with results of experiments
ever done. In both theories, there arise corresponding force mediators, called gauge bosons.
In the GWS theory, electromagnetism is mediated by a massless gauge boson, photon, andthe weak interaction is mediated by massive Z and W ± -bosons. The GWS theory requires
gauge bosons to be intrinsically massless whereas nonzero masses of Z and W ± -bosons are wellestablished experimentally. This contradiction can be solved by introducing a scalar doublet
into the GSW theory. This mechanism is called the Higgs mechanism [5, 6], and the spin 0
quantum of the scalar doublet is called Higgs boson which is widely considered as the lastundiscovered the elementary particle in the SM.
Discovery of the Higgs boson has been regarded as one of the most important goals in theelementary particle physics. The presence of the Higgs boson with a mass below 114.4 GeV[7] and between 158 and 175 GeV [8] has been already excluded with 95 % C.L. (Confidence
Level) by the experiments at the LEP and the Tevatron colliders. Figure 1.1 shows the observed
and expected exclusion limits for the Higgs boson at the 95 % C.L. for the combined CDF and
D0 experiments results at the Tevatron as well as the indication of the excluded mass region.
The QCD has a massless gauge boson, gluon, which interacts with quarks via exchanges ofan additional quantum number, color. The concept of the color was introduced to explain thefact that baryons like ∆++ (u ↑ u ↑ u ↑) or Ω− (s ↑ s ↑ s ↑) behave as fermions. The color charge
has three degrees of freedom which are labeled as R (Red), G (Green) and B (Blue) (the namecame from an analogy to the color of light). The hypothesis of the existence of color charge is
supported by experimental results like the observed R value of e+ e− → hadrons, the decay rate of
π0 → γγ, the study of Drell-Yann process and decay width of the W and Z-bosons. Furthermore,
the three-jet events from e+ e− annihilations observed in PETRA experiments provided the direct
evidence of gluons [9–12].
One of the most important application of the QCD is the concept of the parton distribution functions (PDFs) inside hadrons. The concept of partons, free point-like constituents ofhadrons, have been established through a series of experiments like e-p deep-inelastic scatter-

3

Tevatron Run II Preliminary, <L> = 5.9 fb

95% CL Limit/SM-1

LEP Exclusion

10

1

Expected
Observed±1σ Expected±2σ Expected

TevatronExclusion

SM=1
Tevatron Exclusion

July 19, 2010

100 110 120 130 140 150 160 170 180 190 200
2mH(GeV/c )Figure 1.1: Observed and expected exclusion limits for the SM Higgs boson at the 95 % C.L.
for the combined CDF and D0 experiments at the Tevatron [8].
ing experiments at SLAC [13, 14], and neutrino-nucleon scattering experiment performed at
CERN [15]. Theoretical supports were also given by Bjorken [16] and Feynmann [17]. Now,
partons are understood as gluons and quarks in hadrons.
PDFs evolve depending on the energy scale due to the running of the coupling constantof strong interaction, αS . However, once PDFs are measured at a certain energy scale, theevolution of PDFs can be theoretically predicted by the DGLAP (Dokshitzer-Gribov-LipatovAltarelli-Parisi) evolution function [18–20]. For this reason, a measurement of the PDFs at thehigher energy provides a good test of the QCD.
Despite all the excellent agreements with experiments, the SM has some difficulties to overcome. One such difficulty is the instability of the Higgs boson mass against radiative correction
which needs 1026 orders of fine tuning to be prevented. As a candidate of possible new extension to the SM, the theories including the Supersymmetry (SUSY), which is a symmetry
between bosons and fermions, have been developed. SUSY predicts the existence of new particles, all of which have a SM counterpart. SUSY particles contribute to the radiative corrections
on the Higgs boson mass with opposite direction to the contribution of their SM partners, thus
canceling the instability of the Higgs boson mass.
Precise measurements of the electroweak properties such as W-boson mass can provide anindirect constraint on the SM Higgs boson mass and properties of SUSY particles. Figure 1.2
shows the predicted mass of W-boson as a function of the top quark mass indicating the allowed
region for SM Higgs boson mass and mass scale of the SUSY particles in the Minimally Super-4

Introduction

symmetric Standard Model (MSSM) [21–23].

80.70

experimental errors 68% CL:
LEP2/Tevatron (today)
Tevatron/LHC

MW [GeV]

80.60

ILC/GigaZ

SY

light SU

MSSM

80.50

80.40

80.30

SY

y SU

heav
114
MH =

SM
MH

GeV
SM
MSSM
both models

eV

G
= 400

80.20

Heinemeyer, Hollik, Stockinger, Weber, Weiglein ’10

160

165

170

175

180

185

mt [GeV]Figure 1.2: Prediction for the W-boson mass in the MSSM and the SM as a function of the top
quark mass [21–23].
In the situation described above, the Large Hadron Collider – a proton-proton collider withthe highest center-of-mass energy which surpasses the previous energy frontier – was constructed at the European Organization of Nuclear Research (CERN), Geneva. Along with theunprecedented design luminosity of 1034 cm−2 s−1 , the LHC is expected to bring new knowledge
which enlarge the current understandings of the elementary√ particle physics. The LHC started
proton-proton collisions with a center-of-mass energy of s = 7 TeV on 30 March, 2010.
The ATLAS (A Toroidal LHC ApparatuS) experiments is held using one of the two general
purpose detectors placed at the LHC. The detector is designed to exploit the full physics potential of the LHC such as the discovery of the Higgs boson and the SUSY, precise measurementof the electroweak and top quark physics and stringent test of the QCD. The ATLAS detector
mainly consists of an inner tracking detector with a homogeneous solenoidal magnetic fieldof 2 T, electromagnetic and hadronic calorimeters, and a muon spectrometer with a dedicatedtoroidal magnet system. These detectors have been commissioned during 2008 and 2009 using
cosmic ray and single beam data. Still, further understanding of the detectors is one of the mosturgent tasks to be done using collision data.

5

Figure 1.3: Cumulative luminosity in the ATLAS experiment versus day.
In this thesis, a measurementof the W and Z-boson production cross sections in proton√
proton collisions at s = 7 TeV are presented in the W → µν and Z → µµ processes using
the data collected with the ATLAS detector from April to July, 2010. The integrated luminosity
used in the W → µν analysis is 310 nb−1 and in the Z → µµ analysis is 331 nb−1 . Shown in
Figure 1.3 is the accumulated integrated luminosity in the ATLAS experiment versus day. The
LHC has been steadily delivering proton-proton collisions and ATLAS recorded the event datawith a high efficiency of approximately 95 %.
This production cross sections measurement is particularly significant in two aspects. One
is to perform √the first test of the QCD prediction on the distribution of partons in proton-proton
collisions at s = 7 TeV. Especially, the sensitivity for the PDFs of sea quarks in low-x region
surpasses the previous limitation set by the measurement at the Tevatron collider. The precise
knowledge on the PDFs are indispensable for every physics analysis which will be performedat the LHC.
The other is to establish an event selection criterion for the Z → µµ process. This process
plays a central role in the precise calibrations of the detectors, algorithms and Monte Calrosimulations for its ease of identification and the precise knowledge of the mass and width of
Z-boson. This leads to a series of the precise electroweak measurements which aims to obtain,
for example, new knowledge of the Higgs boson mass and the properties of the SUSY particles.
Muon is the most important physics object in this measurement. Especially, a precise knowledge on the muon identification efficiency is crucial. Hence the muon identification efficiency

6

Introduction

is estimated using the experimental data.
The muon trigger efficiency is estimated with respect to a reconstructed muon track because
one muon track with high transverse momentum is required in both the W → µν and the Z → µµ
candidate event selections. The efficiency is deduced by counting the number of muon trigger
signatures on the path of a given track. The estimation is done using data taken by triggers
which are based on the calorimeter information to avoid trigger biases.
The muon reconstruction efficiency is measured with respect to a reconstructed track in the
inner detector. The efficiency is deduced by counting the number of tracks in the muon spectrometer which has consistent track parameters with a given muons track’s reconstructed in the
inner detector. In the estimation, about half the number of the layers in the muon spectrometer are required to be fired on the extrapolated path of a given inner detector track to reject
non-muon backgrounds.
The results of both efficiency estimations are checked with other independent estimation
using muons in Z → µµ events which are selected thorough the selection criteria established inthis study. This is the first trial of detector performance measurement using Z → µµ process in
the ATLAS experiment.

The Organization of the Thesis
The first part of this thesis is on a introductory purpose. In Chapter 2, a short description
about the theoretical framework of some parts of the SM and expected precise electro-weakmeasurement at the LHC is given to illustrate the motivation and significance of the study.
Chapter 3 and 4 are devoted to give an overview of the LHC and the accelerator complex as wellas the ATLAS detector and its target performance. Muon is the most important physics object
in the analysis, thus Chapter 5 and 6 are devoted to explain the muon trigger and reconstruction
scheme in the ATLAS experiment in some detail.
The second part presents the results of the analysis. In Chapter 7 a brief description of
the actual experimental condition and the dataset used in the analysis are given. Chapter 9
and 10 show the methods and results for the muon efficiency measurement for trigger andreconstruction. Chapter 11 and 12 present the results of W / Z-boson production cross sections
measurement using Z → µµ and W → µν processes. The closing chapter gives a discussion on
the results and overviews the thesis, then presents conclusions.

Chapter 2
Physics Background
This thesis describes measurement of the production cross sections of W
√ and Z-bosons throughthe Z → µµ and W → µν processes in proton-proton collisions at s = 7 TeV. This measurement is the W → µν and Z → µµ production cross section measurement performed at thehighest center-of-mass energy ever.
To illustrate the current situation of the elementary particle physics and the objective of themeasurement concretely, the following items are described in this section.
• An overview of the SM which makes a solid basis of our understanding for nature ofelementary particles and their interactions• A description of the precise electroweak measurement at the LHC• The motivation and significance of the production cross section measurement of W andZ-bosons at the LHC

2.1 The Standard Model of the Elementary Particle Physics
Elementary particles are classified into two categories according to its spin. The particles withhalf-integer spin are called fermions, which are considered as the fundamental building blocksof the matter around us. Fermions are further classified as quarks and leptons. The list of quarks
and leptons are summarized in Table 2.1. Quarks and leptons make up three left-handed isospin
doublet (denoted as L ) and three (lepton) or six (quark) right-handed singlets (denoted as R ).
The fermions in one column in Table 2.1 form one generation. Both quarks and leptons havethree generation structure. The non-existence of 4th generation with neutrino with relevantly
light mass (< mZ /2 ∼ 45 GeV) was proved by the LEP experiments [24–27]. A lepton doublet
consists of one neutrino and one charged lepton, namely e, µ and τ. Bottom part of quark
doublets is marked by dash. This indicates the quarks in eigenstates of the weak interactions, notof mass. The transformation between mass and weak eigenstate is described by the CabbiboKobayashi-Maskawa (CKM) Matrix [28]. Q, T 3 , Y and C in Table 2.1 are charges for eachinteraction. The details are described in the following sections.
The particles with integer spin are called bosons. Especially gauge bosons, which theoretically arise from invariance against arbitrary quantum phase transformations in space-time

8Physics Backgroundcoordinates, play a role of force mediator between fermions. This invariance is called gauge
invariance or gauge symmetry [29]. The explanation of the gauge symmetry is given in subsection 2.1.1 taking the Quantum Electrodynamics (QED [30–35]), which describes the electro
magnetic interaction, as an example.
The Grashow-Weinberg-Salam (GSW) theory [3, 4] is the theory of SU(2)L × U(1)Y gauge
symmetry. This theory describes weak interactions as well as electro magnetic interactions inwhich W and Z-bosons mediate interactions. Further description of the GSW theory is given in
sub-section 2.1.2.
W and Z-bosons are generated in proton-proton collisions at the LHC. Protons are composite particles made of quarks and gluons which are coupled each other by strong interaction
described by Quantum Chromodynamics (QCD), a theory of the SU(3) gauge symmetry. In
sub-section 2.1.3, the description of QCD is given as well as the concept of partons, which ishighly important to describe interactions at the LHC.

Fermions

Quantum Numbers
Q

T3

Y

C

0
−1

+ 12
− 12

−1

0

τR

−1

0

−2

0

Quarks
c
t

+ 23
− 13

+ 12
− 12

1
3
4
+
3
2
−
3

Leptons
!  
ν 
νµ
ντ
e
−
−
e L
µ L
τ− L
eR

µR

u
d0

L

s0

L

b0

L

uR

cR

tR

+ 32

0

dR0

s0R

b0R

− 13

0

+

(R, G, B)(R, G, B)(R, G, B)

Table 2.1: Fermion constituents in the standard model.

2.1 The Standard Model of the Elementary Particle Physics

9

2.1.1 The Quantum Electrodynamics
Regarding ψ(x) as a Dirac field at x in space-time coordinate, U(1) gauge transformation in
QED is written as
ψ(x) → eiQθ(x) ψ(x).
(2.1)
Q is the generator of the gauge transformation physically corresponding to electric chargeof the field ψ(x). θ(x) is the magnitude of the transformation which depends on space and timein a completely arbitrary way. The U(1) gauge symmetry which takes Q as a generator is called
U(1)EM symmetry.
Lagrangean density L (hereafter denoted as Lagrangean) for the free Dirac field is writtenas
L = ψ(iγµ ∂µ − m)ψ.
(2.2)
However, the first term of this L is not invariant under the U(1)EM transformation. To
restoring the gauge symmetry, covariant derivative Dµ is defined as
Dµ = ∂µ − ieAµ .

(2.3)

Aµ is the U(1)EM gauge field, its transformation is defined as
1
Aµ → Aµ + ∂µ α.
e

(2.4)

This transformation keeps the equations of Maxwell unchanged. Here we define fieldstrengthFµν = ∂µ Aν − ∂ν Aµ ,(2.5)
to introduce a gauge invariant kinematic term of the gauge field into the Lagrangean. Then we
obtained the U(1)EM invariant QED Lagrangean1
L = ψ(iγµ Dµ − m)ψ − Fµν F µν .
4

(2.6)

The first term represents the kinetic energy of the Dirac field and interaction with the gauge
field, the second is the mass term of the Dirac field and the last is the kinetic term of the gauge
field. As mentioned above, a requirement of gauge invariance introduces a gauge field anddefines its kinematics and interactions. From the first term, one can see the interaction between
a Dirac and gauge field has the formµ
Qψγµ Aµ ψ ≡ iQ jem
µ A ,

(2.7)

jem
µ is called electro magnetic current. One significant feature of gauge theory is the fact thatinteraction occurs as coupling between vector current of fermion and gauge field. In QED,
gauge field Aµ is identified as photon and couples with the electro magnetic current with thestrength proportional to electric charge.
Note that gauge boson mass term mAµ Aµ is prohibited by the gauge symmetry and consequently, in this case, photon is massless.

10

Physics Background

2.1.2

The Grashow-Weinberg-Salam Theory

Interaction of Gauge Bosons with Fermions
The GSW theory is the theory of SU(2)L ×U(1)Y symmetry which describes the electro magnetic
interaction and weak interaction as a whole. The L attached on SU(2) indicates that SU(2)symmetry is imposed only on the left-handed particles, in other words, particle with the thirdcomponent of the weak isospin T3 = ± 1/2. Isospin is an internal degree of freedom which plays
a role of the charge for weak interactions. Y is called weak hypercharge which was introduced
to explain the origin of the right handed component in neutral current of weak interaction. The
relation between electric charge Q and T3 , Y is written as
Q = T3 +

Y
,
2

(2.8)

Q, T3 and Y for each fermion are summarized in Table 2.1.
Here we define weak isospin current J µ and weak hypercharge current jY which couple toisotriplet of the vector fields Wµi and single vector field Bµ respectively.
1
Jµi (x) = χL γµ τi χL
2with i = 1, 2, 3,

jY = 2(Jµ3 − jem
µ ),

(2.9)
(2.10)

where χL represents a left-handed isospin doublet and τi is the i-th Pauli spin matrix. The
currents and vector fields are assumed to couple each other with the coupling constant of g
(weak isospin) and g0 (weak hypercharge). Then the electroweak Lagrangean has a form
L = gJ µ · Wµ + g0 jYµ Bµ .

(2.11)The physical bosons consist of the charged and neutral weak gauge boson Wµ± , Zµ and photon
Aµ . Define the relations between physical gauge bosons and Wµi , Bµ as
1
Wµ± = √ (Wµ1 ∓ Wµ2 ),2−g0 Bµ + gWµ3,
Zµ = pg2 + g02
gBµ + g0 Wµ3.
Aµ = pg2 + g02(2.12)(2.13)(2.14)The interaction Lagrangean in Eq (2.11) can be transformed asg√ (Jµ− Wµ+ + Jµ+ Wµ− ) (CC)2g+
(Jµ3 − sin2 θW jemµ )Zµ (NC)cosθW
+ g sinθW jemµ Aµ (EM),L =(2.15)

2.1 The Standard Model of the Elementary Particle Physics

11

where Jµ± , θW are defined as Jµ± = Jµ1 ± iJµ2 and g0 /g = tanθW . CC, NC and EM represents the
charged current, neutral current of weak interaction and electro magnetic current respectively.
θW is called Weinberg-angle which determines the ratio of the coupling constants of electro
magnetic and weak interactions. From the third term of Eq (2.15), one can see the relation ofe = g0 sinθW ,(2.16)

where e is the unit electric charge.
Eq (2.15) is well summarizing the interaction of the gauge bosons in the GSW theory. First,
three types of gauge bosons, namely Wµ± , Zµ and Aµ exist. Aµ is photon, the identical gauge fieldarises in the QED couples to electro magnetic current jemµ with the magnitude proportional to the±electric charge. Wµ is called W-boson which couples to charged current with the magnitude of g.
W-bosons interact only with left-handed fermions since charged current is made of purely weakisospin components. Zµ is called Z-boson which couples to neutral current with the magnitudeof g/cosθW . W and Z-bosons are called weak bosons as a whole. Unlike charged current,
neutral current is made of both weak isospin and hypercharge components. Hypercharges forright-handed fermion are non-zero, thus Z-boson couples to right-handed fermions. The formof neutral current in Eq.(2.15) can be transformed as
JµNC = Jµ3 − sin2 θW jemµ1 µ=ψγ (v f − a f γ5 )ψ,2(2.17)

wherev f = T 3 − 2Qsin2 θW ,a f = T3.

(2.18)

v f and a f are the coupling strengths of the vector and axial vector components in the neutral
current to the Z-boson.
The Mass of Weak Bosons
As mentioned above, mass terms of gauge bosons are prohibited by the gauge symmetry. However, actual W and Z-boson have mass [36].
mW = 80.399 ± 0.023GeV,mZ = 91.1876 ± 0.0021GeV.

(2.19)(2.20)

This contradiction is solved by the introduction of a complex scalar (spin-0) isospin doublet
called Higgs doublet φ. Defining weak hypercharge of the Higgs doublet as 1, φ is written as
r
!
1 φ+
,
(2.21)
φ≡2 φ0where +, 0 represent the electric charge of each complex component.

12Physics Background
Then define a Lagrangean which is invariant under SU(2)L × U(1)Y transformation asµ2
L scalar = |Dµ φ| − |φ| −
2λ
2

!2

2

λ > 0,(2.22)

τY+ ig0 Bµ · ,(2.23)
2
2
At high energy, µ2 is considered to be positive. When temperature decreases µ2 become
negative, this lead to the existence of an infinite set of degenerate vacuum state. Define vacuum
expected value of φ asr!
1 hφ+ i,(2.24)hφi =2 hφ0 iDµ = ∂µ + igWµ ·

where

−µ2
.
(2.25)
2λA choice of the the actual vacuum state among them violates the SU(2)L × U(1)Y symmetry.
This is called spontaneous symmetry breaking. However, U(1)EM symmetry still remains after
the spontaneous symmetry breaking. Thus the vacuum state is required to be invariant under
U(1)EM transformation
heiQθ(x) φi = hφi.
(2.26)
hφ+ i2 + hφ0 i2 =This means the operator Q annihilates the vacuum as!
!r!
Y
1 hφ+ i
1 0
Qhφi = T3 +hφi == hφ+ i = 0.
00022 hφ i(2.27)

Hence the vacuum state is selected asrhφi = φ =

!
1 0
,
2 v

(2.28)

where

r
v
µ2
hφi = √ , v = − .
λ2The Higgs doublet can be written using v as
r
!
1
0
i
iτi θ (x)/v
φ=e.
2 v + h(x)(2.29)(2.30)The three fields θi (x) (i = 1, 2, 3) are interpreted as massless Nambu-Goldstone bosons.
Because of the existence of the SU(2)L invariance, these Nambu-Goldstone bosons disappear
after fixing the gauge as
r
!
1
0
0
−iτi θi (x)/v
φ =e
φ=
,
(2.31)
2 v + h(x)h(x) corresponds to a physical particle with spin = 0. This particle is called SM Higgs boson.

2.1 The Standard Model of the Elementary Particle Physics

13

Then the L scalar becomes
L scalar =1∂µ h∂µ h + µ2 h2 +2p
g2 + g02 2
g2 v2 + −W W +v Zµ Z µ +48pg2 + g02
g2 vh + −W W +vhZµ Z µ + O(h2 ).
48(2.32)

The first term is the kinetic term of the SM Higgs, the term from second to fourth are themass terms of Higgs (mH ), W (mW ) and Z (mZ ) bosons, respectivelypmH =−2µ2 .
(2.33)
mW = gv/2.
(2.34)pmZ =g2 + g02 v/2.
(2.35)√The vacuum expectation value is calculated as v = ( 2G F )1/2 ∼ 246 GeV. All the vacuum
expectation value, masses of Higgs, W and Z-bosons exist at the energy scale of order of O(100)
GeV. This energy scale is called the electroweak (EW) energy scale.
The fifth and sixth terms in Eq.(2.32) are the interaction between Higgs and W, Z-bosons.
Decay of the Weak Bosons
W-boson W-bosons are generated and decay only through the interaction with two fermions
which make up a left-hand isospin doublet. The coupling of the W-boson to the left-handed
doublet is expressed in the first term in Eq (2.15). The tree level Feynman diagram of the
W → f f ( f : fermion) vertex is depicted in Figure 2.1.
`+ ; ` ; qW`; `; q 0(a)Figure 2.1: Tree level Feynmann diagram of the W → f f vertex.
Actual possible pairs to which W-bosons can decay are listed in Table 2.2 [37] as well as
calculated partial decay widths and branching ratios assuming αS (mZ ) = 0.1200. Top quark isheavier than W-boson, so decay to a state with top quark is prohibited. Decays to quark states

14

Physics Backgroundwhich contains quarks in different generations like (u, s) is realized through an off-diagonal
element of the CKM Matrix.
The decay width of the W-boson to leptons is written in Eq (2.36) where the assumptionthat lepton mass is negligible is made.
g 2 mW
48π
G F m3W=√
6 2π∼ 226.31 ± 0.07 MeV.

Γ(W ± → l± ν) =(2.36)

Also the decay width to quarks can be written as
Γ(W ± → qi q j ) = Nc |Vi j |2 Γl
G F m3= C √ W |Vi j |22 2π
∼ (706.18 ± 0.22) |Vi j | MeV,

(2.37)

where Nc (=3) is the color factor and Vi j is the corresponding CKM-Matrix element. C is acorrection for QCD effect which is written as!2!3!4
αS (mW )αS (mW )αS (mW )αS (mW )− 12.77− 80.0C = 1++ 1.409ππππ∼ 1.0394 ± 0.0005.
(2.38)The branching ratio of W → µν channel is of the most interest in this study. The current
world average of measured value is [36]
BR(W → µν) = 10.57 ± 0.15%.
Decay mode
eνe
µνµ
τντ
ud
cs
us
cd
cb
ub

(2.39)

Partial width (MeV) Branching ratio (%)
226.3 ± 0.1
10.82 ± 0.00
226.3 ± 0.1
10.82 ± 0.00
226.3 ± 0.1
10.82 ± 0.00
670.3 ± 0.3
32.06 ± 0.00
669.2 ± 0.3
32.00 ± 0.00
35.8 ± 0.1
1.71 ± 0.02
35.8 ± 0.1
1.71 ± 0.02
1.2 ± 0.0
0.06 ± 0.02
0.0
0.00
ΓW = 2091 ± 1 MeV

Table 2.2: Calculated decay width and branching ratio of W-boson (αS (mZ ) = 0.1200) [36].

2.1 The Standard Model of the Elementary Particle Physics

15

Z-boson Z-boson can couple to both left-handed and right-handed fermions thus the possible
decay modes are different from those of W-boson. Most significantly, Z-boson can decay into
oppositely charged lepton pairs such as Z → µµ. Due to the large mass of Z-boson, the leptons have high transverse momenta which result in a clear experimental signal. The tree level
Feynman diagram of the Z → f f vertex is depicted in Figure 2.2.

l; ; qZ= l; ; q(a)Figure 2.2: Tree level Feynmann diagram of the Z → µµ vertex.
Actual possible pairs to which Z-bosons can decay are listed in Table 2.3 as well as calculated partial decay width and branching ratio assuming αS (mZ ) = 0.1200. Top quark is heavier
than Z-boson, so decay to a top pair is prohibited.
The decay width of Z → f f channel is written as
Nc f g2z mz
1(1 − 4x) 2 [v2f (1 + 2x) + a2f (1 − 4x)]48π
Nc f G N m3z
1(1 − 4x) 2 [v2f (1 + 2x) + a2f (1 − 4x)].
=
√
6 2π

Γ(Z → f f ) =(2.40)

where x = m2 /m2Z (m is fermion mass). Nc f accounts for the QCD corrections such as inEq.(2.38) as well as QED corrections [36].
Here, ignoring mass of quarks and leptons, one obtains
Γ(Z → f f ) = 2(v2f + a2f )Nc f Γν ,Γν =G N m3Z√ .
12 2π(2.41)

Γν is a decay width for a certain type of a neutrino pair. The branching ratio of Z → µµ
channel is of the most interest in this study. The current world average of measured value is[36],
BR(Z → µµ) = 3.366 ± 0.007%.
(2.42)

16

Physics Background

Decay mode

vf

af

ν

1
2
1
− + 2xW
2
1 4
− xW
2 3
1 2
− + xW
2 3

1
2
1
−
2
1
2
1
−
2

1
[1 + (1 − 4xW )2 ]2
Nc f
8
[1 + (1 − xW )2 ]
2
3
Nc f
4
[1 + (1 − xW )2 ]2
3300.20 ± 0.06 12.029 ± 0.003””” + mass correction

375.94 ± 0.04 15.064 ± 0.002

e, µ, τ
u, c
d, s
b

Γ f /Γν
1

Part. width (MeV)

BR (%)

167.21 ± 0.02

6.700 ± 0.001

83.99 ± 0.01

3.365 ± 0.001

382.98 ± 0.06 15.346 ± 0.003

ΓZ = 24957 ± 0.3 MeV
Table 2.3: Calculated decay width and branching ratio of Z-boson after QCD and QED corrections assuming αS (mZ ) = 0.1200 [36]. xW represents the sin2 θW .

2.1 The Standard Model of the Elementary Particle Physics

17

2.1.3 The Quantum Chromodynamics and the Parton Model
Proton is not an elemental particle like electron and muon but a composite particle made ofquarks and gluons, the gauge bosons of strong interaction. In proton, interactions like gluon
radiation (q → qg), gluon pair-production (g → gg) and gluon splitting (g → qq) take place
continuously. In this section, an overview of the QCD, which describes the interaction between
quarks and gluons is given followed by a description of the parton model which is crucial tounderstand the weak boson production process in proton-proton collisions.
In QCD, quarks are treated as three dimensional base vector in color SU(3) (SU(3)C ) space.
Gluons, which are belonging to one of the eight states which correspond to SU(3)C octet, intermediate strong interactions through exchanges of color charge. The QCD Lagrangean density
is written as [38, 39]
1 A Aµν
L = − Fµν
F + Σi (iγµ Dµ − mi )qi + Lgauge− f ixing ,4(2.43)F Aµν = ∂µ AνA − ∂ν AµA − αS f ABC AµB ACν ,(2.44)

Dµ = ∂µ − iαS AµA T A ,(2.45)

where AµA is the gluon field (A, B, C passes 1 ∼ 8, these correspond to the degrees of freedom
for gluons), αS is the strong coupling constant and f ABC is the structure constant of SU(3). T A
is the generator of SU(3), satisfying[T A , T B ] = i f ABC T C .

(2.46)

Note that due to the non-Abelian nature of the SU(3) as shown in Eq (2.46), Eq (2.44) has
the self-coupling term of the gluons.
Color Confinement
Despite the vast efforts, no experiments found any evidence for the existence of free quark. All
the composite particles made of quarks such as meson (qq) and baryon (qqq) belong to a color
single state. This fact is understood by assuming the existence of a potential between non color
singlet quarks which increases with the distance between them. Thus colored quark state can’t
exist alone. This phenomenon is called color confinement. The potential between quarks playa role of a string which ties two quarks. Pulling out this string, the stored energy eventuallyreaches the point where it is energetically more favorable to create a qq pair (meson) with two
short strings rather than long one. Since the transverse momenta involved in creating mesons
are of order of a few times mass of the meson only, one obtains two collimated jets of hadrons
traveling in opposite directions following the momentum vectors of the original quarks. For
the massless nature of the gluon, strong interaction intrinsically reaches over long distance.
However the nature is hidden by the confinement.
Asymptotic Freedom
In the classical electromagnetism, it is known that electric fields in a matter is transformed due
to di-electric polarization and eventually results in a change of substantive charge density of18

Physics Backgroundρ → ρ/ (: electric permittivity > 1). This effect is called shielding. Likewise, the vacuum
is filled with charges due to the effect of pair-production and if there is an electric field, could
be polarized. This means that the coupling constant of the interactions between two charges
differs depending on the distance between them. In the electromagnetism, the coupling constantdecreases as the distance between charges increases.
In QCD, since the field is non-Abelian, a gluon can also give rise to a gluon pair. Thus, opposite to the classical electromagnetism case, an anti-shielding effect is produced. The coupling
constant of the QCD, αS (q2 ) , hence has the form in Leading-Logarithm Approximation (LLA).
αS (q2 ) =αS (q20 )1 + BαS (q20 )ln(q2 /q20 )1=,
Bln(q2 /Λ2 )(2.47)

where B = (33 − 2 f )/12π. Such shifting of the coupling constant depending on q2 is calledrunning of the coupling constant. Provided the number of quark flavors f ≤ 16, it follows thatαS (q2 ) decreases as q2 increases. This decrease of αS at large q2 was first discussed in detail by
Gross and Wilczek [40] and Politzer [41]. Eq (2.47) shows that at asymptotically large q2 wehave αS (q2 ) → 0, that is, the quarks behave as if free. This phenomenon is called asymptotic
freedom which guarantee the quasi-free behavior of strongly interacting particles expected in
the parton model described in the next section.
The Parton Model
The invariant variables in deep inelastic lepton-nucleon scattering is defined as depicted in Figure 2.3.

k
k

q

P, M

W

Figure 2.3: The kinematics in deep inelastic lepton-nucleon scattering.

ν=q·P= E − E0,M

Q2 = −q2 = 2(EE 0 − k · k0 ) − m2l − m2l0 ,(2.48)(2.49)

2.1 The Standard Model of the Elementary Particle Physics

19

Q2
.
(2.50)
2Mν
Where E and E 0 represents the incident and emergent energy of the lepton in the rest frameof the nucleus. Thus ν means energy loss of the lepton. q is called momentum transfer written
as q = k − k0 . Q is the invariant mass or energy scale of the interaction and M is the mass of thenucleon. Ignoring the lepton mass, this can be written asx=

Q2 ∼ 4EE 0 sin2 (θ/2),(2.51)

where θ is the scattering angle of the lepton against the beam axis in the rest frame of thenucleus.
If the scattering angle is small enough, Q2 can be approximated as Q2 ∼ (Eθ)2 ∼ (pT )2 , andinvariant mass of the nucleus system scattered by the lepton is written as
W 2 = (P + q)2 = M 2 + 2Mν − Q2 .

(2.52)

Hence all the kinematics of the system can be described by x(ν) and Q2 . Figure 2.4 (a)shows a form factors measured by the ZEUS experiment [42] in e-p deep inelastic scattering.
One can see the x and Q2 dependence of the form factor is well described by the NLO theoretical
calculation.
Figure 2.4 (b) shows the parton distribution functions (PDFs) of proton measured at ZEUS
experiment (Q2 = 10GeV2 ). The horizontal axis is the x and the vertical axis is the form factorof partons. Valence u and d quarks have its peak at x ∼ 0.2 and the ratio between peak heightis 2 : 1 which reflects the structure of proton. If partons were free point-like particle, the peakwould be at 1/3. This shift is due to the QCD effects. The half of the total momentum of proton
is carried by the gluons.
Factorization and PDF Evolution
The cross section of partons in proton-proton collisions are expressed as in Eq (2.53).
XZ
c0 (ab → cX),dxa dxb [ fi (xa , Q2 ) f j (xb , Q2 )] σσ(AB → cX) = K(2.53)

i, j

where fi (x, Q2 ) represents a PDF in a proton for a parton flavor i with energy fraction of x at
c0 (ab → cX) is the production
interaction energy scale of Q2 . a, b are indices for partons and σcross section of c + X (anything) from parton a and b. The K factor is the higher order QCD
correction which scales the cross section without changing shapes of PDFs.
Eq (2.53) means the cross section can be factorized into a soft part and a hard part. This iscalled factorization. The contributions on soft part are coming from exchanges of the soft gluons whereas hard part corresponds to the core parton interaction. Factorization is guaranteed by
the fact that hard process undergo in a very short time compared to soft process. Hence PDFs
do not change during the hard process. Consequently, all the contributions from soft processes
are folded into PDFs. It is proved that factorization is possible in any order of the perturbation
[43].

20

Physics Background

5

ZEUS NLO QCD fit
tot. error

ZEUS
ZEUS 96/97

x=0.0013xfem

F2 -log10(x)ZEUS
x=6.32E-5 x=0.000102
x=0.000161
x=0.000253
x=0.0004
x=0.0005
x=0.000632
x=0.00080.8

x=0.0021

Q =10 GeV

2

0.7

E665

ZEUS NLO QCD fit

NMC

4

2

(a)

BCDMS

x=0.0032

xuv

αs(MZ2) = 0.118

0.6

tot. error

x=0.005

uncorr. error

0.5
x=0.008

30.4

x=0.013xg(× 0.05)
xdv

x=0.0210.3

x=0.03220.2

x=0.05x=0.08xS(× 0.05)

0.1

x=0.13x=0.1810x=0.25

10

-3

10

-2

10

-1

1

x

x=0.4
x=0.65

0
1

10

10

2

10

3

10

4

2

10
2

5

Q (GeV )(a)(b)

Figure 2.4: (a) The form factor measured by the ZEUS experiment at the HERA accelerator,
DESY. (b) The parton distribution function measured at the ZEUS experiment (Q2 = 10GeV2 )[42] .

2.1 The Standard Model of the Elementary Particle Physics

21

Once a PDF is determined at certain Q2 = Q20 , one can determine PDFs at any different
Q2 by the QCD calculation. The equation which describes the Q2 evolution of PDFs is called
DGLAP evolution function [18–20].
In the PDF evolution, x dependence is usually parametrized at a fixed scale Q20 as• valence quarks: f (x, Q20 ) ∼ xλ (1 − x)η
• sea quarks: f (x, Q20 ) ∼ x−λ (1 − x)η
Also different parametrization and number of free parameters are used in different studies. The
prediction is not so accurate in terms of the x dependence of PDFs which has non-perturbative
origin. Hence the in-situ constraint should be provided from experiments to improve the calculation which results in the reduction of the uncertainties on physics results.

22

2.2

Physics Background

Precise Electroweak Measurements at the LHC
proton - (anti)proton cross sections
9

9

10

10

8

8

10

10

σtot

7

10

Tevatron

LHC

6

5

10

5

σb

4

10

4

10

3

3

10

2

10

10

σjet(ET

jet

1

10

0

10

-1

σjet(ETjet> √s/20)

2

10

σW

10

σZ

10

1

0

> 100 GeV)
-1

10

10

-2

-2

10

10

-3

-4

10

-5

10

-3

σt

10

σjet(ETjet

10> √s/4)-4

10

σHiggs(MH=120 GeV)

-510200 GeV

-6

-6

10

-7

-2 -1

10

33

6

events / sec for L = 10 cm s

1010

σ (nb)

7

10

10
WJS2009

500 GeV
-7

10

10
0.1

1

10

√s (TeV)Figure 2.5: Cross sections for physics processes in proton-(anti)proton collisions calculated by
MSTW team [44].
In the proton-proton collisions at the LHC, W and Z-bosons are abundantly produced. Figure 2.5√ shows the calculated cross section of major physics processes. At the current operation
with s = 7 TeV, the cross section for W (Z) boson is about 100 (30) nb. Assuming an integrated luminosity of 10 fb−1 , the total number of generated bosons reaches 100 (30) ×106 .
For this plenty of weak bosons, precise measurement on electroweak properties make up
one of the major objectives in the LHC physics program. A representative electroweak property
is the mass of W-boson (mW ). As mentioned in chapter 1, along with precisely measured top
quark mass, this leads to an indirect constraint on the lower limit for the SM Higgs mass, andproperties of SUSY particles.

2.2 Precise Electroweak Measurements at the LHC

23

In the following subsections, first, experimental methods for mW measurement is described.
For the accurate mW determination, following three items are essential,
1. detailed understanding and extensive calibration of the detector
2. accurate determination on the PDFs especially at EW energy scale
3. precise knowledge on the initial parton kinematics
All of them can be achieved through the measurement using Z → `` process as a control sample where complete kinematics in the final state can be reconstructed and clear experimental
signal (two high-pT leptons, see Figure 2.6) lead to an easy event identification and backgroundsuppression. For the item 1, precisely measured Z-boson mass and width result in an in depth
understanding of the detector performances such as detection efficiencies, momentum resolutions and scales. Actual measurements using Z → µµ events are presented in chapter 9 andonwards. A measurement of Z-boson rapidity distribution put a constraint on the PDFs at EW
energy scale. An overview of the measurement is presented in section 2.2.2. Also the measurement of Z-boson pT distribution gives precise understanding of the initial parton kinematics.
Section 2.2.3 is devoted for the description of the measurement.

py

Z Ѝ εε

ε
u

px

pT Z

ε

Figure 2.6: A transverse view of Z → µµ event [45]. u represents the combined transverse
momentum of the recoil.

24

Physics Background2.2.1

W-boson Mass Measurementpy

W Ѝε ν

ν
u

px

∆φεν

ε

Figure 2.7: A transverse view of W → µν event [45]. u represents the combined transverse
momentum of the recoil.
Figure 2.7 shows a scheme of W → µν event topology in x−y plane (for the definition of thecoordinates, see chapter 4). The presence of a neutrino is detected by a momentum imbalance infinal states. However, due to the presence of the beam-pipe, detectors is not perfectly hermetic
in the longitudinal direction. Hence only a momentum imbalance in the transverse direction(missing ET : ETmiss ) is used for analyses. Consequently, the complete kinematics can not bereconstructed in final states. Hence the invariant mass can not be used to determine the mW
and one should use other variables sensitive to the mW . In collider experiments, the mW isdetermined thorough the following three variables.
• The transverse momentum of charged lepton: p`T• The transverse momentum of neutrino: pνT = ETmissq• The transverse mass of W: MT = 2p`T pµT 1 − cos φ` − φν
The differential cross section of W-boson in terms of p`(ν)
T and MT is written as follows√s
1 − 2p`(ν)2
/ b
dσ
T
∝ q
(2.54)√ ,`(ν)2d p`(ν)T
1 − 4pT / bs2.2 Precise Electroweak Measurements at the LHC

25


√ 
2
b
/
s
2
−
M
dσ
1
T
∝
q
√ ,
dMT (bs − m2W )2 + m2W Γ2W
2
1 − MT / bs(2.55)

dσ / dmT [Arbitrary Unit]Tdσ / dp [Arbitrary Unit]√
where bs is the effective center-of-mass energy of the parton interaction√for W-boson produc√tion. As one can see, dσ/d pT and dσ/dMT have a singularities at pT = b
s / 2 and MT = bs,respectively. The singularities arise as sharp peaks in the distribution of each differential crosssection. This is called Jacobian peak, and mW can be determined by fitting Jacobian peaks.
Figure 2.8 shows calculation results of Eq.(2.54) and Eq.(2.55).

0

10

20

30

40

50

60

0

20

40

60

lepton p (GeV)

100

120

W mT (GeV)

T

(a)

80

(b)

Figure 2.8: Calculated results of (a) dσ/d pT and (b) dσ/dMT showing sharp Jacobian peaks.
In actual experiments, Jacobian peaks are smeared by both detector resolution and W-bosonpT .
• plT has a good detector resolution, but is affected by the limited knowledge of the initial
pT of W-boson• ETmiss has a bad detector resolution and also is affected by the limited knowledge of theinitial pT of W-boson• MT is robust against the limited knowledge of W-boson pT but is affected by poorly
reconstructed ETmiss
Also momentum scale uncertainty, imperfect hadronic recoil modeling bring a large uncertainty. The LHC experiments are aiming at the mW resolution of about 10 MeV [46]. In such a
precision, the uncertainty on the PDFs also affects.
Figure 2.9 shows the combined W-boson mass results measured by the experiments at the
LEP (ALEPH, DELPHI, L3, OPAL) [47] and the Tevatron (CDF, D0) [48] collider. Note that,in the LEP results, the measurement uses WW → lνqq and WW → qqqq events throughcross section measurement just above the pair production threshold and direct invariant mass
reconstruction. The current world average is mW = 80.399 ± 0.023 GeV [36], and the LHC
experiments are aiming to surpass this accuracy.

26

Physics Background

1
ALEPH

Entries080.440±0.051

DELPHI

80.336±0.067

L3
0.75

80.270±0.055

OPAL

80.416±0.053

LEP2 preliminary

80.376±0.033
2χ /dof = 49 / 41

0.5

CDF

80.421±0.043

D∅

80.419±0.039

0.25

Tevatron [Run-1/2]

80.420±0.031
2Overall average

80.399±0.023

χ /dof = 2.7 / 5080.080 80.2 80.4 80.6 80.8 81.0
81MW[GeV]

Figure 2.9: Measurement of the W-boson mass by the LEP and the Tevatron experiments [36].

2.2 Precise Electroweak Measurements at the LHC

2.2.2

27

Z-boson Rapidity Measurement
7 TeV LHC parton kinematics

Tevatron parton kinematics

9

9

10

10
WJS2010

8

10

WJS2008x1,2 = (M/1.96 TeV) exp(±y)

x1,2 = (M/7 TeV) exp(±y)

8

10

Q=M

Q=M

M = 7 TeV
7

7

10

10

6

5

2

(GeV )

10

4

M = 100 GeV

5

10

4

M = 100 GeV

10

Q

Q

2

10

M = 1 TeV

10

2

2

(GeV )

6

M = 1 TeV

10

3

3

10

10
y= 6

2

4

0

2

4

y=

6

2

2

10

10

2

4

0

2

4

M = 10 GeV

M = 10 GeV
1

fixed
target

HERA

10

1

0

10
-7
10

fixed
target

HERA

10

0

-6

10

-5

10

-4

-3

10

10

-2

10

-1

10

0

10

10
-7
10

-6

10

-5

10

-4

-3

10

x

10

-2

10

-1

10

0

10

x

(a)

(b)

Figure 2.10: The allowed parton kinematic region for the LHC and the Tevatron [44].
Figure 2.10 shows a comparison of the allowed parton kinematic region between the LHC
and the Tevatron. As one can see, the LHC has overwhelming reach in terms of measurable
center-of-mass energy region of partons never achieved by any experiments. Hence the in-situ
constraints on PDFs in such energy region is essential for all physics analysis performed in theregion at the LHC.
A convenient variable to put a constraint on PDFs is rapidity (y) of heavy particles. For
the W mass measurement, Z → `` is the√most suitable. Assuming that a heavy particle isproduced in proton-proton collisions with s = 2E from partons with energy fraction of x1 andx2 respectively. The kinematics for the two parton system isb
p1 = (x1 E; 0, 0, x1 E) ,b
p2 = (x2 E; 0, 0, −x2 E) ,(2.56)

b =
E
b
pz =
b
s =

(2.57)(x1 + x2 ) E,
(x1 − x2 ) E,
b2 − bE
p2z = x1 x2 s,

28

Physics Backgroundb is the effective interaction energy and b
where bp1 and b
p2 are four vectors of partons, E
pz is themomentum of the system in the z-direction. Then the rapidity of the heavy particle is expressed
as
b+ b
1 E
pz 1 x1
y = ln= ln .
(2.58)b− b
2 E
pz 2 x2
If one can measure the rapidity distribution of a heavy particle with mass M, the PDF withx1 and x2 at Q2 = M 2 is determined as
x1 =
x2 =

M
√ e+y ,sM
√ e−y .
s(2.59)

Assuming the y acceptance of the ATLAS detector in rapidity as |y| < 2.5, Figure 2.10
shows the fractional energy of partons at the EW scale (∼ mZ , mW ) spans down to x = 10−4 . In
this region, W / Z-bosons are produced from sea quarks and such sea quarks are produced fromgluon splittings in higher energy region. Hence, one can conclude that the Z-boson rapidity
measurement at the LHC is important for its sensitivity to,• sea quark distribution in low-x region at EW energy scale• gluon PDFs in higher energy region.
The experiments at the Tevatron have measured the distribution. However they are looking
different energy fraction region of 0.05 < x < 0.3 and the LHC explores five hundreds times
smaller x region at the EW energy scale.

2.2.3

Z-boson Transverse Momentum Measurement

The primary objective for the Z-boson pT measurement, in the context of the needed process forthe precision W mass measurement, is the in-situ determination of the parton kinematics in the
EW energy scale. This affects not only on the distribution shapes of MT , pT and ETmiss but also
on the production cross section itself through the acceptance calculation. Figure 2.6 and 2.7
show very similar topologies of W → `ν and Z → `` boson events. Indeed, the pT of W is very
correlated that of Z-boson. Moreover, the hadronic recoil in W → `ν events can be calibrated
in Z → µµ events.
Another important objective of the Z-boson pT measurement is the test of non-perturbative
QCD. As already implied in the Eq.(2.56), Z-bosons do not have initial pT in leading order
calculation. The non-zero pT is theoretically only possible when the gluon radiation prior to theparton interaction into account.
At high pT (> 30 GeV), the radiation of single (or double) parton dominates the cross section
and fixed order perturbative QCD calculations should yield reliable results. At low pT theemission of multiple soft gluons is important and calculations in fixed order perturbative QCD
diverges. Formalisms are developed to predict the experimental Z-boson pT distribution in thecontext of soft gluon emission resummation technique [49–51]. The shape of the distribution ispredicted qualitatively but the full result depends on a limited number of free parameters which
need to be extracted from measurement.

2.3 The Motivation and Significance of This Study29

2.3 The Motivation and Significance of This Study
An Inclusive cross sections measurement of W and Z-boson is presented in this thesis. The
motivation of this measurement is to perform the first test of the validity of our understandingon the production mechanism of W and Z-boson in proton-proton collisions at the center-of theenergy of 7 TeV.
The production cross section of W and Z-boson √at hadron colliders was measured previously by the UA1 [52] and UA2 [53] experiments at s = 0.63 TeV at the CERN SppS and by
the CDF [54–56] and D0 [57, 58] experiments at the Fermilab Tevatron colliders. Both colliders utilizes proton-antiproton collisions. Most recently, the RHIC collider experiments[59, 60]√
have reported the first observation of W production in proton-proton collision at s = 0.5 GeV.
The world highest energy of the LHC will result in an exploration in the new parton kinematic region at EW energy scale where low-x sea quarks driven by gluons through their splitting
dominates. This lead to new constraints on the PDFs and stringent test of the QCD.
In this thesis, the total production cross sections measurement of W and Z-boson is performed in the W → µν and Z → µµ processes. Through this measurement, selection criteria
to extract W / Z events in each channel are established. Especially, the study on the Z → µµ
process leads to• A detailed understanding of the detector performance with precise knowledge on the Zboson mass and width• In-situ determination of the PDF of 7 TeV protons through dσ/dyZ measurement• A stringent test for the QCD predictions through dσ/dptZ measurement
These constitute the first major step of the lasting program of the precise electroweak measurements, such as W-boson mass measurement, in the ATLAS. Furthermore, a precise understanding of PDF is essential in most of the measurement and searches which will be performedat the LHC.

Chapter 3
The Large Hadron Collider
The Large Hadron Collider (LHC), the proton-proton collider which achieved the highest centerof-mass energy ever, was built at the European Organization for Nuclear Research (CERN) in
Geneva, Switzerland [61–65]. The LHC main ring is built in the tunnel with circumference of
26.7 km which was excavated at depth varying between 45 and 170 m 1 . The design center-ofmass energy is 14 TeV as well as the peak luminosity of 1034 cm−2 s−1 , both are the unprecedented performance never achieved by any other hadron colliders. The time spacing between
proton bunches are designed to be 25 ns and about 23 events occur in a bunch crossing at thedesign peak luminosity.
The LHC has two general purpose experiments with high luminosity in proton-proton collisions, ATLAS [66] and CMS [67]. At the ±140 m away from the ATLAS interaction point (IP),the LHCf [68] is held to study forward production of neutral particles in proton-proton collisions
at extremely low angles. There are also two low luminosity experiments namely LHCb [69] forB-physics aiming at peak luminosity of 1032 cm−2 s−1 and TOTEM [70] for the detection of protons from elastic scattering as small angles aiming at a peak luminosity of 2 × 1029 cm−2 s−1 with156 bunches. The LHC is also capable to accelerate lead ion beams for heavy ion studies. Thereis one dedicated ion experiment, ALICE [71], aiming at a peak luminosity of 1027 cm−2 s−1 fornominal lead-lead ion operation.
The choice of the use of proton-proton collisions, not electron-positron or proton-antiproton, was made for the following two advantages.
• To achieve a high center-of-mass energy: The accelerated particles lose their energy due
to the synchrotron radiation as in the Eq (3.1),
e2 c E 4
1,(energy loss) =6π0 (mc2 )4 ρ2(3.1)

where 0 is the permittivity of vacuum, e the electron charge, c the speed of light, m andE the mass and energy of the moving particle and ρ the bending radius. According to
the equation, the energy loss heavily depends on the mass of the particle. Thus the LHC
uses protons instead of electron-positron, and uses the world largest LEP tunnel which
1This tunnel was originally made for the Large Electron Position collider (LEP).

3.1 The Injector Chain

31further suppresses the synchrotron radiation due to its large radius. The limitation on
the acceleration for the LHC comes from the maximum magnetic field of the bending
magnets. The field strength of the LHC dipole super-conducting magnet is 8.33 T.
• To achieve a high luminosity: Previous hadron colliders used proton-anti-proton collisions with a configuration which deploys a common vacuum and magnet system for both
circulating beams. However, it is difficult to make anti-proton beam highly intense. Hencethe LHC chose proton-proton collisions and developed a dedicated two-in-one design ofdipole super-conducting magnets to deploy two separated beam pipes.
The LHC started proton-proton collisions on March 30, 2010 with the center-of-mass energyof 7 TeV and provided physics data until the end of October, 2010 then finished the scheduled
operation of the year. The LHC achieved the peak luminosity of 1032 cm−2 s−1 which leads tosensitivities for many new physics in 2011.

3.1 The Injector Chain
The LHC injector chain consists of LINAC – Proton Synchrotron Booster (PSB) – Proton Synchrotron (PS) and Super Proton Synchrotron (SPS) as depicted in Figure 3.1 (PSB is indicatedas BOOSTER in the figure).
At the beginning, hydrogen gas is injected into the duoplasmatron, a metal cylinder which
dissociates hydrogen atoms and generates protons with kinetic energy of 90 keV. Then the
protons are sent to a radio frequency quadrupole, QRF – an accelerating component that bothspeeds up and focuses the particles with RF field provided by four vanes. The spacing of thevanes bunches and accelerates the protons up to 750 keV. From the QRF, the particles are sent to
the LINAC2 (a LINAC which is for the proton acceleration), a linear accelerator whose tank is amulti-chamber resonant cavity tuned to a specific frequency which creates potential differencesin the cavities that accelerate the particle up to 50 MeV.
Protons cross the LINAC2 and reaches PSB, a circular accelerator with circumference of
157 m which consists of four identical rings mounted one above another. The beam line to the
PSB from the LINAC2 is 80 m long. 20 quadrupole magnets focus the beam along the line and2 bending and 8 steering magnets direct the beam. The PSB accelerates them to 1.4 GeV. Then
protons are injected to the PS.
The PS is the circular accelerator with circumference of 628 m. Protons are accelerated to
25 GeV in it. The PS forms the 81 bunch packets of protons with 25 ns spacing for the LHC.
The SPS is the final link in the injector chain to the LHC with circumference of 7 km.
Triplets of 81 bunches formed in the PS are injected to SPS. Three or four triplets are accelerated
in the SPS to 450 GeV and finally transferred to the LHC.

32

The Large Hadron Collider

Figure 3.1: A schematic view of the LHC complex

3.2 The LHC Main Ring33

3.2 The LHC Main Ring
The LHC main ring consists of eight arc sections and eight straight sections called insertions as
depicted in Figure 3.2. The length of each arc is 2.45 km and length of each insertion is 545 m.
Two proton beams are counter-rotate in separate beam pipes and collide at four out of eight
insertions in which experiments are held at the IPs. The ATLAS detector is placed at point
1, CMS is at point 5. The ALICE and LHCb are located at point 2 and point 8 which also
include the injection system for each beam. On upstream of each experiment, beam focusing
systems which deploy three superconducting quadrupole magnets are located. Proton beams
are designed to be focused into transverse radius of 16.7 µm at point 1 and 5, and 70.9 µm
at point 2 and 8. At point 1 and 5, two proton beams collide vertically and at point 2 and 8,
horizontally with the crossing angle of 142.5 µrad (point 1, 5), 150 µrad (point 2), 200 µrad(point 8), respectively.
The remaining insertions are equipped with a dedicated beam instrumentation each. Insertions at point 3 and point 7 have a collimation system to protect the LHC against unavoidable
beam losses by performing beam cleaning. One of the most important facilities located in insertions is the RF cavities which are housed in point 4. The main role of the LHC cavities is tokeep the 2808 proton bunches tightly bunched to ensure high luminosity at the IPs as well asdelivering radio frequency power to the beams during acceleration. The LHC uses eight cavities per beam, each cavity is operated at 4.5 K of temperature and delivering 2 MV accelerating
voltage at 400 MHz of frequency.
An arc is made of 23 arc cells. The configuration of a cell is illustrated in Figure 3.3. Eachcell is 106.9 m long and consists of two 53.45 m long half-cells each of which contains three
14.3 m long superconducting two-in-one dipole magnet. A schematic illustration of the standard cross section of dipole magnet is depicted in Figure 3.4. Those dipoles produce magnetic
fields of 8.33 T which bends the trajectory of protons to keep them along their orbit during
acceleration. Besides dipoles, the LHC also deploys sextupole, octupole, and decapole magnets
which are installed to correct for nonlinear movements due to magnetic field errors. The main
LHC machine and proton beam parameters are summarized in Table.3.1.
The luminosity is describes by the machine parameters as
L=

N 2 nb fr
N 2 nb fr γ
F=F,
4πσ x σy4πn β∗(3.2)

where N is the number of protons in a bunch, nb is the number of bunches stored in the Main
Ring, fr is the revolution frequency and σ x,y characterize the transverse beam profiles in the x(y)direction. Also, n is the normalized transverse beam emittance, the β∗ is the beta function at
the IP and the geometrical luminosity reduction factor F is expressed as
F= q

1
θ2 σ2

,

1 + 4πσc x σz ywith θc the full crossing angle at the IP and the σz the RMS bunch length.

(3.3)

34

The Large Hadron Collider

Figure 3.2: A schematic view of the LHC main ring.

3.2 The LHC Main Ring35

106.90 m

MBB
MCS

MBA
MCS
MCDO

MBB
MSCB

MCS

MQ
MCS
BPM
MO, MQT, MQS

MBA

MBB
MCS

MCDO

MSCB

MBA

MCDO

MQ

MQT: trim quadrupole

MCS: spool piece sextupole

MQS: skew trim quadrupole

MCDO: spool piece octupole + decapole

MO: lattice octupole
MSCB: sextupole (skew sextupole) + orbit corrector

Figure 3.3: A schematic view of the LHC arc corrector magnets.

Figure 3.4: Standard cross section of the LHC two-in-one dipole magnet.

36

The Large Hadron Collider

Maximum proton energy
Relativistic gamma
Number of particles per bunch
Number of bunches
Revolution frequency
Bunch spacing
Longitudinal emittance(4σ)
Transverse normalized emittance
Circulating beam current
Stored energy per beam
RMS bunch length
RMS beam size at the IP1 and IP5
RMS beam size at the IP2 and IP8
Geometric luminosity reduction factor F
Peak luminosity in IP1 and IP5Peak luminosity per bunch crossing IP1 and IP5β∗ at the IP1 and IP5β∗ at the IP2β∗ at the IP8
half crossing angle at the IP1 and IP5
half crossing angle at the IP2
half crossing angle at the IP8[GeV]Injection
450
479.6

Hz
ns
µm rad
[A]
[MJ]
cm
µm
µm
cm−2 sec−1
cm−2 sec−1
m
m
m
µrad
µrad
µrad

1.0
3.5
23.3
11.24
375.2
279.6
18
10
10
± 160
± 240
± 300

Table 3.1: LHC design beam parameters [61].

Collision
7000
7461
1.15 × 1011
2808
11245.5
24.95
2.5
3.75
0.584
362
7.55
16.7
70.9
0.836
1.0 × 1034
3.56 × 1030
0.55
0.5 for Pb / 10 for p
1.0 ↔ 50
± 142.5
± 150
± 200

Chapter 4
The ATLAS Detector

Figure 4.1: A cutaway view of the ATLAS detector.
The ATLAS detector [72], depicted in Figure 4.1, is one of the two general purpose detectors
placed at the LHC. The ATLAS detector is designed to exploit the full physics potential of the
LHC such as the discovery of the Higgs boson and the SUSY, precise measurement of theelectroweak and top quark physics and stringent test of QCD. The general requirements for the
ATLAS detector performance are summarized as follows.
• Good muon identification and momentum measurement over a wide range of momenta
with an accurate determination of the charge of high transverse momentum muons

38

The ATLAS Detector• Good electromagnetic calorimetry with high resolutions on energy, position and directionof photon and electron within a wide geometric range• Full coverage and good hermeticity of hadron calorimetry for accurate jet and missing
transverse energy measurement• Accurate tracking for charged particles with very good momentum resolution and tolerance against high radiation doses• Robust and accurate vertex reconstruction• Efficient triggering with as low as possible transverse momentum thresholds with sufficient background suppression to cover an acceptance for a wide range of the physics
processes of interest• Accurate luminosity determination

These performance will be accomplished by the detectors described in the following sections.
The general concept of particle detections of the ATLAS detector is summarized in Figure 4.2.

Figure 4.2: Particle detection in the ATLAS detector.
The ATLAS detector is designed in a mirror symmetric manner with respect to the interaction point. The dimensions of the detector are 25 m in height and 44 m in length. The overall
weight of the detectors approximately 7000 tonnes.

39
The innermost layer is formed by several types of tracking detectors, which are referred toas the inner detector (ID). The ID is immersed in a 2 T homogeneous solenoidal field parallelto the beam axis. The measurements of charged particle momentum and interaction vertex
reconstruction are performed. A more detailed description of the ID is given in section 4.2.
A liquid argon electromagnetic sampling calorimeters and scintillator-tile hadronic calorimeters are situated outside the solenoid. The calorimeters measure the energy deposits of neutral
and charged particles. More details are described in section 4.3.
The outermost part is formed by the muon spectrometer with a dedicated air-core superconducting toroidal magnet system. A detailed description of the muon spectrometer is presented
in section 4.4.
Additionally, several types of forward detectors are placed up-and-down stream of the ATLAS detector mainly to determine the luminosity. More details are explained in section 4.5.

The ATLAS Coordinate System
The origin of the ATLAS global Cartesian coordinate system is set as coincides with the nominalinteraction point for the ATLAS experiment (IP). The z-axis is oriented parallel to the beam line
in anti-clockwise direction looked from above, the x-axis is pointing in direction of the centerof the LHC ring. The y-axis points upwards. The resulting coordinate system is right handed.
The side-A of the detector is defined as that with positive z and side-C is that with negativez. The azimuthal angle φ is the angle in the xy-plane originating from the x-axis and it increases
clockwise if looking downpthe positive z-direction (side-A). The radial distance r in the transverse plane is defined as x2 + y2 . The polar angle θ is defined as the angle from the positive
z-axis. The pseudo-rapidity is defined as η = −ln(tanθ/2). The transverse momentum is definedas the momentum in xy plane and denoted as pT . Also, transverse energy is denoted as ET andmissing transverse energy is denoted as ETmiss . The distance ∆R in the pseudorapidity-azimuthalpangle space is defined as ∆R = ∆η2 + ∆φ2 . More details on the ATLAS coordinate system ispresented in [73].

40

The ATLAS Detector

4.1

Magnet System

Figure 4.3: A cutaway view of the ATLAS superconducting magnetic system.
The ATLAS detector features a hybrid system of superconducting magnetic system withdiameter of 22 m and length of 26 m with a stored energy of 1.6 GJ. The system consists of,• A solenoid magnet for the pT measurement in the inner detector• Three toroid magnets for the pT measurement in the muon spectrometer. One is placed in
the barrel and the others are placed in each endcap region of the ATLAS detector
Figure 4.3 shows the general layout of the magnet system which provides the magnetic fieldover a volume of approximately 12,000 m3 . Eight barrel and two sets of eight endcap toroidal
magnets are depicted as red windings. The cylinder with four layers indicate the hadronic
calorimeter which plays a role of return york. The solenoid magnet is drawn as a red cylinder inside the hadronic calorimeter. Descriptions for each magnet system are described in thefollowing subsections.

4.1.1

Solenoid Magnet

The solenoid magnet is situated between the inner detector and the calorimeter with inner andouter diameters of 2.46 m and 2.56 m and length of 5.8 m. The solenoid provides homogeneous axial magnetic field of 2 T at the nominal operation current of 7.730 kA and 4.5 K oftemperature. To retain desired calorimeter performance, the material thickness in front of thecalorimeter is reduced as low as possible. The solenoid assembly contribution is suppressed toabout 0.66 radiation length at a nominal incidence. The single layer coil is wound with a highstrength Al-stabilized NbTi conductor. The flux is returned by the steel of the ATLAS hadronic
calorimeter and its girder structure.

4.1 Magnet System

41

4.1.2 Toroid Magnets

8

Transition region∫B dl (T ⋅ m)

The barrel toroid provides the magnetic field in the cylindrical volume surrounding the calorimeters. It consists of eight coils. The overall size of the barrel toroid system is 25.3 m in lengthwith inner and outer diameters of 9.4 m and 20.1 m. The field strength of the barrel toroid isabout 0.5 T at the 20.5 kA operational current and 4.5 K temperature. The conductor and coilwinding technology is based on winding a pure Al-stabilized Nb/Ti/Cu conductor into pancakeshape coils followed by vacuum impregnation.
The two endcap toroids form the magnetic field required in the endcap regions of the muon
spectrometer. These magnets cover 1.65 < r < 10.7 m with axial length of 5.0 m. The fieldstrength of the endcap toroid is about 1.0 T in operation condition. The conductor and coilwinding technology is basically the same as the one used for the barrel toroid.

Barrel region
6
4
2

φ=π/8

End-cap
region

φ=0

0
-2
0

0.5

1

1.5

2

2.5

|η|

Figure 4.4: Bending power of the toroidal magnets in terms of η. The black and red lines show
the bending power sliced at different φ positions in an octant.
Figure 4.4 shows computed toroidal field integrals as a function of |η| from the innermost
to the outermost muon spectrometer layer for infinite momentum tracks. The prediction at
the barrel partially confirmed by the measurement within 0.2 % uncertainty. The field is nothomogeneous especially in the barrel-endcap transition region of 1.3 < |η| < 1.65. This inhomogeneities is caused by the superposition of the barrel and endcap fields.

42

The ATLAS Detector

4.2

Inner Detector

Figure 4.5: A cutaway view of the ATLAS Inner detector (ID).
The ATLAS inner detector [74], depicted in Figure 4.5, consists of three detectors, namely
Pixel Detector (PIXEL), Semiconductor Tracker (SCT) and Transition Radiation Tracker (TRT)from the closest to the beam pipe. The major performance requirements for the inner detector
are as follows.
• A precise transverse momentum measurement for charged particles with
σ pT
= 0.05 × pT (GeV) ⊕ 1% (|η| < 2.5).
pT

(4.1)

• Vertex reconstruction capability which is accurate enough to observe secondary vertices(typically σ = 15 µm in the transverse plane).
As well as the electron identification over |η| < 2.0 within wide range of energies (from 0.5 GeV
to 150 GeV).
The inner detector is situated as a cylindrical envelope of length ±3512 mm and from theinner radius of 50.5 mm to outer radius of 1150 mm. The overall weight of the detectors
approximately 4.5 tonnes. A detailed inner detector configuration is depicted in Figure 4.6.
Also the material distribution in the inner detector is summarized as a function of |η| in Figure
4.7.
All the three detectors are immersed in a 2 T solenoidal magnetic field. A particle originating from the interaction point crosses at least three PIXEL layers, four SCT layers and a4.2 Inner Detector

43

ID end-plate

3512

CryostatSolenoid coil
PPF1
R1150

712

Radius(mm)

R1066

848

PPB1

2710
R1004

TRT(end-cap)

TRT(barrel)
1

R563
R514
R443
R371
R299

2

3

4

5

6

7

8

9 10 11 12

1

2

3

Cryostat
4

5

6

8

7

R644
R560

SCT (end-cap)

SCT(barrel)

R408

Pixel
support tube

R438.8

R337.6

Pixel PP1

R275
R229

R122.5
R88.5
R50.5
0

Beam-pipe

Pixel

R34.3
1299.9934749
400.5 580
1399.7495 650 853.8 1091.5

01771.42115.22505

2720.2z(mm)Envelopes

Pixel

Pixel

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

SCT barrel

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

SCT end-cap

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

TRT barrel

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

TRT end-cap

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

R149.6

R122.5
R88.5

R88.8

R50.5
0
0

400.5

495

580 650

2.5Interaction length (λ )0Radiation length (X )Figure 4.6: A detailed configuration of the ATLAS Inner Detectors.

Services
TRT
SCT
Pixel
Beam-pipe

2
1.5

0.7
Services
TRT
SCT
Pixel
Beam-pipe

0.6
0.5
0.4
0.3

1

0.2
0.5
0.1
0.5

1

1.5

2

2.5

3

2.5

3.5

4

4.5

External
Supports/other
CablesCooling
Electronics
ActiveBeam-pipe

2
1.5

0
0

5
|η|
Interaction length (λ )0Radiation length (X )

0
0

0.5

1

1.5

2

2.5

3

0.7

3.5

4

4.5

5
|η|

External
Supports/other
CablesCooling
Electronics
ActiveBeam-pipe

0.6
0.5
0.4
0.3

1

0.2
0.5
0.1
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5
|η|

0
0

0.5

1

1.5

2

2.5

3

3.5

4

Figure 4.7: Material distribution in the inner detector as a function of |η|.

4.5

5
|η|

44

The ATLAS Detector

large number (typically 36) of TRT straws allowing a precise measurement of its momentum.
To maintain an adequate noise performance after radiation damage, the PIXEL and the SCT isoperated at low temperature of about −10◦ C. In contrast, the TRT is designed to operate at room
temperature. Details of each detector are presented in the following subsections.

4.2.1

Pixel Detectors (PIXEL)

Figure 4.8: A schematic view and a picture of a PIXEL Modules.
The PIXEL is situated directly around the beam pipe which is inside the radius of 36 mm.
The PIXEL has three layers and covers |η| < 2.5 as depicted in Figure 4.6. The PIXEL deploys
1744 modules in total, in which 1456 modules are located in barrel and 288 are in endcap.
A barrel stave is equipped with 13 PIXEL modules and staves are mounted on carbon-fiber
structure as depicted in Figure 4.8. An endcap sector is equipped with six PIXEL modules andeight sectors make up an endcap disk. Both two PIXEL endcaps consist of three identical disks.
The total system has 80 million pixel channels with 50 µm width in the r − φ direction and400 µm length along the z-axis. Three measurements per track determine the impact parameterand are vital for the pattern recognition in the inner detector.
A schematic view and picture of a barrel PIXEL module is presented in Figure 4.8. A
PIXEL module consists the following components.
• 16 front-end electronics chips each has 2880 electronics channels• the sensor tile of area 63.4 × 24.4 mm2 and approximately 250 µm thick• a flexible polyimide printed circuit board with module control chip

4.2 Inner Detector

45

The channels and pixel sensor elements are connected with bump bonds (In or PbSn). A
polyimide pig-tail with Cu lines and a connector (barrel) or a wire micro cable (endcap) are
mounted on the top of them.
The typical resolution of a measurement of the PIXEL is 10 µm in the transverse plane and115 µm in z (barrel) or R (endcap) direction.

4.2.2 Semiconductor Trackers (SCT)

Figure 4.9: A schematic view and a picture of a SCT barrel modules.
The SCT consists of 4088 modules in total in which 2112 modules are forming four coaxial
cylindrical layers. Remaining modules make up each endcap which contains nine disk layers as
depicted in Figure 4.6. The total coverage of the SCT is about 63 m2 and this provides at least
four precision position measurement over |η| < 2.5.
Figure 4.9 shows a schematic view and a picture of a barrel module. The specification of
the endcap module is essentially similar to the barrel one. An SCT module consists of twolayers of silicon strip sensors with a strip pitch of 80 µm providing accurate measurements in
the r − φ plane. A layer consists of two sensors and a polyimide hybrid assembly with a carbon
fiber substrate bridges these two sensors in a layer. The length of the layer is 128 mm (126 mm
active with a 2 mm dead space) and contains 770 (768 active) channels. The two layers arerotated by ± 20 mrad each other. This stereo angle allows a modules to measure the position inz direction. Two layers are mounted on a 380 µm thick thermal pyrolitic graphite (TPG) based
board which provides the thermal and mechanical structure.
The typical resolution of an SCT measurement is 17 µm in the transverse plane and 580 µm
in z (barrel) and R (endcap) direction.

46

4.2.3

The ATLAS Detector

Transition Radiation Trackers (TRT)

Figure 4.10: Pictures of the barrel and endcap TRT.
The TRT consists of a barrel (|η| < 1.0) and two endcaps (1.0 < |η| < 2.0) modules as
depicted in Figure 4.6. The barrel TRT contains up to 73 layers and straws are oriented parallelto the beam axis. The endcap TRT contains 160 layers and straws are pointing towards the beamaxis. Any charged tracks with pT > 0.5 GeV in the TRT fiducial volume transverse at least 36
straws except for the ones generated towards barrel-endcap transition region (0.8 < |η| < 1.0)
where the number of straws decreases to a minimum of 22. Figure 4.10 shows pictures of abarrel and an endcap TRT module.
The basic element of the TRT is a polyimide straw tube with diameter of 4 mm, operatingwith a gas mixture of Xe : CO2 : O2 = 70 : 27 : 3 with 5 – 10 mbar over pressure. The anode for
TRT tube is 31 µm diameter gold plated tungsten (99.95 %). A gain of 2.5 ×104 is achieved at
the operation voltage of −1530 V. The maximum electron collection time is about 48 ns undernominal operating condition. This leads to a typical pT resolution per tube of 130 µm.
The Transition Radiation (TR) is used for the electron identification. In the TRT, 19 µm
diameter polypropylene is used as the TR material. Since the TRT uses Xe based gas mixture,
low energy TR photons are well absorbed and yield much larger signal than normal minimum
ionizing charged particles. The distinction between TR and normal minimum ionizing signal
is achieved on a straw-by-straw basis with separate double (low and high) thresholds scheme
in the front-end electronics. Typically, seven to ten high-threshold TR hits are obtained for aelectron with energy above 2.0 GeV.

4.3 Calorimetry47

4.3 Calorimetry

Figure 4.11: A cutaway view of the ATLAS Calorimeters.
The ATLAS calorimeter [75], depicted in Figure 4.11, covers |η| < 4.9 and consists ofelectromagnetic (EM) and hadronic calorimeters. A summary of the coverage in |η|, granularity
and segmentation in depth are given in Table 4.1. The major performance requirements on theenergy resolution for the calorimeters are as follows.
σE
=
E
σE
•
=
E
σE
•
=
E
•

10
⊕ 0.7% (|η| < 3.2 for EM measurements)√
E (GeV)50⊕ 3% (|η| < 3.2 for hadronic measurements)√
E (GeV)100⊕ 10% (3.2 < |η| < 4.9 for hadronic measurements)√
E (GeV)The ATLAS electromagnetic calorimeters are divided into two parts namely the barrel EM
calorimeter (|η| < 1.475) and the Endcap ElectroMagnetic Calorimeter (EMEC) (1.375 < |η| <3.2). Both deploy the same technology of liquid argon active material with accordion-shaped
lead absorber. Over the fiducial coverage of the inner detector (|η| < 2.5), the EM calorimeters
have finer granularity for precision measurements of electron and photon. The coarser granularity in the other region is sufficient for jet reconstruction and ETmiss measurements.
In the region of |η| < 1.8, a presampler is deployed to correct for the energy deposit in thematerial upstream of the EM calorimeter. The presampler consists of an active liquid argon

48

The ATLAS Detector

X0

layer with thickness of 1.1 cm (0.5 cm) in |η| < 1.52 (1.52 < |η| < 1.8).
The ATLAS hadronic calorimeter is divided into three parts namely scintillator tile calorimeter (|η| < 1.7), Hadronic Endcap Calorimeter (HEC) (1.5 < |η| < 3.2) and Forward Calorimeter(FCal) (3.1 < |η| < 4.9). The HEC and FCal deploys liquid argon technology with different
absorbers.
The total radiation length (X0 ) in the EM calorimeters is > 22 X0 in the barrel and > 24 X0
in the endcap. Also, the approximate total interaction length (λ) is about > 10 over the entire
coverage. Figure 4.12, 4.13 show the material distribution in front of and in the calorimeters in
the unit of X0 and λ. The blue histogram in Figure 4.13 shows the λ distribution in front of thefirst layer of the muon spectrometer. Details of each calorimeter are described in the following
subsections.
12
Before accordion

10

Before presampler

8
6
4
2
0
0

0.5

1

1.5

2

2.5
3
Pseudorapidity

X0

X0

(a)
40
35

Layer 3Layer 2
Layer 1
Before accordion

45
40
35

30

30

25

25

20

20

15

15

10

10

5

5

0
0

Layer 3Layer 2
Layer 1
Before accordion

0.2

0.4

0.6

(b)

0.8

1

1.2
1.4
Pseudorapidity

0

1.6

1.8

2

2.2

2.4

2.6

2.8
3
3.2
Pseudorapidity(c)Figure 4.12: Cumulative amounts of material in units of X0 (radiation length) and as a functionof |η| in front of and in the EM calorimeters. (a) The total amount of material in front of thepresampler layer and in front of the first layer of the EM calorimeters over the full η range. (b)The thickness of each layer as well as the material in front of the first layer in the barrel. (c)The thickness of each layer as well as the material in front of the first layer in the endcap.

4.3 Calorimetry

Presampler
Calorimeter

Presampler
Calorimeter 1st layer

Calorimeter 2nd layer

Calorimeter 3rd layer
Presampler
Calorimeter|η| coverage
number of layers
Granularity ∆|η| × ∆φnumber of readout channels|η| coverage
number of layers
Granularity ∆x × ∆y (cm)number of readout channels|η| coverage
number of layers
Granularity ∆|η| × ∆φfor last layer
number of readout channels

49
BarrelEndcapEM Calorimeter
number of layers and |η| coverage1|η| < 1.52 1
1.5 < |η| < 1.8
3|η| < 1.35 2
1.375 < |η| < 1.5
2
1.35 < |η| < 1.475 3
1.5 < |η| < 2.5
2
2.5 < |η| < 3.2
Granularity ∆|η| × ∆φ vs |η|
0.025 × 0.1|η| < 1.52 0.025 × 0.1
1.5 < |η| < 1.8
0.025/8 × 0.1|η| < 1.40 0.050 × 0.1
1.375 < |η| < 1.425
0.025 × 0.025 1.40 < |η| < 1.475 0.025 × 0.1
1.425 < |η| < 1.5
0.025/8 × 0.1
1.5 < |η| < 1.8
0.025/6 × 0.1
1.8 < |η| < 2.0
0.025/4 × 0.1
2.0 < |η| < 2.4
0.025 × 0.1
2.4 < |η| < 2.5
0.1 × 0.1
2.5 < |η| < 3.2
0.025 × 0.025|η| < 1.40 0.050 × 0.025
1.375 < |η| < 1.425
0.075 × 0.025 1.40 < |η| < 1.475 0.025 × 0.025
1.425 < |η| < 2.5
0.1 × 0.1
2.5 < |η| < 3.2
0.050 × 0.025|η| < 1.35 0.050 × 0.025
1.5 < |η| < 2.5
number of readout channels
7808
1536 (both sides)
10176062208 (both sides)
LAr hadronic endcap (HEC)
1.5 < |η| < 3.2
4
0.1 × 0.1
1.5 < |η| < 2.5
0.2 × 0.2
2.5 < |η| < 3.2
5632 (both sides)
LAr forward calorimeter (FCal)
3.1 < |η| < 4.9
3
FCal1: 3.0 × 2.6
3.15 < |η| < 4.30
FCal1: ∼ 4 times finer
3.10 < |η| < 3.15
4.30 < |η| < 4.83
FCal2: 3.3 × 4.2
3.24 < |η| < 4.50
FCal2: ∼ 4 times finer
3.20 < |η| < 3.24
4.50 < |η| < 4.81
FCal3: 5.4 × 4.7
3.32 < |η| < 4.60
FCal3: ∼ 4 times finer
3.29 < |η| < 3.32
4.60 < |η| < 4.75
3524 (both sides)
Scintillator tile calorimeter
BarrelExtended barrel|η| < 1.0
0.8 < |η| < 1.7
3
3
0.1 × 0.1
0.1 × 0.1
0.2 × 0.1
0.2 × 0.1
57604092 (both sides)

Table 4.1: Coverage in η, granularity and segmentation in depth of the ATLAS calorimeters[72].

The ATLAS Detector

Interaction lengths

50

20
18
16
14
12

HEC3

10
Tile3

HEC2

6 Tile2

HEC1

8

4 Tile1
0
0

0.5

1

1.5

FCal2

HEC0

EM calo

2

FCal3

FCal1
2

2.5

3

3.5

4
4.5
5
Pseudorapidity

Figure 4.13: Cumulative amount of material in units of λ (interaction length) as a function of|η| in front of and in the EM calorimeters, in each hadronic layer, the total amount at the endof the active calorimetry and the total amount of material in front of the first active layer of themuon spectrometer.

4.3.1

LAr Electromagnetic Calorimeter

The EM calorimeter is divided into a barrel part (|η| < 1.475) and two endcap parts (1.375 <|η| < 3.2) each is housed in its own cryostat. The barrel calorimeter consists of two identical
half-barrels which are separated by a small gap (4 mm) at z = 0. Each endcap calorimeterconsists of two coaxial wheels namely an outer wheel (1.375 < |η| < 2.5) and an inner wheel(2.5 < η < 3.2).
Both the barrel and the endcap calorimeters are sampling calorimeters which use accordionshaped lead as absorber and liquid argon as active material. Its accordion geometry provides
a complete φ coverage without azimuthal crack. The ionization charge is collected by copper
clad kapton electrodes which also have accordion-shape. The lead plates in the barrel is 1.53
mm thick in |η| < 0.8 and 1.13 mm thick in |η| > 0.8. In the endcap calorimeters, the plates
is 1.7 mm thick in |η| < 2.5 and of 2.2 mm thick in |η| > 2.5. These optimization are done toimprove the performance in energy resolution.
Figure 4.14 shows a schematic of a barrel EM calorimeter module. A detailed summary of
the granularity of the EM calorimeter is given in Table 4.1 and also in Figure 4.15. Over thefiducial coverage of the inner detector (|η| < 2.5), which is used for precision measurements ofelectron and photon, the EM calorimeters are segmented into three sections in depth. As can beseen in Figure 4.14, the first layer is finely segmented along η. This leads√ to a fine resolution on
the polar direction of a EM shower of approximately ∆θ = 50 mrad/ E (GeV). The remaining
region is segmented into two sections in depth and has a coarser lateral granularity.

4.3 Calorimetry

51
Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Towe∆η = 0 r
.1

2X0

47

0m

m

η=0

16X0
TriggeTow r∆ϕ = 0er
.0982

m

m

4.3X0

15

00

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

Square cells in
Layer 2∆ϕ = 0.0245

ϕ∆η = 0.025
m/8 =4∆η = 0 .69 mm.0031
Strip cells in Layer 1

37.5m

η

Figure 4.14: Sketch of a barrel LAr Calorimeter module.

Figure 4.15: The layout of the signal layers in the EM calorimeters in r − z plane. The figures
on top are for the barrel and the extended endcap. The figure on bottom-left is for the endcap
inner and bottom-right is for the endcap outer wheels.

52

The ATLAS Detector

4.3.2

Hadronic Calorimeters

Scintillator Tile Barrel Calorimeter
The hadronic calorimeter in the barrel region is placed directly outside the EM calorimeterenvelope. The barrel hadronic calorimeter covers |η| < 1.0 and the extended barrel hadronic
calorimeter covers 0.8 < |η| < 1.7.
Figure 4.16 shows the coverage in η and radial segmentation of the barrel and extended
barrel hadronic calorimeters which extends from an inner radius of 2280 mm to an outer radiusof 3865 mm. Both calorimeters are segmented in depth into three layers, approximately 1.5,
4.1 and 1.8 interaction lengths (λ) thick for the barrel and 1.5, 2.6 and 3.3 λ thick for extended
barrel. Azimuthally, both calorimeters are divided into 64 modules.
3865 mm

η=0,0

0,1

0,2

0,4

0,3

0,6

0,5

0,8

0,7

1,0

0,9

1,1

1,2
1,3

D0

D1

D3

D2

D4
D6

D5
BC1 BC2 BC3

BC4

BC5

BC6

BC7

BC8

1,4

C10
B12

B11
B9

E1

A10

E2

B15

B14

B13

1,5

1,6

A1

2280 mm
0

A2 A3
500

~

A4

A5
1000

A6

A7

A8

1500 mm

A9

A12

A13

A14

A15

A16

E3

E4

beam axis

Figure 4.16: Scintillator tile calorimeter segmentation in the radial direction.
Figure 4.17 shows a schematic view of a scintillator tile calorimeter module. The basic
components of the scintillator tile calorimeter are plastic scintillator tile with thickness of 3 mm
and steel absorbers. The shape of each component varies depending on its location. The steel
absorber structure is made of 5 mm thick master plates and 4 mm thick spacer plates. The spacer
plates are glued on the master plate in a staggering fashion to form pockets for plastic scintillator
tiles. The scintillation photons are collected by wave length shifting fiber then transported toand read out by photomultiplier tubes. The readout cells are built by grouping these fibers.

4.3 Calorimetry

53

Photomultiplier

Wavelength-shifting fibre
Scintillator

Steel

Sourcetubes

Figure 4.17: A schematic view of a scintillator tile calorimeter module.

54

The ATLAS Detector

LAr Hadronic Endcap Calorimeter (HEC)The Hadronic Endcap Calorimeter (HEC) consists of two wheels on each endcap covering the
1.5 < |η| < 3.2 region. The HEC is located directly behind the EMEC sharing the same cryostat.
Figure 4.18 shows the layout of the calorimeters in the endcap and forward region. The figure
also includes the FCals.

Figure 4.18: The layout of the calorimeters in the endcap and forward region. All the calorimeters are housed in the same cryostat.
Each HEC wheel is built from 32 identical wedge-shaped modules and each wheel is divided
into two segments in depth (HEC1 and HEC2) as depicted in Figure 4.19. The inner radius of
HEC1 is 372 mm and of HEC2 is 475 mm.
The HEC is a copper - LAr sampling calorimeter with a flat-plate design. Figure 4.20 (a)shows a schematic view of a HEC1 module. The HEC1 (HEC2) consists of 24 (16) copper
plates with thickness of 25 (50) mm. 8.5 mm thick readout gaps are located to house LAr as
active material and electrodes between copper plates. Figure 4.20 (b) shows the structure of a
HEC readout gap. The electrodes are made from carbon loaded kapton.

4.3 Calorimetry

55

Figure 4.19: A schematic view of the HEC segmentation (Dimensions are in mm).

(a)
(b)

Figure 4.20: (a) A schematic view of a HEC1 module. (b) A schematic view of the arrangementof the HEC readout structure.

56

The ATLAS Detector

LAr Forward Calorimeter (FCal)
The Forward Calorimeter (FCal), which covers 3.1 < |η| < 4.9, is integrated into the endcap
cryostats to ensure uniformity of the calorimetric coverage as depicted in Figure 4.18. The FCalon each side is divided into three 45 cm thick modules namely FCal1 for EM measurements andFCal2 and FCal3 for hadronic measurements.
To achieve a tolerance against the high radiation dose, the FCal deploys a design withvery small LAr gaps which is obtained by using an electrode structure of small diameter rods
centered in tubes which are oriented parallel to the beam direction. Figure 4.21 (a) shows aschematic view of an electrode of FCal1, which uses copper as the electrode material, in whicha rad-hard plastic fiber aligned a rod at the center of the tube. Figure 4.21 (b) shows the layoutof the electrodes of FCal1 in which many holes are drilled in copper plates.
FCal2 and FCal3 have the similar structure but tungsten is adopted as the materials forelectrodes and main absorber material to provide containment and minimize the lateral spreadof hadronic showers.

(a)
(b)

Figure 4.21: (a) A schematic view of a FCal1 copper electrode wound by a rad-hard plastic
fiber. (b) The layout of the electrodes of FCal1. RM represents the Moliere radius.

4.4 Muon Spectrometer

57

4.4 Muon SpectrometerR

MDT chambers

12 m
Resistive plate chambers
10
Barrel toroid coil
8

Thin gapchambers

64End-cap
toroid2
Radiation shield

Cathode strip
chambers
0

z

20

18

16

14

12

10

8

6

4

2m

Figure 4.22: A schematic R-Z view of the ATLAS muon spectrometer.
The muon spectrometer [76] is situated at the outermost part of the ATLAS detector. Figure
4.22 shows the cross section in the R - Z plane. The muon spectrometer consists of following
four independent detectors.
1. Monitored Drift Tubes (MDT: |η| < 2.7)
2. Cathode Strip Chambers (CSC: 2.0 < |η| < 2.7, inner station only)
3. Thin Gap Chambers (TGC: 1.05 < |η| < 2.7, |η| < 2.4 for triggering)
4. Resistive Plate Chambers (RPC: |η| < 1.05)
The MDT and the CSC reconstruct a trajectory of a muon for a precision transverse momentum
measurement, whereas the TGC and RPC provide muon triggers with correct bunch crossing
identification. Since precision tracking requires wide time window of about 700 µs, the independent trigger detectors are deployed. The major performance goals of the muon spectrometerare summarized as follows.
• To provide efficient muon identification and transverse momentum measurement for themuons with pT of up to 1 TeV in |η| < 2.7 with a resolution of about up to 10 %.
• To provide muon trigger in |η| < 2.4 with correct bunch crossing identification.

58

The ATLAS Detector

12
11
10
9
8

Contribution to resolution (%)

Contribution to resolution (%)

The momentum measurement in the muon spectrometer is based on the detection of thedeflection of muons in the magnetic field provided by the air-core toroid magnets. The bending
power distribution of the magnets is shown in Figure 4.4.
Figure 4.23 shows a breakdown of the contributions for the calculated muon pT resolution
as a function of pT . At low momentum, resolutions are dominated by fluctuations in energy
loss of muons in front of the muon spectrometer. Multiple coulomb scattering in the muon
spectrometer plays an important role in the intermediate range. At pT above 300 GeV, single hit
resolution, insufficient alignment and calibration dominates the pT resolution.
Tube resolution and autocalibration
Chamber alignment
Multiple scattering
Energy loss fluctuations
Total|η| < 1.5

7
6
5
4
3

12

10
9
8

|η| > 1.5

7
6
5
4
3

2

2

1

1

0

Tube resolution and autocalibration
Chamber alignment
Multiple scattering
Energy loss fluctuations
Total

11

0
10

10

2

10

3

10

10

pT (GeV)
(a)

2

10

3

pT (GeV)(b)

Figure 4.23: A calculated typical momentum resolution for muons reconstructed in the muon
spectrometer. The alignment curve is for an uncertainty of 30 µm in the chamber positions. (a)is for |η| < 1.5 and (b) is for |η| > 1.5.
Trigger detectors are required to have timing accuracy better than 25 ns for the correct
bunch crossing identification. Also the rough position resolution about 10 mm is required since
tracking detectors are dedicated to the measurement in bending (η) coordinate and position in φis provided by trigger detectors in the muon reconstruction algorithms.
The detailed descriptions about muon reconstruction and trigger are presented in the dedicated chapters. The overall layout of the muon spectrometer and the specifications for eachdetector technology are described in the remaining part of this section.

4.4.1

The Detector Layout

A 3-D view of the muon spectrometer is shown in Figure 4.24 as well as the toroid magnets
and other detector structures. In the barrel, the muon chambers are arranged in three concentric
cylinders around the beam axis. In the endcap, chambers form three disks on each side of thedetector, concentric around the beam axis (see also Figure 4.22). Each cylinder and disk iscalled inner, middle and outer station respectively from inside to outside.

4.4 Muon Spectrometer

59

The chambers are placed such that particles originate at the IP traverse three chamber stations. The position of these stations has been chosen to maximize the detector acceptance andto take optimum advantage of the magnetic field configuration.
Figure 4.25 shows the cross section in the R - φ plane. Both the barrel and the endcap toroid
magnets have eight coils and are rotated in the azimuthal direction by 22.5◦ with respect to eachother. There is a 16 fold segmented structure in azimuthal reflecting the magnet configuration.
The muon chambers are arranged in large and small sectors. The large sectors cover the region
between the barrel toroid coils whereas small sectors covers the azimuthal range of the barrel
toroid coils. There are overlap regions at the boundaries between large and small sectors tomaximize the acceptance.

Figure 4.24: 3-D view of the ATLAS detector in the underground hall. The muon chambers(partly removed to show the inner structures) are arranged in three layers around the innerdetector and the calorimeter in the space between 5 and 10 m in radius and 7 and 23 m distancefrom the interaction point.

60

The ATLAS Detector

Small Sector

Large Sector
Resistive plate chambers

MDT chambers
Barrel toroidcoils
End-cap
toroidInner detector

Calorimeters

Figure 4.25: A schematic R - φ view of the ATLAS muon spectrometer.

4.4 Muon Spectrometer

61

4.4.2 Monitored Drift Tubes (MDT)The MDT is the main detector in precision transverse momentum measurement of muons. The
MDT covers the entire muon spectrometer acceptance except for the inner station in the forward
region (|η| > 2.0).
The basic element of the MDT is a pressurized aluminium drift tube with a diameter of
29.970 mm, operating with Ar (97%) / CO2 (3%) gas at 3 bar. The wall thickness of the tube is
0.4 mm. The electrons resulting from ionization are collected at the central tungsten-rhenium
wire with a diameter of 50 µm at a potential of 3080 V. The achieved gas gain is about 2
×104 . The wire is held in position at the tube ends by a cylindrical end-plug which guarantees
the concentricity of the wire with respect to the tube with an accuracy of σ < 10 µm. The
maximum drift time is about 700 ns and average spatial resolution per tube is about 80 µm. The
main parameters of the MDT tube are summarized in Table 4.2.
parameter
designtube materialAlouter tube diameter
29.970 mm
tube wall thickness
0.4 mmwire material
gold-plated W / Re (97 / 3)wire diameter
50 µm
gas mixture
Ar : CO2 = 97 : 3
gas pressure
3.0 bar (absolute)gas gain
2 ×104operating voltage
3080 Vmaximum drift time
∼ 700 µm
average resolution per tube
∼ 80 µm
Table 4.2: The MDT tube main parameters
The MDT tubes are packed together and form a chamber. All regular MDT chambers consistof two multi-layers which consists of three (middle, outer) or four (inner) tube layers. Figure
4.26 shows the structure of a barrel chamber. The shapes and dimensions of chambers werechosen to optimize solid angle coverage.
To achieve the required performance, the position and deformation of the chambers need
to be known to a precision of 30 µm. The MDT deploys a system of optical alignment sensor,
RASNIK [77], which consists of three active elements namely LED, lens and CCD camera. Its
intrinsic precision is about 1 µm. Figure 4.27 shows an endcap MDT chamber equipped withthe optical alignment system.

62

The ATLAS Detector

Cross plate
Multilayer
In-plane alignment
Longitudinal beam
Figure 4.26: A schematic view of a barrel MDT chamber.

RASNIK
Lens mountMultilayer 2

Longitudinal
beams

RASNIK CCDs
Multilayer 1

Cross plates

Figure 4.27: A schematic view of an endcap MDT chamber with the optical alignment system.

4.4 Muon Spectrometer

63

4.4.3 Cathode Strip Chambers (CSC)
In the region |η| > 2.0, the MDT inner station is replaced by the CSC which combines highspatial, time and double track resolution with high-rate capability and low neutron sensitivity.
Due to the small electron drift time of less than 40 ns and the high spatial resolution, operationis considered safe up to counting rates of about 1k Hz/cm2 , which is sufficient for muon tracking
in up to |η| = 2.7 at designed luminosity of the LHC. As in the case of the MDT, the CSC issegmented into large and small chambers in azimuthal. The whole CSC system consists of two
disks with eight small chambers and eight large chambers. The CSC disks are installed withinclining angle of 11.59◦ (see Figure 4.28 (a)). Each chamber contains four cathode strip planes
resulting in four independent η − φ measurements.
The CSC is multi-wire proportional chambers with the wires oriented in the radial direction. Figure 4.28 (b) shows a cutout view of a single CSC layer. Each chamber contains two
orthogonal cathode planes one of which is perpendicular to the wires and the other parallel tothe wires. The anode wire has a diameter of 30 µm and are made of gold-plated tungsten with
3% rhenium. Ar (80%) / CO2 (20%) gas is used at the high voltage of 1900 V which leads to 6
×104 gain. The major CSC parameters are summarized in Table 4.3.

Nomex honeycomb
Wires
Strips

0.5 mm G10
laminates

RohacellGas inlet/
outletAnode read-out
HV capacitor
Conductive epoxy
Wire fixation bar

Cathode read-out
Spacer bar

Sealing rubber

(a)

Epoxy

(b)

Figure 4.28: (a) The CSCs mounted on a rigid wheel inclined by 11.59◦ . (b) A cutout view ofa single CSC layer.

The position of the track is obtained by interpolation between the charges induced on neighboring cathode strip. In the bending direction, with a readout pitch of 5.31 mm and 5.56 mm forthe large and small chambers respectively, the CSC reaches a resolution of 60 µm per cathodeplane. As described above, the CSC preforms measurement in φ-coordinate with resolution of
about 5 mm as well.

64

The ATLAS Detector

parameter
wire material
anode wire diametergas mixturegas gain
operating voltage
η resolution per cathode plane
φ resolution per cathode plane
total ionization for a nominal track

designgold-plated W / Re (97 / 3)
30 µm
Ar : CO2 = 80 : 20
6 ×1041900 V∼ 60 µm∼ 5 mm90 ion pairs

Table 4.3: The CSC chamber main parameters

4.4.4

Thin Gap Chambers (TGC)

The TGC provides muon triggers in the endcap region (|η| > 1.05) of the muon spectrometer.
The TGC is a multi-wire proportional chamber which is designed to operate in the saturated(limited proportional) mode. A schematic structure of a TGC chamber is shown in Figure 4.29(a) with a typical size of 2 × 2 m2 . Actual shapes of TGCs depend on the geometry. The TGC
deploys two dimensional readout which consists of wire groups (η - coordinate) and readout
strips (φ - coordinate). The number of wires in a wire group varies from 4 to 20 (7.2 to 36 mm)
and width of strip channels are about 30 to 50 mm.
Copper Strip

Pick-up strip

2.8mm

Graphite layer

Carbon
FR4
1.8mm

+HV
1 2m

Out)
Wire
ASD(

+HV

1.8 mm

50 µm wire

1.4 mmR

1

2m

ASD(Strip Out)

1.6 mm G-10

(b)

(a)

Figure 4.29: (a) A schematic illustration of a TGC chamber. (b) TGC structure showing anodewires, graphite cathodes, G-10 layers, and a read-out strip orthogonal to the wire.

4.4 Muon Spectrometer

65

The TGC uses a very strong quenching gas mixture of CO2 (55 %) / n-C5 H12 (45 %) whichallows a stable operation in the saturated mode. There are advantages operating in the saturated
mode such as,• high single hit efficiency• small parallax – signals have rather small dependence of the incident angle of muonsMoreover, the highly quenching nature of the n-C5 H12 leads to a no streamer operation even in
the case of the slow neutron interactions.
A significant feature of the TGC is its narrow anode-to-cathode distance (Figure 4.29 (b)).
The anode-to-cathode distance is designed as 1.4 mm and anode-to-anode distance is 1.8 mm.
Note that anode-to-anode distance is also short. This small distance between anodes and strong
electric field reduce the drift component of ionization clusters hence leading to very good timing
resolution required for the accurate bunch crossing identification. The major parameters of TGC
are summarized in Table 4.4.
parametergas gap
wire pitch
anode-to-cathode distancewire material
wire diametergas mixturegas gainwire potential
intrinsic time jitterφ resolution per layer

design2.8 ± 0.1 mm
1.8 ± 0.05 mm
1.4 ± 0.05 mm
gold - plated W / Re (97 / 3)
50 µm
CO2 : n-C5 H12 = 55 : 45
2 ×1052900 ± 100 V
4 ns
3 – 7 mmTable 4.4: The TGC chamber main parameters
As shown in Figure 4.22, the TGC has no outer station and inner station is not used in the
online-trigger, thus whole trigger functionalities are provided by the middle station. The TGC
middle station consists of two doublet and one triplet chambers. A doublet chamber consists of
two wire and two strip readout planes whereas a triplet chamber has three wire and only two
strip readout planes. The cross section of the TGC triplet and doublet is shown in Figure 4.30.
Additional wire plane is to cope with false coincidences from background hits.
Figure 4.31 shows the measured time jitter of the TGC for the 3 GeV π− beam under theseveral incident angle conditions. In the actual experiment, charged particle incident angle for
TGC varies from 10◦ to 45◦ . Thus the intrinsic time resolution is accurate enough for the correct
bunch crossing identification.

66

The ATLAS Detector

1000

0˚

800

500

400

5˚

400

500

600

300

300

400

200

200

200

100

100

600
500

15˚

400

120

700
600
500

200
100
120

140
160
Arrival time (ns)

100
0

0

140
160
Arrival time (ns)

30˚

400
300
200

300

0

0

140
160
Arrival time (ns)

Hits

120

Hits

0
Hits

Hits

Hits

Hits

Figure 4.30: The cross section of five detector layers of the middle station of the TGC.

120

140
160
Arrival time (ns)

700
600
500
400
300
200
100
0

10˚

120

140
160
Arrival time (ns)

45˚

120

140
160
Arrival time (ns)Figure 4.31: Time jitter of the TGC chamber for the various incident angles.

4.4 Muon Spectrometer

67

4.4.5 Resistive Plate Chambers (RPC)
The RPC provides muon triggers in the barrel region (|η| < 1.05) of the muon spectrometer.
The RPC is a gaseous parallel electrode-plate (i.e. no wire) detector. Two resistive plates,
made of phenolic-melaminic plastic laminate, are kept parallel to each other at a distance of 2
mm by insulating spacers. The cross-section of an RPC is depicted in Figure 4.32. The electricfield between the plates of about 4.9 kV/mm allows avalanches to form along the ionizing tracks
towards the anode. The signal is read out via capacitive coupling to metallic strips, which aremounted on the outer faces of the resistive plates. The gas used is a mixture of C2 H2 F4 (94.7%) / Iso-C4 H10 (5 %) / SF6 (0.3 %). At the nominal operating voltage of 9.8 kV, a signal with awidth of 5 ns is generated by the track with a streamer probability of less than 1 %. The position
resolution in φ coordinate is about 10 mm, which is used in the muon reconstruction algorithm.
The major parameters of the RPC are summarized in Table 4.5.

Figure 4.32: The cross section of a RPC chamber.

parameter
designgas gap
2.00 ± 0.02 mm
gas mixture
C2 H2 F4 : Iso-C4 H10 : SF6 = 94.7 : 5 : 0.3
operating voltage
9.80 ± 0.15 kV
Bakelite volume resistivity(1 – 5) ×1010 Ω
intrinsic time jitter< 1.5 ns
time jitter inclu. propagation time< 10 ns
φ resolution per layer
10 mm
Table 4.5: The RPC chamber main parameters

68

The ATLAS Detector

4.5

Forward Detectors

Besides the main ATLAS detectors described in the previous sections, several detectors areplaced in the very forward region. Among them, overviews of the Luminosity Measurement
Using Cherenkov Integration Detector (LUCID), Absolute Luminosity For ATLAS (ALFA)and Minimum Bias Trigger Scintillator (MBTS) are presented in this section.

4.5.1

Luminosity Measurement Using Cherenkov Integrating Detector (LUCID)

(a)

(b)

Figure 4.33: (a) The configuration of the LUCID in a side of the ATLAS detector around thebeam-pipe. (b) A schematic view of a LUCID detector and its readout structure.
The main functionality of the LUCID is to detect inelastic pp scattering in order to bothmeasure the integrated luminosity and to provide online monitoring of the instantaneous luminosity. In principle, the number of inelastic interactions is proportional to the number ofparticles detected in the LUCID. Thus the counting rate of the LUCID is used for luminosity
determination once a scale factor which translates the counting rate to luminosity is obtained.
The two LUCID detectors are installed one in each side of the ATLAS at a distance ofapproximately ±17 m from the IP. The LUCID is placed at a radial distance of approximately
10 cm from the beam-line (|η| ∼ 5.8). A schematic view of the LUCID structure is depicted in
Figure 4.33 (a). The LUCID consists of twenty aluminium tubes surrounding the beam-pipe.
Each tube has 1.5 m length, 15 mm diameter and points towards the IP. The tubes are filledwith C4 F10 gas at a constant pressure of 1.2 – 1.4 bar, providing a Cherenkov threshold of 2.8
GeV for pions and 10 MeV for electrons. The following advantages are obtained by counting
Cherenkov photons by the LUCID.
• Since Cherenkov radiations have no decay time, the LUCID has enough time resolution
for a bunch-by-bunch event counting

4.5 Forward Detectors

69• Since there is no Landau tail in the Cherenkov photon measurement, it is possible todetermine the number of particles entered a tube by pulse-height analyses• Since the tubes are pointing to the IP, the background of low energy secondary particles
can be rejected
The Cherenkov photons are readout by PMTs and FPGAs housed in the front-end electronics calculate the luminosity for each bunch crossing. Since the LUCID system is decoupledfrom the ATLAS trigger and DAQ system, it can provide independent LUCID trigger.

4.5.2 Absolute Luminosity For ATLAS (ALFA)

Front-end boards
Multi-anodephotomultiplierFibre connectors

Upper and lower
Roman pots

10 x u-v fibres

Beam axis

Figure 4.34: A schematic view of the ALFA detector in the Roman Pot.
The absolute luminosities at hadron colliders has been determined via elastic scattering at
small angles. The optical theorem connects the elastic scattering amplitude in the forward
direction to the total cross section. In the ATLAS experiment, the ALFA is used for absolute
luminosity measurements. A schematic view of the ALFA in a Roman Pot is depicted in Figure
4.34. The ALFA provides an absolute luminosity calibration through the measurement of elastic
proton-proton scattering at in the Coulomb-Nuclear Interference (CNI) region as in Eq.(4.2).
 4πα2 α · ρ · σtot · e −B·|t|2
σ2tot · (1 + ρ2 ) · e−B·|t| dN≈ L ·  2 −
+
(4.2)

dt
|t|
|t|
16π

70

The ATLAS Detector

where L is the absolute luminosity and ρ represents the ratio of real to imaginary part of thescattering amplitude, σtot is the total cross-section of pp → X and B is the nuclear slope. The
parameters are extracted by a fit with these four free parameters. t is the momentum transfer
defined as −t = (psinθ)2 ∼ (pθ)2 with p the beam momentum and θ the scattering angle of a
proton. A simulated dN/dt spectrum is shown in Figure 4.35 [78].
x 10 5dN/d(-t)

6000

5000

reconstructed spectrum

4000

L-fit

3000

2000

1000

0
10

-3

10

-2

-t

10

-1

Figure 4.35: A simulated and fitted dN/dt spectrum by PYTHIA.
The ALFA detector is located in Roman Pots located at ±240 m from the interaction point.
On each side there will be two Roman pot stations separated by 4 m. Since the minimum t value
in interest is very small (∼ 5 × 10−4 GeV2 ), The ALFA should be able to count the scattering
rate at very small angle of about 3 µrad. Thus the ATLAS Roman pots have been designed tomove the detectors as close as 1 mm to the beam from above and below.
The ALFA detector consists of ten double-sided scintillating fiber trackers each with 64
square fibers with width of 0.5 mm arranged in stereo u - ν geometry on both sides. The
staggered configuration of the ten trackers leads to a effective spacial resolution of 14.4 µm.
The primary purpose of the ALFA is to measure the absolute luminosity to the precision of ∼3%.
Transportation of the Absolute Calibration to the Nominal Luminosity
Since the extremely small scattering angle is to be measured by the ALFA, the following special
beam condition is needed for absolute luminosity calibrations [79].
• To minimize the beam divergence at the IP, the high beta optics is needed (β∗ = 2625 m)• To have zero beam crossing angle at the IP, the number of bunch should be small

4.5 Forward Detectors

71

These requirements lead the luminosity for the beam condition for the absolute calibration toabout 1027 cm−2 s−1 . The luminosity monitor of the LUCID is also calibrated at this luminosity(by counting inelastic interactions) thus the calibration has to be carried over seven orders ofmagnitude to the nominal luminosity of 1034 cm−2 s−1 . This is done by simply assuming thatthe number of inelastic interactions is proportional to the number of particles detected in the
LUCID at any luminosity value. This wide measurement range is achieved thanks to the goodtime resolution, particle counting capability and background rejection power of the LUCID .

4.5.3 Minimum Bias Trigger Scintillator (MBTS)
The main functionality of the MBTS is to provide the minimum bias trigger within 2.09 < |η| <3.84. The MBTS consists of two sets of scintillation counters located at |z| = 3560 mm andsegmented into two sections in η (divided at |η| = 2.82) and eight sections in φ. Figure 4.36 is a
picture of the MBTS mounted on the endcap calorimeter cryostat (The white disk surrounding
the beam pipe is the MBTS).
The scintillation photons are read out by PMTs. The signals are sent to Central Trigger Processor (see section 4.6.1) after discriminated in the front-end electronics. The Central Trigger
Processor calculates the multiplicity of hits then issues the MBTS trigger. The lowest threshold
MBTS trigger requires only one hit in either side of the MBTS.

Figure 4.36: A picture of the MBTS mounted on endcap calorimeter cryostat.

72

4.6

The ATLAS Detector

Trigger System

The ATLAS trigger system consists of three levels of event selection, namely Level-1 (L1),
Level-2 (L2) and Event Filter (EF) [80, 81]. The L2 – EF chain is also referred to as Higher
Level Trigger (HLT) as a whole. L1 trigger decisions are made in the custom-made front-end
electronics whereas HLT decisions are made in the dedicated computer farm. A schematic viewof the ATLAS trigger system is depicted at Figure 4.37.
I nter action r ate~1 G H z
B unch cr ossing
r ate 40 M H z
LEVEL 1T R IGGE R LV L 1< 75 (100) kH z
L 1A

latencyCAL O

M UON T R A C K I NG

Pipelinememor ies

R oI sR oI B

R oI B uilder

2.5 s

Der andomizer s

R OD

R OD

R OD

R eadout dr iver s (R ODs)
R ead Out L inks (R OL s)

L V L 2 Super visor

LEVEL 2T R IGGE R

L 2SV

L 2Ps

~ 3.5 k H z

R OB

R OB

R OB

L V L 2 & E vent B uilder
Networ ks

R ead Out Systems(R OSs)

40ms

DF M
Data F low M anager

L V L 2 Pr ocessor s

SF I sSub F ar m I nput

SF Os

Sub F ar m Output

few sec

E V E NT F I L T E R~ 200 H z

M ass Str age Data r ecor dingFigure 4.37: Schematic vies of the ATLAS TDAQ system.
The trigger system is responsible for reducing event rate from 1 GHz, which is expected at
the design luminosity of the LHC, to recordable rate of about 200 Hz within allowed latency offew seconds.
The trigger system is designed to be sensitive for one or combinations of the following
physics objects – muon, electron / photon, tau, jets (including b-tagged jets), missing ET (ETmiss )and ET sums. The adequate thresholds are set for each object in terms of pT and multiplicity.

4.6 Trigger System

73

4.6.1 Level-1 Trigger
The L1 trigger is performed based on the information of all calorimeter (LAr, Tile, HEC, FCal)
and the muon spectrometer information. The overall L1 accept decision (L1A) is made by theCentral Trigger Processor (CTP), which combined the information for different object types.
Trigger menus can be programmed in CTP with up to 256 distinct items, each item being a
combination of requirements on the input data. A diagram of the L1 trigger is shown in Figure
4.38.
Calorimeters

Muon detectors

L1 trigger
Calorimeter triggers

EM



Jet

Muon trigger

Emiss
T

∝

ET

Central trigger
processor

Timing, trigger andcontrol distribution

Detector front-ends

Regionsof-Interest

L2 trigger

DAQ

Figure 4.38: Block diagram of the L1 trigger.
The major steps included in the L1 trigger decision are summarized below.
• The number of objects which passed detector specific L1 trigger algorithms for all thresholds are passed from both the calorimeter and the muon spectrometer to the CTP.
• CTP integrates the information and check if any items in the trigger menu are satisfied ornot. If one or more items are satisfied, the CTP provides L1A signal to all detectors.
• Upon receiving an L1A, all detectors send the information for all channels retained intheir pipeline memories to the buffer storage for the HLT. The calorimeter and the muon
spectrometer also send the information about η−φ locations of triggered objects, which iscalled Region of Interest (RoI). The RoI information is used as seeds in HLT algorithms.
The L1 trigger aims to identify high-pT muons, electrons / photons, jets, and tau leptons decaying into hadrons, as well as events with large ETmiss , large total transverse energy (ET sum)

74

The ATLAS Detector

and scalar sum of jet transverse energy. An adequate trigger menu reflecting the situation of theexperiments is used at the CTP stage.
At the L1 output, the 1 GHz event rate is reduced down to about 75 kHz within the L1
decision time of 2.5 µs with the unambiguous identification of the bunch crossing.

4.6.2

Level-2 Trigger

The L2 selection is seeded by the RoI information received from the L1 and provides a refined
analysis of the L1 features based on the detector data with full granularity within RoIs. Also
additional information, which is not available in L1, such as reconstructed track in the ID can beused in the L2 decision. The information from individual detectors can be matched to provide
additional rejection and higher purity. For example, a muon reconstructed in the muon spectrometer can be matched with calorimeter information to utilize isolation information or with
ID track information to reduce backgrounds.
The L2 trigger reduces the event rate below 3.5 kHz within an event processing time of
approximately 40 ms in average.

4.6.3

Event Filter

The EF performs the final online selection on the events which passed L2 selections. As in the
L2, the EF works in a seeded mode in nominal operation (for example, there is alternative modein muon stream for trigger commissioning) with complete data for a given event. Unlike L2,
the EF typically uses the algorithms based on the offline reconstruction.
The EF reduces the event rate down to about 200 Hz with an average processing time oforder of few seconds.

4.7 Analysis Platform and Monte Carlo Samples

75

4.7 Analysis Platform and Monte Carlo Samples
Most of the physics analyses in the ATLAS experiment are performed on the C++ based software framework called ATHENA [82]. In the ATHENA, both simulated and experimental data
are processed through the same ATLAS event reconstruction packages to ensure the consistency
between the Monte Carlo prediction and experimental results in the analyses. In this section, an
overview of the ATHENA framework, with a special emphasis on its data preparation structure,is given.

4.7.1 The Data Preparation Chain in the ATHENA Framework
Shown in Figure 4.39 is a schema of the simulated and experimental data preparation in the
ATHENA framework, which consists of following four major steps.
1. Event generation and immediate decays
2. Simulation of the detector and physics interactions
3. Digitization of the energy deposited in the detectors
4. Event reconstruction with dedicated algorithms to each physics object
Overviews for each step are given in the remaining part of this section.
Event Generation
The most of event generation process in the ATHENA framework is performed by external
event generators such as PYTHIA [83] and POWHEG [84]. Also, the ATHENA uses the Les
Houches Accord PDF Interface (LHAPDF [85]) library with CTEQ PDFs [86] as a default
one. Particles with cτ < 10 mm are decayed by the event generator and their interactions withmaterial or curving in the magnetic field in the ATLAS detector are ignored. The resulted event
information are stored in the format of HepMC event record [87].
Simulation
The standard simulation in the ATHENA relies on the GEANT4 [88] particle simulation kit
which provides models for physics and infrastructure for particle transportation. The geometry
description of the ATLAS detector is provided by the ATHENA side in the format which isdedicated for GEANT4. The energy deposited in the active volume of the detector are recorded
for the digitization stage. The ATLAS detector geometry used in the simulation is designed to
be built from databases containing the information of physical construction and experimental
condition to fairly reflect the situation of the experiment. The same geometry description is also
used in the digitization and event reconstruction stages.

76

The ATLAS Detector

Digitization
In the digitization stage, the information of the energy deposition is converted into the information of detector responses. The detector specific methods of conversion are deployed in thisstage. Typically a digit is produced when the voltage or current on a readout channel crosses acertain threshold within a time window.
Event Reconstruction
The physics object specific reconstruction algorithms, such as for muon, electron and ETmiss ,are deployed in this stage. Both simulated and experimental data can be treated coherently
onwards. The resulted physics object information, in two types of data format with different
level of elaborations, each is called Event Summary Data (ESD) or Analysis Object Data (AOD)
are used in the physics analyses.

Genera on

HepMC

Simula on

G4 Hits

Digi za on

G4 Digits

Reconstruc on

Real Data

ESD, AOD

Figure 4.39: A schematic view of the data preparation chain in the ATHENA.

4.7 Analysis Platform and Monte Carlo Samples

77

4.7.2 Monte Carlo Samples
Theoretical Prediction on the Cross Sections
The theoretical predictions on the W / Z-boson cross section is obtained from next-to-next-to
leading order calculation provided by FEWZ [89, 90] with the MSTW 08 NNLO [91] structure
function parametrization.
FEWZ calculates differential W / Z-boson cross sections. The spin correlation of leptons
in the final states are considered. The calculations are done fully exclusively in each LO, NLO
and NNLO level respectively. FEWZ supports variety of the PDF sets such as CTEQ and
MSTW. In the calculation , the renormalization (µR ) and factorization (µF ) scales are set asµR = µF = MW/Z , where MZ = 91.1876 GeV and MW = 80.403 GeV. The strong coupling
constant αS (MZ ) is dictated by the PDF set.
The MSTW PDF uses 2743 data sets obtained in the previous experiments. The x dependence of each flavor (quarks and gluon) is parametrized with 20 free parameters. Then the PDFs
are evolved using the DGLAP evolution equations toward the energy scale (Q2 ) in consideration. The resulted PDFs at Q2 = 10 and 104 GeV2 are shown in Figure 4.40 with 68 % C.L.
errors from error eigenvectors. For the tt¯ cross section, the top mass is assumed as mt = 172.5
GeV and the corresponding cross section is taken from Ref.[92]. For the QCD process, crosssections are obtained by scaling a leading order Monte Carlo result with a data driven scale
factor. All the cross section values (σ) used in this study are summarized in the third column inTable 4.6 multiplied by the branching ratio (BR) of the processes. The errors correspond to thesystematic uncertainties described hereunder.

1.2

xf(x,Q2)

xf(x,Q2)MSTW 2008 NNLO PDFs (68% C.L.)
Q2 = 10 GeV21

1.2

Q2 = 104 GeV2
1

g/10

g/10

0.8

0.8

u

0.6

0.4

0.6

b,b

0.4

d

0
10-4

s,s
s,s

10

-3

d

c,c

c,c
0.2

u

10-2

u

0.2

d

10-1

u

1

0
10-4

10

-3

10-2

x

Figure 4.40: The MSTW 2008 NNLO PDFs (68 % C.L.).

d

10-1

1

x

78

The ATLAS Detector

For the W / Z processes, the uncertainty of the next-to-next-to leading order calculation isestimated using the MSTW 08 NNLO PDF error eigenvectors at the 90 % C.L limit, variationsof α s in the range 0.1145 - 0.1176, and variations of the renormalization and factorization scales
as MW/Z /2 < µR,F < 2MW/Z by factors. The estimated overall uncertainty for the W / Z processes
are 5 %. For the tt¯ process, the uncertainty of 6 % is assumed. For the QCD scaling factor, theextraction method and uncertainties are described in section 11.4.1.
Monte Calro Sample Generation
Table 4.6 summarizes the generated data samples used in this study. These samples are used to
calculate acceptances and to model the properties of signal and backgrounds. Events are gen∗erated using the PYTHIA (POWHEG only for tt¯) generators with the MRST
√ LO [93] parton
distribution function. All signal and background samples are generated at s = 7 TeV and processed through the ATHENA data preparation chain described in section 4.7.1. The calculationin the PYTHIA is done in the leading order and the resulted cross section is not so reliable (Thereason why PYTHIA is used is for statistics). Thus, in this study, the cross sections for thegenerated samples are normalized by the NNLO cross sections or a data driven scale factor, as
mentioned above.
In the W → µν, Z → µµ, and di-jet samples, the effect of multiple interactions per bunch
crossing (pile-up) is modeled by overlaying simulated minimum bias events over the originalhard-scattering event. However this pile-up modeling is not so accurately. Thus an event-byevent weighting of the number of reconstructed vertices is performed as described in section
8.3.3.

Process
W → µν
W + → µ+ ν
W− →√
µ− ν
Z → µµ ( ŝ > 60 GeV)
W → τν →√ µνν
Z → ττ ( ŝ > 60 GeV)tt¯

Generator
P

di-jet (8 GeV/c single muon filter)P

P
P
P
PH

σ× BR (nb) Calculation order10.46 ± 0.52
NNLO
6.16 ± 0.31
4.30 ± 0.21
0.99 ± 0.05
NNLO
3.68 ± 0.18
NNLO
0.99 ± 0.05
NNLO
NNLO
 0.16 ± 0.011 µ = 0.538
10.6 ×106
LO

Table 4.6: Summary of the Monte Calro samples used in this study. The cross-sections are theones used to normalize number of events except for QCD di-jet samples. For QCD samples, adata driven scale factor is used for a normalization.

Chapter 5
The Muon Trigger at the ATLAS
Experiment
In accordance with the ATLAS trigger scheme, the ATLAS muon trigger consists of following
steps.
• The Level-1 muon trigger provided by the TGC and the RPC in |η| < 2.4• The Level-2 and the Event Filter using other muon spectrometer (MDT and CSC) information as well as the inner detector and the calorimeter information as an auxiliaryuse
In each step, trigger scheme is designed and optimized to select high-pT muons.
Description about general principle of the muon identification and transverse momentum
measurement is given in section 5.1. Then the successive sections are devoted to describe eachlevel of muon trigger – section 5.2 for the Level-1, section 5.3 for the Level-2 and section
5.4 for the Event Filter. Since only Level-1 trigger is used in the W / Z-boson cross sections
measurement, a strong emphasis is placed on it.

5.1 Muon Identification and Transverse Momentum Measurement
Muon is only particle which can penetrate thick dense matters like calorimeter. Most of heavy
particles decay even before they enter the calorimeter. The particles with long life time, suchas electron and light hadrons (π / K) loose all of their energy in the calorimeter. Hence theassumption that a track reconstructed in the muon spectrometer represents a muon trajectory
becomes true. In the first part of this section, a description about energy deposition of particles
in matter is given to illustrate the muon identification principle.
The transverse momentum measurement in the muon spectrometer is based on the detectionof the deflection of muons in a magnetic field. The second part of this section is devoted todescribe this principle of transverse momentum measurement of muons.

80

The Muon Trigger at the ATLAS Experiment

5.1.1

Energy Loss of Charged Particles in Matter

Ionization Energy Loss
Moderately relativistic charged particles (0.1 < βγ < 1000) other than electrons lose theirenergy in matter primarily by ionization and atomic excitation. The mean rate of energy loss in
the region is described by the Bethe-Bloch equation in Eq.(5.1).
Figure 5.1 shows the energy deposition of positive muons in copper. The unit of dE/dx is
MeVg−1 cm2 hence this distribution is also true for other materials. The region where BetheBloch approximation is valid is also indicated.

Stopping power [MeV cm2/g]

"
#
2 2 2
dE
δ(βγ)
2 Z 1 1 2me c β γ T max
2
−
= Kz
ln
−β −
.
(5.1)
dx
Aβ 2
I2
2
K = 4πNA re2 me c2
NA : Avogadro0 s number re : classical electron radius me : electron mass
Z : atomic number of the matter A : atomic mass of the absorberz : electric charge of the incident particle I : mean excitation energy
T max : the maximum kinetic energy imparted to a free electron in a single collisionµ+ on Cuµ−

10LindhardScharff

100

Bethe

Radiative

AndersonZiegler

Eµc
Minimum
ionization

NuclearlossesRadiative
lossesRadiative
effects
reach 1%

Without δ
1
0.001

0.01

0.1

1

10

0.1

1

10

100

1

[MeV/c]

βγ

100

1000

10 4

10 5

10 6

10

100

1

10

100

[GeV/c]Muon momentum[TeV/c]Figure 5.1: −dE/dx for positive muons in copper as a function of βγ (solid curve) [36].
The main features about βγ dependence of mean rate of energy loss are as follows.
1. In the region of 0.1 < βγ < 1, where classical electromagnetism is valid, the dE/dx is
proportional to 1/β2 .

5.1 Muon Identification and Transverse Momentum Measurement81

2. Around βγ = 3, the energy deposition minimizes. In practical cases, most relativistic
particles have mean energy deposition close to the minimum, and are said to be minimum
ionizing particles (MIPs). Most of particles arise from proton-proton collisions at the
LHC is MIPs.
3. In the region of 4 < βγ < 100, the electric field formed by the incident particle flattens
and extends due to the relativistic effect so that distant collision contribution increases asln (βγ). This effect is called relativistic rise.
4. After relativistic rise reaches its maximum around βγ = 100, dE/dx becomes constant.
This region is called Fermi Plateau.
The lower limit of the Bethe-Bloch region comes when the velocity of the incident particle
becomes comparable to that of electrons in atoms. The higher limit is at several hundred GeV
where muons become radiative and begin to lose its energy through bremsstrahlung.
As mentioned above, most of muons arising in the proton-proton collision in the LHC are
MIPs. Concerning the thickness of the ATLAS calorimeter, muons with energy above 3 ∼ 4
GeV can reach to the muon spectrometer.
The Energy Loss of High Energy Electrons – Electromagnetic Cascade

0.20

Positrons

1 Mb

0.15
Bremsstrahlung

0.10

Ionization

0.5

Møller (e −)Bhabha (e +)0.05

Cross section (barns / atom)

Electrons(cm2 g−1)− 1 dE (X 0−1)
E dx

1.0

(b) Lead (Z = 82)

Lead (Z = 82)

σRayleigh1 kb

σg.d.r.
1b0
1

Positronannihilation

10100
E (MeV)1000- experimental σtot

σp.e.

10 mb
10 eV

κe

σCompton

1 keV

κ nuc

1 MeV

1 GeV

100 GeV

Photon Energy

(a)

(b)

Figure 5.2: (a) Fractional energy loss per radiation length in lead as a function of electron or
positron energy (b) Photon total cross section in lead as a function of energy
The radiation length (X0 ) is defined as the average distance that an electron (positron) traverses in matter until it lost their energy down to 1/e, can be expressed as a material dependent
form
716A
(g/cm2 ).
(5.2)
X0 =
√
Z(Z + 1)ln(287/ Z)

82

The Muon Trigger at the ATLAS Experiment

Figure 5.2 (a) shows the fractional energy loss per X0 for electron in lead. As in the figure,energy loss is dominated by the bremsstrahlung for incident energy above 10 MeV.
Figure 5.2 (b) shows the cross section of photons in lead. At the energy higher than 5 MeV,
the energy deposition of the photon is dominated by the electron-position pair production due
to nuclear or electron field (κnuc or κe ). The average mean free path for a photon in terms ofelectron-positron pair production is called conversion length (X p ), which can be expressed as
Xp =

9
X0 .
7

(5.3)

When a high energy electron passes through the matter, it is very likely to create secondary
photons by bremsstrahlung which also results third generation of an electron-position pair production. Third process continues until daughter particles do not have enough energy to create
next particles. In this case, energy of final daughter particles only degraded through ionization.
This phenomenon is called electromagnetic cascade.
The critical energy Ec is defined as the energy when the energy losses by ionization perradiation length equals to the traversing electron energy. Here, consider how many generations
are created until the daughter particles energy become lower than Ec under the assumption thatmean free path of bremsstrahlung and pair production is equals to X0 . Define Ntotal as the total
number of produced electrons (+ positrons), t the length of cascade in the unit of X0 , tmax the twhere final daughter particles are created, E0 the initial energy of the incident electron
Ntotal =

tmax
X

2t

t=0
(tmax +1)

= 2
−1
tmax
∼ 2·2
E0
= 2 ,
Ec
lnE0 /Ec.
ln2
The 95 % of the typical cascade length is expressed astmax =

t95% = tmax + 0.08Z + 9.6.

(5.4)
(5.5)

(5.6)

Taking lead (Ec = 11.8 MeV) as an example the t95% is calculated as 23 (X0 ). The thicknessof the ATLAS EM calorimeter is about 25 X0 hence most of electrons loose its energy throughelectromagnetic cascade and can not reach the muon spectrometer.
In addition, the critical energy for the muons can be expressed as
Ecµ = Ecelec

!
mµ 2
.
me

(5.7)

Here mµ /me ∼ 200, thus muons very unlikely to loose their energy through electromagnetic
cascade.

5.1 Muon Identification and Transverse Momentum Measurement

83

The Energy Loss of High Energy Hadrons – Hadronic Cascade
High energy hadrons loose their energy through the sequential strong interactions, called Hadronic
Cascade, as electrons lose their energy through electromagnetic cascade. Characteristic process
in hadronic cascade is production of secondary hadrons by the strong interaction within a mean
free path of λ, which is defined as the length through which hadrons lose their energy down to
1/e. Figure 5.3 shows the longitudinal depth of hadrons in the unit of λ. The ATLAS hadronic
calorimeter has the thickness of about 10 λ, hence most of hadrons are absorbed in the hadronic
calorimeter and can not reach the muon spectrometer.

Figure 5.3: Energy deposition of hadrons in a matter [1].
tmax for hadrons can be expressed astmax (λ) ∼ 0.2lnE (GeV) + 0.7,

(5.8)

t95% (λ) ∼ alnE + b,

(5.9)

where a and b are material dependent parameters. Taking irons as an example, a = 9.4 and b =39 and λ = 16.7 cm. Then the t95% for a hadron with energy of 100 GeV is calculated as 80 cm.

84

The Muon Trigger at the ATLAS Experiment

5.1.2

Muon Transverse Momentum Measurement

Figure 5.4 shows a drawing which illustrates the motion of a negative charged particle in a
homogeneous magnetic field. As depicted in the figure, the trajectory behaves as a helix with aconstant radius.

magnetic ﬁeld

charged particle

Figure 5.4: Motion of a negative charged particle in a homogeneous magnetic field.
A charged particle is subjected to Lorentz force in the magnetic field as~ ,F~ = q ~v × B(5.10)~ the magnetic flux. Then thewhere q is the electric charge of the particle, ~v the velocity, B
equation of motion is expressed as


mv2
~ ,
= q ~v × Bρ→ pT = qBρ,

(5.11)

where ρ is the radius of helix. Thus pT of the particle with unit charge ispT (GeV) = 0.3Bρ (T · m).

(5.12)The equation means that one can calculate the pT of a charged particles with the knowledge ofthe magnetic field and the curvature of the trajectory.
One of the straightforward approach to measure pT is to fully reconstruct a trajectory withlarge number of precision position measurement. However there also exists useful and practicalapplication for charged particle pT determination, sagitta measurement. Figure 5.5 shows an
overview of the sagitta measurement.

5.1 Muon Identification and Transverse Momentum Measurement

85

L
x
B

s

y

Figure 5.5: Sagitta measurement in a magnetic field.
Here transverse direction is defined as x-coordinate and longitudinal direction as y-coordinate.
In the figure, s is a sagitta and L means the length in the longitudinal direction of the region
where magnetic field exists. An assumption that ρ >> L is made in the discussion hereunder.
L
0.3LB= sinθ/2 ∼ θ/2 → θ ∼,2ρ
pT(5.13)

θ2
0.3 L2 B
∼
.
8
8 pT

(5.14)s = ρ (1 − cos(θ/2)) ∼ ρ

Here s the sagitta. As seen, sagitta s can be measured by the measurement of arbitrary threepoints in the magnetic field. Define each of the point as x1 , x2 and x3 with the error of σ(x), thensagitta can be expressed as1
s = x x − (x2 + x3 ) ,(5.15)
2
here the resolution of pT can be expressed as
q
q
3
3
σ(x)
σ(x) · 8pT22
σ(pT ) meas σ(s)
|
=
=
=
.
(5.16)pTss
0.3 · BL2
As can be seen, the longer L is the more accurate σ(pT )/pT becomes. This is why the ATLAS
muon spectrometer deploys such a long lever-arm.
The ATLAS muon trigger system is based on the concept of the sagitta measurement thus
they basically have three station structure. In barrel, all the RPC three layer immersed in themagnetic field, thus the detector actually measures sagitta. On the contrary in endcap, thedetector configuration does not allow three points measurement in the magnetic field. Thus the
IP is taken as an additional measurement and muons are assumed to be coming from the IP.

86

The Muon Trigger at the ATLAS Experiment

5.2

Level-1 Muon Trigger

The ATLAS L1 muon trigger consists of mainly the following three components.
• The TGC which consists of 144 trigger sectors (1.05 < |η| < 2.4)
• The RPC which consists of 64 trigger sectors (|η| < 1.05)• The MUon to Central Trigger Processor Interface (MUCTPI)
A schematic drawing is shown in Figure 5.6 [94].
RPC-detector

TGC-detector

FE electronics

FE electronics
hit pattern

On detector
Off detector

DSL
(RPC)
64 sectors

Pt thresholds for max.
2 candidates per sector

DSL
(TGC)
144 sectors

MUCTPIDAQDAQInformation on hit strips

Information on hit strips / wire groups

LVL2

CTP

DAQ

ROI information

Multiplicity for different
transverse-momentum cuts

Information on muon candidates
and on multiplicities
CHS01V01

Figure 5.6: A schematic drawing of the ATLAS L1 muon trigger.
Both the TGC and the RPC can send up to two muon candidates per trigger sector to
MUCTPI in an event with corresponding pT threshold values. The MUCTPI calculates overallmuon multiplicity for each of pT threshold with correct overlap solving, After data processing and formatting, results are sent to the CTP, the L2 trigger and the DAQ. In this section,
descriptions about each component are given.

5.2 Level-1 Muon Trigger

87

5.2.1 Level-1 Endcap Muon Trigger
The endcap muon trigger is provided by the TGC placed on the both sides in a mirror symmetricmanner. Figure 5.7 shows the layout of the TGC system on one side.

R(mm)M2(middle)
M3(pivot)
middle MDT

12000

M1
10000

8000

6000

EI

Inner MDT

end-capFI

forward

4000

2000
6000

8000

10000

12000

14000

16000

Z (mm)

Figure 5.7: The cross section in R − Z plane of the TGC system.
The TGC consists of five stations namely EI (Endcap Inner), FI (Forward Inner), M1, M2,
and M3 from inside to the outside. The M1 station is using triplet chambers and M2 and M3
station are using doublet chambers as depicted in Figure 4.30. M3 station is also referred to as
the pivot plane. The TGC stations cover 1.05 < |η| < 2.4 region for triggering except for the
innermost stations (EI / FI) which covers 1.05 < |η| < 1.9. In this section, the trigger algorithm,
detector segmentation and its implementation of the TGC are given.

88

The Muon Trigger at the ATLAS Experiment

Trigger Algorithm
Figure 5.8 shows a scheme of muon pT decision performed by the TGC. The basic principle of
the TGC trigger algorithm is summarized as follows.
M2(middle)
M1(triplet)Rmagnetic
field

o
mu

np

M3(pivot)

ath

R

Z
hi-PT WindowIn
M f inom ite
en
tu
m

Li

ne

Z=~14.5m
Z=~14mam
Be

X
collision point

Z=~13me
L in

low-PT OK!!
R

low-PT Window

Figure 5.8: The pT decision scheme in the TGC.
• The trigger algorithm extrapolates a given hits on the M3 to the interaction point withstraight line assuming an infinite momentum upon a passage of a muon. Then a window
is constructed around the infinite momentum path on each non-pivot plane (M1, M2) inr − φ coordinates separately.
• Hits are searched on non-pivot planes to take coincidence first between M2 and M3 thenbetween M1 and M3. The coincidence between doublet pair of M2 and M3 requires 3out-of-4 condition within a window. This is called low-pT coincidence for its relatively
short lever arm. On the top of low-pT coincidence, the coincidence between M1 and M3
is taken requiring 2-out-of-3 condition in η and 1-out-of-2 condition in φ within the M1
triplet layers. The coincidence conditions are adjustable. In both coincidences, deviations of hits from the infinite momentum path, which is considered as pseudo-sagitta aremeasured to calculate pT of muons.
• The final pT measurement is made by merging the results in both coordinates referring themap which describes the correspondence between measured deviations and pT of muon.
This map is prepared for each RoI. Then the six levels of the pT threshold is applied andmuons are classified according to the highest threshold they passed.

5.2 Level-1 Muon Trigger

89

Detector Segmentation
The coverage of the TGC is divided into several types of logical units. The segmentation in a
M3 octant is shown in Figure 5.9.
∆φ =Sub-sector

1.0

se
ger
g
i
r
T

ctor

η=

0.1

148 sub-sectors
1.5

2.0

1m

64 sub-sectors
2.5

Figure 5.9: A schematic view of the segmentation of a TGC octant.
The TGC coverage is divided into two regions namely endcap (|η| < 1.92) and forward(|η| > 1.92) in η. The endcap region of each octant is divided into six trigger sectors in φ. The
forward octant contains three trigger sectors. There are hence 48 endcap trigger sectors and24 forward trigger sectors on one side of the TGC. Each trigger sector consists of independent
sub-sectors, which corresponds to the TGC RoIs. The number of sub-sectors contained in a
trigger sector is 148 in endcap and 64 in forward.
System Implementation
The trigger algorithm outlined above is implemented in purpose-built electronics, partly mounted
on and near the TGC chambers, and partly located in the underground counting room. A schemaof the trigger and readout chain is shown in Figure 5.10.
• ASD: The wire and strip signals emerging from the TGC are fed into a two-staged amplifier in an Amplifier Shaper Discriminator (ASD [95] ) circuit. Four ASD circuits are built
into a single ASD chip and four ASD chips are incorporated into an ASD board hence
each ASD board handles 16 channels of signals. The ASD board is physically attachedto the edge of a TGC and enclosed inside shielding boxes.
• Patch-Panel: Signals from the ASD boards are sent to a so-called PS board where PatchPanel (PP) ASICs and Slave Board (SLB) ASICs are implemented. Figure 5.11 shows a

90

The Muon Trigger at the ATLAS ExperimentΤΓΧ χηαµβερ φροντ−ενδΤΓΧ 1 ΤΓΧ 2 ΤΓΧ 3ΑΣ∆Μουντεδ ονΤΓΧ χηαµβερσ

∆ελαψ
ΒΧΙ∆

ςΜΕβυσ χρατε

3/4 ηιτσΡεαδουτ

ΑΣ∆

∆ελαψ
ΒΧΙ∆
∆ελαψ
ΒΧΙ∆

ΑΣ∆

ςΜΕβυσ χρατε

Ηιγη−πΤωιρεΣεχτορ
λογιχΗιγη−πΤστριπ∆ουβλετσ∝Χουντινγ ροοµ(ΥΣΑ15)ΠΣ−βοαρδ

∆ελαψ
ΒΧΙ∆

ΕΙ/ΦΙ

Βιγ ωηεελ εδγεΤριγγερΜΥΧΤΠΙ

ςΜΕβυσ χρατε

2/3 ηιτσΣταρ−σωιτχη

ΡεαδουτΡεαδουτΡΟ∆ΡΟΒΤριπλετΡαχκσ νεαρ βιγ ωηεελσ
ΠΣ−βοαρδ ιν ςΜΕβυσ χρατε

∆ελαψ
ΒΧΙ∆

1/2 ηιτσΡεαδουτςΜΕβυσ χρατεΣταρ−σωιτχη

ΕΙ/ΦΙ δουβλετ

Figure 5.10: A schematic view of the TGC electronics system.
block diagram of the Patch-Panel ASIC. The number of input channels is 32. The mainfunctionality of the Patch-Panel is summarized as follows.
1. Signal Delay: The signals from the ASD board are fed into the variable delay logic
at first to adjust the delay difference from TOF, cable length and so forth. The delay
can change from 0 to 25 ns with sub-nanosecond resolution. The Patch-Panel ASIC
is sub-divided to two-parts and each part is responsible to 16 channels come fromthe same ASD board. Setting of the delay is common to these 16 channels.
A block diagram of the variable delay logic is shown in Figure 5.12. The delay logic
consists of two parts – delay part (upper side in the figure) and control part (bottomside in the figure) – both parts deploy 32 stages of delay unit and inverter gate. In thecontrol part, delay units form a Voltage Controlled Ring Oscillator (VCON) and thetotal delay length of VCON is locked to 25 ns using Phase Lock Loop (PLL) logic.
The number of delay unit in VCON (Ncon ) is adjustable. This phase lock realizes
the situation that all the delay units via common voltage control line have the same
delay time of 25 / Ncon ns. The number of delay units used in the delay line (Ndelay )is also adjustable from 0 to 31.
2. Channel Mask: The Patch-Panel ASIC also can mask individual noisy or malfunctioning channels. This functionality is implemented in the BCID circuit shown in
Figure 5.13.
3. Bunch Crossing IDentification (BCID): Figure 5.13 shows the conceptual design

5.2 Level-1 Muon Trigger

Figure 5.11: A block diagram of the Patch-Panel.

Figure 5.12: A block diagram of the variable delay logic in the Patch-Panel ASIC.

91

92

The Muon Trigger at the ATLAS Experimentof the BCID circuit which contains two variable delays. The first delay is used toadjust the phase difference between the signals and 40 MHz clock provided by the
LHC. The second delay is used to adjust the effective gate width from 26 ns to 48
ns. Values set for each delay are common to a group of 16 channels from an ASD
board.

Figure 5.13: A schematic of the BCID circuit on the Patch-Panel ASIC.

The outputs from the Patch-Panel are fed to the on-board logic to solve physical overlap
in the TGCs.
• Slave Board: SLB ASIC typically receives 32 channels of BCID assigned wire and strip
signals from the Patch-Panel and fed them into a so-called coincidence matrix. The SLB
ASIC can be configured to have different five types of coincidence matrices namely fortriplet-wire, triplet-strip, doublet-wire, doublet-strip and EI / FI. Figure 5.14 shows a
block diagram of the SLB ASIC. The functionalities of the SLB are divided into twoparts, namely trigger part and readout part. Overviews of each part is as follows.
1. As mentioned above, the trigger part of the SLB deploys so-called coincidence matrix. The coincidence matrix can be configured to perform different five types ofcoincidence pattern. Figure 5.15 shows the detailed structure of the coincidence
matrix for wire doublets in 3-out-of-4 configuration.
2. The hit data from the Patch-Panel is stored in the pipe-line memory mounted on
the SLB ASIC called L1 buffer during the period of L1 latency. They are read out
upon an arrival of the L1 accepted signal together with the data taken in neighboringbunches (previous and next bunch). Otherwise the stored data will be discarded.
The read out data are sent to the so-called Star Switch module which collects theformatted hit data from the SLBs then multiplexes and randomize them. After thatthe data is sent to the ROD module and shaped into an ATLAS standard readout
format. Finally, the hit data is sent to the ROB i.e. the central DAQ buffer.

5.2 Level-1 Muon Trigger

93

Control P art
Instruction

Data Registers
Tapmatrix

MUX

SD

DEMUX

Mask2

Selector

Test P ulse P attern

Mask1

Delay
Delay

BSC 160ch

WDmatrixWT
matrixST
matrixD

Cmatrix

BSC 40

B

A

JTAG

EI/FI

Input P art

Trigger P art

BSC 4

TTC

Module T ype
TPG T rig Test P ulse
Delay
L1A

Trigger
Output
Data

Input Data

ECR
BCR

CLK
Event
Counter

BCID
Counter

160bit40bit

Level 1 Buffer(Input Data, 160ch)

L1B(Trigger)

12bit
4bit

L1B
(BCID)

Derandomizer 126bit
Start bit

Stop bit

PSC (NXT-BC) [EVID(4) BCID(12) I nputData(160) T rigger(40)]

PSC (PRV-BC) [EVID(4) BCID(12) I nputData(160) T rigger(40)]
PSC (Status) [SLBID(5) MTYPE(3) OVFLW (8) SE U(1) 199’ b0]

Read O ut P art

Figure 5.14: A block diagram in the SLB ASIC.

BSC 4

PSC (CUR-BC) [EVID(4) BCID(12) I nputData(160) T rigger(40)]

94

The Muon Trigger at the ATLAS ExperimentOR’ed YabcC

C=a&b&c+a&b&c

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

8 outputs to encoder section

4x2 (pivot doublet) inputs

12x2 (middle doublet) inputs

7

δR
AB

OR’ed XYC
D

X=Y=A&C+A&D+B&D

SOS043V05

X

Figure 5.15: A schematic illustration of the wire doublet coincidence matrix in SLB ASIC.
• High-pT Board: Trigger signals from the SLBs are combined to identify high-pT track
candidates in coincidence boards combining all three trigger planes (M1, M2 and M3), socalled high-pT boards, located in dedicated mini-racks around the outer rim of the triplet
wheel. Wire (r-coordinate) and strip (φ-coordinate) information is still treated separately
at this point. Figure 5.16 shows the functional structure of a wire high-pT ASIC.
from 4 wire triplet
Slave Boards

18

Phase adjust
18

Phase adjust
18

Phase adjust
18

Phase adjust

Decoder
18

Phase adjust
18

Phase adjust18

Decoderfrom 3 wire doublet
Slave Boards

Clock

192 x 232
2-foldCoin. Matrix
window size: + 20

H/L PtPhase adjust

hit
position

δR
x2

track selector
SOS063V11

Position + δ R
7-bit x 6

Position + δ R
10-bit x 2

Figure 5.16: A schematic illustration of the functionalities in a wire high-pT ASIC.

5.2 Level-1 Muon Trigger

95• Sector Logic: Signals from high-pT boards are sent to Sector Logic (SL) boards containing an r − φ coincidence unit and a track selector to select the highest-pT candidate. The
SL also receives directly the signals from the EI / FI slave boards and can incorporate
them into the trigger logic. The resulting trigger information for 72 separate trigger sectors per side are sent to the MUCTPI. Figure 5.17 shows an example of the coincidence
matrix configured in the SL.
+15

pT1
pT2
pT3
pT4
pT5
pT6

δR

-15 / -7+7

δφFigure 5.17: A coincidence matrix configured in the SL.

96

5.2.2

The Muon Trigger at the ATLAS Experiment

Level-1 Barrel Muon Trigger

The L1 barrel muon trigger is performed by the RPC [96]. For the detector specification and thelayout in the ATLAS detector, see section 4.4.5. In this section, the trigger algorithm, detector
segmentation and its implementation of the RPC are given.
Trigger Algorithm
The trigger algorithm in the RPC consists of two parts – the low-pT algorithm and high-pT
algorithm. A schematic view of the both algorithms are shown in Figure 5.18.

MDT

High-pT

Low-pT

RPC2 (pivot)

MDT

MDT

RPC1

MDT

RPC3

MDT

0

5

10

15 m

Figure 5.18: A schematic view of the trigger principle in the RPC.
The low-pT algorithm deploys two RPC stations attached on the inner surfaces (RPC1) andthe outer surface (RPC2) of the MDT inner station. The RPC2 is also referred to as the pivot
plane. When a hit is generated by a muon in the RPC2, a search for a corresponding hit in the
RPC1 is made within a road centered at the infinite momentum track line. The width of theroad is related to the three pT thresholds assigned to the low-pT algorithm. The algorithm isperformed in both η and φ coordinates. A 3-out-of-4 coincidence of the four layers in the twostations is required.
The high-pT algorithm is performed on the top of a low-pT result. The algorithm operates
in a similar way to the low-pT algorithm but requiring 1-out-of-2 coincidence in the outermost
RPC station (RPC3). As in the low-pT algorithm, three pT thresholds are assigned to the high-pT
algorithm resulting six thresholds in total.

5.2 Level-1 Muon Trigger

97

Detector Segmentation
The RPC is divided into 64 logically identical trigger sectors (32 trigger sectors for each halfbarrel), each one covers a region of ∆η × ∆φ ∼ 1.0 × 0.2. This trigger sector should be distinguished from the physical sector which is sub-divided into two trigger sectors as depicted in
Figure 5.19. Both large and small physical sectors contain two trigger sectors. A trigger sector
is further divided into the fine granularity corresponds to ranges of each electronics element.
Descriptions for each electronics element are given in the next section.

Trigger large sector

Barrel large
sectorTrigger large sector∆η=0.2η-CMPad∆φ=0.1

Trigger small sector∆η=0.1

Trigger small sector

RoI

φ−CM

∆η=0.1∆φ=0.2∆φ=0.1∆φ=0.2∆η=0.2Barrel small
sector

η=0

Figure 5.19: The RPC trigger segmentation.

System Implementation
Figure 5.20 shows a schematic view of the RPC trigger slice in front-end and off detector electronics. The description for each component is as follows.
• The Coincidence Matrix ASIC (CMA) [97] covers a region of ∆η × ∆φ = 0.2 × 0.1 or∆η × ∆φ = 0.1 × 0.2. A CMA performs high-pT and low-pT trigger algorithms, havepipeline memory to store event information during the L1 latency and encode data to aserial readout format. A CMA has two input arrays which correspond to the row andcolumn input for a coincidence matrix, each one is called as pivot input (for RPC2) andconfirm input (for RPC1, RPC3).
In the low-pT algorithm the pivot inputs are connected to the RPC2 and the confirm inputs
are connected to the RPC1. In the high-pT algorithm one of the pivot input is connectedto the low-pT trigger output and the confirm inputs are connected to the RPC3.
• The Splitter board provides a fan-out to serve adjacent inputs to a neighboring CMAs.
• The Pad logic board combines the trigger and readout information from four CMAs, bothin the low and high-pT algorithms. The Pad logic board associates the muon candidates
with a region ∆η × ∆φ = 0.1 × 0.1 and with a correct bunch crossing, solves overlaps

98

The Muon Trigger at the ATLAS Experiment

Figure 5.20: A schematic view of the RPC trigger slice.
and selects the highest pT muon candidate in a coverage of ∆η × ∆φ = 0.2 × 0.2. The
low-pT board sends trigger and readout data to the corresponding high-pT boards, while
the high-pT board sends trigger and readout data to the Sector Logic.
• The Sector Logic (SL) [98] covers a region of ∆η × ∆φ = 1.0 × 0.2 receiving data from
7 high-pT Pad Logic boards in a small physical sectors and 6 high-pT Pad Logic boards
in a large physical sectors. The trigger part of the SL solves the overlap inside a sector,
performs some optional algorithm and selects the two highest pT muon candidates in asector, associating each muon to a RoI (∆η × ∆φ = 0.1 × 0.1) and to a correct bunch
crossing. A trigger output from the SL is sent via parallel LVDS links to the MUCTPI.
The readout part of the SL board multiplexes event packets and sends them to the event
builder.

5.2.3

Muon to Central Trigger Processor Interface (MUCTPI)The MUCTPI receives information on up to two muon candidates per trigger sector from boththe TGC and the RPC then combines the information from all the trigger sectors and calculates
total multiplicity values for each of six pT thresholds. The maximum overall multiplicity is set
at seven. The formatted information are sent to the CTP, the L2 trigger and the DAQ.
In the calculation, the overlaps between the TGC and the RPC or different trigger sectors
are solved to avoid double counting. If a muon produces hits in both the TGC and the RPC, thepriority is given to the RPC muon candidate.
In addition the MUCTPI can hold the trigger data within ± 3 bunch crossings around theL1 trigger. This is needed for setting up the timing of the system and also for monitoring thetiming alignment of the trigger chambers.

5.3 Level-2 Muon Trigger

99

5.3 Level-2 Muon Trigger
The L2 muon trigger algorithms are seeded by the ROI information provided by the L1 trigger
and use all available detector data around the ROI with full granularity and precision. The roleof the L2 is to confirm muon candidates flagged by the L1 and to give precise physics quantities
associated to the muon candidate such as pT .
The muFast algorithm performs a standalone feature extraction using the muon spectrometerdata providing a fast selection of the muon event rated from L1. Subsequently, the muon track
confirmed by muFast is passed to the muComb algorithm which refines the measurement byusing track information reconstructed in the inner detector. The muIso algorithm select isolated
muon candidates using calorimeter information. In this section, descriptions about each muon
L2 algorithm are given.
MuFast
The muFast algorithm consists of the following three steps. The exact procedures are different
between endcap and barrel.
• A global pattern recognition is performed to select clusters in MDT tubes belonging toa muon track without using drift time measurement. First, a pattern recognition is performed on the trigger chamber hits followed by a pattern recognition on the MDT hits.
This is a recursive procedure in which the mean position of the track cluster is computed
and a hit tube having the highest deviation from the mean is removed. It terminates whena single hit tube on each MDT layer is left
• A track fit is performed using drift time measurement and approximated r − t relation
assuming a straight line. A track segment is built if at least four MDT hits (two per MDT
multilayer) can be used and fitted. The position on the middle of the MDT chambercrossed by the fitted result with the best χ2 is chosen and used to sagitta measurement asa precision position measurement.
• The pT is calculated from the position measurements obtained in the previous step referring a pre-calculated look-up table.
MuComb
The muComb algorithm matches a muon track confirmed by the muFast to a L2 ID tracks. The
L2 ID tracks are reconstructed without TRT measurements. The matching algorithm between
muFast and ID tracks are proceeded in the following two steps:• A pre-selection of ID tracks is made using the difference in η and φ between muFast andID tracks. Also the difference in the z-position at the radius of barrel calorimeter surface
is used.
• For each of the pre-selected ID tracks, a combined pT is evaluated with the informationof the muFast track. The combined pT is calculated as a resolution weighted average ofpT given by the muFast and ID tracks. A χ2 is calculated and the ID track which gives
the minimum χ2 is selected as the best matching candidate.

100

The Muon Trigger at the ATLAS Experiment

MuIso
The muIso is seeded by a result of muFast or muComb. The algorithm decodes LAr and Tile
calorimeter quantities (i.e. transverse energy deposit or sums of calorimetric cells above apredefined energy threshold) in cones centered around the muon direction. To remove the contribution of the muon track itself, two different concentric cones are defined.

5.4

Muon Event Filter

In the Event Filter, offline muon reconstruction algorithms have been adopted to work in the
HLT framework. The two offline packages MOORE (Muon Object Oriented REconstruction)and MuId (MuonIdentification) have been used so far for this purpose. These two packages
make up a family of muon reconstruction chain. The detailed description for the reconstruction
algorithm itself is described in chapter 6. The HLT version of the MOORE family is called
TrigMoore, which is modified to work as the RoI seeded mode in online environment. The
TrigMoore has two main strategies,• Seeded strategy: In this strategy TrigMoore accesses ad hoc algorithms that perform aseeded search only around the Region of Interest.
• Full scan strategy: In this strategy TrigMoore accesses directly the pointers of the offline
version of the algorithms allowing it to execute the algorithms as they are in the offline
package.

Chapter 6
The Muon Reconstruction at the ATLAS
Experiment
The ATLAS experiment employs a variety of strategies for identification and reconstruction ofmuon tracks. Among them, two of those are intensively used in the analysis of this thesis.
• Standalone muon tracks are reconstructed only from the information in the muon spectrometer and then extrapolated to the beam line to obtain the track parameters at theclosest approach to the beam axis.
• Combined muon tracks are found by matching standalone muon tracks to nearby innerdetector tracks and then combined the measurement from the two systems.
This chapter is organized as follows. A description about the tracking objects in the ATLAS is given in section 6.1 followed by an overview of the Hough transformation, a common
technique for pattern recognitions, in section 6.2 and tracking in the inner detector presented in
section 6.3. Section 6.4 focuses on the standalone muon track reconstruction strategies. Finally,an overview of the track combination procedure is given in section 6.5.

6.1 The ATLAS Tracking Event Data Model
The ATLAS experiment has developed a common design of data objects which handles thevarious tracking related stuff by the C++ software framework, ATHENA. This common design
is called Tracking Event Data Model (EDM) [99–101].

6.1.1 The Concept of a Track
A reconstructed track is represented by an array of the Track State On Surface (TSOS) objects
as depicted in Figure 6.1. A single TSOS is able to hold polymorphic tracking information suchas track parametrization on a given surface of detector or materials, measurements in various
types of detectors, inert material or integrated material effects and results of fittings.
Among them, the track parametrization and the expression of the detector measurements areof the most important. The details of these two items are described in the following subsections.

102

The Muon Reconstruction at the ATLAS Experiment

track

ex
q/pf

ly

TS
OS
4

lx
ey

z0

d0
ez

hx

lx

TS
OS
3

TS
OS
2
TS
OS
1

Figure 6.1: An image of a reconstructed track in the ATLAS Event Data Model.

6.1.2

The Track Parametrization

A reconstructed track is parametrized on each of detector or material surfaces where the trackpassed. The parametrization is done by a set of five parameters as,
Li = (`1 , `2 , φ, θ, q/p),(6.1)

where `1 and `2 denote the position in two coordinates in the intrinsic local frame on the surface
under consideration. The surface is also expressed by a C++ object which represents various
types of planes or lines. φ, θ, and q/p represent the signed momentum of a track in the ATLAS
global frame.
The ATLAS tracking EDM can deal with five different types of surfaces namely cylinder,
disc, plane, straight line and perigee. In most of the cases, a fitted result of a track is represented
by a track parameters at a perigee, the closest approach of a track to the beam line.
d0 and z0 are defined as the transverse and longitudinal impact parameters. In this thesis,
both d0 and z0 are defined with respect to the IP unless otherwise mentioned. The definition ofd0 and z0 are illustrated in Figure 6.1.

6.1.3

The Expression of Detector Measurements

An abstract common base class (MeasurementBase) is developed so that it is able to represent
various kind of detector measurements. For example, a drift circle from the MDT or TRT, a 3-D
position information from Pixel or SCT. These measurement is to be transformed at each levelof the reconstruction or after an application of a calibration.

6.1 The ATLAS Tracking Event Data Model

103

Figure 6.2 shows a simplified UML diagram which represents the inheritance tree of representative five types of measurements extended from MeasurementBase. A short description
about these items are given below.
MeasurementBase
clone() : MeasurementBase*localParameters() : const LocalParameters&
localErrorMatrix() : const ErrorMatrix&
associatedSurface() : const Surface&
globalPosition() : const GlobalPosition&

SpacePoint
m_clusList : const std::pair<const PrepRawData*, const PrepRawData*>*m_locPar : Trk::LocalParameters*m_elemIdList : std::pair< IdentifierHash, IdentifierHash >m_position : const Trk::GlobalPosition*m_globalErrMat : const Trk::ErrorMatrix*s_numberOfInstantiations : unsigned int
elementIdList() : const std::pair< IdentifierHash, IdentifierHash >&position() : const Trk::GlobalPosition&clusterList() : const std::pair<const PrepRawData*, const PrepRawData* >numberOfInstantiations() : unsigned int
setupGlobalFromLocalErr() : const ErrorMatrix*
CompetingRIOsOnTrackm_localParameters : const LocalParameters*
m_localErrorMatrix : const ErrorMatrix*
m_rotsnum : unsigned int
m_indexMaxAssignProb : unsigned inW
m_assignProb : const std::vector< AssignmentProb >*numberOfContainedROTs() : const unsigned int
indexOfMaxAssignProb() : const unsigned int
rioOnTrack( : unsigned int) : const RIO_OnTrack*
assignmentProbability(indx : unsigned int) : const AssignmentProb
ROTsHaveCommonSurface(withNonVanishingAssignProb : const bool) : const bool

PseudoMeasurementOnTrackm_localParams : const LocalParameters*
m_localErrMat : const ErrorMatrix*
m_associatedSurface : const Surface*m_globalPosition : const GlobalPosition*

RIO_OnTrackm_localParams : const LocalParameters*
m_localErrMat : const ErrorMatrix*
m_identifier : Identifiers_numberOfInstantiations : unsigned int
prepRawData() : const Trk::PrepRawData*
idDE() : const IdentifierHash
detectorElement() : const TrkDetElementBase*identify() : Identifier
numberOfInstantiations() : unsigned int

Segment
m_localParameters : const LocalParameters*
m_localErrorMatrix : const ErrorMatrix*
m_fitQuality : FitQuality*
m_containedMeasBases : DataVector< const MeasurementBase >*s_numberOfInstantiations : unsigned inW
containedMeasurements() : const std::vector< const Trk::MeasurementBase * >numberOfMeasurementBases() : const unsigned int
measurement( : unsigned int) : const MeasurementBase*
fitQuality() : const FitQuality
numberOfInstantiations() : unsigned int

Figure 6.2: A simplified UML diagram showing the extended class of the MeasurementBase.
• RIO OnTrack (Reconstruction Input Object on Track) is an object which represents adrift circle or 3-D position of a hit after applying additional calibrations.
• CompetingRIOsOnTrack is a group of RIO OnTracks on the same detector surface, which
is used to represents unresolved ambiguous measurements compatible with an estimatedtrack positions on a surface.
• Segment contains an array of RIO OnTrack and result of local fitting of them. Figure 6.3
shows a segment reconstructed in the MDT (an array of MDT drift circles). In the MDT

104

The Muon Reconstruction at the ATLAS Experimentsegment reconstruction, a straight line approximation is made since the effect of magnetic
field is negligible in such a small region.

Figure 6.3: A schematic view of a segment in the MDT.
• SpacePoint is a set of a 3-D spatial information of a measurement and its error.
• PseudoMeasurmentOnTrack represents a measurement that can not determine the fulltrack parametrization without information from other detectors.

6.2 The Hough Transformation

105

6.2 The Hough Transformation
The Hough transformation is a feature extraction technique used in image analysis for its robustness in identification of varieties of shapes and patterns. Hough transformation was developed
by Paul Hough in 1962 to analyze bubble chamber pictures at CERN [102, 103]. In the ATLAS track reconstruction, the Hough transformation is used in track pattern recognitions inindividual hits in a detector.
The Hough transformation projects a point in normal space into a curve in a certain parameter space called Hough space.
~ ).
P(~x) = H(~x, α(6.2)
The simplest example of the Hough transformation is a linear transformation for finding lines
in a 2-D space. A line in a 2-D space can be generally expressed as,xcos(φ) + ysin(φ) = r.

(6.3)

Eq.(6.3) represents a line perpendicular to another line which is drawn from the origin to (r , φ)in polar coordinates. Meanwhile, Eq.(6.3) also represents a curve in r − φ space for every (x , y)on the original line in 2-D space. Figure 6.4 shows that every curve in r − φ space which ison the same line in 2-D space intersect at one point and the intersection corresponds to the(r , φ) parameters for the original line. As such, a line in 2-D space is recognized by the Houghtransformation.

5

\














(a)



[








φ UDG(b)

Figure 6.4: Set of points (a) and their representation in the Hough Space (b).
The calculation time of the Hough transformation increases linearly (O(n)) when the numberof points in original space increases whereas a combinatorial approach would be of O(n3 ). This
property of the Hough transformation have huge advantage in the ATLAS experiment where the

106

The Muon Reconstruction at the ATLAS Experiment

expected number of hits at the design luminosity reaches up to 20,000 in an event in the muon
spectrometer.
In practice a search for overlapping points is made in binned Hough space. Figure 6.5 showsthe Hough histogram which corresponds the the curves shown in Figure 6.4 (b). The peaks inthe former correspond to overlaps in the latter.









5






  φ UDG

Figure 6.5: A Hough histogram for the curves in Figure 6.4 (b).

6.3

Tracking in the Inner Detector

The track reconstruction in the inner detector consists of two steps of successive strategies
namely Inside-Out sequence and Outside-In sequence [101, 104, 105]. The Inside-Out sequenceis the primary strategy for the track reconstruction in the inner detector whereas Outside-In
sequence is a complementary approach to find tracks which unlikely to have hits in the silicondetectors (PIXEL and SCT) such as tracks coming from V0 or photon conversion. An overviewsof each sequence are given in the following sub-sections.

6.3.1

Inside-Out Sequence

Inside-Out sequence starts with measurements in the silicon detectors then try to extend thetracks into TRT region following the procedures listed below.
1. The measurements in the silicon detectors, which are bounded on the detector surfaces,
are transformed to a set of 3-D positions in the ATLAS global frame.

6.4 Tracking in the Muon Spectrometer

107

2. Track seeds are searched with or without vertex constraint in z axis taking a balance
between time consumption and seed finding efficiency. Once seeds are found, a trackbuilding is performed with a Kalman filter [106] smoother formalism which follows theroad and include successive hits in the track candidate fit.
3. Ambiguities of shared hits are solved by so-called track scoring strategy [107]. In thisstrategy, a penalty and a benefit are assigned to each morphological features of a track
such as penalty for overlapping hits or benefit for innermost layer hits in the PIXEL. A
likelihood is calculated also taking into account the track fit qualities, then an ambiguous
hits are assigned to the most favorable track.
4. Tracks are extended into TRT region finding comparable TRT measurements with a
Kalman filter based tools [108, 109]. Then a track quality is calculated by track scoring
strategy described above and if the quality is improved with additional TRT measurements, the extended track is stored.

6.3.2 Outside-In Sequence
The Outside-In sequence consists of following two separate steps. In the both steps all themeasurements that have already been assigned to a Inside-Out track are excluded.
1. TRT segments are searched with both a global pattern search and a subsequent local
pattern recognition. Since segments from a track with pT above 500 MeV appear as
almost straight line, the linear Hough transformation is made.
2. The resulting track candidates are then back-extended if at least two comparable measurements are found in the outer three SCT layers. This back-extension uses a Kalmanfilter smoother formalism. An ambiguity resolving and a track refitting are performed
adequately.

6.4 Tracking in the Muon Spectrometer
The ATLAS experiment deploys two independent muon reconstruction algorithm chains – MuId
(Muon Identification) [110–112] and the STACO (Statistical Combined) [113,114]. Both chainscontain entire reconstruction algorithms hence able to provide both standalone and combined
tracks. In the analysis, the STACO chain is used as the primary algorithm. as well as MuId
chain for cross checks and systematic estimations.

6.4.1 Tracking in the STACO Algorithm
This section describes an overview of the standalone muon track reconstruction in the STACO
chain. The standalone muon track reconstruction package in the STACO is called Muonboy
which reconstructs muons in following four procedure.

108

The Muon Reconstruction at the ATLAS Experiment

1. Region of Activity (ROA), a geometrical region defined in the η - φ space with the sizeof about η × φ = 0.4 × 0.4, are identified using information from the trigger chambers.
The center of ROA is placed where there exist at least one TGC or RPC hit in both η − φcoordinate.
2. Local segments of a straight track are reconstructed in multilayers of each muon station
in ROA. The basic procedure is summarized below.
(a) Segment seeds are searched in the region where more than one φ hits are expectedby taking any combinations of two hits in different multilayers in an MDT chamberwith a loose IP constraint. Then a seed is matched with other hits in the samechamber using drift time information and fitting results are examined if the segment
is valid or not. In this matching, δ−ray effect and efficiency of the MDT tubes
are considered. Segments are required to be associated with at least one φ hit andsufficiently good fitting quality. Such segments are called strict segments.
(b) CSC segments are reconstructed in 3-D requiring at least one φ hit.
(c) A looser search, in which no φ hit is required and less stringent χ2 cut, is performed.
The position in the φ is determined by trying five positions along the tube.
In each of these steps, segments are searched in two consecutive passes. The first passreconstructs segments which cross both multilayer in an MDT chamber while the second
pass reconstructs the segments which cross only one multilayer to retain efficiency. In thesecond pass, in order to reduce fake combinations, only the hits left unused in the firstpass are used and a fit quality cut is applied tightly.
3. Segments in different stations are combined by a 3-D tracking to form track candidates.
Effects of the magnetic field is taken into account.
(a) The strict segments are used as seeds for the first rough momentum estimation. Eachsegment is then extrapolated to the neighboring stations assuming several different
values of momentum around the estimation. If some matching exist with one ormore loose segments, the one with the best matching is included in the track candidate and a fit is performed leading to a more accurate momentum estimation.
(b) The resulting track candidates are extrapolated to the all potentially crossed stations
with a finer momentum scan. Any matching loose segment is included in the candidate track and a new fit is performed using all the segments belonging to the track
candidates. Only track candidates with two or more segments are kept after thisstage.
4. A global fit is performed, starting from the best result of the previous fits, but using raw
hit information, such as TDC values and hit strips. In this process all the hits are classified
into good or bad and only good hits are kept. After that, the final fit including the material
effect is performed to achieve a more realistic result.
The covariance matrices of the track candidates are then computed by varying the fitted
parameters taking their correlations into account. To have track parameters at the perigee, the6.4 Tracking in the Muon Spectrometer109

candidate tracks are back-extrapolated to the beam axis and their covariance matrices are propagated taking into account the energy loss and the scattering in the calorimeters.

6.4.2 Tracking in MuId Algorithm
In this section, an overview of the standalone muon track reconstruction in Muid chain is given.
The standalone muon track reconstruction package in Muid is called MOORE (Muon Object
Oriented Reconstruction) [115–118] which reconstructs muons in following procedures.
• CSC segments are reconstructed in 3-D assuming straight line.
• A global track pattern finding is performed deploying the Hough transformation using
MDT, TGC, RPC hits and CSC segments. The suitable assumption for track model depends on the magnetic field distribution which varies region by region. Hence several
types of Hough transformation are performed. The resulting patterns serve as seeds in thenext stage.
• A straight line MDT segment reconstruction is performed. In each station, two hits inthe outermost layer in both sides are taken and four possible tangent lines are drawn. If
the line direction is within 0.2 rad from the pattern direction and more than three hits
are found in the same station within a road with width of 1.5 mm, a straight line fit isperformed. If the χ2 /ndf is over 10, the hit with the largest contribution is dropped andthe segment is refitted. This procedure is repeated until the χ2 /ndf become smaller than 10
and if the number of hits in the segments becomes less than 3, the segment is discarded.
Then φ hits are associated to the segment.
The ambiguous segments, with shared hits, are solved by using track scoring strategy
taking into account the δ-ray effect, noise-induced hits and tracking holes. Then theshared hits are assigned to the track with the highest score.
• The MDT and CSC segments are combined to build track candidates gathering compatible segments along track patterns. For each track candidate, a segment in the outermost
station is used as the seed of the track fit. The seed segment is extrapolated to the next
segment, the second-outermost segment, and this procedure is repeated for all segments.
The resulting set of tracks are sorted by its quality taking into account the number of hits
and the χ2 /ndf. Shared hits are assigned to the track with the highest score. Then the track
is refitted with a detailed geometry description.
Finally tracks are extrapolated to the beam axis to evaluate the track parameters at the theperigee.

110

6.5

The Muon Reconstruction at the ATLAS Experiment

Combined Tracking

Both MuId and the STACO algorithms perform an inner detector track selection for a given
muon spectrometer track using track parameters and covariance matrices. The same definitionof the match χ2 is used in both algorithms as the difference between the inner detector and themuon spectrometer track vectors weighted by the combined covariance matrix,
χ2match = (TMS − TID )T (CMS − CID )−1 (TMS − TID ).

(6.4)

Here T denotes a vector of track parameters expressed at the perigee and C is its covariancematrix.
In the STACO algorithm, several track selection criteria, such as requirement of the samecharge, crude η − φ matching, are applied on both the inner detector and the muon spectrometer
track in addition to match χ2 cut. The track parameters for the combined track is obtained by
the statistical combination as,
−1 −1
−1
−1
T = (C−1
ID − CMS ) (CID TID − CMS TMS ).

(6.5)

In MuId algorithm, a combined refit is performed after the inner detector track selection
using match χ2 . This combined refit accounts all the measurements, scatterer effect, energy loss
and magnetic field effect throughout the path of the track. The resulting track parameters at theat the perigee is stored as the combined track parameters.

Chapter 7
Experimental Conditions and the Datasets√
This study is based on the data sample of s = 7 TeV proton-proton collisions collected from
April to July, 2010. The operation of the LHC and the experiment, as well as the setup of thetrigger, during this period are summarized in this chapter.

7.1 Good Quality Event Selection
The experimental data used in this study are selected in accordance with the good run list (GRL)
criterion developed by the ATLAS experiment to ensure that every analyzer can share the identical events with good quality for the physics analysis in consideration [119].
The concept of GRL criterion based on the selection of luminosity blocks (LB) which are theunit of time for data-taking (∼ 2 minutes period). A GRL is created by applying a Data Quality(DQ) criterion to list all of the valid physics runs and luminosity blocks. Usually physics groups
hold their own GRL by selecting appropriate Data Quality flags (DQ flags), which is simple
indicator of a specific part of DQ such as TGC detector or muon reconstruction in the STACO
algorithm, to be applied on the data used in their analysis. DQ is assessed and DQ flags arefilled in following two stages,• Each sub-system is responsible for filling their DQ flags. The lowest level flags such as fornominal voltages, temperature, humidity are filled automatically. Sub-systems fill flags
at a number of different stages, flagging possible hardware and data-taking problems.
Automatic online flags are set and can be overwritten by the detector shifter during datataking.
• DQ flags are then reviewed by an offline expert. For the dedicated combined performancegroups (such as for muons, taus, jets) the flags are set by a combination of automaticconsistency checks and also by DQ shifters. A distilled summary of these stages are
stored in the database.
Table 7.1 shows the DQ flags required for the W / Z analysis (these requirements are made upona requirement of the stable running of the LHC). Due to the different requirements in the GRL,
the resulted integrated luminosities used in W → µν and Z → µµ are not the same (310 nb−1
for the W → µν and 331 nb−1 for the Z → µµ as listed in Table 7.2).

112

Experimental Conditions and the Datasets

DQ flag
ATLGL
ATLTORATLSOL
L1CTP
MMUIDCBMSTACO
MET

description
DQ information has been reviewed
Good solenoid magnet status
Good toroid magnet status
L1 trigger is working without problems
Requirements for MUID algorithm is fulfilled
Requirements for Staco algorithm is fulfilled
Requirements for ETmiss reconstruction is fulfilled (for W analysis only)
Table 7.1: DQ flags selected for the W / Z analysis

7.2

Operation of the LHC and the Experiment

The LHC has ran stably during the period with good data collection efficiency of ∼ 95 % with the
ATLAS detector. The recorded instantaneous peak luminosity is ∼ 1.6 ×1030 cm−2 s−1 . Figure
1.3 shows the integrated luminosity versus day delivered to (green), and recorded by the ATLAS(yellow) during stable beams condition. The details for the luminosity calculation is given in
section 8.2.
This period is divided into sub-periods according to the changes of the LHC operation modes
or configurations of the ATLAS detector. A summary of the integrated luminosity used in eachW → µν and Z → µµ analysis is given in Table 7.2 with remarks on the LHC operation.
Integrated Luminosity (nb−1 )W → µν GRL Z → µµ GRL
0.13
0.15
8.07
8.76
8.47
8.72
26.89
28.64

Run number range
A: 152884 – 153200
B: 153565 – 155160
C: 152228 – 156682
D1: 158045 – 158392
D2: 158443 – 158582
D3: 158632 – 158975
D4: 159041 – 159086
D5: 159113
D6: 159179 – 159224
Total: 152844 – 159224

29.03
32.85
79.40
28.04
97.05
310.0

31.76
34.71
87.82
28.38
101.85330.8

LHC comments
unsqueezed beam (β∗ = 10 m)
first squeezed beam (β∗ = 2 m)increased number of bunches
increased beam intensity (∼0.9E11
protons/bunch), β∗ = 3.5 m
–
–
–
–
–
–

Table 7.2: A summary of data taking periods
The ATLAS detector have been also operated stably. Table 7.3 shows the luminosity weighted
relative fraction of good quality data delivery by each detector during LHC fills with stablebeams and after ramped up the tracking detectors on between 30 March and 16 July, 2010.

7.2 Operation of the LHC and the Experiment

Inner Detector

Calorimeter

Muon

Sub-detector Good quality fraction (%)
PIXEL
97.1
SCT
98.2
TRT
100.0
LAr EM
93.8
LAr hadronic
98.8
LAr forward
99.1
Tile
100.0
MDT
97.9
RPC
96.1
TGC
98.1
CSC
97.4

Table 7.3: Luminosity weighted relative detector uptime and good quality.

113

114

Experimental Conditions and the Datasets

7.3

Trigger Setups

There were several physics streams operated during the data taking period. Each stream consistsof a particular set of trigger chains. A trigger chain consists of three trigger items, each comesfrom different trigger stages (L1, L2 and EF). An event which passes a certain trigger chain isclassified into the corresponding stream then stored in a dedicated file. If an event passes morethan one trigger chain, the event is stored in all the corresponding files.
Among streams, the MuonswBeam (stands for Muons with Beam) stream and L1Calo stream
are of a particular interest since the former is used in the W / Z-boson cross sections measurement and the latter is in the single muon trigger efficiency estimation. A brief description foreach trigger stream is given below.
- The MuonswBeam stream consists of trigger items which are designed to collect eventswith muons generated in proton - proton collisions. Most of the HLT items are driven bya L1 muon trigger.
- The L1Calo stream consists of trigger items which are designed to collect events withjets, taus, ETmiss , photons and electrons.
The W / Z-boson cross sections measurement utilizes the lowest threshold un-prescaled
L1 single muon trigger available – the L1 MU6 – to avoid the trigger bias as possible. During the data taking period, there exist trigger chains in which trigger decisions are sorely performed with a L1 trigger item – called L1ItemStreamer. Table 7.4 shows the summary of theL1ItemStream for single muons with its prescale factor during lumiblock 746 – 813 in run
159224 (The last stable beam period of the data taking) as an example. The prescale factor forprevious runs are smaller than the values in the table – i.e. all the L1ItemStreamer have notbeen prescaled except for L1 MU0.
Trigger Menu
Prescale

L1 MU0 L1 MU6 L1 MU10 L1 MU0 COMM L1 MU15 L1 MU20
116.7
1.0
1.0
1.0
1.0
1.0

Table 7.4: L1 single muon trigger items for ItemStreamer chain in run 159224, LB 746 – 813.

Special Setups for MUCTPIA Remark should be made on the special configuration on the MUCTPI.
• In design, the MUCTPI can hold L1 trigger information in ± 3 bunches with respect tothe beam collision bunch. Normally only the L1 trigger information coincidenced withthe collision bunch is sent to the L2 trigger but this acceptance has been stretched forthe commissioning of the L1 muon trigger. The resulted timing acceptance for L1 muon
trigger is [-2, -1, 0] in terms of the BCID difference ([BCID for an muon RoI] - [BCIDfor the event]).
• Since the muon rate is not so high during the data taking period, the overlap solving
between the TGC and RPC have not been operated.

7.3 Trigger Setups

115

Level-1 Jet Trigger Configuration
L1 jet trigger is used in the relative trigger efficiency measurement with respect to single muons
to ensure that muons are free from muon trigger biases. Hence a brief description on the L1 jettrigger is made here [120].
The ATLAS EM and hadronic calorimeters are segmented into trigger towers with granularity of about 0.1 × 0.1 in η × φ coordinates. The exact size of trigger towers depends on
its location. The analog signals from calorimeters are transmitted to the L1 hardware and theL1 hardware digitizes the trigger tower signals, associates them with a corresponding bunch
crossings and subtracts pedestals. The L1 system also performs a noise suppression and ET
calibration. The L1 jet trigger constructs so-called jet elements made of four (2 × 2) trigger
towers in both EM and hadron calorimeters. The resulted granularity of the jet element is about
0.2 × 0.2.
The L1 jets are reconstructed with an algorithm which consists of a sliding window with
programmable size. The size of the window could be changed as 2 × 2, 3 × 3 and 4 × 4
jet elements. The step size for the sliding window is set at 0.2 in both η and φ. To prevent
overlapping jets, ET of a cluster defined as a region spanned by 2 × 2 jet elements, should bea local maximum within ± 0.4 units. Then a jet is reconstructed if the total ET withing a given
window is above a given threshold. The L1 jet algorithm is performed within |η| < 3.2. Figure
7.1 shows a schematic diagram of the jet reconstruction algorithm at L1.
Window 0.6 x 0.6

Window 0.4 x 0.4

Window 0.8 x 0.8

Figure 7.1: A schematic diagram of the L1 jet algorithm showing a window of 2 × 2, 3 × 3 and4 × 4 jet trigger elements spanning the EM and hadronic calorimeter.
The L1 jet trigger items are summarized in Table 7.5 with ET thresholds, window size andprescale factor in lumiblock 746 - 813 in run 159224.
Trigger Item (L1 XX)
ET threshold (GeV)
Window size
Prescale factor

J5
5
2×2
115

J10
J15
J30
J55
J75
J95 J115
10
15
30
55
75
95
115
4×4 4×4 4×4 4×4 4×4 4×4 4×4
8.0
1.0
1.0
1.0
1.0
1.0
1.0

Table 7.5: A summary of the Level-1 jet trigger items.

Chapter 8
W / Z Boson Event Reconstruction and
Selection
8.1

Cross Section Measurement Overview

The total production cross-section times branching ratio of the W / Z events, such as Z → µµ or
W → µν, can be factorized into several components as in Eq.(8.1).
σW/Z × BR(W/Z) =N obs − N bkg,
A · C · Lint

(8.1)

where
• σW/Z means the production cross section for W / Z boson, and BR(W/Z) represents its
branching fraction to the W → µν or Z → µµ.
• N obs represents the number of events in the experimental data which passed all the selection criteria applied in the analysis.
• N bkg is the estimated number of background events in the signal region in each analysis.
• A (Acceptance) denotes the acceptance in the phase space. C (Correction f actor) denotes
the correction for the detector effect. These values are derived from MC simulation foreach W → µν or Z → µµ process by calculating the following numbers (for details of
MC samples, see section 4.7.2).
N1 : the total number of generated events
N2 : the number of events generated in the fiducial acceptance defined in the phase space(the exact definitions are specific to each analysis). The fiducial acceptance is defined using Monte Calro truth variables before any QED radiation.
N3 : the number of events which pass the analysis specific selection criteria after event
reconstruction. The selection is made using reconstructed variables.

8.2 Luminosity Calculation

117

Then, the A and C are defined as
A=

N2
N3
, C=
,
N1
N2

(8.2)

In this study, data driven corrections, such as for muon trigger and reconstruction efficiencies, are applied on C to fairly reflect the actual experimental condition.
• Lint represents the integrated luminosity used in each analysis. Current uncertainty for the
Lint is estimated as 11 %. Details for the luminosity calculation is described in section
8.2.
This section is organized as follows: Section 8.2 describes the methodology and current
situation of the luminosity calculation. In section 8.3, the high-pT muon selection and ETmiss
reconstruction used in the W / Z cross sections measurement as well as an overview of the vertex
reconstruction and reweighing technique, and the requirement on the jet quality are presented.
Section 8.4 is devoted to describe the systematic uncertainties which are common to both W /Z-boson cross sections measurement.
Cross sections measurement in W → µν and Z → µµ processes are given in section 11 and
12 respectively.

8.2 Luminosity Calculation
The instantaneous luminosity of pp collision can be written as follows [121].
L=µnb fr µmeas nb fr µmeas nb fr
=
=
,
σinel
σinelσvis(8.3)

where µ is the mean number of inelastic pp interactions per bunch crossing (BC), σinel represents
the inelastic pp cross section, nb is the number of bunches colliding at the IP and fr is therevolution frequency. Also  is the efficiency of the luminosity calculation algorithm of thedetector used in the measurement, µmeas = µ is the average number of interactions per BC
that pass the selection requirements of the algorithm and the visible cross section σvis is thedetector calibration constant for the luminosity measurements. As one can see in the Eq.(8.3)
the luminosity calculation is done with knowledge of the four parameters, namely µmeas , σvis ,nb and fr (11245.5 Hz for LHC).
µmeas is measured by the several detectors such as MBTS, LUCID, LAr calorimeter and theinner detectors for charged particle event counting. The uncertainty for the µmeas measurement
is about 5 % for each method. For the central value used in this study, the one measured with
LUCID is adopted.
As described in the section 4.5, the ATLAS will perform an absolute σvis calibration using
the ALFA detector. Since the ALFA was not ready at the data taking period, σvis is predicted by
MC event generators and measured by the van der Meer (vdM) Scan. The details of the vdMscan are described in section 8.2.1. The dominant uncertainty for the luminosity measurementin this study is coming from the determination of σvis . Estimation using MC event generators
gives ∼20% uncertainty mainly coming from the modeling of the diffractive components of118

W / Z Boson Event Reconstruction and Selection

the pp cross section. Estimations obtained from vdM scans have better uncertainty of ∼11%
which is dominated by the uncertainty on the proton beam current measurement, especiallyby the accuracy of DC transformers [122]. For its smaller uncertainty, the vdM scan result isused for the luminosity calculation. nb , fr are the operation parameters of the LHC and those
uncertainties are zero. The σvis value used for this study is measured by the LUCID as
σvis = 40.2 ± 0.1 (stat) ± 4.4 (syst).

8.2.1

(8.4)

van der Meer (vdM) scanThis method was invented in 1968 by S. van der Meer who found that it was possible to measure
the effective height of the colliding ISR beams by observing the counting rate R in a suitabledetector while scanning one of the two beams in the vertical plane with respect to the other one.
In terms of colliding beam parameters, luminosity is defined as
Z
L = nb fr I1 I2 ρ1 (x, y)ρ2 (x, y)dxdy,(8.5)
where I1(2) is the number of particles per bunch in beam 1 (2) and ρ1(2) (x, y) is the particle density
in the transverse (x − y) plane of beam 1 (2) at the IP. Assuming no correlation between x andy, then the particle densities can be factorized and Eq.(8.5) can be rewritten as
L = nb fr I1 I2 Ω x (ρ1 (x)ρ2 (x))Ωy (ρ1 (y)ρ2 (y)),
where

(8.6)

Z
Ω x (ρ1 , ρ2 ) =ρ1 (x)ρ2 (x)dx,(8.7)

is the beam overlap integral in the x direction, and it is calculated asΩ x (ρ1 , ρ2 ) = R

R x (0)R x (x)dx

,

(8.8)

where R x (x) is the rate measured by the several detectors during a scan. We define Σ x by theequationR
R x (x)dx1
Σx = √.
(8.9)
2π R x (0)Using the last two equations, Eq.(8.5) can be rewritten asL=n b f r I1 I2.
2πΣ x Σy(8.10)

Three vdM scans have been performed at the ATLAS IP on April 26 and May 9 (2 successive
scans), 2010. In each scan, MBTS, Inner Detector and LUCID is used for the rate measurement
and analysis. The results from every detector agreed well within the error. We adopted theresult from the LUCID as the official value, because of the following three reasons.
• The LUCID has good time resolution and event counting capability to provide robust
luminosity measurements for the ATLAS up to luminosities about 1034 cm−2 s−1• The luminosity information provided from the LUCID is independent of the TDAQ, soless sensitive to TDAQ downtime than the other detectors• The background in LUCID is lower than the other detectors

8.3 W / Z Event Reconstruction and Selection
W → µν events are characterized by a high-pT isolated muon and a large ETmiss and Z →µµ events are by two oppositely charged high-pT isolated muons with a Z-boson consistentinvariant mass. In this section, the high-pT muon selection procedure used in the both W → µν
and Z → µµ analysis and how ETmiss is reconstructed are given.
Also, the cross sections measurement in W → µν and Z → µµ processes share common
selection on primary vertices. In each analysis, a event-by-event reweighing on the number ofvertices is applied. A description on these cuts and reweighing are given as well.
Finally, a description on the so-called jet cleaning procedure, which is to reject bad jet
induced by non-physics effect is presented.

8.3.1 High Quality Muon Selection
A set of selections is applied on combined tracks as a part of the W → µν and Z → µµ event
candidate selection. The aim of the selections is to extract prompt muons from W / Z-bosons.
Three types of backgrounds, namely muons from decay-in-flight of π / K mesons, cosmic ray
and QCD processes are mainly considered.
Shown in Figure 8.1 is a distribution of the difference in pT measured in the inner detector(pTID ) and in the muon spectrometer (pTMS ) for combined tracks with pT > 20 GeV and |η| < 1.05.
The events are required to pass the Z → µµ pre-selection (see section 12.1). Since a part of theenergy of π / K meson is lost through in-flight decay, the pTID − pTMS tend to be larger than thatof prompt muons as seen in Figure 8.1 (see a bump in the right-hand side of the distribution).
Making use of this feature, we applied the following cuts.
1. |pTID − pTMS | < 15 GeV
2. pTMS > 10 GeV
The definition of pTMS is a extrapolated pT measurement at the perigee originally measured in
the muon spectrometer then back-extrapolated to the IP. A cut of pT > 20 GeV is applied on thepT of combined tracks in both W / Z-boson cross sections measurement thus cut 2 contributes
to reduce decay-in-flight background.
To reject cosmic ray background, combined tracks are required to point the IP by a cut of
3. |z0 − zvtx | < 10 mmwith z0 the longitudinal impact parameter with respect to the IP and zvtx is the z-position of thegood primary vertex which minimizes |z0 − zvtx |. Figure 8.2 shows the distribution of z0 − zvtx
for combined tracks with pT > 20 GeV in the events which passed the W → µν pre-selection

W / Z Boson Event Reconstruction and Selection

Entries / 1 GeV

120

105

∫ L dt = 331 nb

-1

104

Data 2010 ( s = 7 TeV)
|η| < 1.05

3

10

102
10
1
-30

-20

-10

0

10

20

30

pID - pMS (GeV)
T
T

Figure 8.1: pTID − pTMS distribution for combined tracks with pT > 20 GeV and |η| < 1.05 forthe events which passed the Z → µµ pre-selection
and all the W → µν selection (see section 11.1). The figures show that z0 − zvtx is well modeledby the MC for both QCD and EW events.
Muons from QCD processes are tend to be surround by hadrons. To reject such non-isolated
tracks, the following cut is applied
4. ΣpTID /pT < 0.2 ( ∆R = 4 )where the sum is taken for all inner detector tracks with pT > 1 GeV within a cone with ∆R of
0.4. The denominator is the pT of the combined track in consideration. The contribution fromthe combined track is subtracted from the numerator. This isolation variable is referred to as
relative track isolation hereunder.
Figure 8.3 shows the distribution of relative track isolation for combined tracks with pT >20 GeV in the events which passed the W → µν pre-selection and all the W → µν selection (seesection 11.1). The figures show that relative track isolation is well modeled by the MC for both
QCD and EW events.

106

Data 2010 ( s = 7 TeV)

∫ L dt = 310 nb

-1

105
104

W → µν

Z → µµtt

W → τν

Z → ττ

QCD

121

Entries / 0.5 mm

Entries / 0.5 mm

8.3 W / Z Event Reconstruction and Selection

103

105

∫ L dt = 310 nb

-1

104

Data 2010 ( s = 7 TeV)W → µν

Z → µµtt

W → τν

Z → ττ

QCD

103
102

102
10
10
1

1
10-1
-15

-10

-5

0

5

10

10-1
-10 -8 -6 -4 -2

15

0

2

z0 - zvtx (mm)

4

6

8 10

z0 - zvtx (mm)

(a)

(b)

105
104

∫

Entries / 0.02

Entries / 0.02

Figure 8.2: z0 − zvtx distributions for combined tracks with pT > 20 GeV in the events which
passed the (a) W → µν pre-selection (b) all W → µν selection.

Data 2010 ( s = 7 TeV)

-1

L dt = 310 nb

103

W → µν

Z → µµtt

W → τν

Z → ττ

QCD

104

∫

Data 2010 ( s = 7 TeV)

-1

L dt = 310 nb

103

W → µν

Z → µµtt

W → τν

Z → ττ

QCD

102

102
10

10

1

1

10-1
0 0.05 0.10.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

10-1
0 0.020.040.060.08 0.10.120.140.160.18 0.2

Track Isolation / p

Track Isolation / p

T

(a)

T

(b)

Figure 8.3: Relative track isolation distributions for combined tracks with pT > 20 GeV in theevents which passed the (a) W → µν pre-selection (b) all W → µν selection.

122

8.3.2

W / Z Boson Event Reconstruction and Selection

Missing Transverse Energy Reconstruction

The missing transverse energy (ETmiss ) is defined as a vector with same magnitude and inverse
direction of the vectorial sum of all visible transverse energy. The definition of the ETmiss used in
the W / Z analyses is based on the energy deposits in the calorimeter and reconstructed muons.


X 
X


p~T  .
(8.11)
ETmiss = − E~T +calo cluster

muon

The first term means the vectorial sum of all calorimeter clusters reconstructed by a three
dimensional topological clustering algorithm [123]. Clusters are seeded by a cell which has
an energy significance, which is defined as |Ecell |/RMS noise with Ecell the energy of the celland RMS noise the expected RMS of the electronics noise, above 4. Then the neighboring cells
are added to the cluster if their energy significance is above a defined threshold. The resulted
clusters are classified into EM-like or hadron-like by their shape and calibrated their energy
scale locally depending on their classification [124].
For the ETmiss calculation, muons are classified into two classes. Isolated muon is defined
as muons with no jets within a cone with radius of ∆R ≤ 0.3. The energy deposition of theisolated muon in the calorimeter can be measured explicitly then removed from the first term.
The energy deposition of non-isolated muons cannot be separated from the nearby jet energy.
Therefore, the pT of muon reconstructed as a muon spectrometer standalone track is used unlessthere is a significant mismatch between the track parameters of standalone and corresponding
combined tracks. If there is a mismatch, the pT of the combined track is used and a parametrizedenergy loss in the calorimeter is removed from the first term. For muons in |η| > 2.5, outside
the inner detector acceptance ,the pT of standalone track is used. Details on the performancesof missing transverse energy is found in [125].

8.3 W / Z Event Reconstruction and Selection

123

8.3.3 Primary Vertex Reconstruction
In the cross sections measurement in W → µν and Z → µµ processes, events are required tohave one or more good quality primary vertices to reject events induced by cosmic rays. The
definition of the good vertex is as follows.
• To have three or more tracks• Position in z is within 150 mm from the IP
In this section, an overview of the primary vertex reconstruction in the ATLAS is given.
Primary vertices are reconstructed from tracks reconstructed in the inner detector. Descriptions about the tracking in the inner detector is presented in section 6.3 and Ref.[126, 127].
During the data taking period, tracks are reconstructed from track candidates with pT above 100
MeV in the Inside-Out Sequence and above 300 MeV in the Outside-In Sequence. The primaryvertex reconstruction in the ATLAS consists of two steps [2],• Primary vertex finding algorithm associates tracks to vertex candidates• Vertex fitting algorithm reconstructs vertices position and error matrices. This algorithm
also refits associated tracks constraining them to a reconstructed interaction point.
In the vertex reconstruction, following cuts are applied on the inner detector tracks.
- pT > 150 MeV- |d0 | < 4mm- σ (d0 ) < 5 mm
- σ (z0 ) < 10 mm- at least 4 hits in the SCT- at least 6 hits in the pixel and SCT
Here d0 and z0 denote the transverse and longitudinal impact parameters of tracks withrespect to the center of the beam-spot. Beam-spot is the luminous region in the ATLAS detector
reconstructed during physics run typically in every 10 minutes [128].
Shown in Figure 8.4 and 8.5 are the distributions of reconstructed primary vertices in 6 nb−1of integrated luminosity taken by L1 MBTS trigger. Shown in Figure 8.6 is the position and
RMS in each (x, y, z) coordinate of primary vertices reconstructed in each run. Both position and
RMS vary depending on the run number due to the changes in the LHC operation parameters.
The events are required to fulfill the W → µν GRL selection, L1 MU6 trigger requirement andhave one or more combined tracks in |η| < 2.4 and pT > 6 GeV.

W / Z Boson Event Reconstruction and Selection

Primary Vertex y [mm]

124

1.4

9000

ATLAS Preliminarys = 7 TeV

1.2

8000
7000

1

6000

0.8

5000

0.6

4000
3000

0.4

2000
0.2

RMS x = 0.024 mm

1000

RMS y = 0.040 mm

0-1-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0

Primary Vertex x [mm]0.4

ATLAS Preliminarys = 7 TeV

0.2

2500

0

2000

-0.2

1500

-0.4

Primary Vertex y [mm]Primary Vertex x [mm]Figure 8.4: Two dimensional distribution of reconstructed primary vertices in 6 nb−1 of 7 TeV
data taken by MBTS trigger in x − y plane [2].

1800
1.4

ATLAS Preliminarys = 7 TeV

1.2

1600
1400

1

1200

0.8

1000
800

0.6

1000
-0.6
500

RMS x = 0.024 mm
RMS z = 27.9 mm

-0.8
-1
-200

600
0.4

-150

-100

-50

0

50

100

150

200

0

400
RMS y = 0.040 mm
RMS z = 27.9 mm

0.2
0
-200

-150

-100

-50

0

Primary Vertex z [mm]

(a)

50

100

200
150

200

0

Primary Vertex z [mm](b)

Figure 8.5: Two dimensional distribution of reconstructed primary vertices in 6 nb−1 of 7 TeV
data taken by MBTS trigger in the x − z (a) and the y − z (b) [2].

152844152845152878152933152994153030153134153136153159153200153565153599154810154813154815154817154822155073155112155116155160155228155280155569155634
155669155678155697156682158045158116
158269158299158392
158443
158466158545158548158582
158632158801
158975159041
159086
159113159179159202159203
159224

Vertex z (mm)

-1
-1

-1.5
-1.5

-2
-2

2

1.5 period A
period B
period C100
80 period A
60
40
20
0
-20
-40
-60
-80
-100
period D10.5

period B

Vertex y (mm)Vertex Position and Size(RMS) in x

0
0

-0.5
-0.5

period C
152844152845152878152933152994153030153134153136153159153200153565153599154810154813154815154817154822155073155112155116155160155228155280155569155634
155669155678155697156682158045158116
158269158299158392
158443
158466158545158548158582
158632158801
158975159041
159086
159113159179159202159203
159224152844152845152878152933152994153030153134153136153159153200153565153599154810154813154815154817154822155073155112155116155160155228155280155569155634
155669155678155697156682158045158116
158269158299158392
158443
158466158545158548158582
158632158801
158975159041
159086
159113159179159202159203
159224

Vertex x (mm)8.3 W / Z Event Reconstruction and Selection
125

Vertex Position and Size(RMS) in y

1.5 period A

21

period B(a)period C

Run Number

period D

0.5

Run Number

Vertex Position and Size(RMS) in z(b)period D

Run Number(c)Figure 8.6: The mean position and RMS of primary vertices in (a) x, (b) y and (c) z coordinate
in each run.

126

W / Z Boson Event Reconstruction and Selection

Pile-up Event Reweighting
As mentioned in section 4.7.2, simulated minimum bias events are overlaid over the originalhard-scattering events in the W → µν and Z → µµ MC samples to model the pile-up effect.
Since the pile-up modeling is not perfect, a event-by-event reweighing is applied as describedhereunder.
Shown in Figure 8.7 (a) is the distribution of the number of good vertices in an event in data
and W → µν MC. The events are required to pass W → µν pre-selection (see section 11.1).
Also, the distribution of the z-position of primary vertices reconstructed with three or more
tracks is shown in Figure 8.7 (b). In Figure 8.7 (a), there is a significant difference between data
and MC.
To compensate this difference, an event-by-event weight is applied on the number of goodvertices in an event in the W / Z analyses. The total effect of the reweighing on the acceptanceis about 0.2 %. The reweighing factors for both W → µν and Z → µµ is given in Table 8.1.
number of vertices

fraction of events

number of vertices in Data and MC

10.9

all Data

0.8
MC

0.7
0.6
0.5

900
800

-1

Data 2010 ( s = 7 TeV)W → µ ν MC

700

# of tracks > 2

600
500
400

0.4

300

0.3
0.2

200

0.1

100

0

∫ L dt = 310 nb

0

2

4

6

8

10

0

-200-150-100 -50 0

50 100 150 200
vertices z [mm]number of vertices

(a)

(b)

Figure 8.7: (a) The number of good vertices in an event in data and W → µν MC. (b) z-positionof primary vertices reconstructed with three of more tracks.

Number of good Vertices
0
1
2
3
4
5
6
7

W event weight1
3.851431.03051
0.32755
0.10374
0.05154
0.00766
0.00671

Z event weight1
3.76055
1.062990.354120.113410.05356
0.00980
0.03498

Table 8.1: Event reweighing factors in terms of number of good vertices in an event.

8.3 W / Z Event Reconstruction and Selection

127

8.3.4 Jet Cleaning
To reduce spurious ETmiss generated from detector effects and cosmic rays, the events with jetswith ET in EM scale larger than 10 GeV and at least one of the following characteristics are
rejected in the W → µν analysis.
• A jet with the least number of cells accounting for 90 % of the jet energy (n90) is less orequal to 5 and the energy fraction in the hadronic endcap calorimeter ( fHEC ) is larger than
0.8. This cut is to remove noise bursts in the HEC where most of fake energy deposit isfound in a single or neighboring cells.
• A jet with the fraction of jet energy from bad-quality calorimeter cells ( fQLAr ) is larger
than 0.8 and the energy fraction in the EM calorimeter ( fEM ) is larger than 0.95. fQLAr isthe fraction of LAr cells with a cell Q-factor greater than 4000. The cell Q-factor is thedifference between measured and predicted pulse shape used for a cell energy reconstruction. This cut is to remove fake jets arise from noise bursts in the EM calorimeter.
• A jet with relative timing of the calorimeter deposits from the event time is larger than 50
ns. This cut is to remove out-of-time energy depositions in the calorimeter like cosmics.
Shown in Figure 8.8 are the jet cleaning variables in the events which pass the W → µν
GRL and L1 MU6 trigger with one or more combined tracks with |η| < 2.4 and pT > 6 GeV.
The effect of the jet cleaning on the W → µν acceptance is below 0.01 %.
Events / 0.01

Events / 1.0

104
103
2

10

Bad quality LAr cell fraction

Events / 0.01

Energy deposit fraction in HEC

minimum # of cells containing at least 90 % of the jet energy

106
5

10

104

106
105
104

3

10

103

102

102

10

10

10
1
1

1
0

102

10

0.2

0.4

n90

0.6

0.8

1

Events / 1.0(b)
Jet Timing

Events / 0.01

(a)

5

10

0.2

0.4

0.6

(c)

106
105
104
103

104

102
10

103
0

1
0.2

0.4

0.6

0.8

1

10-1
-100-80 -60 -40 -20 0 20 40 60 80 100
time (ns)emfrac

(d)

0.8

1

fQLAr

fHEC

Energy deposit fraction in EM calorimeters

106

1
0

(e)

Figure 8.8: Jet cleaning variables: (a) n90, (b) fHEC , (c) fQLAr , (d) fEM , (e) Jet timing.

128

8.4

W / Z Boson Event Reconstruction and Selection

Common Systematic Uncertainties

The following three systematic uncertainties which are common to both W / Z cross sections
measurement are evaluated in this section.
• The uncertainty from the muon momentum resolution and scale• The uncertainty from the muon isolation efficiency• The theoretical uncertainty on the acceptance (A and C)

8.4.1

Muon Momentum Resolution and Scale

The uncertainty on the momentum scale and resolution of the muon spectrometer are deduced
by investigating di-muon invariant mass distributions in Z → µµ events. The following two
methods are performed.
1. Fitting with Breit-Wigner function convoluted with a gaussian
2. Chi-square test
In both methods, the muon pT is parametrized as
!
!
1
1
1
=
× (1 + x × C2 ) ,×
pT smear C1
pT MC(8.12)

where (1/pT ) smear is the reconstructed muon curvature smeared by the detector effects which is
not included in the MC. (1/pT ) MC is the reconstructed muon curvature in MC. C1 is the momentum scale term and C2 is the additional momentum smearing term, x fluctuates as a gaussian
distribution with zero mean and unit width.
In the method 1, distributions are fitted with a Breit-Wigner function convoluted with agaussian. The C1 and C2 are determined as the value that fitted mean and gaussian width in data
and MC agree the best. Shown in Table 8.2 is the summary of the determined C1 and C2 .
C1
C2
All
0.991 ± 0.005 0.055 ± 0.012
endcap 0.980 ± 0.012 0.063 ± 0.031
barrel 0.992 ± 0.010 0.031 ± 0.020
Table 8.2: The determined C1 and C2 parameters by di-muon invariant mass distribution fitting.

In the method 2, di-muon invariant mass distributions are investigated by the Chi-square
test. χ2 between smeared distribution in data and in MC is calculated with various C1 and C2 .
Shown in Figure 8.9 is the ∆χ2 distribution in C1 − C2 plane and the di-muon invariant mass

8.4 Common Systematic Uncertainties

129

distribution in data and MC. The distributions in MC are smeared with C1 and C2 which report
the minimum χ2 value (summarized in Table 8.3). Figure 8.9 (a) and (b) are the results for all
Z → µµ events, (c) and (d) are for events in which both muons are generated into the endcap and(e) and (f) are for events in which both muons are generated into the barrel. The χ2 is calculated
within the mass window of 66 < Mµµ < 116 with the binning shown in Figure (b), (d) and (f).
The yellow lines in Figure 8.9 (a), (c) and (e) indicate contour lines where ∆χ2 = 1, 4, 9.... The
results by the method 2 are well consistent with the results from the method 1 within the regionin which ∆χ2 < 1.
C1
All
0.99
endcap 0.99
barrel 0.985

C2
χ2
0.07 0.49
0.07 0.77
0.035 0.58

Table 8.3: The determined C1 and C2 parameters with calculated χ2 value by Chi-square teston the di-muon invariant mass distributions.
The results from both methods are consistent with the estimations from the ATLAS muoncombined performance group based on the comparisons between the measurements in the innerdetector and the muon spectrometer for given combined tracks [129]. Hence the uncertainties
in Ref.[129] are adopted as 0.01 for muon momentum scale and 5 (9) % in endcap (barrel) formuon momentum resolution.

8.4.2 Muon Isolation Efficiency
In the W / Z-boson cross sections measurement, a requirement of relative track isolation isP
applied ( pTID /pT < 0.2 within a cone of ∆R < 0.4). The difference in efficiency for theisolation cut in data and MC is considered as a systematic component.
This effect is estimated using muons selected by tag-and-probe method (see section 10) andresulted efficiency is 0.984 ± 0.010 in data and 0.993 in MC with negligible statistical error. The
difference of ∼ 1 % is observed. This value is taken as a conservative systematic uncertainty
with the central value calculated in MC.

2

0.2
20
18
0.15

16
14

Entries / 5GeV

W / Z Boson Event Reconstruction and Selection

Additional Smearing (C )

130

12

0.1

Data 2010( s = 7 TeV)

30

6

15

4

10

2

5

0
1

35

Z → µµ2080.9 0.92 0.94 0.96 0.98

-1

25

10

0.05

∫ L dt = 331 nb
40
45

0
60

1.02 1.04

70

80

90

100

Momentum Scale Factor (C )

(a)

(b)

0.2
25
0.15

20

Entries / 10 GeV

2120

Mµµ (GeV)

1

Additional Smearing (C )

110

15

0.1

20
18

∫ L dt = 331 nb-1

16

Data 2010( s = 7 TeV)

14

Z → µµ

12
10
8

10

6

0.05
5

4
2

0
0.9 0.92 0.94 0.96 0.98

1

0
60

1.02 1.04

70

80

90

100

Momentum Scale Factor (C )

0.2

9
8

0.15

7
6
5

0.1

0.05

0
1

20
18
16
14

-1

Data 2010( s = 7 TeV)Z → µµ

12
10

4

8

3

6

2

4

1

2
0
60

1.02 1.04∫ L dt = 331 nb

70

80

90

Momentum Scale Factor (C )

100

110

120

Mµµ (GeV)

1

(e)

120

(d)
Entries / 10 GeV

2Additional Smearing (C )(c)

0.9 0.92 0.94 0.96 0.98

110Mµµ (GeV)

1(f)

Figure 8.9: The calculated distributions of ∆χ2 between the di-muon invariant mass distribution
in data and MC in C1 − C2 plane ((a), (b), (c)). (a) is for all Z → µµ events, (c) is for events inwhich both muons are generated into the endcap and (e) is for events in which both muons are
generated into the barrel. The yellow contour lines indicate where ∆χ2 = 1, 4, 9.... The di-muon
invariant mass distributions in data and MC with C1 and C2 which reports the minimum χ2 arealso shown ((b), (d), (f)).

8.4 Common Systematic Uncertainties

131

8.4.3 Theoretical Uncertainty on AcceptanceAs described in section 4.7.2, the central values for the acceptances (A, C) are estimated byusing PYTHIA event generator with the MRST LO∗ [93] PDFs. The uncertainty on these acceptance is estimated by a method which is common to W → µν and Z → µµ analyses [130].
Uncertainties on A
The systematic uncertainties on the acceptances A are dominated by a limited knowledge on
PDFs and the modeling of W / Z-boson production at the LHC. In the uncertainty estimation,
the following three components are considered as independent contributions.
• The uncertainty within a PDF set is estimated using PDF error eigenvectors of the CTEQ6.6
NLO PDF set [131]. The error eigenvectors are obtained by PDF reweighing of a single
sample of events generated using MC@NLO [132] and the CTEQ6.6 NLO PDF set. The
estimated amount of uncertainty on acceptance is 1.8 % for W → µν and 1.6 % for
Z → µµ, respectively.
• The uncertainty between different PDF sets is estimated by comparing three different
PDF sets (MRST LO∗ , CTEQ6.6 and HERAPDF1.0 [133] NLO PDF). The events are
generated with PYTHIA. The estimated amount of uncertainty on acceptance is 1.1 % for
W → µν and 2.0 % for Z → µµ, respectively.
• The uncertainty due to the modeling of W / Z-boson production is estimated from thedifference of the results between PYTHIA and MC@NLO using CTEQ6.6 PDF set. The
estimated amount of uncertainty on acceptance is 1.6 % for W → µν and 2.8 % for
Z → µµ, respectively.
The results are added in quadrature. The resulted uncertainty on A is 3.0 % for W → µν
analysis and 4.0 % for Z → µµ analysis.
Uncertainties on C
The theoretical uncertainty on C is obtained by a PDF reweighing technique due to the limited
statistics. The three PDF sets (MRST LO∗ , CTEQ6.6 and HERAPDF1.0) are used and the 0.3% of uncertainty is obtained for both W → µν and Z → µµ processes.
Besides, the uncertainty coming from low energy (< 1 GeV) FSR is independently estimatedas 0.2 %, and the resulted total theoretical uncertainty on C is 0.4 % for both W → µν andZ → µµ processes.

Chapter 9
Muon Trigger Efficiency Estimation using
Collision Data
The methods and results for the muon trigger efficiency estimation are presented in this chapter.
In this study, the muon trigger efficiency relative to a combined track is estimated since both W /Z-boson cross sections measurement requires at least one combined track in the event selection.
Independent two methods are utilized in this efficiency measurement.
1. Using high-pT combined track samples which pass a selection based on the ones usedin the W / Z-boson cross sections measurement (this method is referred to as the single
combined track method hereunder)
2. Using combined track samples identified as a muon by so-called tag-and-probe method
in Z → µµ events
This section is organized as follows. In section 9.1, a description of the situation of theLevel-1 muon trigger in the data taking period is given. Section 9.2 describes the relative
trigger efficiency estimation by the single combined track method. In section 9.3, an overview
of tag-and-probe method in Z → µµ events is presented followed by a description of actual
analysis and results. Finally the relative trigger efficiency results for the W / Z-boson crosssections measurement are summarized in section 9.4.

9.1

Level-1 Muon Trigger Configuration

The TGC and RPC are designed to be operated with six levels of pT threshold. Both detectors
share a common set of five thresholds throughout the data taking period. Each of them are
named as L1 MU0, L1 MU6, L1 MU10, L1 MU15 and L1 MU20. Remaining one thresholdhave been used for a commissioning purpose.
All the thresholds except for L1 MU0 deploy dedicated coincidence window on the top of
the high-pT coincidence condition. The coincidence window is set to have a pT threshold at thevalue as their name indicates, i.e. L1 MU6 is tuned to have its threshold around 6 GeV. The
efficiency for the L1 MU6 is tuned to be about 80 % at the threshold.

9.1 Level-1 Muon Trigger Configuration

133

In the TGC case, the low-pT and high-pT coincidence are set as the nominal configuration.
low-pT coincidence requires 3-out-of-4 hit coincidence both for wires and strips. High-pT coincidence requires 2-out-of-3 coincidence for wires and 1-out-of-2 for strips on the top of the
low-pT coincidence. The BCID gate width is set at 35 (45) ns for wires (strips).
Figure 9.1 shows a simulated L1 MU6 efficiency map in the endcap (1.05 < |η| < 2.4) formuons with pT = 20 GeV. This trigger item is used in the W / Z analysis as the event trigger.
An inefficient region at the outer edge of the TGC is due to the presence of magnetic field
where muons bend away from TGC acceptance depending on their charges. Ineffective areasin the TGC are due to the presence of the holes for the laser optical alignment and the physicalboundary of the TGC chambers.

Figure 9.1: Simulated TGC L1MU6 trigger efficiency for muons with pT of 20 GeV generated
in 1.05 < |η| < 2.4 in the r − φ plane.
Figure 9.1 shows a simulated L1 MU0 efficiency map in the barrel (|η| < 1.05) for muons
with pT = 10 GeV. This map indicates the acceptance holes in the barrel. Due to the presence ofthe detector support structure (Feet), magnet support, services for the calorimeters and elevator,
the overall coverage of the RPC is about 80 % in the entire barrel region.

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Figure 9.2: A map of the RPC trigger coverage in η − φ plane.

9.1 Level-1 Muon Trigger Configuration

135

9.1.1 Timing Acceptance Stretch for Muon Level-1 Trigger Commissioning
As described in section 7.3, the timing acceptance of the MUCTPI is stretched as [-2, -1, 0] interms of BCID difference ([BCID for a muon RoI] - [BCID for the event]). In the muon trigger
efficiency calculation, RoIs in the stretched time window are adopted.
To see how BCID difference distributes, combined tracks are selected by the following
selection and the BCID difference of the muon RoIs matched with any of the combined tracks
are plotted.
– Reconstructed in the MuId algorithm chain– Matching χ2 < 50
– Number of SCT hits ≥ 4– Number of Pixel hits ≥ 1– |z0 − zvtx | < 10 mm
q1
0.8
ATLAS Preliminarys = 7TeV, Data 20100.6

|η| > 1.05

Fraction of Events

Fraction of Events

In the matching between a given combined track and a muon RoI, ∆R = (∆η)2 + (∆φ)2 of 0.5
is used. If a combined track matches with more than one RoI, the RoI which has larger BCID
is adopted.
Figure 9.3 shows the distributions of the BCID difference for the TGC and the RPC trigger
with respect to the L1 MBTS trigger. The events used in the figures are taken by L1 MBTS
trigger, hence the figures show the difference in BCID between muon RoIs and event timings.
0.8

Calibration with cosmic ray data
First calibration with collision data

0.7
0.6
0.5
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0.4
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ATLAS Preliminary
Data 2010, s = 7 TeV

0.2|η|<1.05

0.1
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1

2

3

4

0

−4

−2

0

TTGC - TMBTS [BC]

(a)

2

4

TRPC − TMBTS [BC](b)

Figure 9.3: Distribution of the trigger time difference in units of bunch crossing (BC) withrespect to the L1 MBTS for the TGC (a) and the RPC (b) triggers.

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9.2

Trigger Efficiency Estimation by the Single Combined
Track Method

This section describes the relative trigger efficiency estimation with respect to combined tracks
which pass a selection based on the one used in the W / Z-boson cross sections measurement.
The estimation is done with the following procedures.
1. Select a combined track
2. Extrapolate the trajectory of the combined track toward the TGC or RPC then define an
RoI search range on the pivot plane
3. Search muon RoIs in the search range
If more than one muon RoIs are found in the search range, the RoI is flagged as fired by the
combined track.
This analysis is done with the data taken via L1Calo stream upon a request that at least one
L1 single jet trigger is issued in a given event (the exact requirement is the OR of all L1 single
jet trigger items, see Table 7.5). Since the single jet triggers are independent to the muon trigger,
no trigger bias is caused in the estimation.

9.2.1

The Combined Track Selection

The selection on combined tracks used is given in Table 9.1. The selection is based on the W /Z event pre-selection (see Table 11.1 and 12.1).
Collision event selection
Good Run List & BCID Z → µµ GRL
Primary vertex
Nvtx ≥ 1 with Ntracks ≥ 3|zvtx | < 150 mm
Trigger
OR of all L1 single jet triggers
High-pT muon selection
Muon selection
STACO combined tracks
pT > 20 GeV, |η| < 2.4
Muon quality
pTMS > 10 GeV|pTMS − pTID | < 15 GeV|z0 − zvtx | < 10 mmTable 9.1: Event and muon selection for trigger efficiency measurement.
The Z → µµ GRL is applied with resulted integrated luminosity is 331 nb−1 . Then theevents are required to pass any of L1 single jet triggers and have one or more good vertices (forthe definition of the good vertex, see section 8.3.3).
Muons are required to be a combined track reconstructed with STACO algorithm with pT >20 GeV in |η| < 2.4. pTMS , pTID are the pT measured only with the muon spectrometer or the9.2 Trigger Efficiency Estimation by the Single Combined Track Method

137

inner detector. z0 means the longitudinal impact parameter with respect to the IP and zvtx is thez-position of a good vertex which minimizes |z0 − zvtx |. Details for the cuts related to pTMS , pTID ,z0 and zvtx are found in section 8.3.1.
The differences between Table 9.1 and the W / Z pre-selection are summarized as follows.
1. pT > 20 GeV, which is consistent with W / Z final selection, is required in the efficiency
estimation.
2. The OR of all L1 single jet triggers is required in this analysis to avoid trigger biases
instead of L1 MU6 in W / Z cross sections measurement
3. No isolation is required since additional activities around a combined track are considered
not to cause any bias in the trigger efficiency estimation (confirmed in section 9.2.4) andisolation requirements largely reduce the available statistics
Figure 9.4 shows event displays for a sample of events used in this efficiency estimation.
All the five samples are taken from the run 159224. The red lines are muons, the purple cones
are jets, the yellow lines are tracks reconstructed in the inner detector and the yellow blocks arecalorimeter clusters. The gray circle represents the projection plane of the endcap TRT. Since
the events are taken by single jet triggers, muons are tend to be immersed in a jet.
Figure 9.5 shows the η, φ and pT distributions for the muons which pass all the selections,
hereafter referred to as denominator muons (the cut of pT > 20 GeV is omitted in the pT distributions just to show the lower pT components). In this figure, positive and negative charged
muons are shown separately and histograms are stacked. In this trigger efficiency estimation,
the entire muon spectrometer acceptance is divided into two bins, namely the endcap (1.05< η <2.4) and the barrel (|η| <1.05), each corresponds to the TGC and RPC respectively. The
number of denominator muons are 2307 (+ :1187, − :1120) in the endcap and 3173 (+ :1670,− :1503) in the barrel.

9.2.2 Track Extrapolation and Search Range Definition
Two independent methods are deployed in the track extrapolation and search range calculation.
In this analysis, the track extrapolator method is used by default. The straight line extrapolation
method is used for a validation of the results and a systematic uncertainty estimation.
Track Extrapolator Method
This method utilizes a tool called track extrapolator [134, 135] to extrapolate the trajectory ofthe denominator muons. In the extrapolation process, the track extrapolator takes into accountthe effect of magnetic field [136] and materials [137].
Extrapolations are done toward artificially defined pseudo trigger pivot planes.
• A cylinder with r = 7500 mm and half-length = 16000 mm along the beam axis fordenominator muons in |η| < 1.05 (barrel)• Two disks with r = 20000 mm at |z| = 15525 mm placed perpendicular to the beam axis
for denominator muons with 1.05 < |η| < 2.4 (endcap)

138

Muon Trigger Efficiency Estimation using Collision Data

(a)

(b)

(c)

(d)

(e)

Figure 9.4: Event displays of the events used in the efficiency estimation. Red lines are muons,yellow lines are tracks reconstructed in the inner detector, purple cones are jets and yellow
blocks are clusters in the calorimeter. Most of muons are immersed in a jet. All events aretaken from RunNumber = 159224, LumiBlock = 260 and (a) EventNumber = 4628851 (b)EventNumber = 4634992 (c) EventNumber = 4636444 (d) EventNumber = 4659650 and (d)EventNumber = 4665286.

Entries / 0.24

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80

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30

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50

60

70

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Muon p (GeV)

T

(d)

40

T

(e)

Figure 9.5: η, φ and pT distributions of muons which passed all the selections listed in Table
9.1 except for the pT distributions (the cut of pT > 20 GeV is not applied on these distributions). Positive and negative muons are shown separately and both are stacked. The φ and pT
distributions are shown for the endcap ((b), (d)) and the barrel ((c), (e)) separately.

140

Muon Trigger Efficiency Estimation using Collision Data

After an extrapolation, track extrapolator reports calculated extrapolation errors, δη and δφ. The
search range is calculated based on this extrapolation error as
search range = (matching tolerance) ×pδη2 + δφ2 + ( RoI size ).

(9.1)

The RoI size represents the half-diagonal length of RoI. The region dependence of RoI size issummarized in Table 9.2.
Region
RoI sizebarrel ( |η| < 1.05) endcap (1.05 < |η| < 1.95)
0.071
0.019

forward (|η| > 1.95)
0.034

Table 9.2: Region dependence of RoI size.
Matching tolerance is an adjustable number and set at 3.0 by default. ∆R is defined as,∆R =p(ηex − ηRoI )2 + (φex − φRoI )2 ,(9.2)

where ( ηex , φex ) represents the extrapolated position on the pseudo pivot plane and ( ηRoI , φRoI )is the center position of the RoI in the η − φ plane.
Straight Line Extrapolation Method
In this method, a track trajectory is extrapolated assuming a straight line ignoring the effects ofmagnetic field and materials. This approximation is valid for high-pT tracks used in W / Z crosssections measurement. A constant size of search range is defined. The default value is ∆R =0.3. This method is much simpler and robust compared to the track extrapolator method.

9.2.3

RoI Finding in a Search Range

If an RoI is found in the search range, the RoI is flagged as fired by the denominator muon. In
case that more than one RoI are found in a search range, one must choose an RoI to be taken.
In searching an RoI, two procedures – called the highest pT procedure and the nearest position
procedure – are deployed. The order of priority adopted in each procedure is as follows.
The Highest pT Procedure
1. The RoI with the highest pT threshold value
2. The RoI at the nearest position from the extrapolated point
3. The RoI with the largest BCID in the stretched timing acceptance9.2 Trigger Efficiency Estimation by the Single Combined Track Method

141

The Nearest Position Procedure
1. The RoI at the nearest position from the extrapolated point
2. The RoI with the highest pT threshold value
3. The RoI with the largest BCID in the stretched timing acceptance
The highest pT procedures is used by default. The nearest position procedures is used for across check and a systematic uncertainty estimation.

142

9.2.4

Muon Trigger Efficiency Estimation using Collision Data

Estimated Efficiency and Scale Factor

The L1 MU6 trigger efficiencies are estimated using the following combination as the default.
• The track extrapolator method in track extrapolation and search range definition• The highest pT procedure in RoI finding
Shown in Figure 9.6 is a two dimensional map of the estimated trigger efficiency for the
L1 MU6. A low efficiency region with η < -1.9 and φ ∼ -1.8 is due to a problematic electronics
board which applies threshold voltages. The condition of the board has not changed throughout
the data taking period. Another low efficiency region around φ ∼ -1.6 in the barrel is due to theacceptance hole on the RPC for the detector support structure (see Figure 9.2). For the figure,pT cut value is relaxed from 20 GeV to 15 GeV to gain statistics.
Shown in Figure 9.7 is the estimated trigger efficiency for the L1 MU6 as a function of η, φand pT . The results for the endcap and the barrel shown separately for the figure in terms of φand pT . The Figure 9.7 (a) shows the η dependence, which shows the low efficiency in η < -1.9
due to the above mentioned problematic electronics board. The efficiency in the barrel is lower
than the endcap reflecting the lower acceptance in the barrel. The Figure 9.7 (c) shows the φdependence in the barrel. The above mentioned support structure region is clearly seen.
A list of the estimated efficiencies for all the L1 single muon trigger items in pT > 20 GeV
are summarized in Table 9.3 along with the trigger efficiencies estimated in MC and trigger
efficiency scale factors (The definition of the scale factor is described later). As shown in thetable, the estimated trigger efficiency is consistent between positive and negative muons within
1 σ. Hence no charge dependence in the trigger efficiency is assumed in this study.

Figure 9.6: Estimated trigger efficiency for L1 MU6 in data in the η − φ. The track selection isbased on Table 9.1 but pT cut value is relaxed to 15 GeV.

Relative MU6 Efficiency

9.2 Trigger Efficiency Estimation by the Single Combined Track Method

143

1
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0.2
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Relative MU6 Efficiency

Relative MU6 Efficiency

(a)

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Relative MU6 Efficiency

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0
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50

60

70

80

Muon p [GeV]

T

(d)

40

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(e)

Figure 9.7: Estimated L1 MU6 trigger efficiency as a function of η, φ and pT for muons which
passed all the selections listed in Table 9.1 except for the cut of pT > 20 GeV in pT distributions. Efficiencies for positive, negative and all muons are shown separately. The φ and pT
distributions are shown for the endcap ((b), (d)) and the barrel ((c), (e)) separately.

144

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Isolation Effect on Trigger Efficiencies
As shown in Figure 9.4, denominator muons are tend to be not isolated. The basic concept of
this relative trigger efficiency measurement is to use the muons with the same quality for trigger
efficiency as the one used in the W / Z-boson cross sections measurement. A naive guess isthat, since both the TGC and RPC utilize hit coincidence in its algorithm, additional hits will
not deteriorate the efficiency unless the density of hits becomes huge. The dependence of thetrigger efficiency on isolation is investigated to ensure this assumption.
Two types of isolation variables are defined. One is utilizing a sum of transverse energy
in the calorimeter within a cone centered at the direction of the muon in consideration with acertain ∆R divided by the pT of the muon.
( relative ET isolation ) =Σ∆R ET (calo).
pT (track)(9.3)

Another is utilizing a sum of pT of charged tracks reconstructed in the inner detector within acone centered at the direction of the muon in consideration with a certain ∆R divided by the pTon the muon. In the calculation, pT of tracks with pT < 1 GeV and the pT of muon itself is not
added.
Σ∆R pT (track)( relative pT isolation ) =.
(9.4)
pT (track)

1
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Data 2010, s = 7 TeV|η| > 1.05, p > 20 GeV

Σ p , ∆ R = 0.1

Σ ET , ∆ R = 0.1

-1

T

T

Σ p , ∆ R = 0.2
TΣ ET , ∆ R = 0.2

TΣ ET , ∆ R = 0.3

Σ p , ∆ R = 0.3
Σ p , ∆ R = 0.4
TΣ ET , ∆ R = 0.4

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Relative MU6 Efficiency

Relative MU6 Efficiency

The contribution from the muon itself is subtracted from the numerator in both types of isolation
variables.
Figure 9.8 shows the dependence of L1 MU6 trigger efficiency on the two isolation variables
with different ∆R values. One can see that relative trigger efficiencies do not depend on theisolation variables. Figure 9.9 shows distributions for both isolation variables in the endcap
and the barrel. The one used in the cross sections measurement of the W / Z is the relative pT
isolation with ∆R = 0.4.
1
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TΣ ET , ∆ R = 0.3

TΣ ET , ∆ R = 0.4

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Isolation Value(a)Σ ET , ∆ R = 0.1

TΣ p , ∆ R = 0.3
Σ p , ∆ R = 0.4

0.4

Data 2010, s = 7 TeVIsolation Value(b)

Figure 9.8: Isolation dependence of L1 MU6 efficiency in the endcap (a) and the barrel (b).

∫ L dt = 331 nb

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1.5

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0

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Relative calo. ET isolation

(c)

(d)

Figure 9.9: Relative pT and ET isolation variables for denominator muons in endcap ((a), (c))
and barrel ((b), (d)) with various cone sizes.

146

Muon Trigger Efficiency Estimation using Collision Data

Trigger Efficiency Scale Factor
In the W / Z-boson cross sections measurement, trigger efficiencies measured in data are used
for the correction of MC efficiency (see section 8.1), thus the actual value used in the crosssections measurement is so called scale factor, the ratio of data efficiency to MC efficiency.
scale factor =efficiency in data.
efficiency in MC(9.5)

In this section the scale factor for single muons is derived. The MC sample used in thisderivation is of W → µν process.
In the efficiency estimation in both data and MC, the completely same method is deployed,
i.e. no truth information is used for MC. In this study, efficiency for L1 MU6 has a special
importance since it is used for the W / Z-boson cross sections measurement. Figure 9.10 showsthe estimated single muon efficiency for L1 MU6 in the endcap and the barrel as a function of
pT . The selection in Table 9.1 is applied except for the pT > 20 GeV just to show the efficiency
in the pT region below the cut value. In the cross sections measurement, the muons with pT >20 GeV is used thus the single muon scale factor is derived using the average efficiency in thepT > 20 GeV region. Table 9.3 summarizes the efficiencies and scale factors for denominatormuons with pT > 20 GeV.
One can see a discrepancy between the efficiency in data and MC for L1 MU6 especially inthe endcap. Currently this is understood as a combination effect of the inefficiency of the TGC
chambers and lack of calibration for the trigger road programmed in the L1 trigger electronics.
efficiency in data
efficiency in MC
scale factor
charge endcap (%) barrel (%) endcap (%) barrel (%) endcap (%) barrel (%)
all
95.1 ± 0.4 76.8 ± 0.7 98.2 ± 0.1 79.5 ± 0.2 96.9 ± 0.5 96.6 ± 1.0+
L1 MU0 µ95.2 ± 0.6 77.4 ± 1.0 98.2 ± 0.1 79.4 ± 0.3 97.0 ± 0.6 97.4 ± 1.3µ−
95.0 ± 0.7 76.2 ± 1.1 98.2 ± 0.1 79.6 ± 0.3 96.7 ± 0.7 95.7 ± 1.4
all86.5 ± 0.7 76.3 ± 0.8 95.0 ± 0.1 79.3 ± 0.3 91.1 ± 0.8 96.1 ± 1.0+
L1 MU6 µ86.5 ± 1.0 76.9 ± 1.0 94.9 ± 0.1 79.3 ± 0.3 91.2 ± 1.1 97.1 ± 1.3µ−
86.4 ± 1.0 75.5 ± 1.1 95.1 ± 0.2 79.5 ± 0.3 90.9 ± 1.1 95.0 ± 1.4
all86.3 ± 0.7 76.2 ± 0.8 94.8 ± 0.1 79.3 ± 0.2 91.0 ± 0.8 96.1 ± 1.0+
L1 MU10 µ86.3 ± 1.0 76.9 ± 1.0 94.7 ± 0.1 79.2 ± 0.3 91.1 ± 1.1 97.1 ± 1.3µ−
86.3 ± 1.0 75.4 ± 1.1 94.8 ± 0.2 79.4 ± 0.3 91.0 ± 1.1 95.0 ± 1.4
all85.1 ± 0.7 61.1 ± 0.9 94.1 ± 0.1 73.2 ± 0.2 90.4 ± 0.8 83.6 ± 1.2
L1 MU15 µ+85.1 ± 1.0 62.0 ± 1.2 94.0 ± 0.1 73.2 ± 0.3 90.5 ± 1.1 84.8 ± 1.7−µ
85.1 ± 1.1 60.1 ± 1.3 94.2 ± 0.2 73.2 ± 0.3 90.3 ± 1.1 82.2 ± 1.8
all82.6 ± 0.8 60.6 ± 0.9 93.6 ± 0.1 73.1 ± 0.2 88.2 ± 0.8 82.9 ± 1.2
L1 MU20 µ+82.8 ± 1.1 61.5 ± 1.2 93.6 ± 0.1 73.1 ± 0.3 88.5 ± 1.1 84.2 ± 1.7−µ
82.4 ± 1.1 59.5 ± 1.3 93.8 ± 0.2 73.1 ± 0.3 87.9 ± 1.2 81.5 ± 1.8
triggerTable 9.3: A summary of the L1 single muon trigger efficiencies. Assigned errors contain only
statistical components.

1

Relative MU6 Efficiency

Relative MU6 Efficiency

9.2 Trigger Efficiency Estimation by the Single Combined Track Method

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Figure 9.10: L1 MU6 trigger efficiencies estimated in data and MC in the endcap ((a)) and thebarrel ((b)). Muons are selected by the selection in Table 9.3 except for pT cut of 20 GeV. In
the scale factor calculation, the average efficiency in the pT > 20 GeV is used.

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9.2.5

Systematic Uncertainty

The L1 MU6 is solely used in the W / Z-boson cross sections measurement since it is the lowest
threshold un-prescaled trigger during the data taking period. In this section, systematic uncertainty on the L1 MU6 efficiency and scale factor is investigated. The results are summarized inTable 9.4. The detailed description for each component is given in the following subsections.

Reconstruction algorithm dependencepT cut value (± 5 GeV)
|pTID − pTMS | cut value (± 5 GeV)
Track extrapolation method
RoI finding criteria
Size of search range in RoI findingη distribution re-weight
Total

eff. in data (%) eff. in MC (%) scale factor (%)
endcap barrel endcap barrel endcap barrel
0.4
2.8
0.0
1.3
0.5
1.5
0.8
1.1
0.1
0.2
0.8
1.0
0.4
0.1
0.0
0.2
0.4
0.1
1.3
0.4
0.3
0.1
1.0
0.4
1.5
0.1
0.3
0.0
1.2
0.1
0.5
0.1
0.4
0.0
0.2
0.1
—
—
—
—
0.3
0.5
2.3
3.0
0.6
1.3
1.9
1.9

Table 9.4: Relative systematics for the L1 MU6 trigger efficiencies and scale factors.

Reconstruction algorithm dependence STACO algorithm, which is used as the default inthis analysis, requires at least one trigger hit in both η and φ coordinates in ROA search whereas
MuId algorithm does not. This requirement could bias the relative trigger efficiency. The sizeof bias differs place by place reflecting the variation in acceptance and efficiency of the trigger
chambers. However the current binning, which divides the muon spectrometer into only twobins namely the endcap (|η| > 1.05) and the barrel (|η| < 1.05), is so coarse that we cannot besensitive to this effect.
To cover this effect, we take the difference in measured efficiency between STACO and
MuId as a systematic component. The L1 MU6 trigger efficiencies for STACO is summarizedin Table 9.3 and for MuId are summarized in Table 9.5. The estimated relative uncertainties,
estimated uncertainty divided by the efficiency or scale factor of STACO muons, on efficiency
in data are 0.4 (2.8) % and in MC are 0.0 (1.3) % in the endcap (barrel) resulting uncertainties
on the scale factors of 0.5 (1.5) %.
eff. in data (%)
eff. in MC (%)
scale factor (%)
chargeendcapbarrelendcapbarrelendcapbarrelall
86.1 ± 0.7 74.2 ± 0.8 95.0 ± 0.1 78.3 ± 0.2 90.6 ± 0.8 94.7 ± 1.0µ+
86.6 ± 1.0 75.0 ± 1.0 94.9 ± 0.1 78.2 ± 0.3 91.2 ± 1.0 95.9 ± 1.4−µ
85.6 ± 1.0 73.3 ± 1.1 95.1 ± 0.2 78.5 ± 0.3 89.9 ± 1.1 93.3 ± 1.4
Table 9.5: A summary of the L1 MU6 trigger efficiencies and scale factors with respect tomuons reconstructed in MuId algorithm.

9.2 Trigger Efficiency Estimation by the Single Combined Track Method

149

1.1

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| > 1.05

0.95
0.9
0.85
0.8

eff. Data
eff. MC

0.75
0.7

scale factor

16

18

20

22

24

Relative MU6 Efficiency / Scale Factor

Relative MU6 Efficiency / Scale Factor

pT Cut Value To take into account the muon momentum scale and resolution fluctuation
resulting an instability of the averaged efficiency in plateau region, the pT cut value is shiftedby ± 5 GeV with 0.5 GeV steps. The results are shown in Figure 9.11 for both in the endcap
and the barrel. The assigned errors are statistical only.
Though fluctuations of the central efficiency / scale factor values are relatively small compared to the statistical error, the maximum shift of central values are counted as a conservative
systematic component. The estimated relative uncertainties on efficiency in data are 0.8 (1.1) %and in MC are 0.1 (0.2) % in the endcap (barrel), resulting uncertainties on the scale factors of
0.8 (1.0) %.
1.1

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| < 1.05

0.95
0.9

eff. Data
eff. MC

0.85

scale factor

0.8
0.75
0.7

16

18

20

Muon p cut (GeV)

24

Muon p cut (GeV)

T

(a)

22
T

(b)

Figure 9.11: Fluctuation of averaged L1 MU6 efficiency for muons with pT > 20 GeV andscale factor with shifting pT cut.
|pTID − pTMS | cut value To estimate the impact of the decay-in-flight contamination in the denominator muons, the effect of changing |pTID − pTMS | cut value is investigated.
In the estimation, the cut value is shifted by 0.5 GeV step and the maximum shift of the central value between 10 GeV and 20 GeV are counted as a systematic component. The resulting
plots are shown in Figure 9.12. The estimated relative uncertainties on efficiency in data are 0.4(0.1) % and in MC are 0.0 (0.2) % in the endcap (barrel), resulting uncertainties on the scale
factors of 0.4 (0.1) %.
Track extrapolation method dependence As described in section 9.2.3, two methods are
deployed for the track extrapolations. By default, the track extrapolator is used but the straightline extrapolation method is also utilized. The difference in the estimated efficiencies between
both methods are taken as a systematic component.
The estimated relative uncertainties on efficiency in data are 1.3 (0.4) % and in MC are 0.3(0.1) % in the endcap (barrel), resulting uncertainties on the scale factors of 1.0 (0.4) %.

Muon Trigger Efficiency Estimation using Collision Data

1.1

Relative MU6 Efficiency / Scale Factor

Relative MU6 Efficiency / Scale Factor

150

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| > 1.05

0.95
0.9
0.85
0.8

eff. Data
eff. MC

0.75
0.7
0

scale factor

5

10

15

20

25

30

1.1

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| < 1.05

0.95
0.9

eff. Data
eff. MC

0.85

scale factor

0.8
0.75
0.7
0

5

10

15

|pID - pMS| (GeV)
T
T
(a)

20

25

30

|pID - pMS| (GeV)
T
T(b)

Figure 9.12: Fluctuation of L1 MU6 efficiency and scale factor with shifting |pTID − pTMS | cut.
The maximum shift of the central value between 10 GeV and 20 GeV are counted as a systematic component.
RoI finding criteria dependence As described in section 9.2.3, two procedures are deployed
for RoI finding in a search range.
By default, in case of more than one RoIs are found in the search range, the first priority isgiven to an RoI with the highest pT threshold number. However one can not guarantee that thisprocedure always selects the RoIs actually fired by the muon. One can give the first priority
to the RoI which is the nearest to the extrapolated point instead and this procedure is equallyvalid as the default one. Thus we take the efficiency difference between this two procedures asa systematic component. The estimated relative uncertainties on efficiency in data are 1.5 (0.1)% and in MC are 0.3 (0.0) % in the endcap (barrel), resulting uncertainties on the scale factorsof 1.2 (0.1) %.
Size of search range in RoI finding The search range in the RoI finding is defined as inEq.(9.1). The dependence of efficiencies and scale factors on matching tolerance is shown in
Figure 9.13. The full width of the fluctuation of central values when we change the matching
tolerance by ± 1 σ from default value (3 σ) are counted as a systematic component.
The estimated relative uncertainties on efficiency in data are 0.5 (0.1) % and in MC are 0.4(0.0) % in the endcap (barrel), resulting uncertainties on the scale factors of 0.2 (0.1) %.
η distribution re-weight Most of the muons used in this trigger efficiency measurement
are considered to be coming from semi-leptonic decay of heavy flavor mesons. Thus the ηdistribution of the muons are different from the muons from W or Z boson decay. Figure 9.14
shows the difference in η distribution on denominator muons and muons in Z → µµ and W → µν
MCs. This difference could enhance or suppress the L1 MU6 trigger efficiency in specific1.1

Relative MU6 Efficiency / Scale Factor

Relative MU6 Efficiency / Scale Factor

9.2 Trigger Efficiency Estimation by the Single Combined Track Method

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| > 1.05

0.95
0.9
0.85
0.8

eff. Data
eff. MC

0.75
0.7

scale factor

1

2

3

4

5

1.1

151

L dt = 331 nb∫Data
2010, s = 7 TeV
-1

1.05
1

|η| < 1.05

0.95
0.9

eff. Data
eff. MC

0.85

scale factor

0.8
0.75
0.7

1

2

Matching tolerance (σ)
(a)

3

4

5

Matching tolerance (σ)(b)

Figure 9.13: Fluctuation of L1 MU6 efficiency and scale factor against the change of matching
tolerance. The maximum shift of the central value between 2 σ and 4 σ are counted as asystematic component.
regions then make the overall efficiency value different from that of true W or Z’s. To evaluate
this uncertainty, the following procedures are taken.
• create L1 MU6 trigger efficiency map as a function of η in data• apply Z → µµ and W → µν muon distributions on the efficiency map and calculated
overall efficiency in the endcap and the barrel bins
The efficiency map is created with two sets of granularity. One is dividing |η| < 2.4 region
into 20 and the other into 40. Both binning report very consistent results. The derived overall
efficiency in the endcap and the barrel is summarized in Table 9.6.
reweighed eff. (20 bins) reweighed eff. (40 bins)
sample for η distribution endcap (%) barrel (%) endcap (%) barrel (%)
data
86.5 ± 0.8 76.3 ± 0.7 86.5 ± 0.7 76.3 ± 0.7
Z → µµ86.2 ± 0.8 75.8 ± 0.8 86.2 ± 0.8 75.8 ± 0.8
W → µν
86.2 ± 0.7 75.9 ± 0.8 86.2 ± 0.7 75.9 ± 0.8
Table 9.6: A summary of the derived L1 MU6 efficiencies in the endcap and the barrel after
reweighed by the η distributions of muons obtained in Z → µµ and W → µν MC. The assigned
errors are statistical only.
The central values in data is the same as in Table 9.3, as expected. The systematic uncertainties assigned to this effect are 0.3 (0.5) % in the endcap (barrel) taking the maximum difference
between data and MC. This effect is directly counted on the scale factor uncertainty.

Muon Trigger Efficiency Estimation using Collision Data

Entries / 0.24

152

700

L dt = 331 nb
∫
600

-1

Data 2010, s = 7TeV
W → µν MC
Z → µµ MC

500
400
300
200
100
0

pT > 20 GeV-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Muon η

Figure 9.14: η distribution of muons in data, Z → µµ and W → µν MC.

9.2 Trigger Efficiency Estimation by the Single Combined Track Method

153

9.2.6 Trigger Efficiency Stability

Relative MU6 Efficiency

The stability of the L1 MU6 trigger efficiency during the data taking period is shown in Figure
9.15. The period is divided into seven sub-periods and each sub-period has at least about 20
nb−1 of data. The results for every period are consistent with the overall average within theerror.
1∫ L dt = 331 nb
0.95

-1

Data 2010 ( s = 7 TeV)
pT > 20 GeV
1.05 < |η| < 2.4

0.9
0.85
0.8
Stat.

0.75

Stat. + Syst

0.7

Per
iod

Per
Per
Per
Per
Per
Per
iod
iod
iod
iod
iod
iod
D6
D5
D4
D3
D2
A-C
D1

Data Taking Period

Relative MU6 Efficiency(a)1∫ L dt = 331 nb
0.95

-1

Data 2010 ( s = 7 TeV)
pT > 20 GeV|η| < 1.05

0.9
Stat.

0.85

Stat. + Syst

0.8
0.75
0.7

Per
iod

Per
Per
Per
Per
Per
Per
iod
iod
iod
iod
iod
iod
D6
D5
D4
D3
D2
A-C
D1

Data Taking Period(b)Figure 9.15: L1 MU6 trigger efficiency stability over the data taking period in the endcap (a)and barrel (b). The dotted line shows the overall average, the light blue band shows the statisticalerror and the yellow band shows the total uncertainty. The error bars on the black square points
shows the statistical error only.

154

Muon Trigger Efficiency Estimation using Collision Data

9.3

Trigger Efficiency Estimation by Z → µµ Tag-and-Probe
Method9.3.1

Tag and Probe Method

Tag-and-probe method is a concrete application of a data-driven technique to collect pure, unbiased samples of probe-like object. In the performance measurement of the muon spectrometerin high-pT regime, tag-and-probe method utilizing Z → µµ process is deployed. In this case,probe-like object is a high-pT muon.
The basic procedure of Z → µµ tag-and-probe method is as follows.
1. A high-pT combined track with high track qualities is taken. This muon is called tag
muon. The tag muon is required to be matched with one or more L1 MU6 RoIs.
2. Another combined track which has Z-boson consistent invariant mass with the tag muonis adopted as a probe muon.
In the procedure, the event trigger is ascribed to the tag muon. Hence the probe muon is freefrom trigger biases. Furthermore, due to the high background rejection power of the invariant
mass cut, very pure muon samples can be collected.

9.3.2

Event Selection and Muon Distribution

Z → µµ candidate are chosen utilizing the same selection criteria used in the Z → µµ crosssections measurement (see Table 12.1). Note that the trigger item used for the event selectionis L1 MU6. There are 109 Z-boson candidates found. For the relative trigger efficiency estimation, both muons can be used for the measurement. Thus number of muon candidates is doubled
from the number of Zs, i.e. total of 218 muons are used for the efficiency measurement. Figure
9.16 shows the distribution of muons coming from Z → µµ decays. In these figures, MC histograms are normalized to the number of events yielded in data. As described in section 12.4,
the estimated amount of the background events is below % level, hence ignored in these figures.

9.3.3

Estimated Efficiency and Scale Factor

The relative trigger efficiencies are measured by using both muons in Z → µµ candidate events
following the steps listed below.
1. Find Z → µµ candidate events with two muons ( each of them is called µ1 and µ2 hereunder)
2. First, µ1 is used for the efficiency measurement using the same procedure described in
section 9.2. In this measurement, prior to the µ1 trial, µ2 is required to be matched withan L1 MU6 RoI to remove a trigger bias from the µ1 measurement.
3. Then µ2 is used for the measurement upon the condition that µ1 is matched with an
L1 MU6 RoI.

60

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9.3 Trigger Efficiency Estimation by Z → µµ Tag-and-Probe Method

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

Z → µµ

50

45

155

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb
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35
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80

90

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120

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2µη

mµµ (GeV)

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb
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(b)
Entries / 0.314

Entries / 0.314

(a)

-1

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16
14
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14
12
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10

8

8
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6

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Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb
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(d)
Entries / 5 GeV

Entries / 5 GeV

(c)

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∫ L dt = 331 nb-1

Z → µµ|η| > 1.05, pT > 20 GeV

35

3

30
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∫ L dt = 331 nb-1

Z → µµ|η| < 1.05, pT > 20 GeV

25
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5
0
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30

40

50

60

70

80

0
20

30

40

50

pµ

70

80
pµ

T

(e)

60

T

(f)

Figure 9.16: (a): Invariant mass distribution of tag and probe muons. (b) (c) (d) (e) (f): η, φ and
pT distribution for probe muons.

156

Muon Trigger Efficiency Estimation using Collision Data

The results of the relative L1 MU6 efficiency measurement using Z → µµ tag-and-probe areshown in Figure 9.17 compared to the results from the single combined track method. Table 9.7
summarizes the efficiencies and scale factors of pT > 20 GeV. One can see that the results fromtag-and-probe method is well consistent with the result from the single combined track method.

L1 MU6

eff. in data
eff. in MC
scale factor
charge endcap (%) barrel (%) endcap (%) barrel (%) endcap (%) barrel (%)
all
86.5 ± 3.5 74.7 ± 4.7 95.2 ± 0.2 79.4 ± 0.4 90.8 ± 3.7 94.1 ± 5.9+µ
84.8 ± 5.3 71.4 ± 6.5 94.9 ± 0.3 79.3 ± 0.5 89.3 ± 5.6 90.1 ± 8.2µ−
88.0 ± 4.6 78.9 ± 6.6 95.4 ± 0.3 79.6 ± 0.5 92.2 ± 4.8 99.2 ± 8.3

Table 9.7: Estimated L1 MU6 trigger efficiencies and scale factors with tag-and-probe method.

9.4

Single Muon Trigger Efficiency Scale Factor

Here, the single muon trigger efficiency measurements described in this section is summarized.
The needed information in the measurement of the W / Z-boson cross sections is the efficiency
scale factor for single muons. The results for independent two methods, namely
1. Single combined track method
2. Tag-and-probe method with Z → µµ eventswere presented. The central values for the scale factors agree well between both methods. As
for the uncertainty, the one from the method 1 is adopted since the available statistics are muchhigher than the method 2. The single muon trigger efficiency scale factors for the W / Z crosssections measurement are summarized in Table 9.8.
regionparametereff. in data
endcap eff. in MC
single muon scale factor
eff. in data
barreleff. in MC
single muon scale factor

result0.865 ± 0.007 (stat) ± 0.016 (syst)
0.950 ± 0.001 (stat) ± 0.006 (syst)
0.911 ± 0.008 (stat) ± 0.017 (syst)
0.763 ± 0.008 (stat) ± 0.015 (syst)
0.793 ± 0.002 (stat) ± 0.010 (syst)
0.961 ± 0.010 (stat) ± 0.018 (syst)

Table 9.8: A summary of the L1 MU6 trigger efficiency and scale factor

9.4 Single Muon Trigger Efficiency Scale Factor

157

Relative L1_MU6 Efficiency

1
0.9
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0.4

Data 2010 ( s = 7 TeV)

0.3

pT > 20 GeV-1tag & probe

0.2

single muons

0.1
0-2 -1.5 -1 -0.5 0 0.5 1 1.5 2µη

1Relative L1_MU6 Efficiency

Relative L1_MU6 Efficiency

(a)

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Relative L1_MU6 Efficiency

(b)

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0.2

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0.1

single muons

0.1
70

80

0
20

30

40

50

pµ

60

70

80
pµ

T

(d)

3

T

(e)

Figure 9.17: Estimated L1 MU6 trigger efficiency by tag-and-probe and single combined track
methods as a function of η, φ and pT for probe muons.

Chapter 10
Muon Reconstruction Efficiency
Estimation using Collision Data
The methods and results for the muon reconstruction efficiency estimation are presented in thischapter. In this study, muon reconstruction efficiency is estimated in the following steps.
1. Identify an ID track which is created by a muon
2. Search a combined track which is considered to be created by the same muon
In proton-proton collisions at the LHC, the average number of ID tracks reconstructed in an
event reaches some tens or hundreds. Most of the reconstructed ID tracks are hadrons and thesetracks form significant background hence the rejection of this background becomes the most
crucial issue for the reconstruction efficiency estimation.
In this study, two methods are used for this purpose. The first one is called the Muon
Spectrometer (MS) Hit Tagging Method, described in detail in section 10.1. The other is the
tag-and-probe method using Z → µµ events. The details and results for the tag-and-probe
method are presented in section 10.2. The results to be used in W / Z-boson cross sections
measurement are summarized in section 10.3.

10.1

MS Hit Tagging Method

In principle, the muon is only particle which can penetrate hadronic calorimeter. Thus, if one
requires activities in the muon spectrometer ahead of an ID track, most of hadron tracks failthis requirement. A tool which counts the associated number of hits in the muon spectrometeraround the extrapolated path of an ID track has been developed. The details of the tool is
described hereunder.

10.1.1

MDT Hits – ID Track Association

The number of MDT hits associated with an ID track is counted by this tool. The word a hit
represents a fired tube. The reason why the MDT hits are utilized is as follows.

10.1 MS Hit Tagging Method

159
extrapolated path

Hit (ﬁr

Surfaceed tub

e)

σex

η

ηex

ηhit

signiﬁcance =ηhit - ηex√(σhit2+σex2)

ηhit : center position of the ﬁred tube in η
ηex : extrapolated position in η
σhit : tube diameter /√12track

σex : extrapolation error (standard deviation)

Figure 10.1: A schematic illustration of the MDT Hits – ID track association.
• One main concern of this method is the measurement bias for the efficiency estimation
inevitably caused by requiring activities in the target detector. Since the MDT covers theentire η range of the muon spectrometer, the bias is more or less uniform. Hence thetreatment of the bias becomes easy.
• The average number of MDT hits on a combined track is about 20. This is large enoughto adjust the amount of bias in case-by-case basis.
To associate MDT hits to an ID track, the track extrapolator [134, 135] is deployed. The
number of MDT hits within a road of certain width around extrapolated track path is counted.
The concrete procedure is summarized as follows.
1. Extrapolate an ID track to an MDT tube layer surface, a plane in which MDT hits arecontained (see Figure 10.1),
2. Calculate a significance from the extrapolated position and error, the center position of
the hit and the tube width asηhit − ηex,(10.1)
significance = q
σ2hit + σ2ex
where ηex is the extrapolated position in η coordinate and ηhit is the center position of the
tube in consideration. σex is the extrapolation
error reported by the track extrapolator and√σhit is the tube diameter divided by 12.

160

Muon Reconstruction Efficiency Estimation using Collision Data

3. If the calculated significance is smaller than a certain cut value, the hit is counted. The
cut value is set at 3.0 by default.
This procedure is repeated over all MDT hits.

10.1.2

Event Selection and Muon Distribution

The ID track selection deployed in the reconstruction efficiency estimation using MS hit tagging
method is summarized in Table 10.1.

QualityPrimary vertex
Trigger

Event selection
W → µν Good Runs List
Nvtx ≥ 1 with Ntracks ≥ 3|zvtx | < 150 mm
L1 MU6

Tagged ID track selection
pT> 20 GeV
Pixel Hits
≥1
Silicon Hits
≥6
TRT Hits≥ 10
P ID
Isolation
pT /pT < 0.2 (∆R = 0.4)
Associated MDT hits 2 of 3: inner ≥ 4, middle ≥ 3, outer ≥ 3
Table 10.1: The event and track selections for muon reconstruction efficiency estimation using
MS hit tagging method.
In this estimation, the GRL for W → µν cross sections measurement is used resulting an integrated luminosity of 310 nb−1 . Events are required to have one or more vertices reconstructedwith at least three ID tracks.
Then the ID tracks are required to pass the cuts of pT and ID hits requirements. Siliconhits mean the sum of the number of SCT hits and Pixel hits. Relative track isolation of ≤0.2 is applied in terms of pT sum of ID tracks within the cone of ∆R = 0.4. In the isolation
calculation, the contributions from the track in consideration itself and tracks with pT < 1 GeV
are subtracted. Finally, the associated MDT hits requirements are applied as in Table 10.1. The
resulting distributions of the selected ID tracks are shown in Figure 10.2.
Combined tracks are looked for within a cone of ∆R = 0.4 centered at a selected ID tracks
in consideration. This matching is done simply using track parameters, not using the track
extrapolator. The efficiency denominator in this estimation is the number of selected ID tracks,
and the efficiency numerator is the number of the ones matched with one or more combined
tracks.
The efficiency is measured regarding the entire muon spectrometer as a single bin. The
estimation results are summarized in Table 10.2. As one can see, a significant discrepancy isseen between the efficiency in data and in W → µν MC. This is considered as mainly comingfrom decay-in-flight contamination. A background rejection method against this decay-in-flightcomponent is described in the next subsection.

10.1 MS Hit Tagging Method

161

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pT > 20 GeV

0-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

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-2

-1

0

1

2

3
µ

µ

η

φ

(a)

(b)

1200

∫ L dt = 310 nb

-1

1000

Data 2010 ( s = 7 TeV)

800
600
400
200
0
20

30

40

50

60

70

80
pµt

(c)

Figure 10.2: (a) η (b) φ and (c) pT distribution of selected ID tracks for the muon reconstruction
efficiency estimation by the MS hit tagging method.

eff. in data (%)
94.7 ± 0.4

eff. in W → µν MC (%)
98.6 ± 0.1

scale factor
96.1 ± 0.4

Table 10.2: Measured muon reconstruction efficiency by the MS hit tagging method withoutbackground subtraction.

162

10.1.3

Muon Reconstruction Efficiency Estimation using Collision Data

Decay in Flight Background Subtraction

To investigate the reason of the discrepancy between the measured muon reconstruction efficiency by the MS hit tagging method in data and MC, the method is factorized into two steps.
1. Search standalone tracks around a selected ID track in consideration
2. Search combined tracks around a selected ID track in consideration which is matchedwith an standalone track
Figure 10.3 shows the ∆R distribution between a selected ID tracks and the corresponding
standalone and combined track. The ∆R value used in the step 1 is set at 0.4 and in step 2 at 0.1.

∫ L dt = 310 nb

-1

103

Data 2010 ( s = 7 TeV)
∆ R (ID - MS)

102∆ R (ID - CO)

pT > 20 GeV

10

1
0

0.1

0.2

0.3

0.4

0.5
∆R

Figure 10.3: Matching ∆R between ID tracks and standalone tracks (black) and ID tracks andcombined tracks (blue).
The resulted efficiency for the standalone and combined tracks are listed in Table 10.3. As
one can see, the main efficiency drop happens in the combining stage.
Sampleeff. standalone (%)
Data
98.2 ± 0.2
W → µν MC
99.4 ± 0.1

eff. combined (%)
96.5 ± 0.4
99.2 ± 0.0

total (%)
94.5 ± 0.5
98.6 ± 0.1

Table 10.3: The breakdown of the measured muon reconstruction efficiency drop in the MS hit
tagging method.
Figure 10.4 shows the distribution of the selected ID tracks which succeeded to pass amatching with an standalone track but failed to match with a combined track. Figure 10.4(a) is a distribution of ∆R between the ID tracks and their nearest standalone tracks.

10.1 MS Hit Tagging Method

163

Figure 10.4 (b) is the distribution of the pT difference between the ID tracks and their nearest
standalone tracks. The ID tracks tend to have harder pT than their nearest standalone tracks.
Figure 10.4 (c) is the 2-D distribution of (a) and (b). Combinations may fail even when
the directions of ID and standalone tracks are reasonably close. This tend to happen when the
ID tracks are much harder than that of the standalone tracks. This suggests the contribution of
decay-in-flight events. The rejection of these decay-in-flight events is crucial for this estimation.

10∫∫ L dt = 310 nb

102

-1

L dt = 310 nb-1

Data 2010 ( s = 7 TeV)

Data 2010 ( s = 7 TeV)

pT > 20 GeV
pT > 20 GeV

10

1
1

0 0.05 0.10.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-30

-20

-10

0

∆ R (ID - MS)

10

20

30

pID - pMS (GeV)T
T(b)
dR (ID - MS)

(a)
0.5
0.45
0.4
0.35
0.3

∫ L dt = 310 nb-1

Data 2010 ( s = 7 TeV)
pT > 20 GeV

0.25
0.2
0.15
0.1
0.05
0
-30

-20

-10

0

10

20

30

pID - pMS (GeV)
T

T

(c)

Figure 10.4: (a) ∆R between the selected ID tracks and their nearest standalone tracks (b)difference in pT between the selected ID tracks and their nearest standalone tracks (c) two
dimensional histogram of (a) and (b).
MDT Hit Residual Template Fit
To subtract the decay-in-flight contamination, template fits for the distribution of MDT hit residuals (distance in η between extrapolated position of selected ID tracks and center of MDT hits)

164

Muon Reconstruction Efficiency Estimation using Collision Data

are performed.The templates are made for the W → µν MC as a prompt muon samples and asingle charged pion MC as the decay-in-flight component. The single pions are flatly generated
in pT between 1 GeV to 100 GeV, thus a reweighing is done according to one over the true pion
pT to the third power based upon a fit to ID track distributions in minimum bias data samples.
Then the two templates are fitted to the residual distribution in data using RooFit [138].
A template fit example for selected ID tracks is shown in Figure 10.5 and derived prompt
muon fraction in the selected ID tracks and that matched with a combined track are summarizedin Table 10.4. Then the derived decay-in-flight components are subtracted from both denominator and numerator. Resulting reconstruction efficiency for prompt muons are in Table 10.5.

Figure 10.5: Fitting result for MDT hit residuals of tagged ID tracks in data and MC.
Selected ID tracks (%)
79.3 ± 0.3

Matched with a combined track (%)
83.0 ± 0.3

Table 10.4: Derived prompt muon fractions by the MDT hit residual template fits.
eff. in data (%) eff. in MC (%) scale factor (%)
99.2 ± 0.4
98.6 ± 0.1
100.5 ± 0.4
Table 10.5: Muon reconstruction efficiency for prompt muons with the MDT hits residual template fits.

10.1 MS Hit Tagging Method

165

10.1.4 Systematic Uncertainty
Systematic
decay-in-flight Contamination
ID tracking efficiency
Cut stability
Trigger bias
Total

Value
2.0%
1.0%
0.5%
0.4%
2.4%

Table 10.6: Systematics for the muon reconstruction efficiency by the MS hit tagging method.
The systematic components for the muon reconstruction efficiency estimation using the MS
hit tagging method are summarized in Table 10.6.
The largest component is coming from the uncertainty for the amount of decay-in-flight
contamination. To evaluate the maximum effect of this, so-called factorizing method is used.
Basically, decay-in-flight components cause negative effect on the reconstruction efficiency estimation in the combining stage. In the factorizing method, reconstruction efficiency estimation isdivided into two parts as in the evaluation in section 10.1.3 and requirements for decay-in-flight
rejection are made before the combination efficiency estimation. The requirements are,
• The selected ID track is matched with a standalone track within ∆R < 0.1• The pT of the standalone track is > 10 GeV• The difference in pT between the ID and standalone track is < 15 GeV
The resulted efficiency is 98.2±0.2% for standalone tracks and 98.9±0.2% for combined tracks
and the overall reconstruction efficiency is 97.1 ± 0.3%. These requirements can not reject all
decay-in-flight contamination. However, compared to the efficiency derived in the template fit
method in Table 10.4, both results are consistent within 2.0 %. Hence a conservative uncertainty
coming from decay-in-flight of 2.0 % is taken, assuming all the efficiency difference is comingfrom decay-in-flight contamination.
The reconstruction efficiency is measured on reconstructed ID tracks. Hence uncertainties
should be put on ID track reconstruction efficiency. The ID tracking efficiency is well modeled(see section 10.2.3) in the MC hence a conservative uncertainty of 1 % is put on it from a MC
study.
The requirement of L1 MU6 trigger causes a bias on the estimation. The amount of theeffect is estimated using truth information in MC and 0.4 % is counted for this effect.
The stability of the efficiency results with respect to variations in the cuts on matching∆R, number of required hits and road size is also examined. The variations are covered by asystematic uncertainty of 0.5 %.

166

10.2

Muon Reconstruction Efficiency Estimation using Collision Data

Z → µµ Tag-and-Probe Method

The muon reconstruction efficiency is also measured with the tag-and-probe method. In thiscase, probe tracks should be reconstructed only with the inner detector. The corresponding
combined tracks are searched as is done in the previous section.

10.2.1

Event Selection and Muon Distribution
Collision event selection
Good Run List & BCID Z → µµ GRL
Primary vertex
Nvtx ≥ 1 with Ntracks ≥ 3|zvtx | < 150 mm
Trigger
L1 MU6
Track Type
Kinematics
Muon quality

TriggerTrack Type
Kinematics
Isolation
ID hitVertex (w.r.t PV)
Opposite Charge
Invariant Mass

Tag track selection
combined tracks
pT > 15 GeV, |η| < 2.4
pTMS > 10 GeV|pTMS − pTID | < 15 GeV|z0 − zvtx | < 10 mm
Matched with L1 MU6 trigger
Probe track selection
ID tracksp > 20 GeV, |η| < 2.4
PT ID
pT /pT < 0.2
Pixel ≥ 1, SCT ≥ 4, Silicon ≥ 6, TRT ≥ 10probe
| < 2mm|d0tag − d0probe | < 2mm, |ztag
0 − z0qtag · q probe < 0|MZ − MT P | < 15 GeV

Table 10.7: Event and muon selection for muon reconstruction efficiency estimation by the
Z → µµ tag-and-probe method.
Table 10.7 summarizes the selection criteria used in the tag-and-probe estimation. The
collision event selection, which is intended to reject events with non-collision origin, is identicalto the one used in the Z → µµ cross section measurement.
Tag tracks are required to be a combined track with pT > 15 GeV generated within themuon trigger chamber acceptance. To reject muons from decay-in-flight events, the cuts on
pTMS > 10 GeV and |pTMS − pTID | < 15 GeV are required. |z0 − zvtx | should be within 10 mm toreject cosmic muons. Finally tag muons are required to be matched with an L1 MU6 RoI. This
matching is done by the method described in section 9.2.
Probe tracks are required to be an ID track with pT > 20 GeV and |η| < 2.4. Relative track
pT isolation and a certain number of inner detector hits are required to reject backgrounds. d0
and z0 measured with respect to the reconstructed primary vertex is required to be with 2 mm

10.2 Z → µµ Tag-and-Probe Method

167

160

Entries / 5 GeV

Events / 5 GeVfrom that of the corresponding tag track. An opposite charge requirement is applied as well as
the mass window cut of |MZ − MT P | < 15 GeV.
Figure 10.6 shows the distributions of resulting probe tracks and invariant mass of tag andprobe tracks. The total number of Z → µµ events found is 135 and 205 probe tracks are adopted.

Data 2010 ( s = 7 TeV)

L dt = 331 nb
140 ∫

-1

Z → µµ

120
100

80
70

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

Z → µµpT > 20 GeV

60
50

80

40

60

30

40

20

20

10

0
60

70

80

90

100

110

0
20

120

40

60

80

100 120 140 160
pµ

mµµ

T

50

(b)
Entries / 0.628

Entries / 0.48

(a)Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

Z → µµpT > 20 GeV

40

40

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

Z → µµpT > 20 GeV

35
30
25

30

20
20

15
10

10

5
0

0

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-3

-2

-1

0

(c)

1

2

3
µ

µ

η

φ

(d)

Figure 10.6: (a) Invariant mass of tag and probe tracks. (b) pT (c) η and (d) φ distributions of
the probe tracks.

168

Muon Reconstruction Efficiency Estimation using Collision Data

10.2.2

Efficiency and Scale Factor

After the probe track selection, a combined track is searched within a cone of ∆R = 0.01 fromeach of adopted probe tracks. The combined tracks are required to satisfy the following cuts.
• |pTMS − pTID | < 15 GeV• pTMS > 10 GeV
These requirements are to ensure that combined tracks have the same quality as the one usedin the W / Z-boson cross sections measurement. The resulting reconstruction efficiencies andscale factors are summarized in Table 10.8 and Figure 10.7. The results in data and MC agrees
well.
eff. in data (%) eff. in MC (%) scale factor (%)
92.2 ± 1.9
92.6 ± 0.2
99.6 ± 2.0

Reconstruction Efficiency

Table 10.8: Measured reconstruction efficiency by the Z → µµ tag-and-probe method.

1
0.95
0.9
0.85
0.8

∫ L dt = 331 nb

-1

0.75

Data 2010 ( s = 7 TeV)

0.7

Z → µ µ MC

0.65
0.6
20

30

40

50

60

70

80
pµ

T

1

Reconstruction Efficiency

Reconstruction Efficiency

(a)
0.95
0.9
0.85
0.8

∫ L dt = 331 nb

-1

0.75

1
0.95
0.9
0.85
0.8

∫ L dt = 331 nb

-1

0.75

Data 2010 ( s = 7 TeV)

Data 2010 ( s = 7 TeV)

0.7

Z → µ µ MC

0.7

Z → µ µ MC

0.65

pT > 20 GeV

0.65

pT > 20 GeV

0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0.6

2

-3

-2

-1

0

η

(b)

1

2

3
µ

µ

φ

(c)

Figure 10.7: (a) pT (b) η and (c) φ distribution of the measured muon reconstruction efficiency
by the Z → µµ tag-and-probe method.

10.2 Z → µµ Tag-and-Probe Method

169

10.2.3 ID Track Reconstruction Efficiency
The track reconstruction efficiency in the inner detector is measured by tag-and-probe methodby using a muon spectrometer standalone track as a probe. In this case, the event and tag selection is identical to the one summarized in Table 10.7. The probe track selection is summarizedin Table 10.9.
Probe track selection
Track Typemuon spectrometer stand alone tracks
Kinematics
pT > 20 GeV, |η| < 2.4
Vertex (w.r.t PV) none
Opposite Charge qtag · q probe < 0Invariant Mass
|MZ − MT P | < 15 GeV
Table 10.9: standalone probe track selection for ID reconstruction efficiency estimation.
ID tracks are looked for within a cone of ∆R = 0.03. The following requirements are appliedon the ID tracks to reject noise or non prompt tracks.
• number of Pixel hits ≥ 1• number of SCT hits ≥ 4• |d0tag − d0probe | < 2 mm (d0 : w.r.t primary vertex)probe| < 2 mm (z0 : w.r.t primary vertex)• |ztag
0 − z0

The resulting ID tracking efficiencies are summarized in Table 10.10 and Figure 10.8. The
reconstruction efficiency in the ID is very close to 100 % both in data and MC. This support
an assumption made in this study that the ID tracking efficiency is well modeled in MC (seesection 10.1.4).

eff. in data (%)
99.5 ± 0.5

eff. in MC (%)
99.5 ± 0.0

scale factor (%)
99.9 ± 0.6

Table 10.10: Measured ID track reconstruction efficiency by the Z → µµ tag-and-probe method.

Muon Reconstruction Efficiency Estimation using Collision Data

ID Reconstruction Efficiency

170

1
0.98
0.96
0.94

∫ L dt = 331 nb

0.92

-1

0.9

Data 2010 ( s = 7 TeV)

0.88

Z → µ µ MC
|η| < 1.05

0.86
20

30

40

50

60

70

80
pµ

T

1

ID Reconstruction Efficiency

ID Reconstruction Efficiency

(a)
0.98
0.96
0.94

∫ L dt = 331 nb

0.92

-1

0.9

Data 2010 ( s = 7 TeV)

0.88

Z → µ µ MC
pT > 20 GeV

0.86
-2

-1.5

-1

-0.5

0

0.5

1

1.5

1
0.98
0.96
0.94

∫ L dt = 331 nb

0.92

-1

0.9

Data 2010 ( s = 7 TeV)

0.88

Z → µ µ MC
pT > 20 GeV

0.86
2

-3

-2

-1

0

1

2

(b)

3
µ

µ

η

φ

(c)

Figure 10.8: (a) pT (b) η and (c) φ distributions of the measured ID tracking efficiency by the
Z → µµ tag-and-probe method.

10.3

Single Muon Reconstruction Efficiency Scale Factor

As in the case for the muon trigger efficiency, the needed information in W / Z-boson crosssections measurement is the efficiency scale factor for single muons. The results for independent
two methods, namely
1. MS hit tagging method & MS hit residual template fit
2. Tag-and-probe method with Z → µµ eventswere presented so far and results for both methods show that single muon reconstruction efficiency is well modeled in the MC. Hence the scale factor center value of 1.000 is taken. As forthe uncertainty, the one from method 1 is adopted since the available statistics are much higher
in this method. The single muon reconstruction efficiency scale factor result issingle muon reconstruction efficiency scale factor = 1.000 ± 0.004 (stat) ± 0.024 (syst)

Chapter 11
Measurement of W Boson Cross Section
11.1 Event Selection
Collision event selection
Good Run List & BCID
W → µν GRL
Primary vertex
Nvtx ≥ 1 with Ntracks ≥ 3|zvtx | < 150 mm
Jet cleaningcleaning cuts
Trigger
L1 MU6High-pT event selection
Muon selection
combined tracks
pT > 15 GeV, |η| < 2.4
Muon quality
pTMS > 10 GeV|pTMS − pTID | < 15 GeV|z0 − zvtx | < 10 mm
W → µν event selection
Tight kinematics
p > 20 GeV, |η| < 2.4
PT ID
ID isolation
pT /pT < 0.2 (∆R = 0.4)
missMissing transverse energy ET > 25 GeVTransverse Mass
MT > 40 GeV
Table 11.1: A summary of the requirements for the W → µν candidate event selection.
A summary of the requirements for the W → µν candidate event selection is given in Table
11.1. The requirements are classified into three stages namely collision event selection, high-pT
event selection and the W → µν event selection. The collision event selection and high-pT event
selection are called pre-selection as a whole.
In the collision event selection, events coming from proton-proton collisions are selected.
First, the official GRL for the W → µν analysis (see section 7.1) is applied and events are
required to have BCIDs of proton-proton collisions. Events are then required to have one ormore reconstructed primary vertices with at least three inner detector tracks. The vertex position

172

Measurement of W Boson Cross Section

along the z-axis required to be within 150 mm from the ATLAS origin to reduce cosmic ray
background. To reduce spurious missing transverse energy from jets generated by detector
effects or cosmic rays, the jet cleaning procedure is applied. The trigger used for this analysis
is L1 MU6.
In the high-pT event selection, first, events are require to have at least one muon reconstructed as a combined track with pT > 15 GeV and |η| < 2.4. Then, the pTMS is required to
be greater than 10 GeV. This is to remove the π/K decay-in-flight contamination as well as
combined tracks resulting from a poor combination of inner detector and muon spectrometerstandalone tracks. To increase further the robustness against π/K background and track reconstruction mistakes, the requirement of |pTMS − pTID | < 15 GeV is applied. Then, |z0 − zvtx | should
be within 10 mm to reject cosmic muons.
Finally, the W → µν event selection is applied. The selection places a pT > 20 GeV on theselected combined track. Also, a requirement of relative track isolation within a cone of ∆R =0.4 is applied to reject QCD background events. Then ETmiss is required to be greater than 25
GeV and final W candidates are counted in the region above transverse mass of 40 GeV.

11.2 Signal Acceptance and Efficiencies

173

11.2 Signal Acceptance and Efficiencies
11.2.1 Overall Acceptance of W → µν Selection
The acceptance is defined as the number of events passing all of the selection divided by the
number of generated events. The acceptance is estimated with a W → µν MC sample which is
described in section 4.7.2. The yielded acceptance is 36.32 % with a negligible statistical error.
The GRL and BCID requirements are omitted from the selection since these are not relevant
for simulated samples. The number of signal events passing each step of the selection, and theefficiencies of each step relative to the previous one and total generated number (denoted as
reduction factor) are given in Table 11.2.
Then the acceptance is corrected to compensate the discrepancy between data and MC in
the number of vertices (see section 8.3.3), muon trigger and reconstruction efficiency. Detailsof the corrections are summarized in section 11.2.2.
selectionAll
Jet cleaning
L1 MU6
Vertexcombined track,|η| < 2.4,
pT > 15 GeV,
pTMS > 10 GeV,
|pTMS − pTID | < 15 GeV,
|z0 − zvtx | < 10 mm,
pµT > 20 GeV,
isolation
missET > 25 GeV
MT > 40 GeV
Correction (vertex)
Correction (trigger)
Correction (reconstruction)

number of events
999885999877630689629399

reduction factor (%) rel. eff. (%)
100.00—100.00100.00
63.08
63.08
62.95
99.80

532776

53.28

84.65

483712479974395955392144

48.38
48.00
39.60
39.22

(W+ :234454, W− :157690)(W+ :39.93, W− :38.21)

391358363141363141

39.14
36.32
36.32

(W+ :217117, W− :146025)(W+ :36.98, W− :35.38)

76.85
99.23
82.50
99.04
—
99.80
92.83
100.00—

Table 11.2: Effect of the W → µν selection criteria on simulated W → µν events.

174

Measurement of W Boson Cross Section

11.2.2

Efficiency Scale Factors

The three correction factors for the W → µν acceptance, namely for the number of vertices,muon trigger and reconstruction efficiency, are applied on the calculated acceptance in MC asin Table 11.2. The details for these corrections are given in the following subsection. In thesecalculation, no difference between positive and negative muons are assumed. All the resulted
scale factor on the W → µν acceptance are summarized in Table 11.3.
Number of Vertices
The discrepancy in the number of vertices between data and MC is corrected as described in
section 8.3.3. An efficiency of 99.8 % is adopted (see Table 11.2) to take into account this effectin acceptance calculations. The amount of correction on acceptance is estimated as about 0.2%. To be conservative, a full range of systematic uncertainty is assigned. The resulted scale
factor is 0.998 ± 0.000 (stat) ± 0.002 (syst).
Trigger Efficiency
The single muon trigger efficiency and scale factor for L1 MU6, which is used in this analysis,
is derived in two bins (endcap and barrel) as in Table 9.8. Since only one muon is required inan event, the single muon trigger scale factor equals to the needed correction for the W → µν
acceptance.
To apply the correction, the fraction of muons flying to each bin is calculated by the W → µν
MC as 0.550 (endcap) and 0.450 (barrel) with a negligible statistical error. In this calculation,
muons are required to pass all the W → µν selection except for the L1 MU6 requirement. The
weighted mean of single muon trigger efficiency is calculated as- 0.819 ± 0.005 (stat) ± 0.014 (syst) (weighted average efficiency in data)- 0.879 ± 0.001 (stat) ± 0.007 (syst) (weighted average efficiency in MC)
After that the ratio of weighted average in data to MC is taken as the trigger efficiency scale
factor for the W → µν acceptance. The resulting scale factor is 0.931±0.006 (stat)±0.017 (syst).
Muon Reconstruction Efficiency
The single muon reconstruction efficiency scale factor also equals to that of the needed correction for the W → µν acceptance. Hence the scale factor for muon reconstruction efficiency istaken from section 10.3 as 1.000 ± 0.004 (stat) ± 0.024 (syst).

11.2 Signal Acceptance and Efficiencies

175

11.2.3 Acceptance Decomposition
The overall acceptance is factorized into two parts as in Eq.(8.1). Each component is referred
to as AW and CW hereafter. The concrete definition and estimated values of AW and CW are as
follows. The values for AW and CW are summarized in Table 11.3.
• AW : Fraction of the generated W → µν events satisfying pµT > 20 GeV, |ηµ | < 2.4, pνT > 25
GeV and MT (µ, ν) > 40 GeV, where all of these quantities refer to the truth-level muon
before any final state radiation. AW is estimated as 0.480. The acceptances for both W +and W − are estimated separately as 0.484 (W + ) and 0.474 (W − ). A common systematic
uncertainty of 3.0 % is assigned to all of them (see section 8.4.3).
• CW : The denominator of CW is the number of events passing the generator-level requirements which equals to the numerator of AW . The numerator is the fraction of events
passing the full analysis selections then corrections by the scale factors are applied. The
resulted CW value is 0.758. The acceptances for both W + and W − are estimated separately
as 0.765 (W + ) and 0.748 (W − ). A common systematic uncertainty of 4.0 % is assigned toall of them (see section 11.3).

11.2.4 Summary of Acceptance and Efficiency
The acceptance for the W → µν event is summarized in Table 11.3. The uncertainty on the total
acceptance is assigned as 5.0 % which is the quadrature sum of the uncertainties of AW and CW .
The scale factors are also summarized.
AW
CW
total acceptancenumber of vertices SF
trigger efficiency SF
reconstruction efficiency SF

W (all)0.480 ± 0.014
0.758 ± 0.031
0.364 ± 0.018

W+W−
0.484 ± 0.015 0.474 ± 0.014
0.765 ± 0.031 0.748 ± 0.030
0.370 ± 0.019 0.355 ± 0.018
0.998 ± 0.002
0.931 ± 0.018
1.000 ± 0.024

Table 11.3: A summary of the acceptance and scale factors for the W → µν events.

176

11.3

Measurement of W Boson Cross Section

Systematic Uncertainty on Acceptance

A summary of the systematic uncertainties is reported here. The decomposition of the systematic uncertainties for CW is given in Table 11.4 as well as a theoretical uncertainty for AW . The
uncertainties on CW coming from muon energy scale and resolution and the cut of ETmiss > 25
GeV have not described yet. The description is given in the following subsections.
parameter
intrinsic uncertainty (%)
number of vertices
0.2
trigger efficiency
2.4 (barrel), 2.1 (endcap)
reconstruction efficiency
2.4
muon momentum scale
1.0
muon momentum resolution
5.0 (barrel), 9.0 (endcap)
associated to the ETmiss cut ( > 25 GeV)
isolation efficiency
1.0
theoretical uncertainty
0.2 (FSR), 0.3 (PDF)
total uncertainty

δCW (%)
0.2
1.8
2.4
1.2
0.2
2.0
1.0
0.4
4.0

parameter
theoretical uncertaintyδAW (%)
3.0

total uncertainty

5.0

Table 11.4: A summary of the systematic uncertainty on the W → µν acceptance.

Muon Momentum Scale and Resolution
The uncertainty on muon momentum scale and resolution are estimated in section 8.4.1 by fitting the Z-boson mass distribution with the Breit-Wigner function convoluted with a gaussian.
The resulted uncertainties are 1.0 % for momentum scale and 9.0 (5.0) % for momentum resolution in endcap (barrel). The acceptance uncertainties coming from them are estimated asfollows.
(a) Shifting C1 in Eq.(8.12) by ± 1.0 % in the acceptance calculation while keeping C2 = 0.
(b) Setting C1 = 1.0 and C2 = 9.0 (5.0) % in endcap (barrel) and calculate the acceptance
To take into account the correlation between muon momentum, ETmiss and relative track isolation,these values are recalculated in event-by-event basis. The uncertainty for (a) is -1.2 (+1.0) %when shifting C1 by -1 (+1) %, hence 1.2 % is adopted as the uncertainty coming from themuon momentum scale. Also, the uncertainty for (b) is 0.2 % and this value is adopted as theuncertainty coming from the muon momentum resolution.

11.3 Systematic Uncertainty on Acceptance177

Uncertainty Associated to the ETmiss > 25 GeV Cut
The W → µν analysis includes a cut of ETmiss > 25 GeV. The systematic uncertainty related tothis cut is estimated as 2.0 % in total [139].
The maximum contribution to the uncertainty is coming from the uncertainty on the energy
scale of the topological calorimeter clusters in the central region (|η| < 3.2). This uncertainty
is derived as the difference between data and MC from E/p studies. At the high-pT region
currently in consideration, the uncertainty on the energy scale is estimated as ± 5 %. The
uncertainty on acceptance from this effect through the cut of ETmiss > 25 GeV is estimated by
MC as ± 1.5 %.
The next largest uncertainty is coming from the imperfect MC modeling of the detector
response. The effect is estimated as the difference between the acceptance calculated ETmiss at
the MC truth level and after reconstruction. The resulted uncertainty through the cut of ETmiss >25 GeV is 1.0 %.
Also, the uncertainty from ETmiss resolution (0.4 %), pile-up (0.01 %), dead regions in thecalorimeter (< 0.2 %), imperfect modeling of the underlying event (0.4 %), energy scale ofthe topological calorimeter clusters in the forward (3.2 < |η| < 4.9) region (0.1 %) and FCal
displacement with respect to the beam spot (0.04 %) are considered.

178

Measurement of W Boson Cross Section

11.4

Background Estimation

11.4.1QCD BackgroundNumber of Background Events Derived by Matrix Method
The estimated number of QCD backgrounds used in this study is derived by so-called matrix
method. In this method, a loose muon sample with Nloose events is defined and impose a tightmuon requirement especially the track isolation criterion used in the analysis upon it. The
number of events in the isolated sample are defined as Nisol . Also nonQCD and QCD are defined
as relative isolation efficiencies for non-QCD and QCD processes. Here, non-QCD represents
the W → µν signals and other electroweak sources. Then the following equations are obtained.
Nloose = NnonQCD + NQCD ,Nisol = nonQCD NnonQCD + QCD NQCD ,then
NQCD =

Nloose nonQCD − Nisol.
nonQCD − QCD

(11.1)(11.2)(11.3)

If one obtains nonQCD and QCD , the estimated number of QCD backgrounds can be expressedas QCD NQCD . The procedure for data driven derivation of these isolation efficiencies are summarized as follows.
• QCD : This efficiency is estimated from muons between 15 and 20 GeV after the preselection. In this region, QCD in data and jet MC samples are almost flat, yielding confidence that the region picked out has only small non-QCD contamination.
In the high-pT region, the efficiency for jet MC falls with pT . Hence the efficiency for 15– 20 GeV data is scaled by the ratio of isolation efficiency in jet MC above and below 20
GeV cut. Then the scaled efficiency of QCD = 0.227 ± 0.006 is obtained. The systematic
uncertainty is assigned as the full range of this extrapolation.
• nonQCD : As the electroweak sample, muons in the Z → µµ selection is taken. The
efficiency nonQCD = 0.984 ± 0.010.
As the loose sample, the events passing all the requirements except for the isolation arechosen. The loose sample has Nloose = 1272 events and isolated sample has Nisol = 1181 events.
Finally, from Eq.(11.3), the estimated number of QCD background QCD NQCD = 21.1 ± 4.5(stat) ± 8.7 (syst) is obtained. The systematic uncertainty emerging from comparing to thenumber with unscaled QCD efficiency.
QCD Scaling Factor Derivation
The QCD scaling factor is derived by comparing the events with non-isolated high-pT muons indata and MC. As a control sample, events passed all W selection criteria before muon isolation
and reversed muon isolation requirement are used.
Figure 11.1 (a) shows the ETmiss distribution of the events with pT > 20 GeV in di-jet MC anddata. MC distribution is normalized to data, and shapes agree well. When the distributions are11.4 Background Estimation

179

normalized to integrated luminosity of 310 nb−1 , we found 6843.9 muons with pT > 20 GeV in
MC distribution and 4186 muons in data. Thus the scaling factor of 0.61 ± 0.01 (stat) ± 0.23
(syst) is derived.
The systematic uncertainties are obtained by comparing the scaling factor with that of theevents with ETmiss > 25 GeV, replacing the relative track isolation with the same cut imposed onrelative calorimeter based isolation and taking absolute difference of the scaling factors between
left and right of the peak. The numbers are summarized in Table 11.5.

Figure 11.1: Shape comparison between di-jet MC and data for pT > 20 GeV.

QCD
Stat.
scaling factor uncertainty
0.61
0.01

High ETmiss
syst.
0.21

Isolation
syst.
0.04

Shape
syst.
0.08

Total
uncertainty
0.23

Table 11.5: QCD scaling factor derived with events with non-isolated muons with pT > 20 GeV

11.4.2 Electroweak and tt¯ Backgrounds
Another background contribution is from sources with real W or Z-bosons, i.e. W → τν,Z → µµ, Z → ττ and tt¯ processes are considered as this type of backgrounds.
The yielded number of these backgrounds is estimated using MC samples. The cross section
are scaled and normalized to the integrated luminosity. Also, the corrections for the number ofvertices, trigger and muon reconstruction are applied. The acceptances and predicted number

180

Measurement of W Boson Cross Sectionof events for the various backgrounds are shown in Table 11.6. For the Z → µµ process, a scale
factor of 109 / 121.9 is applied to compensate the discrepancy observed between the data andMC in the Z → µµ analysis (see Table 12.7).
Systematic components for these background predictions are listed as follows.
• Uncertainty on CW of 4.0 % as summarized in the Table 11.4
• Uncertainty on the PDF dependence of 3.0 % for tt¯• Theoretical cross section uncertainty of 5.0 % for electroweak processes and 6.0 % for tt¯
The total systematic uncertainty is 7.8 % for tt¯ and 6.4 % for electroweak backgrounds. We
treat these uncertainties as 100 % correlated among all the electroweak backgrounds, except
for the tt¯ cross section uncertainty, which is treated as uncorrelated with the other theoreticaluncertainties. The total number of predicted events from electroweak background process is77.8 ± 0.3 (stat) ± 4.8 (syst).

11.4.3

Cosmic Ray BackgroundThe number of cosmic ray backgrounds is estimated in this section. The following two cases
are considered.
1. The events in which cosmic muons overlap with a in-time minimum bias event
2. The events which contain cosmic activity only
For case 1, the cosmic background cross section is written as in Eq.(11.4).
reco
σcosmic = σMB · ptrig
cosmic · pcosmic · Lint ,(11.4)

where σMB is the minimum bias cross section, ptrig
cosmic is the probability that a cosmic ray fires
reco
L1 MU6 trigger in time and pcosmic is the probability that a triggered cosmic background event
passes the W → µν event selection without the requirement on primary vertices. Lint is theintegrated luminosity used for the W → µν analysis.
−5
σMB is assumed as 50 ± 10 (syst) mb. ptrig
by a study of muoncosmic is derived as 3.3 × 10
reco
trigger rate in the bunch with no beam. pcosmic is estimated with the data in non-colliding bunchand resulted probability is (0.34 ± 0.13) · 10−5 . The charge asymmetry of the cosmic muons
are also considered as N + /N − = 1.235 ± 0.004 (stat) ± 0.025 (syst). At the Lint = 310 nb−1 , thenumber of cosmic background in the W → µν acceptance for each charge is estimated as+
Ncosmic= 0.9 ± 0.4 (stat) ± 0.2 (syst),−
Ncosmic = 0.8 ± 0.3 (stat) ± 0.2 (syst).

The main source of the statistical uncertainty is the reconstruction probability for cosmic events.
The main source of the systematic uncertainty is about 20 % of uncertainty on minimum bias
cross section.

11.4 Background Estimation

181

For case 2, a study utilizing non-colliding bunch is performed. With the data which corresponds to the delivered luminosity of 8.4 nb−1 , we have 55581 events in the MuonswBeam
stream. When requirements of more than one muon with pT > 6 GeV and more than one primary vertex are applied, no events remain. Taking into account the calculated results of ptrig
cosmicand preco,
thecosmicraybackgrounds
entirelyinducedbycosmicactivities
areassumedsafelycosmicnegligible in this study.

11.4.4 Background Summary
The overall estimated backgrounds are summarized in Table 11.6.

W

W+

W−

SampleZ → µµZ → ττ
W → τν
tt¯
QCD
CosmicTotal
Z → µµZ → ττ
W → τν
tt¯
QCD
CosmicTotal
Z → µµZ → ττ
W → τν
tt¯
QCD
CosmicTotal

Acceptance (%)
11.4
0.5
3.4
8.7
–
–
–
5.9
0.2
2.0
4.4
–
–
–
5.4
0.2
1.4
4.3
–
–
–

Predicted Events
34.8 ± 0.2 (stat) ± 2.2 (syst)
1.4 ± 0.0 (stat) ± 0.1 (syst)
38.3 ± 0.2 (stat) ± 2.5 (syst)
4.3 ± 0.0 (stat) ± 0.3 (syst)
21.1 ± 4.5 (stat) ± 8.7 (syst)
1.7 ± 0.8 (stat) ± 0.4 (stat)
101.7 ± 10.9
18.2 ± 0.1 (stat) ± 1.2 (syst)
0.7 ± 0.0 (stat) ± 0.1 (syst)
22.4 ± 0.2 (stat) ± 1.4 (syst)
2.2 ± 0.0 (stat) ± 0.2 (syst)
11.1 ± 2.7 (stat) ± 5.2 (syst)
0.9 ± 0.4 (stat) ± 0.2 (syst)
55.5 ± 6.4
16.7 ± 0.1 (stat) ± 1.1 (syst)
0.7 ± 0.0 (stat) ± 0.0 (syst)
15.9 ± 0.1 (stat) ± 1.7 (syst)
2.1 ± 0.0 (stat) ± 0.2 (syst)
10.1 ± 1.8 (stat) ± 3.5 (syst)
0.8 ± 0.4 (stat) ± 0.2 (syst)
46.3 ± 4.5

Table 11.6: The predicted number of electroweak, QCD and cosmic ray background events
after corrections of number of vertices, trigger and muon reconstruction efficiency scale factors.
The predicted number of events are normalized to 310 nb−1 .

182

Measurement of W Boson Cross Section

11.5

Results for W-Boson Analysis

11.5.1

Event Cut Flow in the W → µν Selection

Table 11.7 summarizes the cut flow of the W → µν selection on the events in the 310 nb−1 ofdata in MuonswBeam stream. Total of 1181 (W+ :709, W− :472) W → µν candidates are foundin this analysis.
selection
All
Good Run List
Jet cleaning
L1MU6
VertexCombined µ,|η| < 2.4,
pT > 15 GeV,
pTMS > 10 GeV,
|pTMS − pTID | < 15 GeV,
|z0 − zvtx | < 10 mm,
pT > 20 GeV,
isolation
missET > 25 GeV
MT > 40 GeV

number of events reduction factor (%). relative eff. (%))
50204964
100.00—33613684
66.95
66.95
33611292
66.95
99.99
513393610.23
15.27
4789670
9.54
93.29

20721

4.13 ×10−2

0.43

7052
2921
1220
1181

1.41 ×10−2
5.82 ×10−3
2.43 ×10−3
2.35 ×10−3

34.03
41.42
41.77
96.80

(W+ :709, W− :472)

Table 11.7: Event cut flow of the W → µν selection on data.
Shown in Figure 11.2 is the cut flow of the W → µν signal events as well as the backgroundprocesses. In the figure, the result in data and MC prediction does not agree before preselection.
This is because the di-jet MC sample (denoted as QCD in the figure) is filtered by the cut which
requires the events to have at least one muon with pT > 8 GeV as described in section 4.7.2.

11.5.2Kinematics of Pre-Selected Samples

Figure 11.3, 11.4 show the distributions of selected events in data as well as the MC prediction
after the pre-selection. MC predictions are scaled by the cross section and normalized to thenumber of events in the data. The event-by-event basis weight is applied according to thenumber of vertices distribution. Also the trigger and muon reconstruction efficiency scale factor
is applied. The QCD histogram represents the sum of the contributions from di-jet samples after
0.61 of QCD scale factor applied on them.
Figure 11.3 is the distributions in η, φ and pT of the highest-pT muons. Trigger and reconstruction scale factors are applied according to the direction (endcap or barrel) a given muon
generated. The figures show a good agreement between data and MC prediction.

Events

11.5 Results for W-Boson Analysis

108
107

183

∫ L dt = 310 nb

-1

6

10

Data 2010 ( s = 7 TeV)Z → µµW → µν
tt

W → τν

Z → ττ

QCD

105
104
103
102
10
1

p
p
p
p
p
p
p
p
p
lEve assedBassedJassedMassedPassedHassedMassedI assedMassedM
snt
VCID etCl
i
o
t
u
U
g
hPt onQ latio etean 6uali n
ing
ty

tota

Figure 11.2: A cut flow of the W → µν event selection with backgrounds.
Figure 11.4 shows the ETmiss and MT distributions after pre-selection. In the MT distribution,
if there are more than one muons in an event, the muon which gives the MT value nearest to mW= 80.399 GeV [36] is adopted. The trigger scale factor is applied according to the direction of
the muons selected by this procedure.

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QCD

Entries / 5 GeV

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(c)

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µ

Z → µµtt

W → τν

Z → ττ

QCD

60

70

80

90 100µp (GeV)p (GeV)T(e)

W → µν

T(f)

Figure 11.3: Distributions of the highest-pT muons in events after pre-selection. Histograms
are scaled by the cross section and normalized to the number of events in data. The numberof vertices, trigger and muon reconstruction efficiency scale factors are applied as well as the
QCD scaling factor.

185∫ L dt = 310 nb
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Data 2010 ( s = 7 TeV)

7000

9000

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Z → µµtt

W → τν

Z → ττ

QCD

6000

Events / 5 GeV

Events / 5 GeV

11.5 Results for W-Boson Analysis

5000

106
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Z → µµtt

W → τν

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4000

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3000
2000

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00 10 20 30 40 50 60 70 80 90 100
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(GeV)
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Emiss
(GeV)
T

400
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(b)
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300

W → µν

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QCD

250

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Events / 5 GeV

(a)

105
104
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W → µν

Z → µµtt

W → τν

Z → ττ

QCD

102

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-1

L dt = 310 nb

20

40

60

80

100

120

10-2
0

20

40

60

MT (GeV)
(c)

80

100

120

MT (GeV)(d)

Figure 11.4: ETmiss and MT distributions of the events after pre-selection. The muon which gives
the MT nearest to mW is selected. Histograms are scaled by the cross section and normalized to
the number of events in data. The number of vertices, trigger and muon reconstruction efficiency
scale factors are applied as well as the QCD scaling factor.

186

11.5.3

Measurement of W Boson Cross Section

Kinematics of the W → µν Candidate Events

Shown in Table 11.8 is the number of events after all the W → µν selection in data and MC. The
numbers are separated into the ones coming from W + and W − according to the charge of muons
which is used to calculate the MT . The indicated uncertainties do not include the systematic
contribution from the luminosity.
SampleW
W+
W−
Z → µµ34.8 ± 2.2
18.2 ± 1.2
16.7 ± 1.1
Z → ττ
1.4 ± 0.1
0.7 ± 0.0
0.7 ± 0.0
W → τν
38.3 ± 2.5
22.4 ± 1.4
15.9 ± 1.0¯
tt
4.3 ± 0.3
2.2 ± 0.2
2.1 ± 0.2
QCD
21.1 ± 9.8
11.1 ± 5.4
10.1 ± 4.8
Cosmic1.7 ± 0.8
0.9 ± 0.4
0.8 ± 0.4
Total background 101.7 ± 10.9
55.5 ± 6.4
47.1 ± 4.6
W → µν signal 1194.0 ± 76.4 712.1 ± 45.6 481.5 ± 30.8
Total predicted 1295.7 ± 87.3 767.6 ± 52.0 528.6 ± 35.4
Number observed
1181
709
472
Table 11.8: The number of events which passed the W → µν selection in data and MC with its
error. The error does not contain contributions coming from luminosity uncertainty.
Figure 11.5 and 11.6 show the distributions of selected muons / events in data as well as theMC prediction after all the W → µν selection. In Figure 11.5, muons are selected as the ones
which give the MT result nearest to the mW in an event. In Figure 11.6, in case if there are morethan one muons in an event, the MT result nearest to the mW is adopted. MC predictions are
scaled by the cross section and normalized to the number of events in data. The event-by-event
basis weight is applied according to the number of vertices distribution. Also the trigger andmuon reconstruction efficiency scale factor is applied as well as the QCD scaling factor.

120

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Z → µµtt

W → τν

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QCD

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QCD

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-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

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QCD

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(c)

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QCD

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90 100

10-1
20

30

40

50

µ

70

80

90 100µp (GeV)p (GeV)

T

(e)

60

T

(f)

Figure 11.5: Distributions of the muons used in MT calculation after all the W → µν selection.
Histograms are scaled by the cross section and normalized to the number of events in data. The
number of vertices, trigger and muon reconstruction efficiency scale factors are applied as wellas the QCD scaling factor.

Measurement of W Boson Cross Section

400∫ L dt = 310 nb
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QCD

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188

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(GeV)
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(b)
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250

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W → τν

Z → ττ

QCD

60

MT (GeV)(c)

W → µν

80

100

120

MT (GeV)(d)

Figure 11.6: ETmiss and MT distributions of the events after all the W → µν selection. The muon
which gives the MT nearest to mW GeV is selected. Histograms are scaled by the cross section
and normalized to the number of events in data. The number of vertices, trigger and muonreconstruction efficiency scale factors are applied as well as the QCD scaling factor.

11.5 Results for W-Boson Analysis

189

11.5.4 Cross Section Measurement
The production cross sections times branching ratio of the W → µν process is calculated according to Eq.(11.5) is summarized in Table 11.9.
σW × BR(W → µν) =NWobs − NWbkg.
AW · CW · Lint

(11.5)

N obs for inclusive cross section is 1181, in them, the number of W + is 709 and the number of W − is 472 as listed in Table 11.8. N bkg is also taken from Table 11.8. AW and CW aresummarized in Table 11.3 with the correction factors applied on them. Lint is 310 nb−1 with theuncertainty of 11 %.
σW × BR (W → µν)σW × BR (W + → µ+ ν)
σW × BR (W − → µ− ν)===9.57 ± 0.31 (stat) ± 0.48 (syst) ± 1.05 (lumi) nb.
5.69 ± 0.23 (stat) ± 0.29 (syst) ± 0.63 (lumi) nb.
3.87 ± 0.20 (stat) ± 0.20 (syst) ± 0.43 (lumi) nb.

Table 11.9: Results for the W → µν total cross section measurements.
Figure 11.7 and 11.8 show the comparison of distributions between data and inclusive MC
prediction. Histograms are scaled by the cross section and normalized to the integrated luminosity of 310 nb−1 . For MC, the luminosity uncertainty of 11 % is assigned as the error. In thesefigure, all the scale factors (QCD scaling, number of vertices, trigger and muon reconstruction
efficiency) are applied.

Measurement of W Boson Cross Section

Entries / Charge

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Vertex, Trigger, Reco. SF Corrected

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80

90 100 110 120
MT (GeV)(c)

Figure 11.7: Muon charge, ETmiss and MT distributions of the events after all the W → µν
selection. The muon which gives the MT nearest to mW GeV is selected. MC predictions are
given as an integrated histogram with 11 % of the luminosity uncertainty as the error. MC
predictions are scaled by the cross section and normalized to integrated luminosity of 310 nb−1 .
The number of vertices, trigger and muon reconstruction efficiency scale factors are applied aswell as the QCD scaling factor.

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400

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300
200
100
0
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30

40

50

60

70

80

µ

p (GeV)T(c)

Figure 11.8: η, φ and pT distributions of muons after all the W → µν selection. The muons
which give the MT nearest to mW GeV are selected. MC predictions are given as an integrated
histogram with 11 % of the luminosity uncertainty as the error. MC predictions are scaled by
the cross section and normalized to integrated luminosity of 310 nb−1 . The number of vertices,
trigger and muon reconstruction efficiency scale factors are applied as well as the QCD scaling
factor.

Chapter 12
Measurement of Z Boson Cross Section
12.1

Event Selection
Collision event selection
Good Run List & BCID
Z → µµ GRL
Primary vertex
Nvtx ≥ 1 with Ntracks ≥ 3|zvtx | < 150 mm
Trigger
L1 MU6
Muon selection
Muon quality

High-pT event selection
combined tracks
pT > 15 GeV, |η| < 2.4
pTMS > 10 GeV|pTMS − pTID | < 15 GeV|z0 − zvtx | < 10 mm

Z → µµ event selection
Tight kinematics (both muons) pT > 20 GeV
Muon quality (both muons)(as above)
P ID
ID isolation (both muons)pT /pT < 0.2 (∆R = 0.4)
Chargeq1 · q2 < 0
Invariant Mass
66 < Mµµ < 116 GeV
Table 12.1: A summary of the requirements for the Z → µµ candidate event selection.
A summary of the requirements for Z → µµ candidate events selection is given in Table
12.1. Alike the W → µν event selection, the Z → µµ event selection is divided into three parts.
The collision event selection and high-pT event selection are identical to the W → µν selection
except for GRL (each analysis uses the dedicated GRL) and jet cleaning. Note that the high-pT
event selection only requires a single combined track.
In the Z → µµ event selection, two isolated, oppositely charged muons are required in an
event. Both muons are required to satisfy the same quality as the one in the high-pT event
selection but pT > 20 GeV. The Mass window is set at 66 < Mµµ < 116 GeV.

12.2 Signal Acceptance and Efficiencies

193

12.2 Signal Acceptance and Efficiencies
12.2.1 Overall Acceptance of Z → µµ Selection
The definition of the acceptance is the same as in the W → µν analysis, i.e. the number of events
passing all selections divided by the number of generated events. The acceptance is estimatedwith a Z → µµ MC sample which is described in section 4.7.2. The yielded acceptance is36.90 % with a negligible statistical error. The GRL and BCID requirements are omitted fromthe selection since these are not relevant for simulated samples. The number of signal events
passing each step of the selection, and the efficiencies for each step relative to the previous one
and total generated number (denoted as reduction factor) are given in Table 12.2.
Then the acceptance is corrected to compensate the discrepancy between data and MC in
the number of vertices, trigger and reconstruction efficiency. The correction procedure of thedifference in the number of vertices effect is the same as the one used in W → µν analysis.
Details of the corrections are summarized in section 12.2.2.
selection
number of events reduction factor (%)
Total Events
299811–L1 MU625733085.83
Vertex25681085.66
combined track,|η| < 2.4,
pT > 15 GeV,
23278777.64
pTMS > 10 GeV,MS
ID
|pT − pT | < 15 GeV,
|z0 − zvtx | < 10 mm,
Tight Kinematics (µ × 2)
11808039.38
Isolation
11603538.70
Opposite Charge
11603438.70
Mass Window
11285837.64
Correction (vertex)
112608
37.56
Correction (trigger)
11061536.90
Correction (combined track)
11061536.90

rel. eff. (%)
–
85.83
99.80

90.65

50.72
98.27
100.00
97.26
99.78
98.23
100.00

Table 12.2: Effect of the Z → µµ selection criteria on simulated Z → µµ events.

194

12.2.2

Measurement of Z Boson Cross Section

Efficiency Scale Factors

Number of Vertices
The effect of the correction in terms of the number of vertices is the same as in the W → µν
analysis. The resulted scale factor is 0.998 ± 0.000 (stat) ± 0.002 (syst).
Muon Trigger Efficiency
In the Z → µµ analysis, two muons are required in an event. Thus the single muon trigger
efficiency scale factor does not coincides with the needed correction on the Z → µµ acceptance.
The event trigger efficiency and its uncertainty are expressed as follows.
event = 1 − (1 − 1 ) (1 − 2 ),(12.1)δevent = (1 − 1 ) δ2 ⊕ (1 − 2 ) δ1 .

(12.2)

1 and 2 are the L1 MU6 efficiency for each muon. Since the single muon trigger efficiencies are measured in endcap and barrel separately, events are categorized into three types
according to the direction to which each muon is generated. EE represents the events in which
both muons are generated to the endcap, BB represents the events in which both muons are
generated to the barrel, and EB represents the events in which one muon is generated to theendcap and the other is generated to the barrel. Event trigger efficiency is computed following
the procedure summarized below.
• Estimate the fraction of Z events of each type EE, BB and EB in MC. Events are required
to pass all the Z selection criteria except for the trigger. The resulted fractions are 0.230(EE), 0.286 (BB) and 0.484 (EB).
• Apply Eq.(12.1) on each type of events. Using the single muon trigger efficiency, we
estimated the event trigger efficiency for each type in data and MC.
• Using the fractions, take weighted average of the efficiency separately in data and MC asa scale factor.
- 0.965 ± 0.002 (stat) ± 0.005 (syst) (weighted average efficiency in data)- 0.983 ± 0.000 (stat) ± 0.001 (syst) (weighted average efficiency in MC)
After that the ratio of weighted average in data to MC is taken as the trigger efficiency scale
factor for the Z → µµ acceptance. The resulting scale factor is 0.982±0.002 (stat)±0.005 (syst).
Muon Reconstruction Efficiency
Given that Z → µµ events have two combined muons, the muon reconstruction efficiency scale
factor on the acceptance and its uncertainty are given asevent =  2 ,(12.3)δevent = 2δ.

(12.4)

12.2 Signal Acceptance and Efficiencies

195

The scale factor for muon reconstruction efficiency is taken from section 10.3. The scale
factor on the Z → µµ acceptance become 1.000 ± 0.008 (stat) ± 0.048 (syst).

12.2.3 Acceptance Decomposition
As in W → µν analysis, the overall acceptance is decomposed into AZ and CZ . The definition
and the estimated number are summarized in following.
• AZ : Fraction of the generated Z → µµ events which passed the kinematic and geometricalselection of pT > 20 GeV, |η| < 2.4 and 66 < Mµµ < 116 GeV, where all of these quantities
refer to the truth-level muon before any final state radiation. Estimated value for AZ is
0.486 with 3.0 % of common uncertainty (see section 8.4.3).
• CZ : The denominator is the number of events passing the generator-level requirementsthat form the numerator of AZ , and the numerator is the fraction of events passing the fullanalysis selections. The uncorrected value of CZ is estimated as 0.788. The systematic
uncertainty is assigned as 5.5 %, the details are presented in 12.3.

12.2.4 Summary of Acceptance and Efficiency
The Z → µµ signal acceptance is summarized in Table 12.3. The correction for the number ofvertices distribution, trigger and muon reconstruction efficiency is already applied on the overall
acceptance and CZ . The scale factors are also summarized in the table. The uncertainty on theoverall acceptance is assigned as 6.2 % as the quadrature sum of the uncertainties of AZ and CZ .
Z
AZ
0.486 ± 0.015
CZ
0.774 ± 0.043
overall acceptance
0.369 ± 0.023
number of vertices SF
0.998 ± 0.002
trigger efficiency SF
0.982 ± 0.006
reconstruction efficiency SF 1.000 ± 0.008 (stat) ± 0.048 (syst)
Table 12.3: A summary of the acceptance and scale factors for the Z → µµ events.

196

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12.3

Systematic Uncertainty on Acceptance

Table 12.4 summarizes the systematic components on the Z → µµ acceptance. The uncertainty
on AZ is estimated as 3.0 % and on CZ is estimated as 5.5 %. The effects from muon momentum
scale and resolution are estimated by the same method as in section 11.3. The differences fromthe uncertainty on W → µν acceptance are coming from the fact that, in the Z → µµ analysis,
two muon are required and calorimeter information is not used. The overall uncertainty on theacceptance is 6.2 %.
parameter
number of vertices
trigger efficiency
reconstruction efficiency
muon momentum scalemuon momentum resolution
isolation cut efficiency
theoretical uncertainty
total uncertainty
parameter
theoretical uncertainty
total uncertainty

parameter uncertainty (%)
0.2
2.4 (barrel), 2.1 (endcap)
2.4
1.0
5.0 (barrel), 9.0 (endcap)
1.0
0.2 (FSR), 0.3 (PDF)

acceptance uncertainty (%)
0.2
0.6
4.8
0.5
0.5
2.0
0.4
5.5
δAZ (%)
3.0
6.2

Table 12.4: A summary of the systematic uncertainty on the Z → µµ acceptance.

12.4 Background Estimation

197

12.4 Background Estimation
12.4.1 QCD BackgroundEstimation by Simulated Samples
The combinatorial muon pair comes from QCD process is one of the main background source
for the Z → µµ process due to its huge cross section. The muons originate from semileptonic
decay of heavy flavor hadrons or decay-in-flight of π/K meson.
Since the statistics used in this analysis is so small, the number of QCD background eventsare estimated using MC simulation samples. We used same di-jet MC samples used in the
W → µν analysis with QCD scaling factor of 0.61. Also, due to the fact that the jet production
cross section is not know accurately, the The corrections for the number of vertices, muon
trigger and reconstruction efficiency are applied as well. systematic uncertainty of 100 % isassigned. In 331 nb−1 of data, the predicted QCD background is 0.138±0.085 (stat)±0.138 (sys).
Since the amount of QCD background is expected to be very small, this estimation is used in
the Z-boson cross section calculation.
Estimation from the Number of Same Charged Muon Pair
One of the most straight forward data driven estimations for the number of QCD background is
to count the number of like-sign muon pairs fallen in the invariant mass window passed all theZ → µµ selection. However, the yielded number of such muon pair is zero. Thus only an upper
limit of the number of expected QCD events smaller than 3 is obtained in 95 % C.L.
Estimation using Sideband with Reversed Isolation
In this method the Mµµ − −Isolation space is divided into following four areas.
A: Isolated muons in 66 < Mµµ < 116 GeV
B: Isolated muons in 40 < Mµµ < 60 GeV
C: Non-Isolated muons in 66 < Mµµ < 116 GeV
D: Non-Isolated muons in 40 < Mµµ < 60 GeV
Figure 12.1 shows the Mµµ distributions for isolated and non-isolated muons. An assumptionthat the ratio of isolated to non-isolated muons from jets is independent of Mµµ is made. Uponthis assumption, the number of QCD events in the signal region is given by
NA ∼NB × NC.
ND(12.5)The number of events in each area is NB = 2, NC = 3 and ND = 5. Hence the expected numberof events are(4.0 ± 2.0) × (3 ± 1.7)
= 2.4 ± 2.1.
(12.6)NA ∼5.0 ± 2.2
The assigned error is only statistical component.

Measurement of Z Boson Cross Section

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60

80

100

120

140

160

180

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Figure 12.1: Dimuon invariant mass distributions for isolated and non-isolated muons.

12.4.2

Electroweak and tt¯ Backgrounds

The same set of the processes as in the W → µν analysis, W → µν, W → τν and Z → ττ,are considered as electro weak background process. Since the total amount of the electroweak
background is expected to be very small, we use MC simulation to estimate the various components. For the W → µν process, a scale factor of 1181 / 1194.0 is applied on the number of
events to compensate the discrepancy observed between the data and MC (see Table 11.8).
For the electroweak and tt¯ backgrounds, the following errors are assigned as systematiccomponents.
• Uncertainty on CZ of 5.5 % as summarized in the Table 12.4
• Uncertainty on the PDF dependence of 3.0 % for tt¯• Theoretical cross section uncertainty of 5.0 % for electroweak processes and 6.0 % for tt¯.
The systematics total to 8.7 % for tt¯ and 7.4 % for electroweak backgrounds. All the electroweak backgrounds are treated as 100 % correlated except for tt¯. In 331 nb−1 of data, total of
0.226 ± 0.012 (stat) ± 0.013 (sys) electroweak background events are predicted in this analysis.

12.4.3

Cosmic Ray Background

The model of the cosmic background used in the W → µν analysis is also adopted here asreco
σcosmic = σ MB · ptrig
cosmic · pcosmic · Lint .

(12.7)

12.4 Background Estimation

199−5
σ MB = 50 ± 10 mb and ptrig
are adopted as estimated in section 11.4.3.
cosmic = 3.3 × 10
Even with a loosened z0 cut to |z0 − zvtx | < 150 mm (the cut used in the Z → µµ cross section
measurement is |z0 −zvtx | < 10 mm), no events remain in the non-colliding bunch data of 9.4×105
events. The upper limit is calculated by assuming the case if one event remain, the number of
expected events which pass the Z → µµ selection is 1 × (20/300) = 0.067. This yields a value−8of precocosmic = 7.1 × 10 . The resulted value for the upper limit on the cosmic ray backgroundestimation is
Ncosmic = 50 · 106 × 3.3 · 10−5 × 7.1 · 10−8 × 331 = 0.039.
(12.8)

Since this value is one order smaller than estimated electro weak background and it is just a
upper limit, the background cosmic ray events are considered to be negligible in the Z → µµ
cross sections measurement.

12.4.4 Background Summary
The summary of the backgrounds estimated to Z → µµ in 331 nb−1 of data is presented inTable 12.5. All the values are taken from the prediction of the MC simulation. As backgroundprocesses, we consider W → µν, W → τν, Z → ττ, tt¯ and QCD di-jet events.
As described above, we take 100 % of the predicted number of events as systematics
for QCD events. On the other hand, the uncertainty of the acceptance, PDF and theoretical cross sections are considered for electroweak processes. In 331 nb−1 of data, total of
0.365 ± 0.085 (stat) ± 0.139 (sys) background events are predicted.
sampleW → µν
W → τν
Z → ττtt¯
EW Total
QCD
Total BackgroundAcceptance (%)
Number of events−4
8.68 × 10
0.030 ± 0.010 (stat) ± 0.002 (syst)−41.00 × 10
0.001 ± 0.001 (stat) ± 0.000 (syst)
2.65 × 10−2
0.087 ± 0.004 (stat) ± 0.006 (syst)−12.04 × 10
0.108 ± 0.005 (stat) ± 0.009 (syst)—
0.226 ± 0.011 (stat) ± 0.012 (syst)—
0.138 ± 0.084 (stat) ± 0.138 (syst)—
0.364 ± 0.085 (stat) ± 0.139 (syst)

Table 12.5: The background contributions predicted by MC. Predictions are normalized to 331
nb−1 and vertex, trigger and muon reconstruction scale factors are applied.

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12.5

Results of Z-Boson Analysis

12.5.1

Event Cut Flow in the Z → µµ Selection

Table 12.6 summarizes the effect of each step of Z → µµ event selection. The number of events
passing each step of the selection, the efficiencies of each step relative to the previous one andall the processed events (denoted as reduction factor) are given in Table 12.2. In the 331 nb−1of data triggered by L1 MU6, total of 109 Z → µµ candidates are found.
selection
number of Events reduction factor (%) relative eff. (%)
All49655492
100.00100.00Good run List
35883824
72.27
72.27
L1 MU65476542
11.03
15.26
Vertex5113446
10.30
93.37
Combined µ,|η| < 2.4,
pT > 15 GeV,
pTMS > 10 GeV,
22120
4.45 × 10−3
4.33 × 10−3MSID
|pT − pT | < 15 GeV,
|z0 − zvtx | < 10 mm,
Tight Kinematics (µ × 2)
144
2.90× 10−4
6.51 × 10−3
Isolation
117
2.36× 10−4
81.25
−4Opposite Charge
117
2.36× 10100.00−4
Mass Window
109
2.20× 10
93.16
Table 12.6: Event cut flow of the Z → µµ selection on data.

12.5.2Kinematics of Pre-Selected Samples

Figure 12.2 and 12.3 show the distributions of selected events in data as well as the MC prediction after the pre-selection. MC predictions are scaled by the cross section and normalized
to the number of events in data. An event-by-event basis weight is applied according to thenumber of vertices in a given event. Also the trigger and muon reconstruction efficiency scale
factors are applied. QCD histogram represents the sum of the contributions from di-jet samples
after 0.61 of QCD scale factor is applied on them.
Figure 12.2 is the distributions in η, φ and pT of the highest-pT muons. Trigger and reconstruction scale factors are applied according to the direction (endcap or barrel) of a given muon
generated. The data and MC results show a reasonable agreement.
Shown in Figure 12.3 is the invariant mass distribution of di-muon pairs. If there are morethan two muons in an event, the pair which has the invariant mass nearest to mZ = 91.1876 GeV[36] among any combination is adopted. The data and MC results agree well.

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Z → µµT(f)Figure 12.2: Distributions of the highest-pT muons after pre-selection. Histograms are scaledby the cross section and normalized to the number of events in data. The number of vertices,
trigger and muon reconstruction efficiency scale factors are applied as well as the 0.61 of QCD
scaling factor.

Measurement of Z Boson Cross Section

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the cross section and normalized to the number of events in data. The number of vertices, trigger
and muon reconstruction efficiency scale factors are applied as well as the 0.61 of QCD scaling
factor.

12.5 Results of Z-Boson Analysis

203

12.5.3 Kinematics of Z → µµ Candidate Events
Table 12.7 summarizes the number of events after all the Z → µµ selection in data and MC. The
indicated uncertainties do not include the contribution from luminosity uncertainty.
W → µν
W → τν
Z → ττtt¯
EW Total
QCD
Total backgroundZ → µµ signal
Total predicted
Number observed

0.030 ± 0.010
0.001 ± 0.001
0.087 ± 0.007
0.108 ± 0.011
0.226 ± 0.018
0.138 ± 0.162
0.364 ± 0.163
121.5 ± 9.0
121.9 ± 9.2
109

Table 12.7: The number of events which passed the Z → µµ selection in data and MC with its
error. The error does not contain contributions coming from luminosity uncertainty.
Shown in Figure 12.4 is the cut flow of the Z → µµ signal events as well as the backgroundprocesses. In the figure, the result in data and MC prediction does not agree before preselection.
This is because the di-jet MC sample (denoted as QCD in the figure) is filtered by the cut which
requires the events to have at least one muon with pT > 8 GeV as described in section 4.7.2.
Figure 12.5 and 12.6 show the distributions of selected muons / events in data as well as theMC prediction after all the Z → µµ selection. In Figure 12.5, both muons which comprise Z
candidate are plotted. In case if there are more than two muons in an event, the pair with its
invariant mass the nearest to mZ is selected.
Also in Figure 12.6, the pair with the most Z-like invariant mass is adopted. MC predictions
are scaled by the cross section and normalized to the number of events in data. Event-by-event
basis weight is applied according to the number of vertices distribution. Also the trigger andmuon reconstruction efficiency scale factor is applied as well as the QCD scaling factor.
As can be seen in Figure 12.6, the invariant mass distribution in data has a broader peakthan the MC prediction. This comes from the fact that the momentum resolution of the actual
muon spectrometer is worse than that of in MC. The degradation of the momentum resolution
is estimated as 5 (9) % in the barrel (endcap) in section 8.4.1 and the effect on the acceptance iscounted into the systematic uncertainty.
Figure 12.7 shows the distribution of original Z-boson kinematics after all selections.

Measurement of Z Boson Cross Section

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p
p
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lEve assedB assedT assedP assedH assedM assedI assedC assedM
RIG
nt
CID
V
ighP
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ass
uon solat
Win
io
Qua
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e
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lity ntota

Figure 12.4: A cut flow of the Z → µµ event selection with backgrounds.

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W → τν

Z → ττ

QCD

10

40

1
30

-1

10
20

10-2

10

10-3

0
20

30

40

50

60

70

80

90 100

10-4
20

30

40

50

µ

70

80

90 100µp (GeV)p (GeV)

T

(e)

60

T

(f)

Figure 12.5: Distributions of the muons making up Z candidates after all Z → µµ selection.
Histograms are scaled by the cross section and normalized to the number of events in data. The
number of vertices, trigger and muon reconstruction efficiency scale factors are applied as wellas the 0.61 of QCD scaling factor.

Measurement of Z Boson Cross Section

Events / 5 GeV

206

60

∫

-1

L dt = 331 nb

50

Data 2010 ( s = 7 TeV)Z → µµW → µν

tt

W → τν

Z → ττ

QCD

40
30
20
10
0
20 40 60 80 100 120 140 160 180 200

Events / 5 GeV

Mµµ (GeV)
104
103
102

∫

-1

L dt = 331 nb

Data 2010 ( s = 7 TeV)Z → µµW → µν

tt

W → τν

Z → ττ

QCD

10
1
10-1
10-2
10-3
10-4
20 40 60 80 100 120 140 160 180 200
Mµµ (GeV)

Figure 12.6: Mµµ distributions of the muons after all cuts. Histograms are scaled by the crosssection and normalized to the number of events in data. The number of vertices, trigger andmuon reconstruction efficiency scale factors are applied as well as the 0.61 of QCD scaling
factor.

207

Events / 5 GeV

Events / 5 GeV

12.5 Results of Z-Boson Analysis∫ L dt = 331 nb-1

30

Data 2010 ( s = 7 TeV)

25
20

Z → µµW → µν

tt

W → τν

Z → ττ

QCD

104∫ L dt = 331 nb

-1

103

Data 2010 ( s = 7 TeV)

102
10
1

15

Z → µµW → µν

tt

W → τν

Z → ττ

QCD

10-1
10

10-2

5
0
0

10-3
10-4
0

20 40 60 80 100 120 140 160 180

20 40 60 80 100 120 140 160 180

pZT (GeV)

pZT (GeV)

25 ∫

(b)

Events / 0.5

Events / 0.5(a)Data 2010 ( s = 7 TeV)

-1

L dt = 331 nb

20

Z → µµW → µν

tt

W → τν

Z → ττ

QCD

104∫ L dt = 331 nb
10

Data 2010 ( s = 7 TeV)

102

-1

3

Z → µµW → µν

tt

W → τν

Z → ττ

QCD

10
15

1
10-1

10

10-2
5
0
-3

10-3
-2

-1

0

1

2

3
Y

(c)

10-4
-3

-2

-1

0

Z

1

2

3
Y

Z

(d)

Figure 12.7: pT and rapidity distribution of the Z-bosons after all selections. Histograms are
scaled by the cross section and normalized to the number of events in data. The number ofvertices, trigger and muon reconstruction efficiency scale factors are applied as well as the 0.61
of QCD scaling factor.

208

Measurement of Z Boson Cross Section

12.5.4

Cross Section Measurement

The production cross sections times branching ratio of the Z → µµ process is calculated according to Eq.(12.9) is summarized in Table 12.8.
σZ × BR(Z → µµ) =NZobs − NZbkg.
AZ · CZ · Lint

(12.9)

The 109 Z → µµ event candidates are observed with an integrated luminosity of 331 nb−1
in which 121.9 ± 9.2 events are expected. NZbkg are taken from Table 12.5. AZ and CZ are summarized in Table 12.3 with the correction factors applied on them. Lint is 331 nb−1 with theuncertainty of 11 %.

σZ/γ∗ × BR(Z/γ∗ → µ+ µ− )=0.87 ± 0.08 (stat) ± 0.06 (sys) ± 0.10 (lum) nb.

Table 12.8: Z → µµ total and fiducial cross-section measurement.
Figure 12.8 and 12.9 show the comparison of distributions between data and inclusive MC
prediction. For MC, the luminosity uncertainty of 11 % is assigned as the error. In thesefigure, all the scale factors (QCD scaling, number of vertices, trigger and muon reconstruction
efficiency) are applied.

Events / 5 GeV

12.5 Results of Z-Boson Analysis

100

209

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

MC prediction

QCD scaling: 0.61

80

Normalized to Lint
Vertex, Trigger, Reco. SF Corrected

60
40
20
0
60

70

80

90

100

110

120

Mµµ (GeV)

50∫

Events / 0.5

Events / 5 GeV(a)Data 2010 ( s = 7 TeV)

-1

L dt = 331 nb

MC prediction

QCD scaling: 0.61

40

Normalized to Lint
Vertex, Trigger, Reco. SF Corrected

30
25

∫

Data 2010 ( s = 7 TeV)

-1

L dt = 331 nb

MC prediction

QCD scaling: 0.61
Normalized to Lint

20

Vertex, Trigger, Reco. SF Corrected

30
15
20

10

10
0
0

5
10

20

30

40

50

60

0
-3

-2

-1

0

pZT (GeV)
(b)

1

2

3
Y

Z

(c)

Figure 12.8: Mµµ and Z-boson pT and rapidity distributions after all Z → µµ selection. The
muon pair with Mµµ which is the nearest to mZ is selected. MC prediction is also given as
integrated in one histogram with the error of 11 % of luminosity uncertainty. MC prediction isscaled by the cross section and normalized to 331 nb−1 of integrated luminosity. The numberof vertices, trigger and muon reconstruction efficiency scale factors are applied as well as the
QCD scaling factor.

Measurement of Z Boson Cross Section

25

Entries / 0.314

Entries / 0.24

210

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb-1

MC prediction

QCD scaling: 0.61

20

Normalized to Lint
Vertex, Trigger, Reco. SF Corrected22
20

Data 2010 ( s = 7 TeV)

∫ L dt = 331 nb
18-1

MC prediction

QCD scaling: 0.61
Normalized to Lint

16

Vertex, Trigger, Reco. SF Corrected

14
12

15

10
8

10

6
5

4
2

0

0

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-3

-2

-1

0

1

2

3
µ

µ

η

φ
(b)

Entries / 5 GeV

(a)

90
80

∫

70

Normalized to Lint

Data 2010 ( s = 7 TeV)

-1

L dt = 331 nb

MC prediction

QCD scaling: 0.61
Vertex, Trigger, Reco. SF Corrected

60
50
40
30
20
10
0
20

30

40

50

60

70

80

µ

p (GeV)T(c)

Figure 12.9: η, φ and pT distributions of the muons which make up Z-boson candidate after all
Z → µµ selection. The muon pair with Mµµ which is the nearest to mZ GeV is selected. MC
prediction is also given as integrated in one histogram with the error of 11 % of luminosity uncertainty. MC prediction is scaled by the cross section and normalized to 331 nb−1 of integrated
luminosity. The number of vertices, trigger and muon reconstruction efficiency scale factors areapplied as well as the QCD scaling factor.

Chapter 13
Discussion and Conclusions
The first √measurement of the W and Z-boson production cross sections in proton-proton collisions at s = 7 TeV, the highest center-of-mass energy ever, are performed in the W → µν andZ → µµ processes using the data collected with the ATLAS detector from April to July, 2010.
The integrated luminosity used in the W → µν analysis is 310 nb−1 and in the Z → µµ analysis
is 331 nb−1 .
The muon detection efficiency is estimated using the experimental data. The dedicatedmethods are developed to estimate the efficiencies using single muon tracks since, due to thelimited statistics, the yielded number of Z → µµ events is small.
The muon trigger efficiency is estimated with respect to a reconstructed muon track since
one muon track with high transverse momentum is required in both the W → µν and Z → µµ
event selection. The efficiency is deduced by counting the number of muon trigger signatureson the path of a given track. The estimation is done using data taken by triggers which are basedon the calorimeter information to avoid trigger biases.
The muon reconstruction efficiency is measured with respect to a reconstructed track in the
inner detector. The efficiency is deduced by counting the number of tracks in the muon spectrometer which has consistent track parameters with a given muon track’s reconstructed in the
inner detector. In the estimation, about half the number of the layers in the muon spectrometerare required to be fired on the extrapolated path of the inner detector track to reject non-muonbackgrounds.
Event selection criteria for both W → µν and Z → µµ processes are established.
Figure 13.1 shows the distribution of the energy fraction (x) of partons which constitute Zboson candidates derived from the Z-boson rapidity distribution. The initial transverse momentum of Z-bosons are assumed negligible. The Z-boson flying into the most forward direction is
generated with yZ = 2.2, this corresponds to x = 0.12 and 0.0014. The previous studies held at
the Tevatron [140, 141] measured Z-bosons with |yZ | < 2.8 which corresponds to x > 0.0028.
The results in this thesis are looking the two times finer parton kinematic region.
Figure 13.2 shows the η distribution for muons in Z-boson events including a parton with x <0.0038 ( |yZ | > 2.5 in the Tevatron ). A precise knowledge of the muon spectrometer especiallyin the endcap region is important to put accurate constraints on PDFs in low-x region.

Discussion and Conclusions

Events212

60∫ L dt = 331 nb

Data 2010 ( s = 7 TeV)

50

Mµµ ± Y Zeparton x =7TeV

Z → µ µ MC

-1

40
30
20
10
0 -3
10

10-2

10-1
parton x

Entries / 0.4

Figure 13.1: (a) Parton x distribution in Z-boson candidate events obtained from Figure 12.7(c). The invariant mass of di-muon is used as Q. The Monte Calro prediction is normalized to
the number of events in data and background components are assumed negligible.

∫ L dt = 331 nb

-1

30
25

Z → µ µ events include

Data 2010 ( s = 7 TeV)

a parton with x < 0.0038

Z → µ µ MC

20
15
10
5
0

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2
µ

η

Figure 13.2: η distribution of muons in Z-boson candidate events which have a partons withx < 0.0038. The Monte Calro prediction is normalized to the number of events in data andbackground components are assumed negligible.

213∫ L = 310 nb-1∫ L = 331 nb-1

W (FEWZ + MSTW2008 NNLO)
W+ (FEWZ + MSTW2008 NNLO)

FEWZ + MSTW2008 NNLO-

W (FEWZ + MSTW2008 NNLO)

Data 2010 ( s = 7TeV)

Data 2010 ( s = 7TeV)

2

3

4

5

6

7

8

9 10 11 12

0.5

0.6

0.7

0.8

σW × Br(W → µν) (nb)

0.9

1

1.1

σZ × Br(Z → µµ) (nb)

(a)

(b)

Figure 13.3: Comparisons between the measured cross section times branching ratios and theoretical predictions in (a) W → µν (b) Z → µµ processes.
1181 W-bosons (709 W + and 472 W − ) and 109 Z-bosons are observed in data. The σW ×
BR (W → µν) are measured with a transverse mass cut of MT > 40 GeV and σZ × BR (Z → µµ)
is measured within an invariant mass window of 66 < mµµ < 116 GeV. The results of bothmeasurements are as follows.
σW × BR (W → µν)σW + × BR (W + → µ+ ν)
σW − × BR (W − → µ− ν)
σZ × BR(Z → µµ)

=
=
=
=

9.57 ± 0.31 (stat) ± 0.48 (syst) ± 1.05 (lumi) nb.
5.69 ± 0.23 (stat) ± 0.29 (syst) ± 0.63 (lumi) nb.
3.87 ± 0.20 (stat) ± 0.20 (syst) ± 0.43 (lumi) nb.
0.87 ± 0.08 (stat) ± 0.06 (syst) ± 0.10 (lumi) nb.

The next-to-next-to leading order QCD theoretical predictions are obtained asσW × BR (W → `ν)σW × BR (W + → `+ ν)σW × BR (W − → `− ν)
σZ × BR (Z → ``)

=
=
=
=

10.46 ± 0.52 nb.
6.16 ± 0.31 nb.
4.30 ± 0.21 nb.
0.96 ± 0.05 nb.

For a description of the calculation method, see section 4.7.2.
Shown in Figure 13.3 (a) is a comparison between the yielded σW × BR (W → µν) and thetheoretical predictions. The results for W + and W − are also shown separately. The asymmetry
between the positive and negative charged W-bosons is interpreted as comes from√ the asymmetry in the number of valence u and d quark constituens in protons colliding at s = 7 TeV. All
the results, including the charge asymmetry, are consistent with the theoretical prediction.
Shown in Figure 13.3 (b) is a comparison between the measured σZ × BR(Z → µµ) and thetheoretical prediction. The result agrees well with the theoretical prediction within the error.

214

Discussion and Conclusions

Shown in Figure 13.4 and√ 13.5 are the W / Z-boson production cross sections times branching ratios as a function of s. The results of the previous measurements by the UA1 and UA2
experiments at the CERN SppS, by the CDF and D0 experiments at the Fermilab Tevatron andby the PHENIX experiment at the RHIC are also shown in both figures. Along with the resultsby the previous experiments, the energy dependence of the W / Z-boson production cross section is also well described.
Though the statistics is limited, the uncertainties of the W / Z cross sections measurement isalready dominated by the systematic components.
The largest source is the 11 % uncertainty in the luminosity measurement. This mainly
comes from an inaccuracy in the proton beam current measurement and expected to be improved
with more dedicated measurements. Also the preparation of the absolute luminosity calibration
using the ALFA detector is on going. As described in section 4.5.2, the ALFA detector provide
an accurate absolute luminosity calibration measuring elastic proton-proton scattering at small
angles in the Coulomb-Nuclear Interference region. The expected accuracy of the calibration isabout 3 %.
The second largest systematic source is the uncertainty on the muon detection efficiency.
The major contributions are coming from the contamination of the decay-in-flight muons andlack of statistics. These are expected to be improved significantly with more statistics of Z → µµ
samples. The Z → µµ study in this thesis shows that expected background in the Z → µµ event
selection is below % level. As for statistics, assuming 10 fb−1 of data, the 107 muon samples
from the Z → µµ events are expected within the detector acceptance. This leads to a precise
muon detection efficiency estimation in a phase-space dependent manner.
Another large systematic source comes from the acceptance calculation (3 % for W → µν, 4% for Z → µµ). This is dominated by the uncertainty on PDFs in low-x region (2.1 % (W), 2.6% (Z)) and the W / Z-boson production modeling (1.6 % (W), 2.8 % (Z)). A study shows that,provided well estimated muon detection efficiency, the uncertainty on PDFs improve by a factorof 30 with 10 fb−1 of data [46]. The usage of PYTHIA, a leading order event generator, limits
the accuracy of the W / Z-boson production modeling. Hence the preparation of the MonteCalro production with a next-to leading order generator is on going and this will improve thesituation. Furthermore, the modeling will improve by the feedback from the measurement of an
accurate pT distribution of Z-bosons foreseen in the near future.
In this thesis, muon detection efficiency estimations using the Z → µµ process are performed. These are the first trials of the detector calibrations with the Z → µµ process. The
Z → µµ process plays a central role in the precise calibration of both the detector and MonteCalro simulations. These lead to precise electroweak measurements which make a major objective for the ATLAS. A representative measurement is of the W-boson mass. The ATLAS is
expected to have a potential to measure the W-boson mass with better than 10 MeV accuracy[46]. This leads to a new indirect constraints on the Higgs boson mass and the properties of the
SUSY particles. Furthermore, well constrained PDFs provide a solid basis for every physics
analysis and searches performed at the ATLAS. As such, the works in this thesis constitute thefirst major step for the lasting physics program at the ATLAS.

σW × Br(W → l ν) [nb]215

Data 2010 (10

s = 7 TeV)

∫ L dt = 310 nb-1

W → µν
++W →µ νW →µν

1

NNLO QCD
W (p p)

10-1/

CDF W → (l/e) ν/

D0 W → (e/ µ) ν
UA1 W → l ν

W (pp)

UA2 W → e ν+

W (pp)-W (pp)/

Phenix W ± → (e +/e ) ν
-

1

10

s [TeV]σZ/γ * × Br(Z/ γ *→ ll) [nb]Figure 13.4: Comparison between the measured production cross section times branching ratios
for W → µν channels in this thesis with MT > 40 GeV and theoretical predictions including
next-to-next-to-leading order QCD corrections. The results of the previous experiments are also
shown.

1

Data 2010 (s = 7 TeV)

∫ L dt = 331 nb-1Z/γ *→ µµ (66 < m < 116 GeV)
µµ

10 -1

CDF Z/ γ *→ ee (66 < m
D0 Z/ γ *→ ee/

NNLO QCD
Z/γ * (p p)Z/γ * (pp)

10 -2
1

(70 < meeee

< 116 GeV)
< 110 GeV)CDF Z/ γ *→ ee/ µµ (66 < m
D0 Z/ γ *→ ee(75 < mUA1 Z/ γ *→ ee (m

ee

ee

ee

< 116 GeV)

< 105 GeV)

> 70 GeV)

UA1 Z/ γ *→ µµ (m µ µ > 50 GeV)
UA2 Z/ γ *→ ee (mee> 76 GeV)

10s [TeV]
Figure 13.5: Comparison between the measured production cross section times branching ratios for Z → µµ channel in this thesis with 66 < mµµ < 116 GeV and theoretical predictions
including next-to-next-to-leading order QCD corrections. The results of the previous experiments are also shown.

Acknowledgments
There are a number of people without whom this thesis would not have been written, and towhom I am greatly indebted.
First of all, I wish to express my sincere thankfulness to my supervisor, Prof. Satoru
Yamashita for continuously encouraging and advising me throughout five years of my Ph.D.
course. His true love for physics and attitude to open new frontiers, which is not limited within
particle physics, have affected me so much. He have always respected his duty of education andguided my primitive curiosities into right directions. It is my great fortune that I have been able
to spend my Ph.D course so close to him as his first doctoral student. I am also very grateful
to his wife Ms. Fumiyo Yamashita and his daughter Ms. Mayura Yamashita to allow me to
discuss with him by phone even around midnight and served the members of our laboratory
great dinners many times.
I deeply appreciate Prof. Hiroshi Sakamoto for his constant support over my Ph.D. period.
When my study was going well or I was stumbled by a difficulty, his kind and patient assistancealways helped me a lot. The home party to which he kindly invited me is a very good memory
with delicious dishes prepared by his wife Ms. Riyoko Sakamoto.
I would like to express my gratitude to the director of the International Center of Elementary
Particle Physics (ICEPP), Prof. Sachio Komamiya. All the achievement in my study have been
made as a student of ICEPP and they are obviously based on his tireless effort as the director. I
am also truly thankful to co-spokespersons of the ATLAS Japan group, Prof. Takahiko Kondo,
Prof. Tomio Kobayashi and Prof. Katsuo Tokushuku for giving me this excellent opportunity
to participate in the great experiment.
I am very grateful to Dr. Nicolas Norman Ellis for becoming my supervisor at CERN. He
gave me variety of important advices on my study and career as a researcher and his warmth
encouraged me to carry on my study.
Joao Guimaraes da Costa, a co-convener of the W / Z-boson working group at the ATLAS,
taught me so many things starting from basic techniques for data analyses. We have discussed
a lot for the W / Z cross sections measurement with muons. I really appreciate him for kindly
teaching me as if I am one of his students.
I would like to thank members of the University of Tokyo team. Prof. Tatsuo Kawamoto fortaking care of many aspects of my life at CERN, such as how to refueling a car or how to pay
fines for speeding. Prof. Shoji Asai for kindly arranging my presentation at the ATLAS Japan
physics meetings. Prof. Ikuo Ueda, Prof. Junichi Tanaka and Prof. Shimpei Yamamoto foradministrating excellent computing facility at CERN. Prof. Naoko Kanaya for many discussions

217
on the TGC software development. Dr. Tatsuya Masubuchi for his kind instruction about thetreatment of the batch system.
Prof. Tetsuro Mashimo, Prof. Hiroyuki Matsunaga, Prof. Tadaaki Isobe, Prof. Tomoaki
Nakamura and Mr. Nagataka Matsui for providing me an excellent computing environment fordata analyses and TV meeting system at the University of Tokyo. When needed, they kindly
offered a consultation to solve any problems.
Dr. Susumu Oda has been a great office mate of mine. His amazing skills and proficientknowledge on data analyses stimulated me a lot. Also, he has been a very good friend of mine.
I won’t forget my last night at Geneva when I drank with him until late at night. Dr. Hiroshi
Nomoto and Mr. Takashi Kuwabara were my first colleagues in the TGC Japan team. It was
my great honor that I was able to take over their excellent works. Mr. Kohei Kessoku, Mr. Yu
Suzuki and Mr. Takashi Hayakawa kindly provided me a place to live while I was at CERN.
Mr. Yuya Azuma has been my good room mate. Ms. Katarina Bendtz for giving me excellent
English lessons. I have always enjoyed general discussions with Mr. Hiroshi Yamaguchi.
It is my honor to express my gratitude to members of ATLAS Japan group.
Firstly, I owe to express my acknowledgments to Prof. Osamu Sasaki, the group leaderof the TGC Japan team. He accepted me as a member of his team and provided me expert
knowledge and skills to operate the TGC electronics system. It have been one of the most
crucial asset to complete my study in this thesis.
Prof. Hisaya Kurashige for providing me an opportunity to work on the TGC software,
which played a key role to perform a competent study. I was so lucky that I was able to touch his
general-hearted character through professional discussions in his office and bit non-professionaltalks in a bar near Kobe University.
Prof. Masaya Ishino, I humbly regard him as a mentor of my works at CERN, is one ofthe persons who affected my way of thinking most. He have always disciplined himself to be agood professional. He is a researcher with a practical logical thinking and a strong heart. My
achievements really owe him in so many aspects.
I appreciate Prof. Mitsuaki Nozaki, Prof. Kiyotomo Kawagoe and Prof. Tohru Takeshita
for their great help when I was going to be included into this great experiment. Prof. Hiroyuki
Iwasaki for his strong management for the TGC team which have made a solid basis of mystudy. Prof. Chikara Fukunaga for his consultations about my proceedings for TWEPP2007.
Prof. Yoji Hasegawa for his expert knowledge on the TGC digitization software and a special
entertainment system for relaxations. Prof. Shuji Tanaka and Prof. Atsuhiko Ochi taught mebasics of the TGC chambers and something about stock market and cooking. Prof. Takashi
Matsushita gave me a guidance for the muon trigger efficiency estimation. His great knowledge
and an accurate management of the software was truly amazing. Prof. Yorihito Sugaya for his
collaboration with me in the test of TGC electronics boards. Prof. Makoto Tomoto and Prof.
Takuya Sugimoto for giving me a very good training through the test of the TGC electronics
system. Dr. Akimasa Ishikawa taught me a lot about data analyses. Mr. Yoshiji Yasu and Mr.
Masahiro Ikeno for their expert advices on the TGC software and electronics.
Prof. Yuji Yamazaki, Prof. Shigeru Odaka, Prof. Junichi Kanzaki, Prof. Masahiro Kuze andProf. Takanori Kono gave me important advices in the ATLAS Japan Standard Model meetingand Higher Level Trigger meeting. Prof. Kunihiro Nagano often kindly answered my silly

218

Discussion and Conclusions

questions as a convener of the ATLAS higher level muon triggers. Prof. Takashi Sasaki for
his excellent administrative role on the LCG Grid. Prof. Osamu Jinnouchi for his kind support
for my research career. Dr. Tadashi Maeno for his many advices on TGC software and Panda
system. Prof. Junji Tojo also gave me a lot of advices over cigarettes or a coffee.
Mr. Yasuyuki Okumura and Mr. Yuta Takahashi have been my brothers in arms. The countless discussions with them make up an important basis of my thesis. Their cheerful character
always encouraged me a lot. I wish them a very successful study. Mr. Satoshi Hasegawa,
Mr. Jun Wakabayashi, Dr. Hironori Kiyamura, Dr. Chihiro Omachi, Mr.Takuya Kadosaka, Mr.
Tadashi Niwa, Mr. Shogo Okada, Mr. Matthew King, Mr. Tomonori Nishiyama and Mr. Tomoe
Kishimoto for their collaboration with me and valuable discussions.
I appreciate the conveners and collaborators of the W / Z-boson working group. Dr. Massimiliano Bellomo, Dr. Matthias Schott, Dr. Maarten Boonekamp have shown me excellent
leaderships and relentless scrutinizing in data analyses. I have enjoyed the works and discussions with Dr. Alberto Belloni, Ms. Verena Martinez Outschoorn, Mr. Srivas Prasad, Mr.
Benjamin Smith and Ms. Emily Thompson for the first W / Z cross sections measurement at the
ATLAS experiment.
I also would like to express my thanks to all the LHC crews for bringing us excellent data.
Ms. Ritsuko Anbiru, Ms. Masako Shiota, Ms. Chieko Morita, Ms. Megumi Suzuki of
ICEPP, Ms. Yoko Sasaki and Ms. Ryoko Namba of the Department of Physics of th Universityof Tokyo, Ms. Yuko Honda of KEK, Ms. Connie Potter, Ms. Claire Gibson, Ms. Petya Lilova,
Ms. Christine Demirdjian and Ms. Kate Richardson of CERN have helped me a lot with theirsincere administrative and secretarial supports.
Mr. Yoshindo Miyayama and Ms. Clare Savage, the landlords of my apartments in Japanand France, provided me very comfortable places in which I have cured my fatigues and gained
a power to proceed my study.
It is my pleasure to express my biggest thanks to all the members of the Yamashita laboratory of ICEPP, Dr. Tamaki Yoshioka, Dr. Taikan Suehara, Dr. Tomohiko Tanabe. Dr. Yuichi
Morita, Mr. Hidetoshi Otono, Mr. Hitoshi Hano, Mr. Hideyuki Oide, Mr. Toru Suehiro, Mr.
Takeshi Takahashi, Mr. Takuro Murase, and Mr. Ryo Katayama for sharing many good andhard times with me. Their adventurous attitude for their study have enlarged my eyesight. I amvery proud of being a member of the laboratory.
I wish to extend my heartfelt gratitude to Prof. Takayoshi Oshima for giving me such an opportunity to pursue my study in this great experiment. While I was a student of him at Nagoya
University, he taught me so many things about how to overcome difficulties in life. On my
way to this thesis, these things helped me much more than any technical skills. Prof. Kenji
Inami, the supervisor of my study at Nagoya University, gave me basic knowledge about theexperimental particle physics on detectors and software. I have not done anything without them.
I deeply appreciate my mother Keiko, my father Kazuo, my grandmother Hisako who gave
me so many supports with their eternal love. Also, my sister Chihiro and my brother Masayuki
gave me their selfless encouragements.
Finally, I would like to dedicate this thesis to my late grandfather Yoneji Yamaguchi andlate grandmother Chieko Kubota.

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√
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