CP VIOLATION IN SINGLE TOP QUARK PRODUCTION
By
Weigang Geng

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Physics
2012

ABSTRACT
CP VIOLATION IN SINGLE TOP QUARK PRODUCTION
By
Weigang Geng
We present a search for CP violation in single top quark production with the
DØ experiment at the Tevatron proton-antiproton collider. CP violation in the top
electroweak interaction results in different single top quark production cross sections
for top and antitop quarks. We perform the search in the single top quark final state
using 5.4 fb−1 of data, in the s-channel, t-channel, and for both combined. At this
time, we do not see an observable CP asymmetry.

To Ni.

iii

TABLE OF CONTENTS

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

Chapter 1 Introduction . . . . . . . . . . . . . . . .
1.1 CP Violation . . . . . . . . . . . . . . . . . . . .
1.2 Motivation for searching for CP violation in single
1.3 Samples selection and single top analysis overview

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1
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Chapter 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Fermions . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Gauge Bosons . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Higgs Boson . . . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Limits of the Standard Model . . . . . . . . . . . . . .
2.2 The Top Quark . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Production . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Decay . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The single top quark . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Single top production and decay at the Tevatron . . . .
2.3.2 Motivations for searching for CP Violation in single top
2.4 Outline of CP violation measurement in single top . . . . . . .

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Chapter 3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 The Accelerator Complex and Tevatron . . . . . . . . . . . . . . . . . 31
3.2 Luminosity and Cross Sections . . . . . . . . . . . . . . . . . . . . . . 35
iv

3.3

The DØ detector . . . . . . . . . . . . . . . . . . . .
3.3.1 Particle Signatures . . . . . . . . . . . . . . .
3.3.2 Coordinate System and Pseudorapidity . . . .
3.3.3 The Central Tracking System . . . . . . . . .
3.3.3.1 Silicon Micro-strip Tracker (SMT) .
3.3.3.2 Central Fiber Tracker (CFT) . . . .
3.3.4 The Central and Forward Preshower Detectors
3.3.5 The Calorimeters and ICD . . . . . . . . . . .
3.3.5.1 Calorimeters . . . . . . . . . . . . .
3.3.5.2 Intercryostat Detector . . . . . . . .
3.3.6 The Muon System . . . . . . . . . . . . . . .
3.3.7 The Luminosity Monitor . . . . . . . . . . . .
3.3.8 The DØ Trigger System . . . . . . . . . . . .
3.3.8.1 The Level 1 Trigger . . . . . . . . .
3.3.8.2 The Level 2 Trigger . . . . . . . . .
3.3.8.3 The Level 3 Trigger . . . . . . . . .

Chapter 4 Event Reconstruction
4.1 Tracks . . . . . . . . . . . . .
4.2 Primary Vertices . . . . . . .
4.3 Electrons . . . . . . . . . . . .
4.4 Muons . . . . . . . . . . . . .
4.5 Jets . . . . . . . . . . . . . .
4.6 b Jets . . . . . . . . . . . . . .
4.7 Missing Transverse Energy . .

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Chapter 5 Event Selection . . . . . .
5.1 Strategy . . . . . . . . . . . . . .
5.2 Event selection cuts . . . . . . . .
5.2.1 General selection . . . . .
5.2.2 Electron channel selection
5.2.3 Muon channel selection . .
5.2.4 b-tagging selection . . . .

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Object Identification
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. 60
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Chapter 6 Data and Simulation Samples .
6.1 Data samples . . . . . . . . . . . . . . .
6.1.1 Signal data samples . . . . . . . .
6.1.2 Multijets data samples . . . . . .

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Chapter 7 Event Yields and Data/Simulation Comparison
7.1 Event yields . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Signal acceptance . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Data and Monte Carlo comparison . . . . . . . . . . . . . .

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Chapter 8 Multivariate Analysis . . . . . . . . . . . . . . . . . .
8.1 Split samples . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Output transformation . . . . . . . . . . . . . . . . . . . . . .
8.3 Key for plots . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Boosted Decision Trees (BDT) . . . . . . . . . . . . . . . . . .
8.5 Bayesian Neural Networks (BNN) . . . . . . . . . . . . . . . .
8.6 Neuroevolution of augmented topologies (NEAT) . . . . . . .
8.7 A combined BNN using BDT, BNN and NEAT discriminants

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Chapter 9 Statistical Analysis . . . .
9.1 Poisson distribution likelihood . . .
9.2 Bayesian analysis . . . . . . . . . .
9.3 Posterior probability density for the

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6.2

6.3

6.1.2.1 Multijets in the electron channel . . . .
6.1.2.2 Multijets in the muon channel . . . . . .
Simulation samples . . . . . . . . . . . . . . . . . . . . .
6.2.1 Signal simulation samples . . . . . . . . . . . . .
6.2.2 Background simulation samples . . . . . . . . . .
6.2.3 Simulation samples corrections and normalization
6.2.3.1 Simulation efficiencies corrections . . . .
6.2.3.2 W +jets and multijets backgrounds . . .
Lepton charge mis-ID measurement samples . . . . . . .

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CP asymmetry

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Chapter 10 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . 142
10.1 Uncertainties affecting normalization only . . . . . . . . . . . . . . . 143
10.2 Uncertainties affecting normalization and shape . . . . . . . . . . . . 150
Chapter 11 CP Violation Measurement
11.1 Cross section measurement . . . . . .
11.2 Expected results . . . . . . . . . . .
11.3 Observed results . . . . . . . . . . .
vi

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Chapter 12 Results and Conclusions . . . . . . . . . . . . . . . . . . . . 167
Appendix A Plots After Splitting by the Lepton Charge . . . . . . . . 169
Appendix B SAM Definitions of Dataset Used in This Analysis . . . 183
Appendix C Plots for discriminants after the binning transformation 185
Appendix D Lepton Charge Mis-Identification
D.1 Electron Charge Mis-ID Rate . . . . . . . .
D.2 Muon Charge Mis-ID Rate . . . . . . . . . .
D.3 Conclusion . . . . . . . . . . . . . . . . . . .

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Appendix E W Asymmetry Check . . . . . . . . . . . . . . . . . . . . . . 199
Appendix F b/¯ Jet Energy Scale (JES) Check . . . . . . . . . . . . . . 202
b
Appendix G Production and decay asymmetries . . . . . . . . . . . . . 212
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

vii

LIST OF TABLES

Table 2.1

Standard Model gauge bosons . . . . . . . . . . . . . . . . .

12

Table 2.2

Single top quark production cross sections [1]. . . . . . . . .

17

Table 6.1

Integrated luminosity for the datasets used in this analysis. .

81

Table 6.2

The Monte Carlo samples event samples . . . . . . . . . . . .

85

Table 7.1

One b tagged event yields . . . . . . . . . . . . . . . . . . . .

94

Table 7.2

Two b tagged event yields . . . . . . . . . . . . . . . . . . . .

95

Table 7.3

Expected and observed yields in “positive” samples . . . . .

96

Table 7.4

Expected and observed yields in “negative” samples . . . . .

97

Table 7.5

Combined (Electron+Muon, Run IIa+Run IIb) signal acceptances. 99

Table 8.1

BDT discriminant used in the current analysis. . . . . . . . . 112

Table 11.1

Expected results for CP asymmetry in s, t, s+t channels. . . 161

Table 11.2

Observed results for CP asymmetry in s, t, s+t channels. . . 166

Table D.1

Overall Charge mis-ID Rates. . . . . . . . . . . . . . . . . . . 198
viii

Table F.1

Event yields for signals in “positive” samples . . . . . . . . . 203

Table F.2

Event yields for signals in “positive” samples b/bbar JES . . 203

Table F.3

Event yields for signals in “negative” samples . . . . . . . . . 204

Table F.4

Event yields for signals in “negative” samples b/bbar JES . . 204

Table F.5

Ratio of integrals for variables before and after b/¯ JES . . . 205
b

ix

LIST OF FIGURES

Figure 1.1

Flow chart of the stages of the analysis overview . . . . . . .

5

Figure 2.1

The Standard Model of elementary particles . . . . . . . . .

8

Figure 2.2

Feynman diagram for the quark-antiquark annihilation

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16

Figure 2.3

Feynman diagram for single top s-channel production. . . . .

18

Figure 2.4

Feynman diagram for single top t-channel production. . . . .

19

Figure 2.5

Decay branching ratio of a top quark . . . . . . . . . . . . .

20

Figure 2.6

Feynman diagram for single top s-channel . . . . . . . . . . .

20

Figure 2.7

Feynman diagram for single top t-channel . . . . . . . . . . .

21

Figure 2.8

The transverse momentum for s-channel . . . . . . . . . . . .

22

Figure 2.9

The transverse momentum for t-channel . . . . . . . . . . . .

23

Figure 2.10

The pseudorapidity for s-channel . . . . . . . . . . . . . . . .

24

Figure 2.11

The pseudorapidity for t-channel . . . . . . . . . . . . . . . .

25

Figure 2.12

Feynman diagram for W ′ boson decaying into single top. . .

27

x

Figure 2.13

FCNC via exchange of a gluon in single top production. . . .

28

Figure 3.1

Fermilab’s accelerater chain. . . . . . . . . . . . . . . . . . .

32

Figure 3.2

Fermilab’s Tevatron Tunnel . . . . . . . . . . . . . . . . . . .

36

Figure 3.3

Side view of the DØ detector . . . . . . . . . . . . . . . . . .

39

Figure 3.4

A schematic of a hermetic detector . . . . . . . . . . . . . . .

41

Figure 3.5

High energy particle signatures left in the detector components 42

Figure 3.6

The Tracking System at DØ. . . . . . . . . . . . . . . . . . .

45

Figure 3.7

The disk/barrel design of the silicon microstrip tracker. . . .

47

Figure 3.8

Illustration of the calorimeter systems. . . . . . . . . . . . . .

49

Figure 3.9

Intersecting view of a quarter of the DØ calorimeter . . . . .

50

Figure 3.10

Trigger-related data flow in L1 and L2 trigger systems.

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58

Figure 4.1

Illustration of a primary vertex. . . . . . . . . . . . . . . . .

64

Figure 4.2

Illustration of jet formation. . . . . . . . . . . . . . . . . . .

68

Figure 4.3

Illustration of a secondary vertex . . . . . . . . . . . . . . . .

70

Figure 7.1

A pie chart illustration of backgrounds and signals . . . . . .

92

Figure 7.2

Lepton transverse momentum . . . . . . . . . . . . . . . . . 100

Figure 7.3

HT for positive and negative samples . . . . . . . . . . . . . 101

Figure 7.4

The Lepton Eta . . . . . . . . . . . . . . . . . . . . . . . . . 101
xi

Figure 7.5

Single top mass distribution . . . . . . . . . . . . . . . . . . 102

Figure 7.6

Top Mass distribution for positive and negative samples . . . 102

Figure 7.7

W Transverse mass distribution . . . . . . . . . . . . . . . . 103

Figure 8.1

Flowcharts of the MVA analyses. . . . . . . . . . . . . . . . . 106

Figure 8.2

Color scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 8.3

Decision tree illustration . . . . . . . . . . . . . . . . . . . . 111

Figure 8.4

BDT output for s+t channel . . . . . . . . . . . . . . . . . . 113

Figure 8.5

BDT output for s-channel

Figure 8.6

BDT output for t-channel . . . . . . . . . . . . . . . . . . . . 115

Figure 8.7

An illustration of a simple Neural Network. . . . . . . . . . . 116

Figure 8.8

BNN output for s+t channel . . . . . . . . . . . . . . . . . . 118

Figure 8.9

BNN output for s channel

Figure 8.10

BNN output for t channel . . . . . . . . . . . . . . . . . . . . 120

Figure 8.11

NEAT output for s+t channel . . . . . . . . . . . . . . . . . 122

Figure 8.12

NEAT output for s channel . . . . . . . . . . . . . . . . . . . 123

Figure 8.13

NEAT output for t channel . . . . . . . . . . . . . . . . . . . 124

Figure 8.14

Combined BNN output for s+t channel . . . . . . . . . . . . 126

Figure 8.15

Combined BNN output for s channel . . . . . . . . . . . . . 127
xii

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. . . . . . . . . . . . . . . . . . . 119

Figure 8.16

Combined BNN output for t channel . . . . . . . . . . . . . . 128

Figure 8.17

s+t channel discriminant plots . . . . . . . . . . . . . . . . . 129

Figure 8.18

Zoomed s+t channel discriminant plots . . . . . . . . . . . . 129

Figure 8.19

t channel discriminant plots . . . . . . . . . . . . . . . . . . . 130

Figure 8.20

Zoomed t channel discriminant plots . . . . . . . . . . . . . . 130

Figure 8.21

s channel discriminant plots . . . . . . . . . . . . . . . . . . 131

Figure 8.22

Zoomed s channel discriminant plots . . . . . . . . . . . . . . 131

Figure 9.1

Illustration of flat probability density . . . . . . . . . . . . . 135

Figure 9.2

Illustration of cross section measurement . . . . . . . . . . . 136

Figure 9.3

Illustration of two dimensional posterior probability density . 139

Figure 11.1

Illustration of a 2d posterior . . . . . . . . . . . . . . . . . . 155

Figure 11.2

Illustration of measuring CP violation . . . . . . . . . . . . . 156

Figure 11.3

Expected CP Violation results in s + t-channel . . . . . . . . 158

Figure 11.4

Expected CP Violation results in t-channel . . . . . . . . . . 159

Figure 11.5

Expected CP Violation results in s-channel . . . . . . . . . . 160

Figure 11.6

Observed CP Violation results in s + t-channel . . . . . . . . 163

Figure 11.7

Observed CP Violation results in t-channel . . . . . . . . . . 164

Figure 11.8

Observed CP Violation results in s-channel . . . . . . . . . . 165
xiii

Figure A.1

Color scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Figure A.2

Transverse momentum of lepton for both samples . . . . . . 171

Figure A.3

Centrality for All Jets for both samples . . . . . . . . . . . . 171

Figure A.4

Delta Phi between Lepton MET for both samples . . . . . . 172

Figure A.5

HT for both samples . . . . . . . . . . . . . . . . . . . . . . 172

Figure A.6

HT-AllJets-MinusBTaggedJet for both samples . . . . . . . . 173

Figure A.7

Invariant Mass of two leading jets for both samples . . . . . . 173

Figure A.8

InvariantMass-LightQuarkJets1-2 for both samples . . . . . . 174

Figure A.9

Leading b Tagged Jet for both samples . . . . . . . . . . . . 174

Figure A.10 LeadingBTaggedJetEta for both samples . . . . . . . . . . . 175
Figure A.11 LeadingBTaggedJetLeptonDeltaPhi for both samples . . . . . 175
Figure A.12 LeadingBTaggedJetPt for both samples . . . . . . . . . . . . 176
Figure A.13 LeadingLightQuarkJetBTagNN for both samples . . . . . . . 176
Figure A.14 LeadingLightQuarkJetEta for both samples . . . . . . . . . . 177
Figure A.15 LeadingLightQuarkJetLeptonDeltaPhi for both samples . . . 177
Figure A.16 LeadingLightQuarkJetPt for both samples . . . . . . . . . . 178
Figure A.17 LeptonEta for both samples . . . . . . . . . . . . . . . . . . 178
Figure A.18 METPt for both samples . . . . . . . . . . . . . . . . . . . . 179
xiv

Figure A.19 QTimesEta for positive and negative samples . . . . . . . . . 179
Figure A.20 SecondLightQuarkJetPt for positive and negative samples . . 180
Figure A.21 Single top mass for positive and negative samples

. . . . . . 180

Figure A.22 SpinCorr for positive and negative samples . . . . . . . . . . 181
Figure A.23 TopMassMinChiSqr for positive and negative samples . . . . 181
Figure A.24 WT for positive and negative samples . . . . . . . . . . . . . 182
Figure C.1

s+t channel discriminant plots . . . . . . . . . . . . . . . . . 187

Figure C.2

Zoomed s+t channel discriminant plots . . . . . . . . . . . . 187

Figure C.3

t channel discriminant plots . . . . . . . . . . . . . . . . . . . 188

Figure C.4

Zoomed t channel discriminant plots . . . . . . . . . . . . . . 188

Figure C.5

s channel discriminant plots for . . . . . . . . . . . . . . . . 189

Figure C.6

Zoomed s channel discriminant plots . . . . . . . . . . . . . . 189

Figure D.1

Muon charge mis-ID rate as a function of pT . . . . . . . . . 197

Figure E.1

Expected posterior density for W + jets asymmetry . . . . . 200

Figure E.2

Observed posterior density for W + jets asymmetry . . . . . 201

Figure F.1

HT for all jets before and after b/¯ JES
b

Figure F.2

Leading jet transverse momentum before and after b/¯ JES
b

Figure F.3

Single top mass before and after b/¯ JES . . . . . . . . . . . 208
b
xv

. . . . . . . . . . . 206
207

Figure F.4

HT for all jets before and after b/¯ JES
b

Figure F.5

Leading jet transverse momentum before and after b/¯ JES
b

Figure F.6

Single top mass before and after b/¯ JES . . . . . . . . . . . 211
b

xvi

. . . . . . . . . . . 209
210

Chapter 1
Introduction
This thesis gives an overview of the first search for CP violation in single top quark
production at the DØ experiment at the Fermilab Tevatron Collider. Chapter 1 gives
an introduction to CP violation and the motivation for this search in the single top
process; Chapter 2 sketches the theory background; Chapter 3 gives an introduction
of the experimental facilities used in this analysis; Chapter 4 describes how to identify
basic physics objects; Chapter 5 presents the data and simulation samples used
in this analysis; Chapter 6 shows the event selection cuts and describes how the
background samples are normalized; Chapter 7 presents the multivariate methods
used; Chapter 8 describes how the statistical methods are implemented; Chapter 9
discusses systematic uncertainties encountered in this analysis; Chapter 10 shows the
specific methods used to measure the CP asymmetry and the results; Chapter 11
1

concludes this thesis by summarizing the results of the analysis and giving an outlook
for future analyses.

1.1

CP Violation

Charge conjugation and Parity (CP) symmetry states that the laws of physics should
be the same if a particle were interchanged with its antiparticle (C symmetry), and
left and right were swapped (P symmetry). CP-symmetry was proposed in 1957 by
Lev Landau as the true symmetry between matter and antimatter [2]. CP violation
occurs when there is a difference in the way that particles and anti-particles interact.
CP violation was first discovered in 1964, in the decays of neutral kaons by J. Cronin
and V. Fitch [3]. Their discovery showed that weak interactions violate not only the
charge-conjugation symmetry C between particles and antiparticles and the parity
P, but also their combination. The violation of CP-symmetry plays an important
role both in the attempts to explain the dominance of matter over antimatter in the
universe, and in the study of weak interactions in particle physics.
The Standard Model Lagrangian contains two ways to break CP-symmetry. The
first of these is in the QCD strong sector, which has yet not been found experimentally. The second way, involving the weak force, has been experimentally verified,
but only accounts for a small portion of the CP violation required to explain baryogenesis. Here we present a search for CP violation involving the top quark.
2

1.2

Motivation for searching for CP violation in
single top

The top quark was discovered in 1995 at the Fermilab Tevatron by the CDF and D0
collaborations[4]. It is the heaviest elementary particle found to date. Its large mass
and corresponding coupling strength to the Higgs boson suggests that CP violation
in the top sector might be accessible [5].
CP violation processes can exist within the Standard Model (SM) through a
CP-violating phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. However,
it is estimated that the amount of CP-violation in the SM is not enough to explain
baryogenesis, suggesting the possibility that new physics is needed to account for all
CP-violating processes [6].
CP violation is a very rare phenomenon that was confirmed in the decay of KL mesons [3]. However, the amount of CP violation observed in these systems can
be accommodated within the SM [7]. More interesting are systems involving Bmesons where the expected CP-violating effects within the SM are much larger [8].
On the other hand, the SM predicts very low CP violation for top physics because
of the Glashow-Iliopoulos-Maiani (GIM) mechanism which suppresses changes in
strangeness by 2 in weak interactions, making any large CP-violation effect direct
evidence of physics beyond the SM [6, 8].
3

The single top process provides a direct measurement of the CKM Matrix element
|Vtb |. One of the assumptions in measuring |Vtb | from single top is that the W tb
vertex is CP-conserving, and we test that assumption here.

1.3

Samples selection and single top analysis overview

This analysis is based on the single top cross section measurement in s+t, s and t
channels. (See Section 2.3 for definitions of these channels.) The data and simulation
samples went through various selection cuts and processing stages before multivariate
and statistical analysis. Sketch of the analysis is shown in Figure 1.1. These items
will be discussed in detail in Chapters 4 through 11.

4

$

!
"

#

%
"

#

Figure 1.1: Flow chart of the stages of CP violation analysis in single top. For
interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation.

5

Chapter 2
Theory
Elementary particles are the building blocks of the world around us and their interactions have been successfully described by the Standard Model of Elementary
Particles [9, 10, 11, 12]. High energy experimentalists conduct experiments either to
test the SM’s predictions in great detail, or to search for new interactions that are not
predicted by the SM (Beyound SM). At the energy frontier, high energy accelerators
can produce heavy particles such as top quarks to probe new physics.
The top quark is the most massive observed elementary particle. It was postulated
in 1973 by Makoto Kobayashi and Toshihide Maskawa to explain CP violation in
kaon decays [7]. The top quark was discovered at the Tevatron collider at Fermilab
in 1995, with the production of a top-antitop pair via strong interactions [4].
C.-P. Yuan et al [13] and S. Willenbrock [14] predicted a top quark production
6

mode by means of the electroweak interaction, in which the top quark is produced
singly, thus also called “Single Top” quark production. This production mode has
been observed at the Tevatron [15, 16] in 2009 by the DØ and CDF collaborations.
Single top is sensitive to many new physics models, and CP violation would be
a significant manifestation of them. Moreover, this measurement is unique in the
Tevatron (p¯ collider), and is not easily measured at the Large Hadron Collider
p
(LHC). The last section of this chapter explains how CP Violation in single top
manifest itself and how we intend to measure it.

2.1

The Standard Model

The Standard Model includes two major theories – quantum electroweak theory and
quantum chromodynamics. It describes the interactions between all known particles
(electromagnetic, weak, and strong interactions) in terms of one internally consistent
framework, the quantum field theory (QFT). The particles in the Standard Model
are divided into two groups – fermions and bosons.
The Standard Model has had extensive success in explaining a wide variety of
experimental results. Among other examples, the Standard Model predicted the
existence of the W and Z bosons, gluon, and the top and charm quarks before
these particles were observed. Their predicted properties were also experimentally
confirmed with good precision.
7

Three Generations
of Matter (Fermions)

mass→ 2,4 MeV
charge→ ⅔

u

spin→ ½

4,8 MeV

-⅓
½

d

0

½

171,2 GeV

c

⅔
½

t

⅔
½

charm

-⅓
½

4,2 GeV

s

b

-⅓
½

<0,17 MeV

<15,5 MeV

1

photon
0

νe νμ ντ

1

gluon
91,2 GeV

0

½

1

tau
neutrino

0,511 MeV

105,7 MeV

1,777 GeV

½

electron

Z

0

½

e

g

0

0

muon
neutrino

-1

γ

0

bottom

strange

electron
neutrino

Leptons

0

top

104 MeV

down
<2,2 eV

III

1,27 GeV

up

name→

Quarks

II

-1

½

μ

-1

½

τ
tau

muon

0

Z boson
80,4 GeV

W

±1

1

±

W boson

Figure 2.1: The Standard Model of elementary particles. [17]

8

Gauge Bosons

I

The Standard Model depends on 19 parameters, whose numerical values are established by experiment.

2.1.1

Fermions

The Standard Model includes 12 elementary particles of spin 1 known as fermions,
2
which observe the Pauli exclusion principle [18]. There are the six quarks (up,
down, charm, strange, top, bottom), and six leptons (electron, electron neutrino,
muon, muon neutrino, tau, tau neutrino). Each quark/lepton has a corresponding
antiparticle with the same mass but opposite electric charge.
The fermions are the building blocks of matter. They are further grouped into
three generations, where the lightest are in the first generation and the heaviest in the
third. Each generation contains a charged lepton with charge −1, a charge-neutral
neutrino, and up-type and down-type quarks with charges + 2 and − 1 respectively.
3
3
All ordinary (baryonic) matter is made of first generation charged particles (electrons,
and up and down quarks), since these do not decay. On the other hand, the two
higher generation charged particles decay within very short half lives.
Some properties of quarks and leptons can be seen in Figure 2.1. Note by massenergy equivalence, we usually express mass in units of eV/c2 , where c is the speed
of light in a vacuum, and we set c2 = 1 in this thesis, and then leave out c from
equations. The masses of hadrons are mostly of the order of 1 GeV/c2 , which makes
9

the GeV (gigaelectronvolt, or a billion electronvolt) a very convenient unit of mass.
For example the proton has a mass of 0.938 GeV.

The quarks carry color charge (red, green, blue), and hence interact through the
strong interaction. Quarks also carry electric charge and weak isospin (a component
of the weak hypercharge, which unifies weak with electromagnetic interactions.), so
they can interact with each other both elctromagnatically and via the weak interaction. At lower energy, or larger distance, the strong interaction becomes very
strong, resulting in a phenomena called color confinement, which results in quarks
being bound to one another, forming color-neutral composite particles called hadrons.
Hadrons are strongly interacting particles built from two types of quark combination:
¯
Baryon = QQQ (3 quarks), Meson = QQ (quark-antiquark pair). The familiar proton (uud) and the neutron (udd) are the two baryons composed of quarks with the
smallest masses.

The electrons, muons, and taus do not carry color charge, but carry an electric
charge, and so they all interact electromagnetically. The neutrinos do not carry color
charge or electric charge, so they only interact with the other particles through the
weak force, which makes them very difficult to detect.
10

2.1.2

Gauge Bosons

In the Standard Model, gauge bosons are force carriers that mediate the strong, weak,
and electromagnetic fundamental interactions. The gauge bosons of the Standard
Model all have spin 1 (thus the name bosons).
Photons mediate the electromagnetic force between particles that carry electric charges. The photon is massless and is described by quantum electrodynamics
(QED) [11].
The W + , W − , and Z gauge bosons mediate the weak interactions between
particles of different flavors (all quarks and leptons). They are massive, with the Z
boson the heaviest. These three gauge bosons along with the photons are grouped
together, as collectively mediating the electroweak interaction.
The eight gluons mediate the strong interactions between color-charged particles
(the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled
by a combination of color and anticolor charge (e.g. red-antigreen). Because the
gluon has an effective color charge, they can also interact among with each other,
which is different from photons, which do not carry electric charge and therefore do
not interact with each other. The gluons and their interactions are described by the
theory of quantum chromodynamics (QCD) [11].
Table 2.1 gives a summary of the properties of the gauge bosons in the SM.
11

Table 2.1: Standard Model gauge bosons
Gauge Bosons spin = 1
Force

Mass [GeV ]

Electric Charge

Strong

Gluon (g)

0

0

Weak

W±

80.398 ± 0.023

±1

Weak

Z

91.1876 ± 0.0021

0

EM

2.1.3

Gauge boson

Photon (γ)

0

0

Higgs Boson

The Standard Model also predicts the existence of another boson, the Higgs boson,
which gives mass to all elementary particles, including the massive W/Z bosons and
the lighter fermions, i.e. quarks and leptons, and even the Higgs boson itself. In this
way the Higgs boson is a key building block in the Standard Model.
The Higgs particle was theorized by R. Brout, F. Englert, P. Higgs, G. Guralnik,
C. R. Hagen, and T. Kibble in 1964 [19, 20, 21]. It has no intrinsic spin (spin 0), and
for that reason is classified as a boson (like the gauge bosons integer spin 1). Because an exceptionally large amount of energy and beam luminosity are theoretically
required to observe a Higgs boson in high energy colliders, it is the only fundamental
particle predicted by the Standard Model that has yet to be observed. It is hoped
that the LHC at CERN will confirm the existence of the Higgs boson.
12

2.1.4

Limits of the Standard Model

In spite of extensive experimental successes, the Standard Model is not a complete
theory of fundamental interactions. It has its own intrinsic defects, and there are
numerous phenomena that the SM can not explain. This leads to various Beyond
the Standard Model (BSM) searches. Listed below are some of the limitations of the
SM:
• It does not incorporate the physics of dark energy, which is the reason that
the universe is expanding at an accelerating rate, and accounts for 73% of the
total mass-energy of the universe [22].
• It does not explain gravitation, and it can’t describe general relativity consistently in terms of quantum field theory.
• It does not correctly account for neutrino oscillations and their non-zero masses
observed by the oscillation experiments [23]. Although mass terms for the
neutrinos can be added to the standard model by hand, the specifics of neutrino
mass are still unclear.
• It depends on 19 numerical constants, whose values are obtained from experiment, but the origin of the values is unknown.
• It has several apparently unnatural properties giving rise to puzzles like the
strong CP problem, where QCD strong interaction is CP-symmetric, and the
13

hierarchy problem, such as why the weak force is 1032 times stronger than
gravity [24].
• It does not contain any dark (i.e. nonluminous) matter particle that possesses
all of the required properties deduced from cosmology observations [25].
• It is also difficult to accommodate the predominance of matter over antimatter
(matter/antimatter asymmetry).

2.2

The Top Quark

The existence of the top quark was postulated (together with bottom quark) in 1973
by Makoto Kobayashi and Toshihide Maskawa to explain the observed CP violations
in kaon decay [7]. In hadron colliders, it can be produced via both the strong and
electroweak interactions. The top quark was discovered in 1995 by the DØ and
CDF Collabrations at Fermilab via strong interactions [4]. The production of single
tops via weak interaction was discovered also at Fermilab by the DØ and CDF
experiments in 2009 [15, 16] .

2.2.1

Properties

The top quark is an up-type quark with spin 1/2 and charge +2/3e. It has the largest
mass of any known elementary particles. Its mass is measured 172.9 ± 1.5 GeV [26].
14

Due to its large mass, it needs high energy colliders to be created, such as Tevatron
or LHC. It participates in strong, weak and electromagnetic processes.

2.2.2

Production

In hadron collisions, top quarks are produced dominantly in pairs through the QCD
¯
¯
processes q q → tt and gg → tt. Approximately 85% of the production cross sec¯
tion at the Tevatron is from q q annihilation, with the remainder from gluon-gluon
¯
fusion. Smaller cross sections are expected from electroweak single-top productions
mechanisms, mediated by virtual s-channel and t-channel W bosons, respectively. A
virtual particle is one having mass not equal to that of the free particles, also called
“off mass shell”.
A Feynman diagram for top pair production is shown in Fig. 2.2

2.2.3

Decay

Top quarks decay almost exclusively into a W boson and a b quark, with a branching
ratio B(t → W + b) ≈ 99.8%. Thus the final decay products are determined by the
W boson decay.
The fraction of top events containing b quarks is expected to be close to 100%,
and the quarks to be rather energetic, since they come from the decay of a massive
object.
15

Figure 2.2: Leading order Feynman diagram for the production of top quark pairs in
strong forces, where a quark-antiquark pair form a very energetic gluon, which then
decays into a top-antitop pair. From here and below, for the Feynman diagrams, the
time axis is always from left to right, and the space axis is from bottom up, unless
otherwise noted.
Because of its enormous mass, the top quark has an extremely short lifetime of
only 5 × 10−25 s, which is about 20 times smaller than the time scale of the strong
interaction (10−23 s). As a result, unlike other quarks, the top quark is expected
to decay before top-flavored hadrons or tt-quarkonium bound states can form. This
provides a unique opportunity to study directly the decay of quarks.

2.3
2.3.1

The single top quark
Single top production and decay at the Tevatron

Electroweak top quark production is usually referred to as single top quark production because only one top quark is produced per event. At hadron colliders,
16

there are three Standard Model single top quark production modes, the s-channel
p
b
(p¯ → t¯ + X) 2.3 and t-channel (p¯ → tq¯ + X) 2.4 exchanges of a virtual W , and
p
b
the tW production (p¯ → tW + X). The next to leading order (NLO) cross sections
p
with NNLL corrections for these processes at the Tevatron at 1.96 TeV are listed in
Table 2.2. The central values of the cross sections for single top are for estimated
172.5 GeV top quark mass. The uncertainties include components from the choice
of scale and parton distribution functions, but not for the top quark mass.
Table 2.2: Single top quark production cross sections [1].
Process

Cross Section (pb)

t-channel

2.26 ± 0.12

s-channel

1.04 ± 0.04

At the Tevatron, the two dominant single top quark production channels are the
s-channel and t-channel. In the s-channel, an intermediate virtual time-like W -boson
decays into a top and antibottom quark, as shown in Figure 2.3. The final state is
therefore a W boson and two bottom jets. In the t-channel, a bottom quark (originating from gluon radiation) transforms to top quark by exchanging a virtual space-like
W boson with an up or down quark, as shown in Figure 2.4. The accompanying
bottom quark is typically at large pseudorapidity (See definition in Equation 3.6)
and low transverse momentum, defined as pT =
17

p2 + p2 . Thus they usually esx
y

cape detection, and are often not reconstructed in the analysis. The t-channel final
state results also dominantly in W +2 jets, with just one of the jets coming from a
bottom quark. Occasionally, the initial or final-state quark can radiate a hard gluon
or quark at a large angle. That can be detected as additional jets. Together with
the light quark, this will lead to W +3 and W +4 jets events. The number of jets
reconstructed in the detectors depends on the decay kinematics. Although as shown
in Figure 2.4 is a 2 → 3 process, it contributes similar large cross section in the NLO
calculation to s-chanel [27]. The tW production mode, where a single top quark is
created in association with a real (on-shell) W boson, has too small of a cross section
(0.14±0.03 pb [1]) at the Tevatron energy, so it’s not included in our search channels.

Figure 2.3: Feynman diagram for single top s-channel production.

As mentioned in the top quark section 2.2, the top quark decays to a W boson
18

Figure 2.4: Feynman diagram for single top t-channel production.

and a b quark. The W boson further decays to two jets or to a lepton plus neutrino
(Figure 2.5). The all-jets channel is immersed in a large QCD background. In
our analysis, the electron and muon leptonic final states are the most useful. The
Feynman diagrams for the single top production and decay modes for s- and tchannel are shown in Figure 2.6 and Figure 2.7 separately.
Due to its large mass, the top quark is produced almost at rest, and the b quark
from the top quark decay tends to be central and have large transverse momentum,
as shown in Figure ??. For the decay products of W boson, the lepton has a softer
pT spectrum than that of the neutrino. This is due to the W boson polarization,
so the lepton from the W boson decay preferentially points in the same direction
as the incident proton or antiproton. The lepton appears as an isolated track of
19

Figure 2.5: Decay branching ratio of a top quark. Source: CP Yuan class notes.

Figure 2.6: Feynman diagram for single top s-channel production and decay.

20

Figure 2.7: Feynman diagram for single top t-channel production and decay.
high momentum in the cetnral tracking detector, matched with a shower in the
electromagnetic segments of the calorimeter or the muon chamber. The transverse
momenta of neutrinos from the W boson decay are reconstructed from the imbalance
in transverse energy measured in each event (missing ET):

ET =−
/

i
ET .

(2.1)

(Other quarks involved in the collision generate secondary hadrons, but they are
mostly low pT .)
Several single top parton level kinematics distributions for both channels are
shown in Figure 2.8 to Figure 2.11 .
The light quark produced in the t-channel has reasonably large pT , but its most
distinguishing feature is the asymmetric Q(l) × η distribution, where Q(l) is the
21

dσ/dpT [fb/5 GeV]

2 (a)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

b from top
b with top
lepton
neutrino

50

100

150
pT [GeV]

Figure 2.8: The transverse momentum for s-channel

22

dσ/dpT [fb/5 GeV]

b from top (b)
light quark
b from gluon
lepton
neutrino

5
4
3
2
1
0
0

50

100

150
pT [GeV]

Figure 2.9: The transverse momentum for t-channel

23

dσ/dη [fb/0.2]

b from top
b with top
lepton

16 (c)
14
12
10
8
6
4
2
0
-4

-2

0

2

Figure 2.10: The pseudorapidity for s-channel

24

4
η

dσ/dη [fb/0.2]

b from top
light quark
b from gluon
lepton

35
30
25

(d)

20
15
10
5
0
-4

-2

0

2

Figure 2.11: The pseudorapidity for t-channel

25

4
η

charge of the lepton in the event, which is used to keep the multiplication positive.
This asymmetry arises because the final state light quark produced during the single
top production most often is a d quark that moves in the same direction as the proton
(antiproton). The light quark η will hence tend to have the same sign as the charge
of the lepton from the top decay.
Event selection therefore requires a high pT electron or muon, two to four jets,
one of which must be identified as originating from a bottom quark, and missing ET
(Details of event selection see Chapter 5).

2.3.2

Motivations for searching for CP Violation in single
top

The main significance of measuring the cross sections for single-top production is that
it is directly proportional to the |Vtb |2 component of the CKM matrix. Moreover,
no assumption is needed on the number of families or on the unitarity of the CKM
matrix to measure |Vtb |. If there is CP violation, it would show up for amplitude in
|Vtb |.
Single top quark production offers excellent opportunities to probe physics beyond
the standard model. There are several ways new physics could produce a single
top quark differently for top and anti-top through processes such as new exchange
particles, flavor changing neutral currents (FCNC), anomalous W tb couplings or
26

other processes.
Single top can be produced by the decay of a resonance, for example, a W ′
boson, which have the same final states as the SM single top production, as shown
in Figure 2.12. If this resonance couples differently to top and anti-top, this could
produce different cross sections.

Figure 2.12: Feynman diagram for W ′ boson decaying into single top.

Non-SM interactions, such as flavor changing neutral currents (FCNC), can also
enhance the total single top cross section for t-channel, and possibly introduce a
difference in top and anti-top production rates. The Feynman diagrams for FCNC
via exchange of a gluon are shown in Figure 2.13.
In summary, the s-channel (tb) single top production is most sensitive to new,
heavy charged bosons. The t-channel (tqb) single top quark production would similarly be enhanced by flavor-changing neutral currents (FCNC). Either could produce
27

Figure 2.13: FCNC via exchange of a gluon in single top production.
a CP asymmetry effect, providing sensitivity to new physics.

2.4

Outline of CP violation measurement in single
top

Combining the CP symmetry with simultaneous time reversal (T) produces a combined symmetry called CPT symmetry. As of now, no violations of CPT symmetry
have been observed. CPT symmetry must be preserved in any Lorentz invariant
local quantum field theory with a Hermitian Hamiltonian.
We exploit that Tevatron is a p¯ collider, meaning that the initial state is a CP
p
eigenstate and therefore, any difference between the cross sections for p¯ → tX and
p
¯
p¯ → tX would be a clear indication of CP violation [8, 28].
p
28

The purpose of this measurement is to measure the top and anti-top quark production separately. The theoretical cross section for each of them is half that of the
total single top cross section.
The asymmetry AP in the single top production can be expressed as follows:
AP =

¯
σ(p¯ → tX) − σ(p¯ → tX)
p
p
.
¯
σ(p¯ → tX) + σ(p¯ → tX)
p
p

(2.2)

where σ denotes the production rate.
¯
The strategy of this analysis is to identify the production of single t or t quarks
using the charge of the lepton when the W boson decays leptonically and then
¯
measure the individual single t and t production cross sections. We assume that no
significant CP violation is present in background samples.
This analysis uses the same event selection and signal and background modeling
as the measurement of the single top quark production cross section using 5.4 fb−1
of DØ Run IIa and Run IIb data [29]. We split by lepton charge the discriminant
that was used to measure the single top quark production cross section [30], and
use it to measure top and antitop production cross sections separately. Therefore all
the systematic uncertainties in the single top quark cross section measurement are
applied to this analysis [29, 30]. A new systematic uncertainty is added to account
for the misidentification of the lepton charge, discussed in detail in Appendix D.

29

Chapter 3

Experimental Setup

The Fermi National Accelerator Laboratory (Fermilab) [31, 32] is located in the west
surburbs of Chicago, Illinois in the USA. Fermilab is the only facility in the world
where high energy protons and anti-protons collide at a center-of-mass energy of
√

s = 1.96 TeV [32, 33]. The Tevatron completed its physics program in September

2011 and stopped running. All the other elements in the accelerator chain except the
Tevatron and recycler are still being used for neutrino physics and other experiments.
A complex detection system is required to “see” the details of these energetic
collisions, and study interesting physics processes such as single top quark production. The two main detectors at Fermilab are known as DØ and CDF. This chapter
presents a description of accelerator complex and the DØ detector at Fermilab.
30

3.1

The Accelerator Complex and Tevatron

Fermilab uses a series of accelerators to create the high energy proton and antiproton
beams that collide in the Tevatron collider. The proton beams are created starting
with hydrogen gas from a linac at the beginning of the accelerator cycle. A portion
of the proton beams are taken from the Main Injector to create antiprotons. Once
enough antiprotons are accumulated, they are loaded into the Tevatron, where they
are accelerated to the final highest energy stage. The accelerated protons and antiprotons are grouped into a number of bunches, and they collide at two points where
the CDF (B0) and DØ (D0) detectors are located. Figure 3.1 is a picture illustrating
Fermilab’s accelerator chain. Below we talk about each part separately.
• Cockcroft-Walton Pre-accelerator
Producing negatively charged hydrogen ions (H − ) is the first step in creating proton and antiproton beams. This takes place in the Cockcroft-Walton
generator. Hydrogen gas is converted into H − ions by introducing it into a
container lined with molybdenum electrodes. The ions are accelerated out of
the container by a 750 keV electrostatic field applied by the Cockcroft-Walton
generator.
• Linear Accelerator
The Fermilab Linac is a 500-foot long linear particle accelerator that accelerates
31

Figure 3.1: Fermilab’s accelerater chain.

32

the negative hydrogen ions H − from the Cockcroft-Walton pre-accelerator to
400 MeV before injecting them into the Booster accelerator. The H − ions
pass through a carbon foil, which removes electrons from the hydrogen ions,
creating positively charged protons or H + .
• Booster
Located nearly 20 feet below ground, the Booster is a circular accelerator with a
diameter of 500 feet that uses magnets to bend electrically charged particles in
a circular path. Boosting means the protons coming from the linac experience
a repeated acceleration from electric fields during each revolution, increasing
their energy by a small amount each time. The protons travel around the
Booster about 20,000 times, and their energy is boosted to 8 GeV by the end
of the acceleration cycle. Then the Booster sends the protons to the Main
Injector.
In the synchrotron, the final beam energy is determined by the ring radius and
the maximum value of field:
p = 0.3Bρ,

(3.1)

where p is the proton momentum, B is the magnetic field in Tesla, and ρ is the
ring radius in meters.
• Main Injector The Main Injector (MI) is the next link in the accelerator chain.
33

The MI performs three functions: it accelerates protons and antiprotons for
injection into the Tevatron, it delivers protons for antiproton production, and it
transfer antiprotons between antiproton storage rings and from the antiproton
storage rings to the Tevatron. Protons from the Main Injector are also delivered
to several neutrino targets.

• Antiproton Source
Antiprotons do not exist freely in nature like normal matter. To produce antiprotons, a 120 GeV beam of protons taken from the main injector is steered
onto the side of a drum shaped nickel target. The drum is rotated quickly to
prevent the beam from hitting the same spot and thus preventing the destruction of the target. The collisions produce many secondary particles including
antiprotons. The aniprotons then enter a beamline in which they are captured
and focused, before being injected into a storage ring. After accumulating
a sufficient number of antiprotons in the storage ring, they are sent to the
Recycler before they are injected into the Tevatron.

• The Recycler
The Fermilab Recycler is a 8 GeV permanent magnet storage ring for the
accumulation of antiprotons from the antiproton source, and the recovery of
the antiprotons remaining at the end of a Tevatron store. It is located in the
34

Main Injector tunnel directly above the Main Injector beamline.

• The Tevatron
The Tevatron is the most powerful proton-antiproton accelerator in the world.
The Tevatron ceased operations on September 30th, 2011. It accelerates beams
of protons and antiprotons to nearly the speed of light at an energy of 0.98
TeV around a four-mile circumference vacuum pipe mostly surrounded by superconducting electromagnets. 774 niobium-titanium superconducting dipole
magnets cooled in liquid helium are used to produce a magnetic filed of 4.2 Teslas. Another 240 NbTi quadrupole magnets are used to focus the beam [31].
The collisions reproduce conditions in the early universe (≈ 10 ps after the Big
Bang, in comparison to 1 ps for LHC) and probe the structure of matter at a
very small distance. Picture 3.2 shows the Tevatron tunnel.

3.2

Luminosity and Cross Sections

In particle physics, collision rates are measured in terms of instantaneous luminosity,
L. The luminosity is an important value to characterize the performance of an
accelerator. Luminosity is defined as the number of particles per unit area per unit
time, usually expressed in cgs units, cm−2 s−1 .
For an intersecting storage ring collider, the instantaneous luminosity can be
35

Figure 3.2: Fermilab’s Tevatron Tunnel. The upper magnets are not in use. The
lower magnets are part of the Tevatron Collider. Protons and antiprotons travel
through a vacuum pipe located inside the string of magnets. On the roof are the
cables and cooling pipes.

36

characterized by the parameters:

N N
L = fn 1 2
A

(3.2)

where
f is the revolution frequency,
n is the number of bunches in one beam in the storage ring,
Ni is the number of particles in each bunch,
and A is the cross area of the beam.
The higher the luminosity, the greater the chance that a proton will collide with
an antiproton. The Tevatron had been able to deliver luminosities up to 4 × 1032
cm−2 s−1 [34]. At the interaction point, the beams are squeezed very narrowly to
increase the chance of hard collisions.
The rate of a physics process is given by

dN
= Lσ
dt

(3.3)

where σ is the total cross section of the process, N is the count of physics events,
and L is the (instantaneous) luminosity.
The total number of collisions which result in a given physics process in a period
37

of time can thus be written as

N =σ

where L ≡

Ldt = σL

(3.4)

Ldt, the integrated luminosity, is defined as the integral of the instan-

taneous luminosity with respect to time.
Therefore, the collision count can be calculated by multiplying the integrated luminosity by the cross-section for that collision process. The total number of collisions
is directly proportional to the integrated luminosity over this time.
The integrated luminosity has the unit of inverse area, usually expressed as inverse
picobarns pb−1 or inverse femtobarns f b−1 (1 barn = 10−24 cm2 ; 1 fb = 10−15
barns = 10−39 cm2 ).
This analysis uses 5.4 f b−1 of data collected at DØ.

3.3

The DØ detector

Detectors are our “eyes” to record and identify the useful events to reveal the nature
of fundamental interactions. DØ is one of two detectors used to study collisions produced in the Tevatron. Proton-antiproton collisions create showers of new particles
at the center of both CDF and DØ detectors at a rate of more than 2 million Hz.
We cannot record all those events. The trigger system decides whether an event
38

is interesting enough to be worth keeping. About 20 events per second are stored
on computer tape. For these interesting events, the detectors record each particle’s
flight path, energy, momentum and electric charge.
DØ is a typical high energy particle detector. It measures thirty feet tall and
fifty feet long and consists of four major parts: a tracking system, calorimeter, muon
system, trigger system. Figure 3.3 gives a sketch of the DØ detector components.

Figure 3.3: Side view of the DØ detector. The proton/anti-proton beam travels from
left/right to right/left.

39

3.3.1

Particle Signatures

Stable particles such as p, p, e± , γ will show up in the detector as energy deposits in
¯
hadronic and electromagnetic calorimeters or charged tracks in the tracking system.
Muons have a long lifetime and interact less with matters in the detector, which
means they pass through the entire detector before they decay, and leave tracks
in the muon detectors. Most of the particles produced in high-energy collisions
are short-lived. In order to observe all possible decay products of an collision, one
needs a hermetic detector and electronic system to record the events for further
offline analysis. Besides, since the presence of a neutrino is inferred from the missing
energy, it’s important that the calorimeters have 4π solid angle coverage, so that
missing energy is not due to any failure to detect all produced particles. Figure 3.4
shows a typical cylindrical modern detector:
Figure 3.5 shows what signatures particles will leave in the components of the
detector.

• Most charged particles, like electrons and protons, are detected both in the
tracking chamber and the electromagnetic calorimeter.

• Muons have a long life time, and have small interactions with matters in
calorimeter, so they are detected in all parts of the detector. They pass through
the entire detector, and leave tracks in the muon chamber.
40

Figure 3.4: A schematic of the basic components of a hermetic detector. I.P. refers
to the region containing the interaction point. This is a cross section of the typical
cylindrical design. [35].

41

Figure 3.5: High energy particle signatures left in the detector components [36].
• Neutral particles, like neutrons and photons, are not detectable in the tracking
chamber.

• Photons are detected by the electromagnetic calorimeter, while neutrons are
evidenced by the energy they deposit in the hadron calorimeter.

• Neutrinos rarely interact with matter, and will escape from detection by the
detector. Their presence can only be inferred using missing energy by looking
at the momentum balance (Eq. 2.1).

An event consists of all data pertaining to a single p¯ interaction as measured in
p
the detector.
42

3.3.2

Coordinate System and Pseudorapidity

For the convenience of the DØ detector description and data analysis, we use a righthanded coordinate system, in which the z-axis is defined along the beam pipe in the
direction of the proton beam, and the y-axis is upward, and thus x-axis directed into
the paper by right-handed rule (Figure3.3). The (x, y)-plane is usually referred to
as the transverse plane, which is vertical to the beam direction (z-axis). The polar
angle θ is the angle relative to the positive z-axis, and the azimuthal angle φ is the
angle from the positive x-axis on the transverse plane.
The rapidity of a particle of momentum pµ is defined as

y=

1
ln
2

|p| + pz
|p| − pz

,

(3.5)

where pz is the component of the momentum along the beam axis.
In the Tevatron, the particles are traveling close to the speed of light, thus the
mass of the particle is neglectable, and E ≈ |p| establishes. In this limit, the rapidity
becomes equal to the pseudorapidity:

y=

1
ln
2

E + pz
E − pz

θ
where η ≡ − ln tan 2

1
1 − cos θ
= − ln tan
2
1 + cos θ

= − ln tan

θ
2

≡ η,

(3.6)

is called the pseudorapidity, and θ is the angle between

the particle momentum p and the beam axis.
43

We use the term “forward” to describe the regions that are close to the beam
axis at large |η| (e.g. 2.5), and “central” means the regions with small |η| (e.g. 1.5).
Pseudorapidity depends only on the polar angle of the trajectory of a particle, and
not on its energy as seen from Eq. 3.6.
The detector pseudorapidity η det is defined as the pseudorapidity of the calorimeter cluster (electron, jet, or central track muon) with respect to the geometric center
θ
of the DØ detector, η det ≡ − ln tan det
2

, where θdet is relative to the center

of the detector.

3.3.3

The Central Tracking System

The point where the beams collide is surrounded by tracking detectors to record the
tracks (trajectories) of high energy particles produced in the collision. The Tracking
System is closest to the interaction point. It includes a silicon micro-strip tracker
(SMT) and a central fiber tracker (CFT) right outside the silicon detector. The
whole tracker is immersed in a 2 T superconducting solenoidal magnet, thus particle
tracks are curved; from the curvature we can deduce their momentum. The SMT
and CFT are optimized for tracking and vertexing at pseudorapidities |η| < 3 and
|η| < 2.5, respectively. A schematic view of the central tracking system is shown in
Figure 3.6.
The Tracking System is used to identify and measure the momentum of electrons
44

Figure 3.6: The Tracking System at DØ.

45

and muons, and to determine the position of the primary interaction vertex. The two
tracking detectors are able to locate the primary interaction vertex with a resolution
of about 35 µm along the beamline. They are also used to identify jets originating
from b quarks, which is an important decay product of single top.

3.3.3.1

Silicon Micro-strip Tracker (SMT)

The silicon micro-strip tracker (SMT) is located closest around the interaction region.
It gives very precise information, but silicon is expensive, so it is installed closest to
the beam where they cover a smaller area. The SMT is used for both tracking and
vertexing.
The SMT is designed of barrel modules interspersed with disks in the center, and
disks in the forward region (Figure 3.7). The barrel detectors primarily measure the
r − φ coordinate and the disk detectors measure r − z and r − φ. Vertices of particles
in the forward region are reconstructed in three dimensions by the disks, and vertices
of particles in the central region are measured in the barrels, and the central fiber
tracker. The detector has in total six barrels and sixteen disks.

3.3.3.2

Central Fiber Tracker (CFT)

Outside the silicon, DØ has an outer tracker made of scintillating fibers, which
produce photons of light when a particle passes through. The CFT consists of scintillating fibers mounted on eight concentric support cylinders and occupies r from
46

Figure 3.7: The disk/barrel design of the silicon microstrip tracker.
20 to 52 cm from the center of the beampipe. The fibers are double clad and are
835 microns in diameter. The two innermost cylinders are 1.66 m long; the outer six
cylinders are 2.52 m long. The outer cylinder provides coverage for |η| < 1.7 (See
Fig. 3.6).
Each cylinder supports two layers of fiber doublets. One doublet layer of fibers
is oriented along the beam direction (z) and a second doublet layer is oriented at a
stereo angle in +3◦ or −3◦ .
The scintillating fibers are coupled to clear fiber waveguides which carry the
scintillation light to visible light photon counters for read out. The entire detector
has 71,680 channels.

3.3.4

The Central and Forward Preshower Detectors

The central and forward preshower detectors are located between the solenoid and
the calorimeters. The preshower detectors aid in electron identification and back47

ground rejection during both triggering and offline reconstruction. They function as
calorimeters as well as tracking detectors, enhancing the spatial matching between
tracks and calorimeter showers.
The central preshower detector (CPS) covers the region |η| < 1.3. The CPS
consists of three concentric cylindrical layers, each having 1280 triangular scintillator
strips. The resolution of the CPS is about 6 mm. The two forward preshower
detectors (FPS) cover 1.5 < |η| < 2.5.

3.3.5

The Calorimeters and ICD

The DØ calorimeter system consists of three uranium/liquid-argon calorimeters and
an intercryostat detector (ICD).

3.3.5.1

Calorimeters

The calorimeters are located outside the tracking system. They use uranium metal
bathed in liquefied argon to capture particles and measure their energies. The
calorimeters provide energy measurements for electrons, photons, and jets, as well
as assist in identification of electrons, photons, jets, and muons and measure the
transverse energy imbalance in events (missing transverse energy E T ). They play
/
crucial role in this analysis. The calorimeter systems are illustrated in Figure 3.8
below.
48

Figure 3.8: Illustration of the calorimeter systems.

49

As can be seen in Figure 3.8, each calorimeter contains an electromagnetic section
closest to the interaction region followed by fine and coarse hadronic sections.
As shown in Figure 3.9, the calorimeter has a central section (CC) covering
pseudorapidities up to |η| ≈ 1.1, and two end calorimeters (EC) that extend coverage
to very forward region |η| ≈ 4.2. All three calorimeters are housed in separate
cryostats that maintain a temperature of approximately 90 K.

Figure 3.9: Intersecting view of a quarter of the DØ calorimeter, showing the trigger
towers and pseudorapidity coverage. The shading pattern indicates groups of cells
ganged together for signal readout. The rays indicate pseudorapidity intervals from
the center of the detector. The ICD is also denoted in the figure.

The signals generated by particle interactions in the calorimeters are grouped
into showers. Calorimeter readout cells form pseudo-projective towers as shown
50

in Figure 3.9, which are called Trigger Towers, which are essential for L1 and L2
triggers. There are 55,296 calorimeter electronic channels to be read out in total.

3.3.5.2

Intercryostat Detector

There are two issues with the calorimeters:
• The three calorimeters provide incomplete coverage in pseudorapidity.
• There is substantial material in the region we do not analyze, thus degrading
the energy resolution.
To address these problems, additional single-cell structure layers of sampling have
been added between the central and end cryostats. This Intercryostat detector (ICD)
consists of scintillator sampling that is attached to the exterior surfaces of the end
cryostats. It covers the region 1.1 < |η| < 1.4. Its rough location is shown in
Figure 3.9.

3.3.6

The Muon System

Surrounding all of the rest of the detector, the muon system resides at the most
outside layer beyond the calorimeter, and as the name implies, detects muons. Unlike
most common particles, muons don’t get absorbed in the calorimeter; they interact
small with the calorimeter and live long enough to leave the detector. By putting
51

detectors outside, we can identify muons relatively easily. High energy muons are
quite rare and a sign of interesting collisions.
The central muon system uses proportional drift tubes (PDTs), central scintillation counters. The PDTs and scintillators are emerged in toroidal magnets in order
to bend charged particles. The scintillators are also used for triggering. The central
muon system provides coverage for |η| < 1.0.
The forward muon system extends muon detection to |η| ≈ 2.0, and uses mini
drift tubes (MDTs) rather than PDTs, and includes trigger scintillation counters and
beam pipe shielding.

3.3.7

The Luminosity Monitor

Luminosity at the DØ interaction region is measured by plastic scintillator arrays
placed in front of the EC cryostats. A dedicated Luminosity Monitor (LM) is used
to detect inelastic pp collisions. The LM also serves to measure beam halo rates and
as a fast measurement of the z coordinate of the interaction vertex.
The LM detector consists of two arrays of twenty-four plastic scintillation counters
with Photomultiplier tubes (PMTs) readout. The arrays are located in front of the
end calorimeters and occupy the radial region between the beam pipe and the forward
preshower detector. They cover the pseudorapidity range 2.7 < |η| < 4.4.
52

3.3.8

The DØ Trigger System

Proton-antiproton collisions delivered by the Tevatron happen inside the detector
2.5 million times every second. We cannot record all those events on computer tape.
Instead, trigger and data acquisition systems are designed to accommodate the high
interaction rates. The trigger is a system of fast electronics and computers that
decides whether an event is interesting enough to be kept using information from a
small subset of the DØ detector signals. The task of the trigger system is to suppress
background events as efficiently as possible while not losing precious physics events.
Three distinct levels form this trigger system with each succeeding level examining
fewer events but in greater detail.

• The first stage (Level 1 or L1) comprises a collection of hardware trigger elements that provide a trigger accept rate of about 2 kHz.
• In the second stage (Level 2 or L2), hardware engines and embedded microprocessors associated with specific subdetectors provide information to a global
processor (L2GBL) to construct a trigger decision based on individual objects
as well as object correlations. Once there is a L2 accept, the complete detector
information is read out. The L2 system has an accept rate of approximately 1
kHz.
• Events passed by L1 and L2 are sent to a farm of Level 3 (L3) microprocessors;
53

sophisticated algorithms reduce the rate to about 50 Hz to be recorded for
offline reconstruction.

The overall coordination and control of DØ triggering is handled by the software
package COOR running on the online host. COOR interacts directly with the trigger
framework (for L1 and L2 triggers) and with the data acquisition supervising systems
(for the L3 triggers).

3.3.8.1

The Level 1 Trigger

The Level 1 Trigger is implemented in hardware and programmable firmware. The
calorimeter trigger (L1Cal) inputs consist of electromagnetic and hadronic trigger tower energies made up of sums over depth and transverse coordinates (in a
∆η × ∆φ = 0.2 × 0.2 region). The central track trigger (L1CTT) does a fast track
identification and momentum estimate using FPGAs and firmware. The muon system trigger (L1Muon) looks for patterns consistent with muons using hits from muon
wire chambers, muon scintillation counters, and tracks from the L1CTT. The L1 forward proton detector trigger (L1FPD) selects diffractively-produced events in which
the outgoing protons or antiprotons are scattered at very small angles. The trigger
framework (TFW) gathers digital information from each of these L1 trigger devices
and determines whether a particular event is to be accepted for further examination
by L2, or rejected. The L1 trigger makes a decision in 3.5 µs.
54

3.3.8.2

The Level 2 Trigger

The L2 trigger provides detector-specific preprocessors (L2Cal, L2Muon, L2PS, L2CTT,
L2STT) and a global stage (L2Global) to refine objects coming from L1 and test for
correlations in physics signatures across detector subsystems. L2 includes preprocessors for each detector subsystem and a global processor for integration of the
data. Preprocessor subsystems include tracking, calorimeter, preshower, and muon
systems. The subsystems work in parallel and trigger decisions are made in the
L2Global stage based on physics objects reconstructed in the preprocessors.
L2 preprocessors collect data from the front-ends and L1 trigger system and
analyze these data to form physics objects. L2 can also combine data across detectors
to form higher quality physics objects and examine event-wide correlations in all L2
physics objects. The full detector is read out for events passing L2 and further
analysis in the L3 trigger.
Data arrive at the L2 system via three transmission protocols. Calorimeter and
tracker data and signals from the TFW are transmitted by 1.3 Gbit/s serial GLinks on optical fibers [37]. The muon system uses 160 Mbit/s Cypress Hotlink
transmitters on coaxial cables or standard CAT/6 cables, unshielded twisted pair
(UTP) Hotlinks [38].
• L2Cal The calorimeter preprocessor system identifies jets and electrons/ photons and calculates event E T for the global processor. Each processor uses the
/
55

ET data from the 2560 calorimeter trigger towers, including both electromagnetic towers and the electromagnetic and hadronic tower sums.
• L2Muon L2Muon receives the L1Muon output and data from approximately
150 front-end modules (from the PDTs, MDTs, and the scintillation counters).
The muon candidates contain the track pT , η and φ coordinates, and quality
and timing information.
• L2PS L2PS is used for electron refinement at the trigger level by providing
evidence for early shower development and by giving a good spatial point for
comparison with calorimeter clusters or tracks. At L2, the CPS and FPS are
treated as separate detectors and their data are processed independently.
• L2STT The L2STT performs online pattern recognition in the data from the
SMT. It reconstructs charged particle tracks found in the CFT at L1 with
increased precision by utilizing the much finer spatial resolution of the SMT.
The L2STT improves the momentum measurement of charged particle tracks at
the trigger level. Requiring hits in the SMT helps reject spurious L1 triggers
from accidental track patterns in the CFT. L2STT is able to measure the
impact parameter of tracks precisely enough to tag the decays of long-lived
particles, specifically B hadrons.
• L2CTT The L2CTT preprocessor takes inputs from the L1CTT and the
56

L2STT. It operates in two different modes: i) with input tracks straight from
L1CTT and ii) with input tracks from L2STT which receives input from the
L1CTT and SMT barrels. The pT or impact parameter sorted list of L2 tracks
are passed on to L2Global.
• L2Global L2Global is the first level of the trigger to examine correlations
across all detector systems. L2Global is responsible for making trigger decisions
based on the objects identified by the L2 preprocessors. Trigger decisions are
made by creating global physics objects. L2Global imposes requirements on
the global physics objects according to configuration information it receives
from the Trigger Control Computer (TCC) based on the downloaded trigger
menu from COOR. Level 2 Trigger Control Computer (L2TCC or TCC2) is a
computer that runs L2 Relay Software (or L2RS). It provides an interface to
COOR and monitor servers, and configures and controls all L2 crates.
After an L1Accept is issued, the TFW sends a trigger decision mask to L2Global,
and the SCL sends notification of an L1 accepted event to every geographic
sector. For each event, L2Global uses the 128 L1 trigger decision bits (each
trigger decision bit represents a pass or fail of a certain trigger condition) and
preprocessor inputs to make a trigger decision, and returns this decision to the
TFW. The trigger list specifies which trigger conditions L2 will impose for each
run. The trigger list is downloaded to L2Global by the TCC, which receives
57

its instructions from COOR.
A block diagram of the L1 and L2 trigger systems is shown in Figure 3.10.

Detector Level1
CAL

L1CAL

CPS
FPS

Level2
L2CAL
L2PS

L1CTT
L2CTT

CFT

L2STT

SMT
MUO

L1MUO

FPD

L1FPD

Lumi

Trigger
Framework

L2MUO

Global
L2

Figure 3.10: Trigger-related data flow in L1 and L2 trigger systems.

3.3.8.3

The Level 3 Trigger

The L3 trigger provides additional rejection at a higher level through a fully programmable software trigger. L3 has the full readout information available from all
detector elements. L3 performs a limited reconstruction of events, reducing a nomi58

nal 1 kHz input rate to 50 Hz for offline analysis. Its decisions are based on complete
physics objects as well as on the relationships between such objects. The trigger list
includes blocks of filter scripts that specify one or more filters. Only when all filters
in a script are satisfied, is the trigger satisfied and the event sent out to be recorded.

59

Chapter 4
Event Reconstruction and Object
Identification
This chapter describes how the detector subsystems are used in order to identify
physics objects, such as jets and electrons, which are created from a p¯ collision.
p
Particle identification is essential for many physics analyses at the DØ experiment.
The hits with a corresponding position and measured energy are clustered to form
either a track or a calorimeter energy cluster, depending on their locations in the
detector. From these physics objects are created: vertices, electrons, muons, jets and
E T . The DØ offline reconstruction software [39] is responsible for reconstructing
/
those objects that are used to perform all DØ physics analyses.
The reconstructed objects are related to each other. By extrapolating all tracks
60

to the beam line, the crossing point with the most tracks is used as the vertex.
Different detector systems help in separating physics objects from each other. For
example, muon will have signal at muon detector, while electron does not, which
will discriminate from electron. Jets have a bigger and wider shower shape, while
electron are isolated signals in calorimeter, and usually have tracks in the tracking
system. MET is the sum of all energies measured in calorimeter. Since there will
be some energy missing to get the balance in each direction, we assume there is a
neutrino, which can not be detected. Even though physics objects are reconstructed
separately, objects are not allowed to overlap and share hits or energy or tracks.

4.1

Tracks

Charged particles are identified in the CTT, which is discussed at Section 3.3.3. It
can be used to measure the particle momentum. Matching with calorimeter energy
deposits or muon hits, we can determine the particle trajectories more precisely.
In the plane perpendicular to the direction of the magnetic field, the trajectory
of a charged particle is a circle. Trajectories originating from the interaction point
can be characterized by two parameters (ρ, φ), where φ is the direction of the track
at the point of closest approach to (0, 0), and the curvature:

ρ=

qB
pt

61

(4.1)

where q is charge, B is magnetic filed, and pt is transverse momentum.
Due to the large number of hits in the event, pattern recognition in the tracking
system can not be achieved by conventional combinational approach. One must
reduce the combinations of track candidates before feeding them to the final Kalman
filter based local road finders, which is highly CPU consuming. In this analysis two
preselection pattern recognition algorithms are used:

• Histogram Track Finding (HTF): divides the detector into slices in (φ, ρ)
and uses the Hough transform [40] to preselect a initial number of combinations
of groups of hits of relatively small size [41].
• Alternative Algorithm (AA): starts from combinations of hits in at least
three SMT super-layers. Track candidates are extended to CFT detectors [42].

Of these two methods, AA is better at low pT and high impact parameter and
has a lower fake rate. HTF has higher efficiency at high pT, and has higher efficiency
in difficult η regions like the overlap region (region with partial CFT coverage), and
is less affected by high luminosity.
Having done these preselections, a Kalman filter based global track-finding reconstructor is applied to these track candidates to find the final global tracks in the
event, and write a list of found tracks back into the event. A Kalman filter gives
a weighted average of the predicted and measured track values, with more weight
62

to the ones with smaller uncertainty. The estimates produced by the Kalman filter
method tend to be closer to the true values than the original measurements because
the weighted average has a better estimated uncertainty. As implied by their name,
the global tracks are not specific to any one detector, instead to all the tracking
detector subsystems (CFT, SMT, Muon).

4.2

Primary Vertices

The real or physics location of the hard scatter interaction point is named primary
vertex (PV). See figure 4.1 for an example. In DØ primary vertices are reconstructed
by means of an adaptive primary vertex algorithm [43]. This algorithm first selects
tracks coming from different interactions by clustering them according to their zposition; in the second step, the location and width of the beam is determined and
then used to re-fit tracks and finally each cluster of tracks is associated with a vertex
using the “adaptive” technique of giving all tracks a weight and reiterating the fit;
the third and last step consists of choosing the vertex that has the lowest probability
of coming from a minimum bias interaction (event with no trigger requirements).
63

Figure 4.1: Illustration of a primary vertex.

64

4.3

Electrons

Electrons are defined as clusters of energy depositions in the electromagnetic section
of the calorimeter, matched with a track from the Central Tracking System. We
require electrons to be within the central calorimeter with |η det | < 1.1 (CC) 3.3.2.
This analysis uses three types of electrons:

• Loose isolated electron
The fraction of cluster energy deposited in the electromagnetic section of the
calorimeter, over the total energy deposited in both the electromagnetic and
hadronic sections of the calorimeter, is defined as the EM fraction. For electrons, we require its EM fraction > 0.9. The electron must also meet shape
requirements. The energy deposition in the calorimeter must be matched to a
charged particle track from the tracking detectors with pT > 5 GeV and originating from the primary vertex. The electron is also required to be isolated
(not within a jet), and the transverse momentum pT (e) > 15 GeV.
• Tight isolated electron
The definition of a loose isolated electron is used as the basis for the definition
of a tight isolated electron. A tight isolated electron must pass all the loose
isolated electron requirements and have a value of EM-likelihood L > 0.85.
Electron likelihood is the probability to discriminate a real electron from faked
65

ones, using a discriminant based on several electron identification variables.
• Multijets modeling electron
A multijet electron is defined as a Loose no-track electron. It must have EM
fraction > 0.9, satisfy shape requirement, isolation < 0.2, and pT (e) > 15 GeV.
There are no requirements for a matching track. We use thus defined electrons
to model the multijet background sample as shown in Section 6.1.2.1.

4.4

Muons

Muons are identified by combining tracks in the muon spectrometer ( η det < 2.0)
with central detectors tracks. We use the following definitions in this analysis:
• Loose isolated muon
Loose muons must hit 3 layers in the muon section and pass the cosmic ray rejection requirements. The track reconstructed in the muon system must match
a track reconstructed in the central tracker with medium track quality and
match requirements. The track must be close to the primary vertex: z(track,
PV) < 1 cm. The muon’s transverse momentum must be pT (µ) > 15 GeV,
and it must not be in a jet, determined by requiring ∆R(µ, jet) > 0.5.
• Tight isolated muon
The definition of a loose isolated muon is used as the basis of the tight isolated
66

muon. Tight isolated muons are loose muons with the additional isolation
criterion that: (a) the momenta of all tracks in a cone of radius R < 0.5
around the muon direction, except the track matched to the muon, add up to
less than 20% of the muon pT ; and (b) the energy deposited in an annular
cone of radius 0.1 < R < 0.4 around the muon direction is less that 20% of the
muon pT .
• Multijets modeling muon
The multijet muon is defined as one which passes all selection cuts (before
b tagging), but no isolation or ∆R(muon, jet) requirements are made on the
muon. Any jets close to the muon are removed from the event, and E T is
/
recalculated to regain momentum balance. Thus defined muons are used to
model the multijet background samples.

4.5

Jets

A jet is a narrow cone of hadrons and other particles produced by the hadronization of
a quark or gluon. Because of QCD confinement, when two quarks reach a separation
distance of around 10−15 m (diameter of a hadron), they fragment into jets of mesons
and baryons, that are actually recorded by the detector. The jets are measured
and studied through jet reconstruction, correction and flavor tagging, in order to
67

determine the properties of the original quark. Figure 4.2 shows how the quark
evolves to a jet in the detector.

Figure 4.2: Illustration of jet formation.
In DØ, jets are reconstructed using the RunII cone algorithm, with a cone size of
0.5. Jet energy scale corrections [44] are applied to jets in the data and MC to convert
jet energies from reconstruction to particle-level. Jets containing a muon within
∆R(µ, jet-axis) < 0.5 are considered to originate from a semileptonic b-quark decay
68

and are corrected for the momentum carried away by the muon and the neutrino.
For this correction, it is assumed that the neutrino carries the same momentum as
the muon.
Monte Carlo jets need to be corrected for differences in the reconstruction and
identification efficiency between data and simulation, and for different calorimeter
responses. The “jet shifting, smearing, and removal algorithm” (JSSR) [45] is applied.
Jets are accepted in the analysis if they satisfy the Jet-ID selection criteria [46],
and have pT > 15 GeV and |η| < 3.4. For RunIIb only, we require that tracks
associated with jets originate from the primary vertex.

4.6

b Jets

b jets are jets originating from bottom quarks. They are identified (“tagged”) by the
b-tagging algorithm. Because top quarks nearly always decay to a bottom quark,
identifying bottom quarks helps to identify the decays of top quarks. The most important feature of b jets is that they have sufficient lifetime and travel some distance
before decaying, resulting in a secondary vertex, as show in figure 4.3.
Given that single top quark events have at least one b jet in the final state, we
use a neural network (NN) based b jet tagger [47] to identify jets originating from b
quarks. Jets are first required to be “taggable” and then are “tagged”. “taggable”
69

Figure 4.3:
Illustration of the secondary vertex of a b jet.
http://www-d0.fnal.gov/Run2Physics/top/singletop_observation/.
d0
is distance between the secondary track and primary vertex. A displaced track is
one with large d0 . The 2D distance between the primary vertex and the secondary
vertex is the transverse decay length, which we denote Lxy .

70

means a jet has enough tracking information that the b-tagging will be reliable. If a
jet has no tracks, or is too forward where there is no tracker, then b-tagging makes
no sense so we can’t use it. We only try to b-tag jets which are taggable. This is
done by looking at the secondary vertex information and seeing if it’s consistent with
a b hadron decay.
Both taggability and tagging are applied directly on the Monte Carlo samples,
and the efficiencies are corrected by a scale factor derived from comparing MC to
data. We select events that either have one b jet that has b-tag NN output > 0.775,
or two b jets with b-tag NN output > 0.5.

4.7

Missing Transverse Energy

In the Tevatron, the initial momentum of the colliding partons along the beam axis
is unknown (parton distribution). However, the initial momentum transverse to the
beam axis is zero. Even though neutrinos escape detection, the component of their
momentum in the transverse plane (“missing transverse energy”) can be inferred from
conservation of momentum in the collision. The sum of the transverse momenta
of undetected neutrinos is therefore equal to the negative sum of the transverse
momenta of all particles observed in the detector. In practice, we compute the
missing transverse energy by adding up vectorially the transverse energies in all cells
of the electromagnetic and fine hadronic calorimeters. Cells in the coarse hadronic
71

calorimeter are only added if they are part of a good jet. This raw quantity is
then corrected for the energy corrections applied to the reconstructed objects, and
the momenta of all muons in the event are corrected for their energy loss in the
calorimeter.

72

Chapter 5
Event Selection
At the Tevatron, single top quark production is a very rare process relative to its
major backgrounds (cross section ≈ 3 pb−1 ). A general event selection strategy is
implemented to maximize signal acceptance, and thereafter a multivariate technique
is used to separate signal from background, which will be discussed in the next
chapter.

5.1

Strategy

The experimental signal for single top events is one isolated high transverse momentum central lepton, and missing transverse energy from the decay of W boson from
the top quark decay, accompanied by a b jet from the top decay, and a second jet
which is sometimes also from the decay of a b hadron. Since there may be significant
73

initial- or final- state radiation, we include our search events with between two to
four jets.
The composition of the background components is different for events with different jet multiplicities (2, 3, 4) and lepton flavors (electron, muon). The signal to
background ratio and signal acceptance in each subsample set also differ significantly.
Thus the data is divided into many orthogonal sub-samples (i.e. channels) according to jet and b-tag multiplicities. The event selection criteria in this analysis are
applied separately for the different channels, and then several channels are combined
to increase statistics.

5.2

Event selection cuts

We apply a loose event selection to find events containing an isolated lepton, missing
transverse energy, and two to four jets with high transverse momentum. Then we
make a series of topological cuts to reduce the multijet background in each channel
to an acceptable low level.

5.2.1

General selection

These selection cuts are applied for both electron and muon channels.

• Good quality (for data).
74

• Instantaneous luminosity > 0.
• Pass Mega-OR trigger requirement, in which at least one of the selected “reasonable” triggers has to fire. For details of which triggers are included in the
Mega-OR trigger and their efficiencies, see Appendix ??.
• Good primary vertex: |zPV | < 60 cm with at least three tracks attached.
• Two, three, or four good jets with pT > 15 GeV and |η det | < 3.4. For Run
IIb jets are required to be vertex-confirmed.
• The leading jet pT > 25 GeV.
• For Run IIb only, the second leading jet pT cut is raised to 20 GeV in events
with exactly three good jets.
• For Run IIb only, the second leading jet pT cut is raised to 25 GeV in events
with exactly four good jets.
• Jet triangle cut of |∆φ(leading jet, E T )| vs. E T :
/
/
• |∆φ| from 1.5 to π rad when E T = 0 GeV, and E T from 0 to 35 GeV
/
/
when |∆φ = π rad.
• Missing transverse energy
• 20 < E T < 200 GeV in events with exactly two good jets.
/
75

• 25 < E T < 200 GeV in events with three or more good jets.
/
• Scalar sum of the transverse energies of all good jets
• HT (alljets) > 50 (55) GeV in events with exactly two good jets for Run IIa
(Run IIb) period.
• HT (alljets) > 75 (80) GeV in events with exactly three good jets for
Run IIa (Run IIb) period.
• HT (alljets) > 100 (110) GeV in events with exactly four good jets for
Run IIa (Run IIb) period .
• Jet triangle cut of second leading jet pT vs. HT (alljets) for Run IIb in events
with exactly two good jets.
• second leading jet pT from 0 to 27.5 GeV when HT (alljets) = 0 GeV, and
HT (alljets) from 0 to 165 GeV when second leading jetpT = 0 GeV.
• Scalar sum of the transverse energies of all good jets, the lepton transverse
momentum, and the missing transverse energy
• HT (alljets, lepton, E T ) > 120 GeV in events with exactly two good jets.
/
• HT (alljets, lepton, E T ) > 140 GeV in events with exactly three good jets.
/
• HT (alljets, lepton, E T ) > 160 GeV in events with exactly four good jets.
/
76

5.2.2

Electron channel selection

These selection cuts are applied for electron channels only.
• Only one tight electron with |η det | < 1.1 and pT > 15 (20) GeV in events with
2 (3 or more) good jets.
• No additional loose electron with pT > 15 GeV.
• No tight isolated muon with pT > 15 GeV and within |η det | < 2.0.
• Electron coming from the primary vertex: |∆z(e, PV)| < 1 cm.
• Electron triangle cuts of |∆φ(e, E T )| vs. E T
/
/
• |∆φ| from 2 to 0 rad when E T = 0 GeV, and E T from 0 to 40 GeV when
/
/
|∆φ| = 0 rad.
• |∆φ| from 1.5 to 0 rad when E T = 0 GeV, and E T from 0 to 50 GeV
/
/
when |∆φ| = 0 rad.
• |∆φ| from 2 to π rad when E T = 0 GeV, and E T from 0 to 24 GeV
/
/
when |∆φ| = π rad.

5.2.3

Muon channel selection

These selection cuts are applied for muon channels only.
• Only one tight muon with pT > 15 GeV and |η det | < 2.0.
77

• No additional loose muons with pT > 4 GeV.
• No loose electron with pT > 15 GeV and within |η det | < 2.5.
• Muon coming from the primary vertex: |∆z(µ, PV)| < 1 cm.
• Muon triangle cuts of |∆φ(µ, E T )| vs. E T
/
/
• |∆φ| from 1.2 to 0 rad when E T = 0 GeV, and E T from 0 to 85 GeV
/
/
when |∆φ| = 0 rad.
• |∆φ| from 2.5 to π rad when E T = 0 GeV, and E T from 0 to 30 GeV
/
/
when |∆φ| = π rad.
• Muon track curvature significance cuts of |TrackCurvSig| vs. |∆φ(µ, E T )|, where
/
|TrackCurvSig| = |

q/pT
|, and q and pT are the charge and transverse moσ(1/pT )

mentum of the charged track associated with the muon.
• |∆φ| from 0.875π to π rad when |TrackCurvSig| = 0, and |TrackCurvSig|
from 0 to 4 (6) when |∆φ| = π rad for Run IIa (Run IIb) period.
• |∆φ| from 2 to π rad when |TrackCurvSig| = 0, and |TrackCurvSig| from
0 to 2 (3) when |∆φ| = π rad for Run IIa (Run IIb) period.
These cuts are needed to reject events with poorly measured muons that cause
an excess in data over background model in the ∆φ distributions.
78

• Transverse momentum of the leading jet within the ICD region of the detector:
leading jet pT > 30 GeV when 1.0 < |leading jet η det | < 1.5.
• Transverse momentum of the second leading jet within the ICD region of the
detector: leading jet pT > 25 GeV when 1.0 < |leading jet η det | < 1.5 only
for Run IIb period with exactly three good jets.

5.2.4

b-tagging selection

To be able to extract single top events we also look for the presence of one or two btagged jets. We select events that have exactly one jet with b-tag NN output > 0.775
and no other jet with b-tag NN output > 0.5, or two jets with b-tag NN output >
0.5. This ensures that there is no overlap between the one tag and two tags samples.

79

Chapter 6
Data and Simulation Samples
In this chapter, the data and simulation samples used for this analysis are presented.
The corrections to multijet and MC simulation samples are discussed.

6.1

Data samples

The data sample was collected from the p¯ collisions in the Tevatron at a center of
p
mass energy of 1.96 TeV, using the DØ detector.

6.1.1

Signal data samples

The data sample was collected between August 2002 and February 2006 (Run IIa)
and between June 2006 and June 2009 (RunIIb), corresponding to 1.08 + 4.28 =
80

5.35 fb−1 of good quality data in each of the e and µ channels, as shown in Table 6.1.
The datasets used in this analysis are listed in Appendix B.
Table 6.1: Integrated luminosity for the datasets used in this
analysis.
Trigger Version

Integrated Luminosity [pb−1 ]

Run IIa

v8 – v14

1078.81

Run IIb

v15a

534.44

v15b

688.02

v15c

397.31

v16

2661.90

v8-16

5360.48

Data sample

Total

We require events to pass the Mega-OR trigger requirement, in which at least
one of the selected “reasonable” triggers has to fire. We measure that the Mega-OR
trigger efficiency for the events that pass our selection is 100% within the assigned
systematic uncertainties and thus no additional trigger efficiency correction factors
are needed in our MC samples. Details of trigger efficiencies measurement are described in Appendix ??.

6.1.2

Multijets data samples

Multijet events form the second largest background after W +jets. We use data
events to model it. We select those events that pass all our event selection criteria
81

except the lepton requirements.

6.1.2.1

Multijets in the electron channel

The multijets background in the electron channel is modeled with data events that
pass all selection cuts (before b tagging) except that the EM object is not required
to have a matching track. In addition, the EM object is required to fail the electron
likelihood cut.
This sample suffers from a kinematic bias that can be corrected by reweighting
the events with a kinematic correction factor [48]. The kinematic correction factor
is defined as
QCDWeight = εfake−e /(1 − εfake−e ),

(6.1)

which depends on the parameter εfake−e , which is the efficiency for a multijet faked
electron (See definition in Section 4.3.) to pass the tight electron criteria.
εfake−e is measured as the ratio of the number of events with a tight electron over
the number of events with an multijet faked electron in the E T < 10 GeV region.
/
Even though the low- E T region is dominated by multijet events, there is a non/
negligible contamination from real electrons, in particular for the tight sample. This
signal contamination originates mostly from Z+jets events and to some extent also
from W +jets events. The expected contributions to the multijet and tight electron
samples originating from W +jets and Z+jets events are estimated from Monte Carlo
82

and subtracted from the number of events in data before computing εfake−e .

6.1.2.2

Multijets in the muon channel

The multijets background in the muon channel is modeled with data events that pass
all selection cuts (before b tagging), but no isolation or ∆R(muon, jet) requirements
are made on the muon. In order to make the jets in these events match those in
the signal data, any jets close to the muon are removed from the event, and E T is
/
recalculated to regain momentum balance.

6.2
6.2.1

Simulation samples
Signal simulation samples

Simulated single top event samples are generated with the comphep-singletop [49]
Monte Carlo event generator. singletop produces events whose kinematic distributions match those from NLO calculations. The top quark mass is 172.5 GeV, and
this applies to all top quark samples. The PDF set is CTEQ6M [50] and the scales
are m2 for the s-channel and (mt /2)2 for the t-channel. The top quarks and the
t
W bosons from the top quark decays are decayed in comphep-singletop to ensure
the spins are properly transferred. pythia [51] is used to add the underlying event
and initial- and final-state radiation. evtgen [52] is used to decay b hadrons.
83

6.2.2

Background simulation samples

¯
The W +jets, Z+jets, and tt background samples for this analysis are generated using
alpgen [53] (version 2.11). Zero-bias overlay events are used to better model the
high instantaneous luminosity. All MC simulated events have an additional number
of zero bias p¯ events superimposed, dependent on the luminosity profile.
p
Table 6.2 shows the cross sections, branching fractions, and initial numbers of
events for the Monte Carlo samples. The W +jets and Z+jets cross sections are from
alpgen.

6.2.3

Simulation samples corrections and normalization

The expected number of Monte Carlo events coming from the simulated backgrounds
samples are obtained in three steps:
• First, apply scale factors such that the MC reconstruction and selection efficiencies match those found in data, as explained in Section 6.2.3.1 below.
¯
• Second, the tt, Z+jets, dibosons, and single top samples are normalized to
the integrated luminosity of our dataset using the cross sections and branching
fractions listed in Table 6.2. The normalization weight is calculated as:

w=

σT heory × Integrated Luminosity
.
Number of events produced by MC
84

(6.2)

Table 6.2: The cross sections, branching fractions, and initial numbers of events in
the Monte Carlo event samples. The symbol ℓ stands for electron plus muon plus
tau decays. We only include tau decays to leptons.
The Monte Carlo Event Sets
Cross Section

Branching

No. of p17

No. of p20

[pb]

Fraction

Events

Events

1.04+0.04
−0.04

0.324 ± 0.003

0.6M

0.5M

0.6M

0.5M

+0.16
3.30−0.16

0.324 ± 0.003
0.324 ± 0.003

1.2M

1.0M

7.46+0.48
−0.67

0.438 ± 0.004

1.5M

1.3M

1.5M

1.3M

+0.48
7.46−0.67

0.105 ± 0.001
0.543 ± 0.005

3.0M

1.6M

90.5

0.324 ± 0.003

2.7M

3.0M

W c¯ → ℓνcc
c

260

0.324 ± 0.003

2.7M

3.0M

W jj → ℓνjj

23, 831

0.324 ± 0.003

55M

97M

W+jets total

24, 182

0.324 ± 0.003

60.4M

103M

Zb¯ → ℓℓbb
b

38.7

0.0337 ± 0.0000

0.7M

0.7M

Zc¯ → ℓℓcc
c

106

0.0337 ± 0.0000

0.7M

0.7M

Zjj → ℓℓjj

7, 032

0.0337 ± 0.0000

14M

4.0M

Z+jets total

7, 177

0.0337 ± 0.0000

15.4M

5.4M

W W → anything

11.6 ± 0.4

1.0 ± 0.0

2.0M

0.7M

W Z → anything

3.25 ± 0.11

1.0 ± 0.0

1.0M

0.6M

ZZ → anything

1.33 ± 0.04

85 1.0 ± 0.0

1.0M

0.5M

Diboson total

16.2 ± 0.6

1.0 ± 0.0

4.0M

1.8M

Event Type
Signals
tb → ℓ+jets
tqb → ℓ+jets
Signal total
Backgrounds
¯
tt → ℓ+jets
¯
tt → ℓℓ
Top pairs total
W b¯ → ℓνbb
b

2.26+0.12
−0.12

7.46+0.48
−0.67

• Finally, the W +jets background is corrected for the reconstruction efficiencies,
but normalized to the data before tagging, as explained in Section 6.2.3.2 below.

6.2.3.1

Simulation efficiencies corrections

The efficiencies to reconstruct, identify and select objects in the MC are higher than
in data, so the following scale factors are used to correct for those differences:

• Primary vertex position reweighting
We reweight the position of the primary vertices along the beamline in z to
make the distribution in MC events match data.
• Instantaneous luminosity reweighting
We reweight the instantaneous luminosity distributions of the MC events to
match those in Run IIa and Run IIb data.
• Z pT distribution reweighting
We reweight the inclusive Z boson pT spectrum to match the theory model.
• EM ID efficiency correction factor
We correct each event in the electron channel with a scale factor that accounts
for the differences in electron cluster finding and identification efficiency [54]
[55]. For multijet background model electrons, the MC to data scale factor is
consistent with one.
86

• Muon ID and isolation efficiency correction factor
We correct each event in the muon channel for the muon ID efficiency, the
track match, and the isolation. The ID scale factor is parametrized in (ηdet ,φ);
track match is parametrized in track-z and ηCFT ; and the isolation in η. The
parametrizations derived in Z → µµ data and MC, as described in Ref. [56]:
There is an additional mismodeling correction applied to the muon-ID as a
function of ηdet in W +jets events.

• Jet shifting, smearing, and removal (JSSR)
We use the JSSR processor [45] for the W +jets and Z+jets samples (including
W bb, W cc, Zbb and Zcc), and dibosons.

• Taggability and b-tagging efficiency correction factor
The taggability and tagging algorithms are directly applied to both data samplesand the simulated samples (direct tagging), and the efficiencies corrected
by a scale factor derived from comparing MC to data. Random tagging is used
for W +light and W + c samples to ensure proper MC statistics after tagging.
The random tagging algorithm replaces the standard b-tag NN output with
one that is chosen randomly between a probability p = 1/2 and p = 1/24. This
causes many more of the W +light jet events to fall into the one and two tagged
samples.
87

6.2.3.2

W +jets and multijets backgrounds

The W +jets background is taken from Monte Carlo samples and corrected for reconstruction efficiencies as described in Section 6.2.3.1 above. The samples are weighted
by the leading-log (LL) cross sections (including branching fractions) from alpgen
and the integrated luminosity. Comparisons of LL and NLO calculations to data [57]
show the need for K ′ -factors to scale alpgen cross sections for W jj, W cj (j rep′
resents light partons, including u, d, s), W b¯ and W c¯, and also KHF -factors for
b,
c
W b¯ and W c¯ (HF represents Heavy Flavor partons, which include b and c). Similar
b
c
cross section correction is done to the Z+Jets samples. The flavor composition of
W +jets and Z+jets samples are normalized to NLO.
The multijets background is modeled with the orthogonal data samples described
in Section 6.1.2. The multijets and the W +jets backgrounds are normalized using
an iterative Kolmogorov-Smirnov-test normalization method (IKS).
In the IKS method, two anti-correlated scale factors are applied to the W +jets
and multijets samples to get the proper normalization to data. The scale factors
are determined by measuring the agreement between data and background model
on three distributions sensitive to the W +jets and multijets normalizations: lepton
pT , E T , and W transverse mass. The final W +jets and multijets scale factors are
/
the ones that maximize the product of the Kolmogorov-Smirnov (KS) test values of
each distribution. The KS-test tries to determine if two datasets differ significantly.
88

It has the advantage of making no assumption about the distribution of data.
In order to deal with the mismodeling observed for some angular variables, the
W +jets and Z+jets samples are reweighted to reproduce the jet η distributions in
data. The reweighting is done by comparing the W +jets and Z+jets samples to data
after subtraction of all other backgrounds. It is done successively on the leading and
second leading jet η, the ∆R between them, and on the third and fourth jet η when
applicable. The reweighting is done with a fitted function that excludes the ICR
region and preserves the overall normalization.
It is found that the normalization is preserved after applying b-tagging, and no
further IKS normalization is needed.

6.3

Lepton charge mis-ID measurement samples

Charge measurement is important for this analysis since the CP violation can be
diluted by the mis-identification (mis-ID) of the lepton charge. We rely on the track
charge to determine whether the selected lepton carries positive or negative charge.
We select Z → ee or Z → µµ events to measure the charge mis-ID rate. For
this purpose, we use samples of events which have two electrons or muons with
high transverse momentum in them. The charge mis-ID rate is defined as the ratio
between the number of same sign events and the total number of di-lepton events.
We make the same lepton and jet requirements to select this sample as in the single
89

top analysis. We make no MET cut.
Details of the sample definitions can be found in Appendix D.

90

Chapter 7
Event Yields and Data/Simulation
Comparison
In this chapter we present data and simulation sample event yields after the event
selection described in Chapter 5.

7.1

Event yields

The samples after selection, which we call “pretagged”, “onetagged” and “twotagged”
¯
samples, are dominated by W +jets events, with some tt contributions that become
more significant for higher jet multiplicities, and smaller contributions from multijets,
Z+jets and diboson events. Figure 7.1 gives a pie chart illustration of the composition
91

2 jets

3 jets

4 jets

pretag

1 tag

2 tag
Figure 7.1: A pie chart illustration of the components of each background and signal
sample in each jet channel in pretag, one tag, and two tag bins.

of each background and signal sample in each jet channel after this selection.
We use the term “yield” to mean the number of events of the signal or background
in question predicted to be in the nearly 5.4 fb−1 of data analyzed here. Thus, the
event yield for a specific sample is defined as:

Y = σ × L = σ × 5.4 fb−1

(7.1)

where, σ is the cross section for that sample, and L = 5.4 fb−1 is the integrated
luminosity used in this analysis. On the other hand, the event yield for a MC sample
92

can also be expressed as:

Y=

Nselected

ε(i)corrections

(7.2)

i

where Nselected is the number of events remaining after selection in that MC sample,
and ε(i)corrections is the overall efficiency correction factor for the ith event after
selection to account for differences between data and MC from particle ID, vertex
confirmation, taggability and b-tagging, that is:

ε(i)corrections = ε(i)particle ID × ε(i)vertex confirmation ×
ε(i)taggability × ε(i)b−tagging × N σ
MC

(7.3)

, where σ is cross section and NMC total number of events in MC sample. For
data, the event yield is equal to the number of events.
Tables 7.1 and 7.2 show the yields for all signals and backgrounds for events with
one and two b-tagged jets respectively.
For the CP violation measurement, an extra cut applied is to split the samples by
lepton charge. Tables 7.3 and 7.4 show these yields for all signals and backgrounds
after splitting samples by lepton charge (“positive” and “negative” samples). The
sum of the positive and negative yields is identical to the total. We do not redo the
normalization of W +jets and QCD separately for positive and negative samples.
93

From these tables we can see that in all of the sum of yields of all MC samples
equal to the number of events in data. b tagging improves signal to background ratio
radically, however, we also lose event statistics in the 1-tag and 2-tag samples. Note
that the yield values shown in these and subsequent tables have been rounded for
clarity, so that the sums of the components do not always equal exactly the values
given for these sums, however all calculations have been done with full-precision
values.
Table 7.1: One b tagged event yields with statistical uncertainty for each jet multiplicity and for all analysis channels combined (Electron+Muon, Run IIa+Run IIb).
2 jets

3 jets

4 jets

All Channels

198 ± 0.91

85 ± 0.63

26 ± 0.36

309 ± 1.2

¯
tt

313 ± 1.8

545 ± 2.8

499 ± 2.8

1,356 ± 4.4

W +jets

3,222 ± 20

961 ± 9.9

239 ± 4.0

4,421 ± 23

Z+jets & dibosons

357 ± 6.8

123 ± 4.3

29 ± 1.7

510 ± 8.2

Multijets

258 ± 2.2

117 ± 1.9

37 ± 0.83

412 ± 3.1

Background Sum

4,150 ± 22 1,745 ± 11 804 ± 5.2

6,699 ± 25

Backgrounds+Signals

4,348 ± 22 1,830 ± 11 830 ± 5.3

7,008 ± 25

Data

4,284 ± 65 1,772 ± 42

851 ± 29

6,907 ± 83

1:31

1:22

Source
Signals
tb+tqb
Backgrounds

S:B

1:21

1:21

94

Table 7.2: Two b tagged event yields with statistical uncertainty for each jet multiplicity and for all analysis channels combined (Electron+Muon, Run IIa+Run IIb).
Source

2 jets

3 jets

4 jets

All Channels

46 ± 0.37

31 ± 0.34

13 ± 0.22

90 ± 0.55

¯
tt

121 ± 0.97 285 ± 1.8

361 ± 2.2

767 ± 3.0

W +jets

338 ± 5.1

139 ± 3.2

45 ± 1.7

522 ± 6.3

Z+jets & dibosons

42 ± 1.7

18 ± 1.1

5.9 ± 0.53

66 ± 2.1

Multijets

19 ± 0.62

13 ± 0.64 6.3 ± 0.33

39 ± 0.95

Background Sum

520 ± 5.5

456 ± 3.9

418 ± 2.8

1,394 ± 7.3

Backgrounds+Signals

566 ± 5.5

487 ± 3.9

431 ± 2.8

1,484 ± 7.3

Data

597 ± 24

535 ± 23

432 ± 21

1,564 ± 40

S:B

1:11

1:15

1:33

1:16

Signals
tb+tqb
Backgrounds

95

Table 7.3: Number of expected yields and observed data counts in ”positive” samples
after b-tagging.
2 jets

3 jets

4 jets

All Channels

tb

53 ± 7.6

22 ± 3.7

6.4 ± 1.7

81 ± 13

tqb

70 ± 5.6

37 ± 4.4

13 ± 2.9

119 ± 13

tb+tqb

122 ± 13

59 ± 8.1

19 ± 4.6

200 ± 26

¯
tt

218 ± 41

418 ± 66

429 ± 77

1,066 ± 183

1,773 ± 199

549 ± 67

149 ± 42

2,471 ± 307

Z+jets & dibosons

197 ± 28

73 ± 21

16 ± 9.0

286 ± 57

Multijets

133 ± 12

63 ± 5.8

21 ± 2.0

217 ± 20

Source

W +jets

Total prediction

2,443 ± 292 1,162 ± 166 635 ± 134

4,239 ± 592

Data

2,386 ± 49

1,161 ± 34

645 ± 25

4,192 ± 65

S:B

1:19

1:19

1:32

1:20

96

Table 7.4: Number of expected yields and observed data counts in “negative” samples
after b-tagging.
2 jets

3 jets

4 jets

All Channels

tb

52 ± 7.6

22 ± 3.7

6.5 ± 1.6

80 ± 13

tqb

71 ± 5.5

36 ± 4.2

13 ± 2.9

120 ± 13

tb+tqb

123 ± 13

58 ± 7.9

20 ± 4.5

200 ± 25

¯
tt

217 ± 42

415 ± 65

433 ± 78

1,065 ± 185

1,789 ± 191

551 ± 86

135 ± 40

2,474 ± 316

Z+jets & dibosons

203 ± 29

68 ± 19

18 ± 9.6

289 ± 56

Multijets

144 ± 13

67 ± 6.2

22 ± 2.1

233 ± 21

Source

W +jets

Total prediction

2,475 ± 287 1,157 ± 183 628 ± 133

4,261 ± 603

Data

2,495 ± 50

1,146 ± 34

638 ± 25

4,279 ± 65

S:B

1:19

1:19

1:31

1:20

97

7.2

Signal acceptance

The signal acceptance is defined as:

A=

B

Ninitial

εcorrections
Nselected

where B is the branching fraction for the MC sample, Ninitial is the initial number of events in each MC sample, Nselected is the number of MC events remaining
after selection, and εcorrections are efficiency correction factors to account for differences between data and MC from particle ID, vertex confirmation, taggability and
b-tagging.

Table 7.5 shows the percentage of each single top quark signal that remain after
selection in each channel before and after b-tagged jets have been required. The
entries in this table are calculated using the yields shown in Section 7.1 and the
following equation:
A=

Yield
σ×L

in which σ is the predicted cross section (for tb or tqb) and L is the integrated
luminosity for each sample.
98

Table 7.5: Combined (Electron+Muon, Run IIa+Run IIb) signal acceptances.
2 jets

3 jets

4 jets

All Channels

tb

3.0%

1.3%

0.39%

4.7%

tqb

2.6%

1.2%

0.41%

4.3%

tb+tqb

2.8%

1.2%

0.40%

4.4%

tb

1.9%

0.78%

0.23%

2.9%

tqb

1.2%

0.60%

0.21%

2.0%

tb+tqb

1.4%

0.65%

0.22%

2.3%

PreTag

1,2 Tags

The final combined signal acceptances are:

s − channel tb = (2.9 ± 0.4)%
t − channel tqb = (2.0 ± 0.3)%
s + t channels tb + tqb = (2.3 ± 0.3)%

7.3

Data and Monte Carlo comparison

We examine various important kinematic variables to make sure the Monte Carlo
simulated samples model the data. To judge whether a variable is well modeled or
not, the variable distribution for data is compared with the sum of the signal and
99

backgrounds. We normalize each sample in the model to the integrated luminosity
of data (5.4 ifb), and overlay their sum to the data.
The data-MC comparison plots after the selection cuts in Section 5.2 for both
pretagged and tagged samples are shown in Appendix ??.
The data-MC comparison plots after splitting by the lepton charge are shown in
Appendix A. The data-MC comparison plots for the combined BNN discriminants
after splitting are shown in Appendix C.
Good agreement is seen between the prediction and data in all channels. Selected

DØ 5.4 fb -1
Data
s+t-channel
W+bb
W+cc
W+lp
Z+jets
Diboson
tt
Multijets

1000

500

0

Yield [Events/10GeV]

Yield [Events/10GeV]

plots after splitting by the lepton charge are shown below.

50

100

DØ 5.4 fb -1
Data
s+t-channel
W+bb
W+cc
W+lp
Z+jets
Diboson
tt
Multijets

1000

150
200
Lepton pT [GeV]

500

0

50

100

150
200
Lepton pT [GeV]

Figure 7.2: The transverse momentum of the lepton in the electron+muon channel
for positive (left) and negative (right) samples.

100

Yield [Events/20GeV]

Yield [Events/20GeV]

DØ 5.4 fb -1
600

400

200

0
100

200

300

DØ 5.4 fb -1
600

400

200

0
100

400
HT [GeV]

200

300

400
HT [GeV]

Yield [Events/0.25]

Yield [Events/0.25]

Figure 7.3: The HT in the electron+muon channel for positive (left) and negative
(right) samples.

DØ 5.4 fb -1
400

200

0

DØ 5.4 fb -1

400

200

-2

-1

0

1

0

2
Lepton η

-2

-1

0

1

2
Lepton η

Figure 7.4: The LeptonEta in the electron+muon channel for positive (left) and
negative (right) samples.

101

Yield [Events/5GeV]

Yield [Events/5GeV]

DØ 5.4 fb -1

(d)
600

400

200

DØ 5.4 fb -1

(d)
600

400

200

0

140

160

0

180
200
220
Top Quark Mass [GeV]

140

160

180
200
220
Top Quark Mass [GeV]

Yield [Events/20]

Yield [Events/20]

Figure 7.5: Reconstructed top mass distribution in the electron+muon channel for
positive (left) and negative (right) samples.

DØ 5.4 fb -1

1000

1000

500

0

DØ 5.4 fb -1

500

0

100

200

χ2

300
400
of top mass

0

0

100

200

300
400
χ2 of top mass

Figure 7.6: Top mass minimum Chi squared distribution in the electron+muon channel for positive (left) and negative (right) samples. TopMassMinChiSqr gives the
minimum value of the differences between constructed top mass and theory top mass
for all possible reconstructed top quarks.

102

Yield [Events/10GeV]

Yield [Events/10GeV]

DØ 5.4 fb -1

1000

500

0

0

DØ 5.4 fb -1

1000

500

0

50
100
150
W Boson Transverse Mass [GeV]

0

50
100
150
W Boson Transverse Mass [GeV]

Figure 7.7: The W Transverse mass distribution in the electron+muon channel for
positive (left) and negative (right) samples.

103

Chapter 8
Multivariate Analysis
Given the increasing complexity of modern HEP experiments, multivariate analysis
(MVA) techniques have been applied to extract the maximum information content
out of the data. Multivariate classification is one of the techniques used for “data
mining”, which is automatic or semi-automatic analysis of large amount of data in
order to extract previously unknown interesting patterns. MVA involves analysis of
multiple statistical variables at a time.
Three different MVA techniques are used in the single top analysis: (i) Bayesian
neural networks (BNN), (ii) boosted decision trees (BDT), and (iii) neuroevolution
of augmented topologies (NEAT). A combined new BNN discriminant is formed by
further combining those three methods.
A big advantage of multivariate techniques compared with a conventional cut
104

based analysis is that events which fail an individual selection criterion will continue
to be considered by the algorithm. In a multivariate technique, the separation power
of the many discriminating variables x is combined into a single discriminant D(x).
This way we do not cut out signal events, while obtaining an improved separation
power beyond that of any of the single variables alone. This combined single variable
corresponds to a one-to-one function of the probability P r(S|x) that an event characterized by the variables x belongs to the signal class S. For each MVA, a background
event is more likely to give an output in the low-discriminant region (D(x) ≈ 0 ),
while a signal event will tend to output to the high-discriminant region (D(x) ≈ 1),
thus separating signal from the backgrounds. The cross section and other info can
be derived from the D(x) distributions observed in data using Bayesian calculations
which will be discussed in Chapter 9.
Figure 8.1 shows how each of the MVA’s is applied in the flow chart of the single
top analysis.

8.1

Split samples

The signal and background samples are divided into three independent subsets, which
are used by the three MVA’s.
• the first subset (“training”) contains one fourth of the samples and is used to
created the multivariate filters for (i.e. train) BDT, BNN and NEAT;
105

Figure 8.1: Flowcharts of the MVA analyses.

106

• the second subset (“testing”) also contains one fourth of the samples and is
used to created the multivariate filter (i.e. train) the combination BNN of the
three different multivariate analyses (BDT, BNN and NEAT) used in the single
top analysis;
• the last subset (“yield”) contains the remaining half of the samples and is used
to verify the BNNs convergence, do the final measurements with all the MVAs
(BDT, BNN, NEAT, and combination BNN) and make all the plots.
The original MC samples are split by putting the first event in the testing, the
second event in the training and the 3rd and 4th event in the yield sample, and
repeating the process until the end of the sample was reached. All three resulting
samples are normalized back to the full dataset: testing/training weights multiplied
by 4.0 and yield weights multiplied by 2.0, where the actual factors are calculated
as yield in the original over yield in the subsample.

8.2

Output transformation

The MVA output is a number between 0 and 1, with background-like (signal-like)
events populating mostly in the low (high) discriminant region. In the high discriminant region there may be some bins in which there are some signal but no background
events. To avoid this, we apply a monotonic transformation to the discriminant that
107

ensures a minimum number of background events in each bin. For details see Appendix D of DØ Note 5811 [58]. All the discriminant plots shown in this chapter are
after applying this binning transformation, unless otherwise noted.

108

8.3

Key for plots

For each MVA output plot, the signal and background distributions use the color
scheme illustrated in Figure 8.2.

Figure 8.2: Illustration of the color scheme used in plots of signals and backgrounds
in the single top analyses.

109

8.4

Boosted Decision Trees (BDT)

Decision trees (DT) originated in the fields of data mining and pattern recognition.
Several methods were developed to improve the DT classification power by creating
an ensemble (forest) of decision trees. One of these extensions is boosting decision
trees (BDT).
In a decision tree, the internal nodes contains various tests, and terminal nodes
are called leaves. Each leaf has an assigned decision tree output value. An event will
start from the root node, follow a unique path through the decision tree, and end up
at a leaf and the classification of the event is the decision tree output value of this
leaf. All nodes continue to be split until they become leaves.
Figure 8.3 shows an example of a decision tree.
A powerful technique to improve the performance of any weak classifier (defined
as any classifier that does a little better than random guessing) is boosting [59]. The
basic principle of boosting is to create a tree, calculate an associated error function
then regenerate a tree with a smaller error function by re-weighting the misclassified
events. The boosting algorithm used in DØ’s single top quark search is adaptive
boosting (AdaBoost) [59].
In this analysis we find that boosting typically improves the performance by 20%.
The increase in performance saturates in the region of 25 boosting cycles, therefore
30 boosts were used in this analysis. The full set of parameters used in this analysis
110

Figure 8.3: An example decision tree. Nodes with associated splitting test are shown
as blue circles and terminal nodes with purity output are shown as green leaves. An
event (observation) defined by variables xi of which HT < 242, and mtop > 162 will
return D(xi ) = 0.82. An event with variables xj of which HT ≥ 242 and pT ≥ 27.6
will result a decision tree output value 0.12.

111

Table 8.1: BDT discriminant used in the current analysis.
parameter

value

Number of Boosting Cycles:

30

Ada Boost Parameter:

0.20

Minimal Leaf Size:

100

Impurity Measure:

Gini

Boosting Purity Limit:
Number of Bags:
Bagging Fraction:
Random Forest Fraction:

0.5
1
0.75
1.0

is as shown in Table 8.1.
Figs. 8.4, 8.5, and 8.6 show the distributions for BDT, for the 6 analysis channels
and the combination, for s+t-, s- and t- channels, respectively.

112

Event Yield

BDT OUTPUT FOR s+t CHANNEL

e+µ-channel
1-2 tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tbtqb DT output

Figure 8.4: BDT output for s+t channel for the six analysis channels combined.

113

Event Yield

BDT OUTPUT FOR s CHANNEL

e+µ-channel
1-2 tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tb DT output

Figure 8.5: BDT output for s-channel for the six analysis channels combined.

114

Event Yield

BDT OUTPUT FOR t CHANNEL

e+µ-channel
1-2 tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tqb DT output

Figure 8.6: BDT output for t-channel for the six analysis channels combined.

8.5

Bayesian Neural Networks (BNN)

Artificial “neural networks” (NN) are widely used as flexible models for classification.
Bayesian methods can improve the power of these models, so that they can be safely
115

exploited when training data is limited. Figure 8.7 shows an example of a simple
Neural Network.

Figure 8.7: An illustration of a simple Neural Network.

The BNN analysis proceeds as follows.

1. The BNN analysis starts from the lepton and jet 4-vectors variables with good
discrimination between signal and background for 6 channels.
2. The training of the networks is performed and the discriminant D(x) is built.
We then check that the performance of the BNN is adequate.
3. Compute the expected and observed posterior densities of the single top cross
section for each of the 6 analysis channels and its combinations using binned
116

likelihoods formed from the BNN output distributions of the 6 analysis channels, and determine the cross sections.
For each of the 6 analyses channels we built a training set T by combining 10,000
signal and 10,000 background events, which were sampled proportionally to their
weights from the signal and background in the MC training samples. From the
training set T we constructed a posterior density p(w|T ) over the network parameter
space. A sample of K = 100 networks pertaining to the last 100 of 300 epochs
was drawn from the posterior density using a Markov Chain Monte Carlo (MCMC)
technique [60, 61] and used to approximate the discriminant, D.
Figures 8.8, 8.9, and 8.10 show the BNN output distributions for the 6 analysis
channels and the combination, for s+t-, s- and t- channels, respectively.

117

Event Yield

BNN OUTPUT FOR s+t CHANNEL

-1
DØ Run II, 5.4fb

e+µ channel
1-2 b-tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tbtqb BNN Output

Figure 8.8: BNN output for s+t channel for the six analysis channels combined.

118

Event Yield

BNN OUTPUT FOR s CHANNEL

-1
DØ Run II, 5.4fb

e+µ channel
1-2 b-tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tb BNN Output

Figure 8.9: BNN output for s-channel for the six analysis channels combined.

119

Event Yield

BNN OUTPUT FOR t CHANNEL

-1
DØ Run II, 5.4fb

e+µ channel
1-2 b-tags
2-4 jets

1000

500

00

0.2

0.4

0.6

0.8
1
tqb BNN Output

Figure 8.10: BNN output for t-channel for the six analysis channels combined.

8.6

Neuroevolution of augmented topologies (NEAT)

NeuroEvolution of Augmenting Topologies (NEAT) is a method for evolving artificial
neural networks with a genetic algorithm. It is most effective to start evolution
120

with small, simple networks and allow them to become increasingly complex over
generations, just as organisms in nature increased in complexity since the first cell.
The training for NEAT is based on a genetic algorithm which evolves a population of possible discriminators. The decriminators of NEAT are defined by neural
networks (NN) that are similar to those used in BNN. An initial population of NNs
is created with zero hidden neurons and randomly assigned weight connections. This
population is then evolved by a series of operations that can be classify as mutations,
crossovers and selection. Mutations change the weight of existing connections or add
new hidden nodes to the network. Crossovers create a new NN by combining two
different parent NNs, allowing the combination of those features that potentially can
create better discriminators. After these operations, NNs are selected to be part of
the next generation depending on the “fitness” of each discriminator.
Figs. 8.11, 8.12, and 8.13 show the NEAT output distributions for the 6 analysis
channels and the combination, for s+t-, s- and t- channels, respectively [62].

121

Event Yield

NEAT OUTPUT FOR s+t CHANNEL

D0 Run II, 5.4 fb-1
e+µ-channel
1-2 b-tags
2-4 jets

1000

800

600

400

200

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 0.8 0.9
1
tbtqb NEAT output

Figure 8.11: NEAT output for s+t channel for the six analysis channels combined.

122

Event Yield

NEAT OUTPUT FOR s CHANNEL

D0 Run II, 5.4 fb-1
e+µ-channel
1-2 b-tags
2-4 jets

1200

1000

800

600

400

200

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9
1
tb NEAT output

Figure 8.12: NEAT output for s-channel for the six analysis channels combined.

123

NEAT OUTPUT FOR t CHANNEL

Event Yield

1200

D0 Run II, 5.4 fb-1
e+µ-channel
1-2 b-tags
2-4 jets

1000

800

600

400

200

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 0.8 0.9
1
tqb NEAT output

Figure 8.13: NEAT output for t-channel for the six analysis channels combined.

124

8.7

A combined BNN using BDT, BNN and NEAT
discriminants

Ensemble tests with datasets containing contributions only from backgrounds and
SM signals, shows a 70% correlation among the outputs of the individual MVA
methods above. Thus, to achieve the maximum sensitivity, a second level of BNN is
used to construct a combined discriminant for each channel, for tb, tqb, and tb+tqb
events, using BDT, BNN and NEAT discriminants as the inputs.
In this combination BNN, we have two sets of trainings. The combined tb and
tqb discriminants take as inputs the three discriminant outputs of BDT, BNN, and
NEAT, and they are trained by assuming tb or tqb as signals, respectively. The
combined tb+tqb discriminant takes inputs from the six discriminant outputs of BDT,
BNN, and NEAT that are trained separately for the tb and the tqb signal. The
training for the combined tb+tqb BNN treats the combined tb+tqb contribution as
signal with production rates ratio predicted by SM. In both trainings, we followed the
same procedure as in the non-combination BNN training, described in Section 8.5.
The CP violation analysis uses this combined BNN output as the basis.
Figs. 8.14, 8.15, and 8.16 show the NEAT output distributions for the 6 analysis
channels and the combination, for s+t-, s- and t- channels, respectively.

125

Event Yield

BNN Combination OUTPUT FOR s+t CHANNEL

e/µ+jets
1-2 b-tags
2-4 jets

1000

500

0
0

0.2
0.4
0.6
0.8
1
tbtqb BNNComb Output

Figure 8.14: Combined BNN output for s+t channel for the six analysis channels
combined.

126

Event Yield

BNN Combination OUTPUT FOR s CHANNEL

e/µ+jets
1-2 b-tags
2-4 jets

1000

500

0
0

0.2

0.4
0.6
0.8
1
tb BNNComb Output

Figure 8.15: Combined BNN output for s channel for the six analysis channels
combined.

127

Event Yield

BNN Combination OUTPUT FOR t CHANNEL

e/µ+jets
1-2 b-tags
2-4 jets

1000

500

0
0

0.2

0.4
0.6
0.8
1
tqb BNNComb Output

Figure 8.16: Combined BNN output for s+t channel for the six analysis channels
combined.

Figures C.1 to C.6 show the combined discriminants distributions for positive
and negative samples separately after splitting by lepton charge.

128

400

DØ 5.4 fb -1
Data
tb+tqb
W+jets
tt
Multijets

200

Yield [Events/0.04]

Yield [Events/0.04]

(e)

(e)

400
300

DØ 5.4 fb -1
Data
tb+tqb
W+jets
tt
Multijets

200
100

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

DØ 5.4 fb -1

10

5

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Yield [Events/0.04]

Yield [Events/0.04]

Figure 8.17: The s+t discriminant plots in the electron+muon channel for positive
(left) and negative (right) events.

(f)

DØ 5.4 fb -1

10

5

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure 8.18: The BNNcomb6SortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

129

400
300
200

DØ 5.4 fb -1
Data
tqb
tb
W+jets
tt
Multijets

Yield [Events/0.04]

Yield [Events/0.04]

(e)

DØ 5.4 fb -1
Data
tqb
tb
W+jets
tt
Multijets

400

200

100

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

DØ 5.4 fb -1

6

4

2

0
0.8

Yield [Events/0.04]

Yield [Events/0.04]

Figure 8.19: The t discriminant plots in the electron+muon channel for positive (left)
and negative (right) events.

8

DØ 5.4 fb -1

6

4

2

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure 8.20: The BNNcombTSortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

130

(e)

400

DØ 5.4 fb -1
Data
tb
tqb
W+jets
tt
Multijets

Yield [Events/0.04]

Yield [Events/0.04]

600

200

(e)
600

400

DØ 5.4 fb -1
Data
tb
tqb
W+jets
tt
Multijets

200

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

DØ 5.4 fb -1

6

4

15

(f)

DØ 5.4 fb -1

10

5

2

0
0.8

Yield [Events/0.04]

Yield [Events/0.04]

Figure 8.21: The s discriminant plots in the electron+muon channel for positive
(left) and negative (right) events.

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure 8.22: The BNNcombSSortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

131

Chapter 9
Statistical Analysis
In order to obtain a measurement of the CP asymmetry, the top and antitop cross
sections need to be measured simultaneously. The cross sections are determined using
the signal and background binned distributions of the combination BNN outputs.
The cross section calculations are performed employing Bayesian statistics with the
top statistics [63] package.

9.1

Poisson distribution likelihood

The basic assumption of particle physics is that event counts follow a Poisson distribution, that is, if the expected number of events is d, the probability to observe a
132

count of D, is given by:
L(D|d) =

e−d dD
,
D!

(9.1)

The expected number of events d come from signal and background sources:
N

N

d = αLσ +
i=1

bi ≡ aσ +

bi ,

(9.2)

i=1

where α is the signal acceptance, L is the integrated luminosity, σ is the signal cross
section (the quantity to be measured), bi the expected event count for background
source i, and a ≡ αL is defined as the effective luminosity for the signal. N is the
total number of background sources.

We measure the likelihood for each individual histogram bin and regard them as
independent measurement channels. The total likelihood for each analysis channel
is thus a product of the likelihood of each histogram bin:
M
L(D|d) ≡ L(D|σ, a, b) =

i=1

L(Di |di ),

(9.3)

where D and d represent vectors of observed data counts and expected signal plus
background event counts, and a and b are vectors of effective luminosity and backgrounds. M is the total number of bins in the channel.
133

9.2

Bayesian analysis

Bayes’ theorem links the uncertainty of a probability model before and after observing
the modelled system. From Bayes’ theorem, we obtain:

p(σ, a, b|D) =

L(D|σ, a, b)π(σ, a, b)
,
p(D)

(9.4)

We regard the probability to observe a given number of counts for data p(D) is
a constant. Further integrating over the parameters a and b gives the probability
density for the signal cross section given observed event counts D:

p(σ|D) =

1
N

L(D|σ, a, b)π(σ, a, b)da, db.

(9.5)

σ
where N is an overall normalization factor from the requirement 0 max p(σ|D)dσ =
1, where the integral upper bound σmax is chosen as when the posterior probability density p(σ|D) is sufficiently close to zero. The function p(σ|D) is called the
posterior probability density, which is the probability density of observing a certain
cross section assuming event counts D is observed. The function π(σ, a, b) is called
the prior probability density. L(D|σ, a, b) is the Poisson likelihood detailed in last
section.
In general, our prior knowledge of a and b is independent of that of cross section
134

σ. Thus,
π(σ, a, b) = π(a, b|σ)π(σ) = π(a, b)π(σ)

(9.6)

We assume that the prior probability density of signal cross section is evenly
distributed, which is equivalent to a flat prior for the signal cross section: π(σ) =
1/σmax , as shown in the Figure 9.1 below.

Figure 9.1: An illustrative plot of a flat prior probability density for the signal cross
section.
Thus, the posterior probability density for the signal cross section Eq. 9.5 can be
written as:
p(σ|D) =

1
N σmax

L(D|σ, a, b)π(a, b)da, db.
135

(9.7)

We choose the peak of the posterior density distribution as the measured cross
seciton, and the 68% confidence interval about the peak as an estimate of its uncertainty, as shown in Figure 9.2.

Figure 9.2: An illustrative plot demonstrating cross section measurement from a
posterior probability density.

To measure top and antitop quark cross sections, we generalize the method above
to measure simultaneously the cross sections of two signals, σ+ and σ− , by building
a two-dimensional posterior probability density. The expected event count in this
case will be:
N
d = a+ σ+ + a− σ− +
136

bi ,
i=1

(9.8)

where a+ and a− are the effective luminosities of the two signals respectively.
As before, we assume a flat prior for each of the two signals:

π(σ+ ) = 1/σ1,max

(9.9)

π(σ− ) = 1/σ2,max

(9.10)

where σ1,max and σ2,max is a sufficiently high upper bound for the first and second
signal cross section to be close to zero.

Finally we get a two dimensional posterior probability density for different values
of σ+ and σ− :
1
p(σ+ , σ− |D) =
N σ1,max σ2,max

L(D|σ+ , σ− , a, b)π(a, b)da, db.

(9.11)

Replacing the likelihood with the Poisson distribution, we obtained

L(D|σ+ , σ− , a, b) =

Dp
e−dp dp
p=1

Γ(Dp + 1)

n=1

e−dn dDn
n
Γ(Dn + 1)

(9.12)

where the dp and dn is the expected number of events with positive and negative
137

leptons respectively in each bin:

dp = σ+ ap + bp
dn = σ− an + bn .

(9.13)

Here ap and an represent the effective luminosities for single top and antitop, and bp
and bn are the background yields for events with leptons with positive and negative
charges, respectively.
π(a, b) encodes our knowledge of the effective signal luminosities and background
yields. The posterior density distribution is obtained by creating a large number
of samples of systematic shifts in a and b. A separate likelihood distribution is
obtained for each sample, and the final posterior is the sum over all of the individual
likelihoods.
From this likelihood the 2d posterior probability density Eq. 9.11 is rewritten as:
Dp
e−dp dp

1

p(σ+ , σ− ) =
N σ+,max σ−,max

p=1

Γ(Dp + 1)

n=1

e−dn dDn
n π(a, b)dadb.
(9.14)
Γ(Dn + 1)

We can then define a contour plot of equal probability that encloses a volume CL
around the peak of the posterior density, as illustrated in Figure 9.3.
The one dimensional posterior probability density for each positive and negative
signal can be derived by integrating the two-dimensional posterior density Eq. 9.11
138

Figure 9.3: An illustrative plot demonstrating a contour plot derived from a two
dimensional posterior probability density.

139

over the other signal:

p(σ+ |D) =

σ−,max

0

p(σ+ , σ− |D)dσ− ,

(9.15)

p(σ+ , σ− |D)dσ+ .

(9.16)

and
p(σ− |D) =

σ+,max
0

Then we can determine the cross section measurements for positive and negative
signals each in the same way as in the one dimensional case, as shown in Figure 9.2.

9.3

Posterior probability density for the CP asymmetry

To obtain the posterior probability density for the asymmetry, we utilize the relationships (Eq. 2.2):
σ − σ−
; σ = σ+ + σ−
A= +
σ+ + σ−

(9.17)

where A is the definition of the top production asymmetry, and σ the total production
cross section.
140

Combining with Eq. 9.14, we obtain

p(σ, A) =

σ
2N σmax

L(D|σ(1 + A)/2, σ(1 − A)/2, a, b)π(a, b)dadb.

(9.18)

The posterior probability density for the asymmetry p(A) thus can be computed
by integrating over the total cross section σ:

p(A) =

p(σ, A)dσ

141

(9.19)

Chapter 10

Systematic Uncertainties

Systematic uncertainties expresses our inability to model the detector accurately.
Systematic errors are often difficult to assess, because they do not show up as fluctuations in the results of repeated measurements, as statistical uncertainties do. It is
important to think about possible sources of systematic errors and to try to correct
them or rule them out.

Systematic uncertainties enter the single top measurements in two ways: as uncertainty on the normalization of the signal and background samples, and as effects
that change the shapes of the distributions of those samples and the shapes of the
expected signal distributions, i.e. the combination BNN outputs.
142

10.1

Uncertainties affecting normalization only

These systematic uncertainties affects only the normalization of the signal and background samples.
• Integrated luminosity
¯
The 6.1% uncertainty on the luminosity estimate affects the signal, tt, Z+jets,
and diboson yields.
• Theory cross sections
¯
The uncertainties on the single top and tt cross sections come from Refs. [1]
and [64], and are calculated for 3 top quark mass points: 170 GeV, 172.5 GeV,
and 175 GeV. The resulting values for the uncertainties for 172.5 GeV are
¯
±3.8% for s-channel tb, ±5.3% for t-channel tqb, and +6.4%, −9.0% for tt. For
tb+tqb combined, the uncertainty is ±4.8%. (NB, the uncertainty on the signal
cross section does not of course enter the experimental measurement of it.) The
uncertainties on the Z+jets cross section is set to 3.3% as per reference [65].
The uncertainties on the diboson cross sections is set to 7% in accordance with
the Higgs group current practice [66].
• Branching fractions
From the Particle Data Book, the branching fractions for a W boson to decay
to an electron, muon, or tau lepton, have an average uncertainty of 1.5% and
143

we include this in the MC normalization uncertainties.
• Parton distribution functions
We have estimated the effect of changing the parton distribution functions on
the signals and assign a systematic uncertainty of 2% to the signal acceptances
from this source. PDF uncertainties on the acceptance can be calculated by
reweighting the MC events before selection using 40 CTEQ PDF sets and then
calculating the acceptance for each of the eigen sets [50]. The square root of
the sum of the squares of the difference between the PDF eigen sets with the
nominal PDF set is quoted as uncertainty.
• Trigger efficiency
We use an OR of many trigger conditions which give us a trigger efficiency of
close to 100%. We assign an uncertainty of 5% to the trigger efficiency in all
channels and treat it as uncorrelated between p17 and p20.
• Instantaneous luminosity reweighting
We reweight the instantaneous luminosity distributions of all MC samples to
make them match Run IIa or Run IIb data distributions as appropriate. The
uncertainty on this reweighting is 1.0%.
• Primary vertex modeling and selection
We reweight the distribution of the primary vertices along the beamline in MC
144

to match that in data [67], [68]. The uncertainty on this reweighting is 0.05%
(negligible). The uncertainty on the difference in primary vertex selection
efficiency between data and MC is 1.4%.

• Color Reconnection
We estimate the systematics due to color reconnections by taking the difference in signal efficiency between a sample generated with PYTHIA TuneAPro
and PYTHIA TuneACPro [69]. The relative difference on preselection and btagging efficiency between both simulations is found to be 1.0% and is assigned
¯
as an additional uncertainty to the central efficiencies for tt background and
signal MC.

• Relative b/light jet response
This uncertainty takes into account the difference between the nominal inclusive jet response and the response for B- hadrons. To estimate this difference,
¯
particle jets in a tt lepton+jets sample were constructed and classified as b- or
light jets. Single particle response curves for both data and MC were then
applied to the particle jets to predict the energy of a reconstructed jet in the
calorimeter. From these reconstructed energies, the ratio pdata /pMC was
T
T
then calculated separately for both b-jets and light jets and the double ratio
145

evaluated:

pdata /pMC
T
T

b-jet

pdata /pMC
T
T
light jet
resulting in a differnce of 1.8% [70]. The systematics uncertainty is then obtained by shifting down by 1.8% the nominal response of b-jets (identified based
on the MC truth information).
• Electron reconstruction and identification efficiency
The electron scale factor uncertainty is taken from Ref. [55], but adapted to
the electron acceptance cuts used in this analysis in accordance with [71]. The
uncertainty includes contributions from the fit used to evaluate the background
in the Z boson sample, as well as dependencies on the luminosity, distance to
closest jet, jet multiplicity, and electron pT . The resulting total uncertainty is
2.8% for p17, and 3.8% for p20 data.
• Muon reconstruction and identification efficiency
The muon scale factor uncertainties for muon reconstruction (1.4%), muon
identification (1.2%) and muon isolation (0.4%) are taken from Table 6, 4 and
8 of Ref. [72]. They were estimated by the muon ID group, for the tag/probe
method, background subtraction, and limited statistics in the parameterization.
An additional uncertainty of 1% is added in quadrature to take into account the
latest muon ID as explained in Appendix 5.1. The assigned total uncertainty
146

is 2.1%.
• Jet Fragmentation and higher-order effects
We have measured the systematic uncertainty due to jet fragmentation by com¯
paring the acceptance of the nominal tt events generated with alpgen+pythia
(as used in the analysis) to ones generated with alpgen+herwig. The resulting uncertainty of 0.7%, 3.7% and 4.7% for events with 4, 5 and 6 jets, is
applied to the signal samples in the 2, 3 and 4 jet bin, respectively.
We have also measured the systematic uncertainty due to a combination of jet
fragmentation and higher order effects (We take the variations observed in the
top pair cross section analysis described in DØ Note 6025, averaged over run
¯
period and lepton type.) comparing the acceptance of the nominal tt sample to
ones generated with MC@NLO+HERWIG. The resulting uncertainty is 1.6%
for events with 2 jets, 1.7% for events with 3 jets, and 7.0% for events with
4 jets. The variation is anti-correlated between events with 2 or 3 jets and
¯
events with 4 jets. This uncertainty is applied exclusively to the tt sample and
accounts for both jet fragmentation and higher order effects.
• Initial-state and final-state radiation
¯
We use tt samples that were generated varying the ISR/FSR settings and we
have evaluated this uncertainty in those samples as follows: for signal MC,
¯
which have 2,3, or 4 jets, we take the uncertainties from the tt events with 4,
147

¯
¯
5, 6 jets. For the tt background, we take numbers from the tt samples with
2, 3, and 4 jets directly. All uncertainties are averaged over the electron and
muon channels, and are half the difference between the ISR and FSR samples.
We find an uncertainty ranging from 0.8% to 10.9% and apply it to signal and
¯
tt samples.

• b-jet fragmentation
¯
The size of the uncertainty from the b-jet modeling was evaluated in the tt
pairs cross section analysis following the method described in Ref. [70]. The
uncertainty arises from the difference between the fragmentation parameterizations preferred by SLD vs. LEP data. A 2.0% value is measured and applied
¯
to signal, tt and Zbb samples.

• Taggability
The uncertainty associated with b-tagging in MC events includes components
for the taggability and the tagging efficiency. The taggability uncertainties are
evaluated by raising and lowering the taggability scale factor values by one
standard deviation on each MC sample and repeating the entire analysis. The
taggability uncertainties affect the normalization of the MC samples only and
the values are between 3.1% and 21.5%.

• W+jets heavy-flavor scale factor correction
148

The heavy-flavor scale factor correction, λHF , for W b¯ and W c¯ is measured
b
c
in a sample that is orthogonal to the one in the analysis and found to be
consistent with 1, with a 12% uncertainty. Two other methods based on the
candidate sample also confirm that λHF is consistent with one.
• Z+jets heavy-flavor scale factor correction
′
The heavy-flavor scale factor KHF for Zb¯ and Zc¯ is determined from NLO
b
c
calculations, and we set the correction to it, λHF to be 1.0 (since we cannot
normalize to data to check it) with an uncertainty of 12%, taken from the λHF
for W +jets events.

• W+jets and multijets normalization
We use a fit to the pretagged data to determine the W +jets and multijets
background normalizations. The uncertainties are estimated to be 30% for the
multijets backgrounds (40% for the Run IIb MU channel), and 1.8% for the
W +jets backgrounds.

• Lepton Charge Mis-Identification
The CP violation measurement needs to separate the samples into positive and
negative subsets, according to the lepton charge in the final state. We select
the Z → ee or Z → µµ events to measure the charge mis-ID rate. We require
each event to have exactly two electrons or two muons, and the invariant mass
149

of the leptons between 80 and 100 GeV (Z peak). We measured the fake rate
below 1%. And since we are not sensitive to effects of the order of 1% compared
to the existing much larger systematic uncertainties, we decide to simply add a
systematic uncertainty of 1% anti-correlated between the positive and negative
charge samples. Details see Appendix D.
• Sample statistics
The MC and data samples we use to estimate the signal and background shapes
are limited in size. As In particular the multijets background samples have low
statistics after b tagging. We take the background sample statistics into account
for each sample in each bin of the final discriminant distribution.

10.2

Uncertainties affecting normalization and

shape
The following systematics affects the shapes of the distributions of the signal
and backgrounds, and the shapes of the combination BNN outputs.
• Jet reconstruction and identification
The efficiency to reconstruct and identify jets has an uncertainty varying from
0.04% to 3.7% for all MC samples.
150

• Jet energy resolution
We assign a normalization and shape-changing uncertainty ranging from 0.2%
to 11.6% as the jet energy resolution uncertainty for all signals and backgrounds.

• Jet energy scale
The JES correction is raised and lowered by one standard deviation on each
MC sample and the whole analysis repeated, which produces a shape-changing
uncertainty, and an overall normalization uncertainty. The normalization part
ranges from 0.3% to 14.6% for all MC samples.

• Vertex confirmation
The efficiency to identify vertex-confirmed jets has an uncertainty varying from
0.1% to 9.6% for all MC samples.

• b-tagging
The uncertainty associated with b-tagging in MC events includes scale factor
uncertainties (SF) in the case of applying direct tagging and tag rate (TRF)
uncertainties in the case of using random tagging. This is done simultaneously
for heavy flavor and light jets, as it was done in the single top observation analysis. The SF and TRF uncertainties originate from several sources: statistical
errors of MC event sets; the assumed fraction of heavy flavor in the multijets
151

MC events for the mistag rate determination; and the parameterizations. The
SF and TRF uncertainties affect both shape and normalization of the MC samples. The values range from 4.3% (5.8%) to 14.0% (11.2%) for single-tagged
(double-tagged) samples.
• V +jets angular corrections
We reweight the alpgen W and Z+jets background based on several pretagged
data distributions. The uncertainty from these reweightings affects the shapes
of the W and Z+jets background components. The reweighting procedure does
not change the normalization of the W and Z+jets samples before b-tagging.
After b-tagging, small normalization variations (≈ 0.3%) are introduced by
taggability and b-tagging scale factors.
• Response to b and ¯ quarks
b
The measurement of the top-antitop cross section difference could be affected
by a different response of the calorimeter to quark and antiquark jets. Such a
bias could come from a different calorimeter response to the b and the ¯ decays,
b
respectively. To estimate this uncertainty, we rescale the pT (the 4-vectors
accordingly) of the b and ¯ by a factor of 0.9971 and 1.0021 respectively [73],
b
depending on b or ¯ and then re-apply the MVA filters. The measured effect
b,
is small, and we add another 1% flat systematic uncertainty to account for it.
See Appendix F for details.
152

Chapter 11
CP Violation Measurement
This chapter discusses the final cross section measurements for both top and antitop
quarks, and the expected and observed CP asymmetry measurement results for all
single top production channels, i.e. s-channel, t-channel and s + t-channel.

11.1

Cross section measurement

As can be seen from Section 2.4, to measure the CP Violation in single top, we must
measure the cross sections separately both for top and antitop quarks. The cross
section is determined in a Bayesian approach using the top statistics software
package [63]. The inputs are the BNN combined output distributions shown in
Section 8.7.
These split MVA outputs are further fed into the top statistics package to
153

obtain the desired posteriors.

The cross section is measured by forming a two-dimensional (2d) posterior as a
function of both the positive and the negative top cross sections. In this approach,
the 2d posterior is constructed with no theoretical assumption on either the positive
or negative cross sections. From this 2d posterior, we extract the individual positive
(negative) cross section by integrating over the negative (positive) axis. Figure 11.1
shows an example of a 2d posterior as a function of both the positive and the negative
top cross sections.

The procedure is done separately for s+t (considering s+t as signal and all other
contributions as background), s (considering s as signal and adding the t contribution
to the backgrounds), and for t (considering t as signal and adding the s contribution
to the backgrounds), in order to obtain a posterior density curve as function of the
cross section asymmetry (defined in Section 2.4) for each individual channel. The
central value of the asymmetry is taken from the peak (mode) in the posterior density
function, and the 68% interval about the peak gives the uncertainty. One can see an
example of this measurement from the illustrative Figure 11.2.

The next two chapters show the expected and observed results of the CP asymmetry measurement. Appendix ?? gives more supplement plots and results.
154

Figure 11.1: An illustrative example demonstrating a 2d posterior as a function of
both the positive and the negative top cross sections. This plot is obtained using
the top statistics package. The red small square denotes the Standard Model
prediction (no CP violation). The black dot is the peak of the posterior which
is close to our final results of top-antitop quark cross sections. The 68%, 90%, and
95% Confidence Limit (C.L.) are shown in contours of various colors. We also draw a
diagonal line to visually show, how far away the measured peak is from CP symmetry,
and whether it is shifted to the positive or negative side.

155

Figure 11.2: An illustrative example demonstrating how to measure the CP violation from an asymmetry posterior. This plot is obtained using the top statistics
package. We take the peak of the plot as the central value of the CP violation. The
yellow area denotes the 68% CL interval, which is taken as the uncertainty of the
CP violation measurement. We also draw a 95% CL area with the light blue color.

156

11.2

Expected results

The expected cross section is measured by setting the number of data events in
each analysis channel to the expected number of background events plus the number
of signal events, predicted when using the SM cross section value of 0.52 pb for
s-channel, 1.13 pb for t-channel, and 1.65 pb for s + t-channel (for a top mass of
172.5 GeV). The expected CP asymmetries are further calculated from the cross
section measurements.
The posterior density functions for the 2d, single top production asymmetry, and
cross sections, separately for top and antitop quarks, are shown in Figs. 11.3 to 11.5
taking into account all systematics.
From all the plots, we can see in each analysis channel, the expected cross section
is very close to the standard model prediction, and thus the expected CP asymmetry
is close to zero. This means the systematics do not bias our measurement.
Expected results for CP asymmetry in s, t, s+t channels for different systematics
are shown in Table 11.1.
The expected values are zero within large errors. The error is smallest in the s+t
channel, and largest in the s channel.

157

Figure 11.3: Expected posterior density distributions and measurements of top and
anti-top cross sections in the s + t-channel. The top left plot shows the 2d posterior
of top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
158

Posterior density

σt [pb]

h2

DØ 5.4 fb -1
3

Expected Peak
68% C.L.
90% C.L.
95% C.L.
SM

2

3

DØ Run II, 5.4 fb

-1

2.5

Expected
Asymmetry

2

+0.19

= 0.01-0.19
1.5
1

1

0.5

1

2

1.2

DØ Run II, 5.4 fb

-1

1

Expected
Cross Section

0.8

0
-1 -0.8 -0.6 -0.4 -0.2 0

3
σt [pb]

+0.41

= 1.25 -0.37 pb

0.2 0.4 0.6 0.8

Cross section asymmetry A

Posterior density

Posterior density

0
0

DØ Run II, 5.4 fb

1.2
1

1
top

-1

Expected
Cross Section

0.8

+0.40

= 1.16 -0.36 pb

0.6

0.6

0.4

0.4

0.2

0.2

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

Figure 11.4: Expected posterior density distributions and measurements of top and
anti-top cross sections in the t-channel. The top left plot shows the 2d posterior of
top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
159

Posterior density

σt [pb]

h2

DØ 5.4 fb -1

2

Expected Peak
68% C.L.
90% C.L.
95% C.L.
SM

1.5

1

3

DØ Run II, 5.4 fb

-1

2.5

Expected
Asymmetry

2

+0.27

= -0.05 -0.27
1.5
1

0.5
0.5

1.4

0.5

1

1.5

DØ Run II, 5.4 fb

1.2

-1

Expected
Cross Section

1

+0.34

= 0.55 -0.29 pb

0.8

0
-1 -0.8 -0.6 -0.4 -0.2 0

2
σt [pb]

0.2 0.4 0.6 0.8

Cross section asymmetry A

Posterior density

Posterior density

0
0

1.4

DØ Run II, 5.4 fb

1.2

1
top

-1

1

Expected
Cross Section

0.8

= 0.58 -0.29 pb

+0.35

0.6

0.6

0.4

0.4

0.2

0.2

0
0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

t cross section [pb]

0
0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

t cross section [pb]

Figure 11.5: Expected posterior density distributions and measurements of top and
anti-top cross sections in the s-channel. The top left plot shows the 2d posterior of
top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
160

Table 11.1: Expected results for CP asymmetry in s, t, s+t channels.
Discriminant

CP Asymmetry

tb

−0.05+0.28
−0.27

tqb
tb+tqb

0.02+0.19
−0.19

−0.02+0.14
−0.13

161

11.3

Observed results

The approach described in Sec. 11.2 is repeated using the data events to obtain the
observed cross sections. The observed CP asymmetries are further calculated from
the cross section measurements.
The posterior density functions for the 2d, single top production asymmetry,
and cross sections separately for top and antitop quarks, are shown in Fig. 11.6 to
Fig. 11.8 taking into account of all systematics. The colors show the 68%, 90%, and
95% CL regions.
Unlike the expected results, we can see the measured peak is shifted farther away
from the Standard Model prediction, mostly around one standard deviation away.
The s-channel deviates more than the t-channel, which is again larger than s + t
combined. The measured asymmetries all deviate in the same direction, i.e. to the
negative part. This might be due to data fluctuation. We expect this bias will disappear as we have more statistics of events. Our analysis currently is still background
dominated (S:B approximately 1:20). The 2d plots show that the measured values
are about one standard deviation away from the SM, while the asymmetry plot shows
they are more than one standard deviation away. This is due to the integration in
top statistics, when converting the 2d plot into 1d asymmetry plot. We need at
least three standard deviation to claim evidence, so we don’t observe CP violation
yet at this point.
162

Posterior density

σt [pb]

h2

DØ 5.4 fb -1
Measured Peak
68% C.L.
90% C.L.
95% C.L.
SM

4

3

3

DØ Run II, 5.4 fb

-1

2.5

Observed
Asymmetry

2

+0.16

= -0.24 -0.16
1.5

2
1

1

0.5

1

2

3

DØ Run II, 5.4 fb

1.2
1

-1

Observed
Cross Section

0.8

= 1.11 +0.38 pb
-0.36

0.6

0.2 0.4 0.6 0.8

Cross section asymmetry A

DØ Run II, 5.4 fb

1
top

-1

1

Observed
Cross Section

0.8

+0.41

= 1.75 -0.40 pb
0.6

0.4

0.4

0.2

0.2
0
0

0
-1 -0.8 -0.6 -0.4 -0.2 0

4
σt [pb]

Posterior density

Posterior density

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

Figure 11.6: Observed posterior density distributions and measurements of top and
anti-top cross sections in the s + t-channel. The top left plot shows the 2d posterior
of top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
163

Posterior density

σt [pb]

h2

DØ 5.4 fb -1
3

Measured Peak
68% C.L.
90% C.L.
95% C.L.
SM

2

3

DØ Run II, 5.4 fb

-1

2.5

Observed
Asymmetry

2

+0.18

= -0.25 -0.18
1.5
1

1

0.5

1

2

DØ Run II, 5.4 fb

-1

1.4
1.2

Observed
Cross Section

1

0
-1 -0.8 -0.6 -0.4 -0.2 0

3
σt [pb]

+0.32

= 0.86 -0.29 pb
0.8

0.2 0.4 0.6 0.8

Cross section asymmetry A

Posterior density

Posterior density

0
0

1.4

DØ Run II, 5.4 fb

1
top

-1

1.2
1

Observed
Cross Section

0.8

= 1.39 -0.31 pb

+0.35

0.6

0.6
0.4

0.4

0.2

0.2

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

0
0

0.5

1

1.5

2

2.5

3

3.5

4

t cross section [pb]

Figure 11.7: Observed posterior density distributions and measurements of top and
anti-top cross sections in the t-channel. The top left plot shows the 2d posterior of
top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
164

Posterior density

σt [pb]

h2

DØ 5.4 fb -1

2

Measured Peak
68% C.L.
90% C.L.
95% C.L.
SM

1.5

1

3

DØ Run II, 5.4 fb

-1

2.5

Observed
Asymmetry

2

+0.29

= -0.43 -0.35
1.5
1

0.5
0.5

0.5

1

1.5

DØ Run II, 5.4 fb

-1

2.5

Observed
Cross Section

2

+0.19

= 0.12 -0.12 pb

1.5

0
-1 -0.8 -0.6 -0.4 -0.2 0

2
σt [pb]

0.2 0.4 0.6 0.8

Cross section asymmetry A

Posterior density

Posterior density

0
0

1.8

DØ Run II, 5.4 fb

1
top

-1

1.6

Observed
Cross Section

1.4

+0.26

1.2

= 0.51-0.23 pb

1
0.8

1

0.6
0.4

0.5

0.2
0
0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

t cross section [pb]

0
0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

t cross section [pb]

Figure 11.8: Observed posterior density distributions and measurements of top and
anti-top cross sections in the s-channel. The top left plot shows the 2d posterior of
top and antitop production cross sections; top right plot shows the posterior of the
top-antitop production cross section assymmetry Atop ; bottom left plot shows the
posterior of the top production cross section; bottom right plot shows the posterior
of the antitop production cross section. The top (antitop) cross section are extracted
by integrating over the antitop (top) axis respectively from the 2d posterior.
165

The observed results for CP asymmetry in s, t, s + t channels for different systematics are summarized in Table 11.2.

Table 11.2: Observed results for CP asymmetry in s, t, s+t channels.
Discriminant

CP Asymmetry

tb

−0.43+0.29
−0.35

tqb
tb+tqb

−0.25+0.18
−0.18

−0.24+0.18
−0.16

166

Chapter 12
Results and Conclusions
In this thesis we present a search for CP violation using the single top quark final state
with the DØ detector at the Fermilab Tevatron. We perform the search separately
in the s-, t- and s + t-channel using 5.4 fb−1 of data. This analysis is an extension
of the single top cross section measurement, and is the first analysis searching for
CP violation in single top quark production.
The measured asymmetry A for s-, t- and s+t-channel are −0.43+0.29 , −0.25+0.18
−0.35
−0.18

and −0.24+0.16 respectively.
−0.16

167

APPENDICIES

168

Appendix A
Plots After Splitting by the
Lepton Charge
Figures A.2 to A.24 show various kinematic distributions in the tagged final samples
after being splitted by the lepton charge. The plots are shown on the left for the positive samples and on the right for the negative samples. The legends are only shown
in the first pair of plots (Fig. A.2). All other plots assume the same legend. The
signal and background distributions use the color scheme illustrated in Figure A.1.

169

Figure A.1: Illustration of the color scheme used in plots of signals and backgrounds
in the single top analyses.

170

Yield [Events/10GeV]

Yield [Events/10GeV]

DØ 5.4 fb -1
Data
s+t-channel
W+bb
W+cc
W+lp
Z+jets
Diboson
tt
Multijets

1000

500

0

50

100

DØ 5.4 fb -1
Data
s+t-channel
W+bb
W+cc
W+lp
Z+jets
Diboson
tt
Multijets

1000

500

0

150
200
Lepton pT [GeV]

50

100

150
200
Lepton pT [GeV]

Yield [Events/0.08]

Yield [Events/0.08]

Figure A.2: The transverse momentum of the lepton in the electron+muon channel
for positive (left) and negative (right) samples.

DØ 5.4 fb -1
600

400

200

0

DØ 5.4 fb -1
600

400

200

0

0.2

0.4

0.6

0

0.8
Centrality

0

0.2

0.4

0.6

0.8
Centrality

Figure A.3: The Centrality for All Jets in the electron+muon channel for positive
(left) and negative (right) samples.

171

Yield [Events/0.2]

Yield [Events/0.2]

500

DØ 5.4 fb -1

400
300

DØ 5.4 fb -1
400
300

200

200

100

100

0

0

1

0

2
3
∆φ(Lepton,MET)[Rad]

0

1

2
3
∆φ(Lepton,MET)[Rad]

Yield [Events/20GeV]

Yield [Events/20GeV]

Figure A.4: The Delta Phi between Lepton MET in the electron+muon channel for
positive (left) and negative (right) samples.

DØ 5.4 fb -1
600

400

200

0
100

200

300

DØ 5.4 fb -1
600

400

200

0
100

400
HT [GeV]

200

300

400
HT [GeV]

Figure A.5: The HT in the electron+muon channel for positive (left) and negative
(right) samples.

172

Yield [Events/10GeV]

Yield [Events/10GeV]

DØ 5.4 fb -1
600

400

200

0

0

50

DØ 5.4 fb -1
600

400

200

0

100
150
200
HT light jets [GeV]

0

50

100
150
200
HT light jets [GeV]

Yield [Events/20GeV]

Yield [Events/20GeV]

Figure A.6: The HT-AllJets-MinusBTaggedJet in the electron+muon channel for
positive (left) and negative (right) samples.

DØ 5.4 fb -1

800
600
400
200
0

DØ 5.4 fb -1
800
600
400
200

0

100

200
300
Minv jets [GeV]

0

0

100

200
300
Minv jets [GeV]

Figure A.7: The Invariant Mass for the two leading jets in the electron+muon channel
for positive (left) and negative (right) samples.

173

Yield [Events/20GeV]

Yield [Events/20GeV]

400

DØ 5.4 fb -1

300

200

100

0

DØ 5.4 fb -1

400
300
200
100

0

100

0

200
300
Minv light jets [GeV]

0

100

200
300
Minv light jets [GeV]

3000

Yield [Events/0.2]

Yield [Events/0.2]

Figure A.8: The InvariantMass-LightQuarkJets1-2 in the electron+muon channel for
positive (left) and negative (right) samples.

DØ 5.4 fb -1

3000

2000

2000

1000

0

DØ 5.4 fb -1

1000

0

0.8
0.85
0.9
Leading tagged jet NN output

0.8
0.85
0.9
Leading tagged jet NN output

Figure A.9: The Leading b Tagged Jet in the electron+muon channel for positive
(left) and negative (right) samples.

174

Yield [Events/0.25]

Yield [Events/0.25]

DØ 5.4 fb -1
400

200

0

-2

-1

DØ 5.4 fb -1
400

200

0

0
1
2
Leading tagged jet η

-2

-1

0
1
2
Leading tagged jet η

500

Yield [Events/0.2]

Yield [Events/0.2]

Figure A.10: The LeadingBTaggedJetEta in the electron+muon channel for positive
(left) and negative (right) samples.

DØ 5.4 fb -1

400
300

DØ 5.4 fb -1
500
400
300

200

200

100

100

0

0

0
1
2
3
∆φ(Lepton,Leading tagged jet)[Rad]

0
1
2
3
∆φ(Lepton,Leading tagged jet)[Rad]

Figure A.11: The LeadingBTaggedJetLeptonDeltaPhi in the electron+muon channel
for positive (left) and negative (right) samples.

175

Yield [Events/10 GeV]

Yield [Events/10 GeV]

800

DØ 5.4 fb -1

600
400
200
0

800

DØ 5.4 fb -1

600
400
200
0

50
100
150
200
Leading tagged jet p [GeV]
T

50
100
150
200
Leading tagged jet p [GeV]
T

105

Yield [Events/0.2]

Yield [Events/0.2]

Figure A.12: The LeadingBTaggedJetPt in the electron+muon channel for positive
(left) and negative (right) samples.

DØ 5.4 fb -1

4

10

103
102

105

DØ 5.4 fb -1

4

10

103
102

10

10

1

1

10-1 0

10-1 0

0.2
0.4
0.6
0.8
1
Leading tagged jet NN output

0.2
0.4
0.6
0.8
1
Leading tagged jet NN output

Figure A.13: The LeadingLightQuarkJetBTagNN in the electron+muon channel for
positive (left) and negative (right) samples.

176

Yield [Events/0.4]

Yield [Events/0.4]

DØ 5.4 fb -1

600

400

200

0

DØ 5.4 fb -1

600

400

200

-4

-2

0

0
2
4
Leading tagged jet η

-4

-2

0
2
4
Leading tagged jet η

Yield [Events/0.2]

Yield [Events/0.2]

Figure A.14: The LeadingLightQuarkJetEta in the electron+muon channel for positive (left) and negative (right) samples.

DØ 5.4 fb -1
400
300
200

300
200
100

100
0

DØ 5.4 fb -1

400

0

0

1
2
3
∆φ(Lepton,Leading light jet)[Rad]

0

1
2
3
∆φ(Lepton,Leading light jet)[Rad]

Figure A.15: The LeadingLightQuarkJetLeptonDeltaPhi in the electron+muon
channel for positive (left) and negative (right) samples.

177

Yield [Events/10 GeV]

Yield [Events/10 GeV]

DØ 5.4 fb -1

800
600
400
200

DØ 5.4 fb -1

800
600
400
200

0

50

0

100
150
200
Leading light jet p [GeV]

50

T

100
150
200
Leading light jet p [GeV]
T

Yield [Events/0.25]

Yield [Events/0.25]

Figure A.16: The LeadingLightQuarkJetPt in the electron+muon channel for positive (left) and negative (right) samples.

DØ 5.4 fb -1
400

200

0

DØ 5.4 fb -1

400

200

-2

-1

0

1

0

2
Lepton η

-2

-1

0

1

2
Lepton η

Figure A.17: The LeptonEta in the electron+muon channel for positive (left) and
negative (right) samples.

178

Yield [Events/10 GeV]

Yield [Events/10 GeV]

DØ 5.4 fb -1

1000

500

0

50

100

DØ 5.4 fb -1

1000

500

0

150
200
Missing E [GeV]

50

T

100

150
200
Missing E [GeV]
T

600

(c)

Yield [Events/0.4]

Yield [Events/0.4]

Figure A.18: The METPt in the electron+muon channel for positive (left) and negative (right) samples.

DØ 5.4 fb -1

400

200

0
-4

600

(c)

DØ 5.4 fb -1

400

200

0
-4

-2
0
2
4
Q(lepton) X η(light-quark jet)

-2
0
2
4
Q(lepton) X η(light-quark jet)

Figure A.19: The QTimesEta in the electron+muon channel for positive (left) and
negative (right) samples.

179

Yield [Events/5GeV]

Yield [Events/5GeV]

DØ 5.4 fb -1
400

200

0

20

DØ 5.4 fb -1
400

200

0

40
60
80
Second light jet p [GeV]

20

T

40
60
80
Second light jet p [GeV]
T

Yield [Events/5GeV]

Yield [Events/5GeV]

Figure A.20: The SecondLightQuarkJetPt in the electron+muon channel for positive
(left) and negative (right) samples.

DØ 5.4 fb -1

(d)
600

400

200

0

DØ 5.4 fb -1

(d)
600

400

200

140

160

0

180
200
220
Top Quark Mass [GeV]

140

160

180
200
220
Top Quark Mass [GeV]

Figure A.21: The SigTopMass in the electron+muon channel for positive (left) and
negative (right) samples.

180

Yield [Events/0.2]

Yield [Events/0.2]

300

DØ 5.4 fb -1

200

100

DØ 5.4 fb -1

300

200

100

0
-1

0
-1

-0.5
0
0.5
1
Top Quark Spin Correlation

-0.5
0
0.5
1
Top Quark Spin Correlation

Yield [Events/20]

Yield [Events/20]

Figure A.22: The SpinCorr in the electron+muon channel for positive (left) and
negative (right) samples.

DØ 5.4 fb -1

1000

1000

500

0

DØ 5.4 fb -1

500

0

100

200

χ2

300
400
of top mass

0

0

100

200

300
400
χ2 of top mass

Figure A.23: The TopMassMinChiSqr in the electron+muon channel for positive
(left) and negative (right) samples.

181

Yield [Events/10GeV]

Yield [Events/10GeV]

DØ 5.4 fb -1

1000

500

0

0

DØ 5.4 fb -1

1000

500

0

50
100
150
W Boson Transverse Mass [GeV]

0

50
100
150
W Boson Transverse Mass [GeV]

Figure A.24: The WT in the electron+muon channel for positive (left) and negative
(right) samples.

182

Appendix B
SAM Definitions of Dataset Used
in This Analysis
The dataset is obtained from the MUinclusive and EMinclusive common sample
group (CSG) skims:
• CSG CAF skim PASS3 p18.13.01 for RunIIa
• CSG CAF skim PASS2 p21.10.00 for Run IIb1
• CSG CAF skim PASS4 p21.10.00 p20.12.00-04 and
CSG CAF skim PASS4 p21.12.00 p20.12.05 allfix for RunIIb2
and the following VJets definitions
• VJets EM/MUinclusive Moriond09 RunIIa v1 for Run IIa
183

• VJets EMinclusive Summer09 extended RunIIb v3 for Run IIb electrons
• VJets MUinclusive Summer09 extended allfix RunIIb for RunIIb muons

184

Appendix C
Plots for discriminants after the
binning transformation
Figures C.1 to C.6 show various discriminants distributions in the tagged final samples after the binning transformation applied to the discriminants [58, 30]. When
trying to calculate the cross section, in the high discriminant region there may be
some bins in which there are some signal but no background events. To avoid this,
we applied a binning transformation to MVA outputs that ensures that there is a
minimum amount of effective background events in each bin. We followed the same
procedure as described in detail in Appendix D of Ref. [58] and applied the same
binning transformation function derived for the BNNComb discriminants in Ref. [30]
to both positive and negative charge samples. The signal region with discriminant
185

output from 0.8 to 1 are zoomed to show that there are in fact signals in that region.
The “Sort” or “Ranked” plots sorted each bin according to their S/B ratios from left
to right.

186

400

Yield [Events/0.04]

Yield [Events/0.04]

(e)

DØ 5.4 fb -1
Data
tb+tqb
W+jets
tt
Multijets

200

(e)

400
300

DØ 5.4 fb -1
Data
tb+tqb
W+jets
tt
Multijets

200
100

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

Yield [Events/0.04]

Yield [Events/0.04]

Figure C.1: The s+t discriminant plots in the electron+muon channel for positive
(left) and negative (right) events.

DØ 5.4 fb -1

10

5

0
0.8

(f)
10

5

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

DØ 5.4 fb -1

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure C.2: The BNNcomb6SortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

187

400
300
200

Yield [Events/0.04]

Yield [Events/0.04]

(e)

DØ 5.4 fb -1
Data
tqb
tb
W+jets
tt
Multijets

DØ 5.4 fb -1
Data
tqb
tb
W+jets
tt
Multijets

400

200

100

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

Yield [Events/0.04]

Yield [Events/0.04]

Figure C.3: The t discriminant plots in the electron+muon channel for positive (left)
and negative (right) events.

DØ 5.4 fb -1

6

4

2

0
0.8

8

DØ 5.4 fb -1

6

4

2

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure C.4: The BNNcombTSortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

188

(e)

400

Yield [Events/0.04]

Yield [Events/0.04]

600

DØ 5.4 fb -1
Data
tb
tqb
W+jets
tt
Multijets

200

(e)
600

400

DØ 5.4 fb -1
Data
tb
tqb
W+jets
tt
Multijets

200

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

0

0.2
0.4
0.6
0.8
1
Ranked BNNcomb6 discriminant

(f)

Yield [Events/0.04]

Yield [Events/0.04]

Figure C.5: The s discriminant plots in the electron+muon channel for positive (left)
and negative (right) events.

DØ 5.4 fb -1

6

4

(f)

DØ 5.4 fb -1

10

5

2

0
0.8

15

0
0.8

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

0.85
0.9
0.95
1
Ranked BNNcomb6 discriminant

Figure C.6: The BNNcombSSortZoom plots in the electron+muon channel for positive (left) and negative (right) events.

189

Appendix D
Lepton Charge Mis-Identification
The charge measurement is important for this analysis since CP violation can be
diluted by the mis-identification (mis-ID) of the lepton charge. We rely on the track
charge to determine whether the selected lepton carries positive or negative charge.
We select Z → ee or Z → µµ events to measure the charge mis-ID rate. We
require each event to have exactly two electrons or two muons, and the invariant
mass of the leptons to be between 80 and 100 GeV (Z peak). We assume that all
same sign events (defined as the events containing two same sign leptons) under the
Z peak must have one lepton with the wrong charge, and that opposite sign events
(defined as the events containing two opposite sign leptons) have correctly measured
lepton charges. Therefore the charge mis-ID rate is defined as the ratio between the
number of same sign events and the total number of di-lepton events.
190

We measured the lepton charge mis-ID rate dependences on lepton detector eta
and lepton transverse momentum using CSG 2EMhighpt and 2MUhighpt data samples. The luminosity of the data is 1.1 f b−1 for p17 and 4.3 f b−1 for p20.
We also measured the mis-ID rate from MC samples as a cross check.
The data and simulation samples used in this analysis are listed below. Electron
Channel data samples:
• CSG CAF 2EMhighpt PASS3 p18.13.01 for RunIIa
• CSG CAF 2EMhighpt PASS4 p21.10.00 p20.12.00 for RunIIb
• CSG CAF 2EMhighpt PASS4 p21.10.00 p20.12.01 for RunIIb
• CSG CAF 2EMhighpt PASS4 p21.10.00 p20.12.02 for RunIIb
• CSG CAF 2EMhighpt PASS4 p21.10.00 p20.12.05 for RunIIb
• CSG CAF 2EMhighpt PASS2 p21.10.00 for RunIIb
Electron Channel MC samples:
• AFB-Zee-60-130GeV-p21 for RunIIb
• AFB-Zee-60-130GeV-NoExtraSmear for RunIIa
Muon Channel data samples:
• CSG CAF 2MUhighpt PASS3 p18.14.00 for RunIIa
191

• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.00 for RunIIb
• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.01 for RunIIb
• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.02 for RunIIb
• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.03 for RunIIb
• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.04 for RunIIb
• CSG CAF 2MUhighpt PASS4 p21.10.00 p20.12.05 summer2009 for RunIIb
• CSG CAF 2MUhighpt PASS2 p21.10.00 for RunIIb
Muon Channel MC samples:

• Zmumu-weigang-60-130GeV-p20 2 for RunIIb
• Zmumu-weigang-60-130GeV-p17 for RunIIa
For both channels we used the selection cuts as close as possible to the single top
cross section measurement, except that we have 2 leptons instead of 1 (same isolation
requirements for both leptons.), and we used the 2 jet inclusive bin while single top
analysis uses 2, 3, 4 jet exclusive bins. Also there is no MET requirement.
192

D.1

Electron Charge Mis-ID Rate

Electrons are defined as clusters of energy depositions in the electromagnetic section
of the calorimeter, consistent in shape with an electromagnetic shower. We used
these cuts for electrons in the charge mis-ID measurement:

• We require invariant mass 80 < M12 < 100 GeV
• We require electrons to be within the central calorimeter with |η det | < 1.1
(CC).
• electron transverse momentum pT > 15 GeV
• z(track, primaryvertex) < 1 cm
• At lease 90% of the energy of the cluster must be contained in the electromagnetice section of the calorimeter. EMF> 90%
• The isolation requirement is ISO< 0.15
• EM-likelihood> 0.85
• 7 × 7 H-matrix χ2 < 50 HMx7cut = 50.
• Track pT > 5 GeV
• RDCA< 2. (= no rdca requirement.)
193

• Track match changed from spatial match only to also EOP match included
(track match spatialchi2prob() => track match chi2prob()).

This further

lowers electron misid rate from 0.6 to 0.3 percent.
The mis-ID rate is less than 0.5% for both MC and data, in all bins.

194

D.2

Muon Charge Mis-ID Rate

Muons are identified by combining tracks in the muon spectrometer ( η det < 2.0)
with central detectors tracks. We used these cuts for muons in the charge mis-ID
measurement:
• We require Invariant Mass 80 < M12 < 100 GeV
• We require muons to match the central calorimeter with |η det | < 2.0
• muon pT > 15 GeV
• z(track, primaryvertex) < 1 cm
• We require muon not in a jet: ∆R(muon, jet) > 0.5
• Momenta of all tracks are within R < 0.5 except muon track < 20% of muon
pT: etTrkCone5/pT< 0.2
• energy in cone 0.1 < R < 0.4 less than 20% of muon pT: etHalo/pT< 0.2
• pass 3 layers of muon scintilators: |nseg| = 3
• not from cosmic rays
• has a central track
• track Chi2Ndf () < 4.0
195

• when there is no SMT hits, require DCA < 0.2 (track match muon in η, φ.)
Figure D.1 shows the muon charge mis-ID rate as a function of lepton pT for
Run IIa (left) and Run IIb (right).
The mis-ID rate is less than 1% for both MC and data, in all bins.

196

p17 muon mis ID rate over muon transverse momentum
Entries 69208

Lepton mis-ID rate

0.07

Mean
RMS

0.06

66.7
17.39

0.05
0.04

data
mc

0.03
0.02
0.01

0
20 30 40 50 60 70 80 90 100
Transverse momentum of lepton [GeV]
p20 muon mis ID rate over muon transverse momentum
Entries 116916

Lepton mis-ID rate

0.08
Mean
73.58
RMS
20.74
0.07
0.06
0.05
data
0.04
mc
0.03
0.02
0.01
0
20 30 40 50 60 70 80 90 100
Transverse momentum of lepton [GeV]

Figure D.1: The muon charge mis-ID rate as a function of lepton pT for Run IIa
(left) and Run IIb (right).

197

D.3

Conclusion

In both MC and data, the fake rate is always below 1%, as shown in Table D.1. And
since we are not sensitive to effects of the order of 1% compared to the existing much
larger systematic uncertainties, we simply add a systematic uncertainty of 1% anticorrelated between the positive and negative charge samples. One may note that the
data charge mis-ID rate is significantly higher than MC. This is because MC does
not simulate our detector well. As long as they are all very small, it shouldn’t affect
the final result.
Table D.1: Overall Charge mis-ID Rates.

Overall charge mis-ID rates
Run IIa

Run IIb

Electron

Muon

Electron

Muon

Data

0.22%(1 ± 0.11)

0.52%(1 ± 0.053)

0.32%(1 ± 0.074)

0.50%(1 ± 0.041)

MC

0.12%(1 ± 0.036) 0.15%(1 ± 0.016)

198

0.068%(1 ± 0.054) 0.18%(1 ± 0.0068)

Appendix E
W Asymmetry Check
We performed a cross-check, for measuring the W + and W − asymmetry in the
W +jets sample. This check was done by using W +jets samples as the signal and
tbtqb sample as a part of the backgrounds in the 2-jet and 1-tag bin. The expected
and observed posterior density funcions are shown in Fig. E.1 to Fig. E.2, taking
into account all systematics. The W asymmetry is found to be consistent with 0 (as
expected) and compared to the single top asymmetry we are trying to measure. This
check is sensitive to possible bias from the detector effect, and we find that there are
none.

199

Posterior density

20

DØ Run II, 5.4 fb -1

18
16
14

Expected
Asymmetry

12

= -0.011+0.025
-0.025

10
8
6
4
2
0
-0.2 -0.15 -0.1 -0.05

0

0.05 0.1 0.15 0.2

Cross section asymmetry Aw
Figure E.1: Expected posterior density distributions for W + jets asymmetry in the
s + t-channel 2-jet 1-tag bin.

200

Posterior density

20

DØ Run II, 5.4 fb -1

18
16
14

Observed
Asymmetry

12

= -0.025 +0.026
-0.024

10
8
6
4
2
0
-0.2 -0.15 -0.1 -0.05

0

0.05 0.1 0.15 0.2

Cross section asymmetry Aw
Figure E.2: Observed posterior density distributions for W + jets asymmetry in the
s + t-channel 2-jet 1-tag bin.

201

Appendix F
b/¯ Jet Energy Scale (JES) Check
b
The measurement of the top-antitop cross section difference could be affected by a
different response of the calorimeter to quark and antiquark jets. Such a bias could
come from a different calorimeter response to the b and the ¯ decays, respectively.
b
In principle, c and c responses in the calorimeter could affect b/¯ JES also, but it’s
¯
b
an even smaller effect, thus we only check b and ¯ responses check.
b
We rescale the pT (the 4-vectors accordingly) of the b and ¯ by a factor of 0.9971
b
and 1.0021 respectively [73], depending on b or ¯ and then re-apply the MVA filters,
b,
for all MC samples. Then, we evaluate the difference in the CP violation extracted
from the original and modified samples. We only do this for the signal, which we
expect will have the largest effect, because our main measurements come from the
signal region of the signal asymmetry posteriors.
202

The Jet Energy Scale (JES) is applied before the event selection and can introduce
changes not only to event yields, but also because the jet kinematics are changed. It
can change the jet multiplicity distribution of the events, and thus affect the number
of events passing the selection. Tables F.1 to F.4 shows the expected event yields for
the signals after b-tagging before and after applying b/bbar JES for both “positive”
and “negative” samples. We can see that within errors the event yields do not change.
Table F.1: Number of expected yields for signals in “positive” samples after btagging.
Source

2 jets

3 jets

4 jets

All Channels

tb

53 ± 7.6

22 ± 3.7

6.4 ± 1.7

81 ± 13

tqb

70 ± 5.6

37 ± 4.4

13 ± 2.9

119 ± 13

tb+tqb

122 ± 13 59 ± 8.1

19 ± 4.6

200 ± 26

Table F.2: Number of expected yields for signals in “positive” samples after b-tagging
for b/bbar JES.
Source

2 jets

3 jets

4 jets

All Channels

tb

53 ± 0.84 22 ± 0.54 6.5 ± 0.26

81 ± 1.5

tqb

70 ± 1.2

36 ± 0.95

13 ± 0.53

120 ± 2.4

tb+tqb

123 ± 1.9

58 ± 1.4

19 ± 0.74

200 ± 3.9

To check the normalization effects, we compare a few variables before and after
203

Table F.3: Number of expected yields for signals in “negative” samples after btagging.
Source

2 jets

3 jets

4 jets

All Channels

tb

52 ± 7.6

22 ± 3.7

6.5 ± 1.6

80 ± 13

tqb

71 ± 5.5

36 ± 4.2

13 ± 2.9

120 ± 13

tb+tqb

123 ± 13 58 ± 7.9

20 ± 4.5

200 ± 25

Table F.4: Number of expected yields for signals in “negative” samples after btagging for b/bbar JES
Source

2 jets

3 jets

4 jets

All Channels

tb

52 ± 0.84 22 ± 0.54 6.4 ± 0.26

80 ± 1.5

tqb

71 ± 1.2

36 ± 0.94

13 ± 0.52

120 ± 2.4

tb+tqb

123 ± 1.9

58 ± 1.4

19 ± 0.73

200 ± 3.9

204

b/¯ JES. To obtain a numerical estimate, we integrate from the peak bin, and look
b
into the ratios of the integrals before and after this JES. This is done for tb + tqb
combined for the one tag two jet bin for positive and negative samples separately.
We looked into several variables that are sensitive to this b/¯ JES: HT for all jets,
b
Leading jet transverse momentum, Single top mass. The results are summarized in
Table F.5. The plots are show in Figure F.1 to Figure F.6.
Table F.5: Ratio of integrals for several kinematic variables before and after b/¯ JES:
b
HT for all jets, Leading jet transverse momentum, Single top mass, in the positive
and negative tbtqb samples in one tag two jet bin. The integral is from the peak
bin.
positive

negative

HTAllJets

0.987

0.993

P TJet1

0.986

0.994

Mtop

0.990

0.982

Based on these findings, we apply another 1% anti-correlated flat uncertainty on
single top and ttbar and Wbb samples, i.e. 0.01 for the top files and -0.01 for the
antitop files.

205

HT : All Jets
Entries 42545

5

Mean
RMS

4

114.6
50.3

Before b/ b JES
After b/ b JES

3
2
1
0
0

100 200 300 400 500 600 700 800
H : All Jets [GeV]

Figure F.1: HT for all jets before and after b/¯ JES for positive tbtqb samples in
b
one tag two jet bin.

206

Jet1 pT
Entries 42545

7

Mean
RMS

6

72.51
30.87

Before b/ b JES

5

After b/ b JES

4
3
2
1
0 20 40 60 80 100120140160180200220240
0
Jet1
p [GeV]
Figure F.2: Leading jet transverse momentum before and after b/¯ JES for positive
b
tbtqb samples in one tag two jet bin.

207

Top mass corresponding to minimal significance

14

Entries 42545
Mean

10

173.7

RMS

12

21.49

Before b/ b JES

8

After b/ b JES

6
4
2
0
0

50 100 150 200 250 300 350 400 450 500
Top mass

Figure F.3: Single top mass before and after b/¯ JES for positive tbtqb samples in
b
one tag two jet bin.

208

HT : All Jets
Entries 42648
Mean

4

115.1

RMS

5

52.1

Before b/ b JES
After b/ b JES

3
2
1
0
0

100 200 300 400 500 600 700 800
H : All Jets [GeV]

Figure F.4: HT for all jets before and after b/¯ JES for negative tbtqb samples in
b
one tag two jet bin.

209

8

Jet1 pT
Entries 42648

7

Mean
RMS

6

72.72
31.24

Before b/ b JES

5

After b/ b JES

4
3
2
1
0 20 40 60 80 100120140160180200220240
0
Jet1
p [GeV]
Figure F.5: Leading jet transverse momentum before and after b/¯ JES for negative
b
tbtqb samples in one tag two jet bin.

210

Top mass corresponding to minimal significance
Entries 42648

14

Mean
RMS

12
10

173.9
21.76

Before b/ b JES
After b/ b JES

8
6
4
2
0
0

50 100 150 200 250 300 350 400 450 500
Top mass

Figure F.6: Single top mass before and after b/¯ JES for negative tbtqb samples in
b
one tag two jet bin.

211

Appendix G
Production and decay asymmetries
The asymmetry in single top production can be expressed as follows:

AP =

¯
σ(p¯ → tX) − σ(p¯ → tX)
p
p
.
¯
σ(p¯ → tX) + σ(p¯ → tX)
p
p

(G.1)

¯
The asymmetry can also originate from the top decay t → bW + or t → ¯ − ,
bW
quantified by the partial rate asymmetry:

AD =

¯ bW
Γ(t → bW + ) − Γ(t → ¯ − )
¯ bW
Γ(t → bW + ) + Γ(t → ¯ − )

(G.2)

where Γ denotes the decay rate.
It is customary when measuring a cross section to assume that the top quark
decays exclusively in t → bW and ignore any possible CP violation contribution from
212

the decay process. However, in the more general case, the measured asymmetry A
is equal to

A=

¯
¯ bW
σ(p¯ → tX)B(t → bW + ) − σ(p¯ → tX)B(t → ¯ − )
p
p
.
¯
¯ bW
σ(p¯ → tX)B(t → bW + ) + σ(p¯ → tX)B(t → ¯ − )
p
p

(G.3)

where B denotes the branching ratio. Note the asymmetry defined in this way is
always smaller than one.

The decay asymmetry can be written as a function of Γ(t → bW + ) = Γt B(t →
¯
bW + ) and Γ(t → ¯ − ) = Γt B(t → ¯ − ) where Γt and Γt are the total decay
bW
bW
¯
¯ ¯
¯
width for t and t quark. Because of the conservation Γt = Γt = Γ, the measured
¯
asymmetry can be expressed in terms of the partial decay rates
¯
¯ bW
σ(p¯ → tX)Γ(t → bW + ) − σ(p¯ → tX)Γ(t → ¯ − )
p
p
A=
¯
¯ bW
σ(p¯ → tX)Γ(t → bW + ) + σ(p¯ → tX)Γ(t → ¯ − )
p
p

(G.4)

Therefore the measured asymmetry contains contributions from both production and
partial rate asymmetries. In particular, it can be shown that

A=

AP + AD
1 + AP AD

(G.5)

If one assumes that CP violation only happens in the top production or AD is
negligible [5], then we have AD ≈ 0, A = AP . On the other hand, if one assumes
213

that AD = AP , then A =
A

2AP
. In this analysis, we only measure the asymmetry
1+A2
P

214

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