MEASUREMENT OF SINGLE-TOP T -CHANNEL PRODUCTION USING ATLAS
DATA
By
Jenny Lyn Holzbauer

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

ABSTRACT
MEASUREMENT OF SINGLE-TOP T -CHANNEL PRODUCTION USING
ATLAS DATA
By
Jenny Lyn Holzbauer
This document reports the measurement of the single-top t-channel cross-section using data
from the ATLAS detector, located at the Large Hadron Collider on the border of France and
Switzerland. The data used were collected during the first half of 2011, from proton-proton
collisions with a 7 TeV center-of-mass collision energy. Single-top is electroweak top-quark
production and t-channel is one of the standard model production modes. To isolate this
production, selections are applied to find events with a similar final state. A cut-based
analysis is used to further isolate the signal using a series of selections in several orthogonal
kinematic regions. Finally, a statistical analysis is performed to determine the measured
cross-section and the CKM matrix element |Vtb |. The cross-section for top and anti-top
production is considered separately and the resulting cross-sections are σ + = 59+18 pb for
−16
t
the positive charge channel and σ − = 33+13 pb for the negative charge channel. The total
−12
t
measured single-top t-channel cross-section using all kinematic channels in this analysis is
92+29 pb with an expected cross-section of σt = 65+22 pb. The 95% confidence level limit
−26
−20
on the standard model |Vtb | value is determined to be |Vtb | > 0.67.

Copyright by
JENNY LYN HOLZBAUER
2012

To my parents, who only ever asked me to do my best, and to my husband, who has always
been encouraging, even when I am the most pessimistic.

iv

ACKNOWLEDGMENTS

This dissertation is the result of many years of work and effort, and I could not have completed it without the support of many people. First, I would like to acknowledge my advisor,
Bernard Pope, and Reinhard Schwienhorst, whom I have worked closely with over the years.
The support and encouragement has been much appreciated. Additionally, the ATLAS
single-top group and collaboration in general have been much involved, and certainly this
analysis would not be possible without the efforts of many individuals to collect, process and
understand the data used here. In particular, I would like to acknowledge my fellow t-channel
analysis colleagues, especially Philipp Sturm, Kathrin Becker, Chad Suhr, Wolfgang Wagner,
Julien Donini, Dominic Hirschbuehl, and Reinhard Schwienhorst. I will always appreciate
the help and input that has been provided over the years by my many colleagues. I would
also like to thank my fellow students as well as my family for keeping me grounded. Finally,
I would like to acknowledge my parents, who inspired me to learn physics, and my husband,
who has always encouraged and supported me in my quest to become a physicist.

v

TABLE OF CONTENTS

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

ix

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Introduction

1

2 Single-top Production and the Standard
2.1 The Standard Model Particles . . . . . .
2.1.1 Leptons . . . . . . . . . . . . . .
2.1.2 Quarks . . . . . . . . . . . . . . .
2.1.3 Force Carriers . . . . . . . . . . .
2.2 Particle Properties and |Vtb | . . . . . . .
2.3 Overview of Physics Processes . . . . . .
2.3.1 Single-top and Other Processes .
2.3.2 Cross-section . . . . . . . . . . .
2.4 New Physics Possibilities . . . . . . . . .

Model
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .

3 ATLAS and the LHC
3.1 The Large Hadron Collider . . . . . . . . . . . .
3.2 The ATLAS Detector . . . . . . . . . . . . . . .
3.2.1 Detector Variables and Geometry . . . .
3.2.2 The Inner Detector . . . . . . . . . . . .
3.2.3 The EM Calorimeter . . . . . . . . . . .
3.2.4 The Hadronic and Forward Calorimeters
3.2.5 The Muon Spectrometer . . . . . . . . .
3.2.6 Magnets . . . . . . . . . . . . . . . . . .
3.2.7 The Trigger and Data Collection . . . .
3.2.8 Data Quality . . . . . . . . . . . . . . .
4 Particle Reconstruction
4.1 Electrons . . . . . . . . . . . . . . . . . . . . .
4.2 Muons . . . . . . . . . . . . . . . . . . . . . .
4.3 Quarks and Jets . . . . . . . . . . . . . . . . .
4.3.1 b-tagging . . . . . . . . . . . . . . . . .
4.3.1.1 How b-quarks are Identified .
4.3.1.2 Impact of Different Operation
4.4 Taus . . . . . . . . . . . . . . . . . . . . . . .
vi

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.

3
4
6
7
8
8
11
12
16
18

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

21
21
25
25
28
29
30
31
33
34
35

.
.
.
.
.
.
.

37
38
40
41
43
43
46
47

. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
Points on the Analysis
. . . . . . . . . . . . .

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

4.5

Neutrinos and Missing Energy . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Monte Carlo Simulation and Corrections
5.1 MC Generator and Showering . . . . . . . . . . . . . .
5.2 Monte Carlo Weighting and Corrections . . . . . . . .
5.2.1 Theoretical cross-section and luminosity weight
5.2.2 Pile-up weight . . . . . . . . . . . . . . . . . . .
5.2.3 Lepton scale factor . . . . . . . . . . . . . . . .
5.2.4 Mis-tagging and b-tagging scale factor . . . . .
5.2.5 Energy corrections in the analysis . . . . . . . .

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

47
52
53
54
55
55
56
56
57

6 Preselection

59

7 Modeling the Signal and the Backgrounds
7.1 Multijets Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 W +jets Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63
63
65

8 Event Yields and Discriminating Variables
8.1 Event Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Discriminating Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70
70
71

9 The Cut-Based Analysis
9.1 Analysis Channels . . . . . . . . . . . . . .
9.2 Analysis Method . . . . . . . . . . . . . .
9.2.1 Selection Optimization . . . . . . .
9.2.2 b-tagging Threshold and Cut-Based
9.3 Selection Choices . . . . . . . . . . . . . .

78
78
79
79
83
85

. . . . . .
. . . . . .
. . . . . .
Selections
. . . . . .

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

10 The Measurements
10.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.1 Effect of Pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1 Cross-section Calculation . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1.1 Two and Three jet Single Top Quark t-channel Production .
10.2.1.2 Positively and Negatively Charged Single Top Quark t-channel
Production . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1.3 Combined t-channel Production Cross-section Result . . . .
10.2.2 Estimate of |Vtb | . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.3 Comment on Significance . . . . . . . . . . . . . . . . . . . . . . . . .

108
109
112
113

11 Conclusions and Implications for Future Work

116

vii

93
93
100
105
105
108

Appendices

120

¯
A Data Based Cross-check of tt Background
B Multivariate Analysis
B.1 Boosted Decision Tree Overview . . . . . .
B.1.1 Classifier Formation and Parameter
B.1.2 Cut-based Analysis Variables . . .
B.1.3 Additional Variables . . . . . . . .

120

. . . . . . . .
Optimization
. . . . . . . .
. . . . . . . .

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

127
127
130
132
138

C Alternative Analysis Channels

151

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

viii

LIST OF TABLES

2.1

(N)NLO cross-sections for single-top processes [1, 2, 3] . . . . . . . . . . . .

18

2.2

Cross-sections for various processes including branching ratios and k-factors.
Values shown for one lepton decay (ex. electron) in the case of Z+jets and
¯
W +jets processes and leptonic decays only for tt. The diboson sample is
filtered to require at least one electron or muon with pT > 10 GeV. Singletop s-channel and t-channel list different lepton decays for the W separately
to show the branching ratios used. . . . . . . . . . . . . . . . . . . . . . . . .

19

Estimate of multijets yields for the pretag and preselection samples for different number of jet selections, separated by lepton type. . . . . . . . . . . . .

65

Scale factors for the overall normalization factor used to normalize MC to
data for W +jets. The uncertainties are statistical only. . . . . . . . . . . . .

66

Correction factor WSF for each W +jets flavor for the muon and electron samples combined, with statistical (first) and systematic (second) uncertainties.

69

Event yields for the two-jets and three-jets tag positive and negative lepton charge channels after the preselection, except for the b-tagging selection.
The multijets and W +jets backgrounds are normalized to the data, all other
samples are normalized to theory cross-sections. Lepton types (muon and
electron) are combined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Event yields for the two-jets and three-jets tag positive and negative lepton
charge channels after the preselection. The multijets and W +jets backgrounds
are normalized to the data, all other samples are normalized to theory crosssections. Lepton types (muon and electron) are combined. . . . . . . . . . .

72

Event yields for the two-jets and three-jets tag positive and negative leptoncharge channels after the cut-based selection. The multijets and W +jets backgrounds are normalized to the data, all other samples are normalized to theory
cross-sections (including single-top t-channel). Uncertainties shown are systematic uncertainties. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

7.1

7.2

7.3

8.1

8.2

9.1

ix

10.1 Percent systematic uncertainties for the 2 jet plus channel. Here, XS means
cross-section, Z means Z+jets, and Dib. means diboson. Norm refers to
normalization, s indicates single-top s-channel. If two values are given, the
top value is the upshift and the bottom value is the downshift. . . . . . . . . 101

10.2 Percent systematic uncertainties by process for the 2 jet minus channel.
Here, XS means cross-section, Z means Z+jets, and Dib. means diboson.
Norm refers to normalization, s indicates single-top s-channel. If two values
are given, the top value is the upshift and the bottom value is the downshift. 102

10.3 Percent systematic uncertainties by process for the 3 jet plus channel. Here,
XS means cross-section, Z means Z+jets, and Dib. means diboson. Norm
refers to normalization, s indicates single-top s-channel. If two values are
given, the top value is the upshift and the bottom value is the downshift. . . 103

10.4 Percent systematic uncertainties by process for the 3 jet minus channel. In
this table, XS means cross-section, Z means Z+jets, and Dib. means diboson.
Norm refers to normalization, s indicates single-top s-channel. If two values
are given, the top value is the upshift and the bottom value is the downshift. 104

10.5 The fit values by process and channel. The 2 or 3 jet channels include both
lepton charges, and the lepton charge channels include both 2 and 3 jet events.
All channels is the combination of plus and minus lepton charge events with
2 and 3 jets. Dib. means diboson and Z means Z+jets. . . . . . . . . . . . . 107

10.6 Systematic uncertainties for the expected t-channel cross-section measurement, where the final line includes all systematic uncertainties and the data
statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

10.7 Systematic uncertainties for the observed t-channel cross-section measurement, where the final line includes all systematic uncertainties and the data
statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
¯
A.1 Event yield for the various tt normalization estimate channels. The multijets
and W +jets backgrounds are normalized to the data, all other samples are
normalized to theory cross-sections (including single-top t-channel). Other
refers to Z+jets, dibosons, s-channel single-top and W t single-top contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
x

B.1 Event yield for the 2 jet and 3 jet 1 b-tag positive and negative lepton-charge
channels after the selection on the BDT formed using the cut-based analysis variables. The multijets and W +jets backgrounds are normalized to the
data; all other samples are normalized to theory cross-sections. The t-channel
single-top contribution is normalized to the observed cross-section determined
using all four channels. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B.2 Systematic uncertainties for the expected t-channel cross-section measurement
for the BDT formed using cut-based analysis variables, where the final line
includes all systematic uncertainties and the statistical uncertainty of the
data. Uncertainties that were re-estimated versus the cut-based analysis (Section 10.2.1) are listed individually. Others are not listed but are included in
the totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
B.3 Event yield for the 2 jet and 3 jet 1 b-tag positive and negative lepton-charge
channels after the selection on the BDT formed using ten analysis variables.
The multijets and W +jets backgrounds are normalized to the data; all other
samples are normalized to theory cross-sections. The t-channel single-top contribution is normalized to the observed cross-section determined using all four
channels. Other top refers to the s-channel and W t single-top contributions.

145

B.4 Systematic uncertainties for the expected t-channel cross-section measurement
determined using the BDT created with ten analysis variables, where the final
line includes all systematic uncertainties and the statistical uncertainty of
the data. Uncertainties that were re-estimated versus the cut-based analysis
(Section 10.2.1) are listed individually. Others are not listed but are included
in the totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
C.1 Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and
negative lepton-charge channels after the preselection. The multijets are neglected and all other samples are normalized to theory cross-sections. . . . . 152
C.2 Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and
negative lepton-charge channels after the preselection and |η(ju )| > 2.0. The
multijets are neglected and all other samples are normalized to theory crosssections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.3 Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and
negative lepton-charge channels after the preselection, |η(ju )| > 2.0, and
m(lνb) < 190GeV. The multijets are neglected and all other samples are
normalized to theory cross-sections. . . . . . . . . . . . . . . . . . . . . . . 153
xi

C.4 Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and
negative lepton-charge channels after the preselection, |η(ju )| > 2.0, m(lνb) <
190GeV, and either m(AllJetsMinusBestJet) > 450GeV for the 4 jet channel
or m(AllJetsMinusBestJet) > 250GeV for the 3 jet channel. The multijets are
neglected and all other samples are normalized to theory cross-sections. . . 155

xii

LIST OF FIGURES

2.1

The known standard model particles. Different generations of quarks and
leptons are indicated by different shades in the bottom two rows. The top
row of particles have different shades indicating the forces they are associated
with. 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

2.2

The standard model leptons (left) and quarks (right), by mass. . . . . . . . .

9

2.3

Feynman diagrams for single-top production. The diagrams in the top row are
for the signal, t-channel single-top production. In the second row, diagrams on
the left are W t production and the diagram on the right is s-channel single-top
production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

¯
Feynman diagrams for backgrounds to single-top production. The tt is the
diagram on the top left, W +jets is the top central diagram and multijet
production is the top right diagram. The final two diagrams are the smallest
backgrounds, Z+jets on the bottom left and diboson on the bottom right. .

15

Average number of interactions per crossing for the 2011 ATLAS data set for
different values of β ∗ used by the LHC. The β ∗ = 1.5 m data set was used
for the analysis in this document [4]. ATLAS Experiment c 2011 CERN. . .

24

2.4

3.1

3.2

Cut away view of the ATLAS detector [5], ATLAS Experiment c 2008 CERN. 26

3.3

Graphic showing absolute values of η for various values of θ. . . . . . . . . .

27

4.1

Event display for a b-jet, with the secondary vertex shown in the dashed box
and primary vertex shown as a round ball [6], ATLAS Experiment c 2011
CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Distribution of the 2 jet yields for the signal (t-channel) and its backgrounds,
given a selection on the JetFitterCombNN b-tagging variable at the given xaxis value (1 b-tag). Selections at higher x-axis values have lower b-tagging
efficiencies but higher mis-tagging efficiencies. The black vertical line shows
the threshold used in the analysis. . . . . . . . . . . . . . . . . . . . . . . . .

48

4.2

xiii

4.3

6.1

8.1

8.2

8.3

8.4

9.1

Distribution of the 3 jet yields for the signal (t-channel) and its backgrounds,
given a selection on the JetFitterCombNN b-tagging variable at the given xaxis value (1 b-tag). Selections at higher x-axis values have lower b-tagging
efficiencies but higher mis-tagging efficiencies. The black vertical line shows
the threshold used in the analysis. . . . . . . . . . . . . . . . . . . . . . . . .

49

Feynman diagram for t-channel single-top production, showing the final state
after the top quark decay. The other t-channel diagram is the same as this
one, except without the gluon in the initial state and thus without the ¯
b-quark
in the final state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

Discriminating variables for the pretag sample (no b-tagging) for 2 jet
events. Hatched bands show the jet energy scale uncertainty. The last bin
contains the sum of the events in that bin or higher. Other top refers to
the s-channel and W t single-top contributions. Pred. refers to the predicted
signal plus background model. . . . . . . . . . . . . . . . . . . . . . . . . . .

74

Discriminating variables for the pretag sample (no b-tagging) for 3 jet
events. Hatched bands show the jet energy scale uncertainty. The last bin
contains the sum of the events in that bin or higher. Other top refers to
the s-channel and W t single-top contributions. Pred. refers to the predicted
signal plus background model. . . . . . . . . . . . . . . . . . . . . . . . . . .

75

Discriminating variables for the preselection sample (with b-tagging) for 2
jet events. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions. . . . . . .

76

Discriminating variables for the preselection sample (with b-tagging) for 3
jet events. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions. . . . . . .

77

Distribution of the significance (y-axis) for the reconstructed top mass, for
the 2 jet channel after preselection. The vertical lines show the optimal cut
thresholds for the two selections shown (less than and greater than some
reconstructed top mass value) and the arrows indicate the region that is kept
after the selection is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

xiv

9.2

9.3

9.4

Distribution of the significance (x-axis) for various variables (each y-axis entry
is a separate variable), given a JetFitterCombNN b-tagging operating point,
denoted by different marker shapes. The plots are all for the 3 jets, positively
charged lepton channel. The top left plot is preselection only, the top right is
preselection plus a requirement that the reconstructed top mass be less than
210 GeV, and the bottom plot is preselection plus a requirement that the |η|
of the highest pT untagged jet be greater than 2.0. The 2.4 operating point
is used in the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Discriminating variables for the preselection sample (with b-tagging) for 2
jet events normalized to unit area. The last bin contains the sum of the events
in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

Discriminating variables for the preselection sample (with b-tagging) for 3
jet events normalized to unit area. The last bin contains the sum of the events
in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

9.5

Distribution of the lepton charge after the full cut-based selection for 2 jets and
3 jets. These are the four primary analysis channels. The t-channel single-top
contribution is normalized to the observed cross-section determined using all
four channels. Other top refers to the s-channel and W t single-top contributions. 89

9.6

Discriminating variables for 2 jet events after applying all cut based cuts
except for the cut on the variable shown. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels.
Other top refers to the s-channel and W t single-top contributions. The last
bin contains the sum of the events in that bin or higher. . . . . . . . . . . .

90

Discriminating variables for 3 jet events after applying all cut based cuts
except for the cut on the variable shown. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels.
Other top refers to the s-channel and W t single-top contributions. The last
bin contains the sum of the events in that bin or higher. . . . . . . . . . . .

91

9.7

10.1 Pseudo-experiment distribution used for the final cross-section uncertainty
determination. This distribution is for the observed cross-section uncertainty,
for all channels combined. The β value is the fit for a given pseudo-experiment
with yields scaled by the values in Table 10.5, and the uncertainty is determined from the distribution RMS and deviation of the mean from 1. . . . . . 108
xv

10.2 Distribution used to determine the expected significance for the 3 jet channel
(all lepton charges are allowed) and negative charge channel (2 and 3 jets
allowed). The two curves are ensembles with and without the assumption of
a standard model signal. The vertical line shows the mean of the standard
model signal and background distribution. . . . . . . . . . . . . . . . . . . . 115
¯
A.1 Scale factors for tt production using six separate channels, the combination of
electron channels, the combination of muon channels, and the combination of
all six channels. Statistical uncertainties are given by colored portions of the
black lines unless the statistical uncertainties are so small as to be covered by
the marker itself. The black line shows the data statistical, b-tagging scale
factor, mis-tagging scale factor, and jet energy scale uncertainties combined.
Other uncertainties are neglected in this cross-check. . . . . . . . . . . . . . 126
B.1 A pictorial representation of a single decision tree, where A and C are variables
values, X and Y are selection thresholds. The node is designated as S for signal
and B for background. The S and B circles are the final nodes, or leaves, in
the tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
B.2 BDT classifier distributions for the 2 jet (top) and 3 jet (bottom) selections,
formed using cut-based analysis variables. The left column is before the selection on the BDT classifier in a log scale, and the right column is after. The
t-channel single-top contribution is normalized to the observed cross-section
determined using all four channels. Other top refers to the s-channel and W t
single-top contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B.3 Discriminating variables for the 2 jet selection after a selection on the BDT
classifier formed using cut-based analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels.
Other top refers to the s-channel and W t single-top contributions. . . . . . . 136
B.4 Discriminating variables for the 3 jet selection after a selection on the BDT
classifier formed using cut-based analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels.
Other top refers to the s-channel and W t single-top contributions. . . . . . . 137
B.5 Discriminating variables for the 2 jet selection before any BDT classifier selection. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions. . . . . . . 140
xvi

B.6 Discriminating variables for the 3 jet selection before any BDT classifier selection. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions. . . . . . . 141
B.7 Discriminating variables for the 2 jet selection before any BDT classifier selection normalized to unit area. The last bin contains the sum of the events
in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
B.8 Discriminating variables for the 3 jet selection before any BDT classifier selection normalized to unit area. The last bin contains the sum of the events
in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.9 BDT classifier distributions for the 2 jet selection on the top line and the 3 jet
selection on the next line, for the BDT formed using ten analysis variables.
The left figures are before the selection on the BDT classifier, the right figures
are after. Note that the BDT distributions before selections are in a log scale.
The t-channel single-top contribution is normalized to the observed crosssection determined using all four channels. Other top refers to the s-channel
and W t single-top contributions. . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.10 Discriminating variables for the 2 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last
bin contains the sum of the events in that bin or higher. The t-channel
single-top contribution is normalized to the observed cross-section determined
using all four channels. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.11 Discriminating variables for the 2 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last
bin contains the sum of the events in that bin or higher. The t-channel
single-top contribution is normalized to the observed cross-section determined
using all four channels. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
B.12 Discriminating variables for the 3 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last
bin contains the sum of the events in that bin or higher. The t-channel
single-top contribution is normalized to the observed cross-section determined
using all four channels. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
xvii

B.13 Discriminating variables for the 3 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last
bin contains the sum of the events in that bin or higher. The t-channel
single-top contribution is normalized to the observed cross-section determined
using all four channels. Other top refers to the s-channel and W t single-top
contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

xviii

Chapter 1
Introduction
A rock smashes against another rock and shatters into pieces. Some are shiny, some are
differently colored. However, if you were to take one of these rock pieces and zoom in, divide
it into pieces until you can’t divide further, you would see that it is composed of the same
bits of matter as any other rock. In such ways, people have searched for the fundamental
building blocks of matter, the elementary particles.
In the modern era, we have found these blocks are very small indeed and require a lot
of human ingenuity to study. It has taken the work of many men and women over the
years to reach the point where we can do the experiments we now perform. We have found
that colliding very small bits of matter (protons) composed of smaller particles (quarks and
gluons) at very high speeds causes the creation of a flurry of new, fundamental particles.
These particles may have unintuitive properties, such as masses larger than the particles
which originally collided (made possible by the large amount of energy used to collide them).
In this dissertation we will study one such fundamental particle.
Thousands of scientists are now working at the Large Hadron Collider (LHC) on four
1

experiments located at different points around the collider ring. Two are general purpose
machines, ATLAS and CMS. These machines are designed to try to find not only particles and
processes we know exist but also new ones. The LHC smashes bits of atoms that are already
quite small (protons) together at incredibly high speeds, producing new particles which
decay or smash into others and eventually some particles hit the detectors. Scientists use
large computing clusters to take this information and attempt to reconstruct what happened
when the original bits of protons collided, and to sort out the collisions with particles and
processes they don’t want from the ones they do.
Clearly this is challenging, cutting-edge work only possible in the modern era. But the
questions we look to answer are fundamental. What is the world really made of at the
smallest level? What are the properties of the smallest particles? How do they interact with
other particles at this scale and what do those interactions produce?
In this dissertation, we will discuss specifically the search for the t-channel single-top
quark production. The top quark is the most massive fundamental particle yet observed
and the t-channel production mode refers to a particular way it is created. We will overview
the particles known to exist and the current theory related to these. Then we will examine
the collider and detector used in this study (the ATLAS detector). Finally we will discuss
the procedure to isolate this process from so many others, as well as the measurement and
kinematics of this process.

2

Chapter 2
Single-top Production and the
Standard Model
High energy physics deals with the very fundamental parts of our universe, the fundamental particles and forces. Our present understanding is that there are four forces: gravity,
electromagnetism, strong and weak. As energies increase, it is predicted that these forces
can be united into one force, starting with the electromagnetic and weak forces, which form
the electroweak force. Each force has a mediating particle, a force carrier, which governs
interactions of various particles. These particles are discussed in the next section.
Single-top production is the process where a top quark is created in an electroweak
interaction. As stated previously, the top quark is the most massive of the elementary
particles. Only one top quark is produced in an electroweak interaction. There is another
¯
version of top quark production using the strong force and involving a top and anti-top (tt).
This was the process detected in 1995 to claim discovery [7, 8], meaning a likelihood of less
than 0.0000006 of background events imitating the signal. Single-top itself was only recently
3

discovered [9, 10, 11] and the particular channel (t-channel) discussed in this document was
separately observed in 2011 [12] by the D0 collaboration at the Tevatron. Shortly afterwards,
measurements of t-channel single-top production were reported by the CMS experiment [13]
and the ATLAS experiment [14, 15] at the LHC (see the next chapter for more details
on the LHC and ATLAS). Direct limits on the CKM matrix element |Vtb | have also been
set [16, 17, 13] via studies of single-top production and indirect limits, which are more precise,
¯
have been set using studies of tt production [18, 19, 20]. |Vtb | has also been estimated most
precisely from knowledge of the other various matrix elements, via a global fit [18].
This single-top t-channel process investigation is still just starting, so this process has
not been fully studied yet. It is possible that deviations from expectation could be found in
its various fundamental properties, which could indicate new particles or anomalous parts
of the standard model. In this document, we will measure the cross-section of this process
and consider its kinematics. But first, before performing a new measurement, we must
understand what is already known.

2.1

The Standard Model Particles

The standard model is the basic theory of particle physics [21, 18, 22, 23] and was formulated
in the 1960’s and 1970’s. It describes and predicts various particles and their properties based
on symmetry relations. The model divides the fundamental particles into several categories
and subcategories, pictured in Figure 2.1. There are three major particle categories: leptons,
quarks and bosons (force carriers). There are also three generations of the quarks and leptons,
where each generation is designated by a different shade in the figure. In this figure and
elsewhere in this document (unless noted) we use the so-called natural units where c = ℏ = 1.
4

Particles

γ W Z g
Photon W Boson Z Boson

Gluon

uc t e µ τ
s b νe νµ ντ
d

Up
Quark

Charm
Quark

Down
Quark

Strange Bottom
Quark
Quark

Top
Quark

Electron

Muon

Tau

Electron Muon
Tau
Neutrino Neutrino Neutrino

Figure 2.1: The known standard model particles. Different generations of quarks and leptons
are indicated by different shades in the bottom two rows. The top row of particles have
different shades indicating the forces they are associated with. 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

2.1.1

Leptons

One category of particles are the leptons. Leptons typically include electrons (e), muons
(µ), taus (τ ), and their corresponding neutrinos. However, we will use this term in this
document to generally refer to electrons, muons and/or taus, while neutrinos are considered
as a separate set of particles. The leptons do not interact via the strong force and so are
not involved in hadronic bound states like the proton. The electron is a stable lepton and
is involved in the structure of the atom. Muons and taus are heavier than the electron and
decay to other particles. This is particularly true for the tau. Unlike the tau, the muon
survives long enough to escape our detector which is important for particle identification,
but has a short decay time relative to the electron. For each lepton there is a corresponding
anti-lepton with opposite charge.
There is also a corresponding neutrino flavor for each lepton flavor, or type (electron
neutrino, muon neutrino, and tau neutrino). Each lepton and its corresponding neutrino
form a set of particles where each lepton type is considered a separate generation (there are
three generations). Neutrinos are the lightest of the known particles and have no charge. In
the standard model there are no known right handed neutrinos or left handed anti-neutrinos,
where right handed indicates spin and momenta are in the same direction and left handed
indicates the opposite. This difference, rather than a difference in charge, distinguishes the
neutrino and anti-neutrino.
Because neutrinos only interact via the weak force, they are very difficult to detect.
Neutrinos usually pass right through detectors without interacting. This makes neutrino
astrophysics possible, because neutrinos from distant sources will travel from the source
without interacting and scattering off clouds of matter between the source and the Earth.
6

However, this is problematic for collider physics. Particles from collisions need to interact
with matter and deposit their energy into the detector to be detected. While this may not
always happen, it should happen nearly 100% of the time to prevent uncertainties on the
measurements from getting large. To handle neutrinos, we don’t build a dedicated neutrino
detector but instead make use of event kinematics to account for the neutrino via missing
energy in the event. This will be discussed further in Section 4.5.

2.1.2

Quarks

Quarks are arranged like the leptons into generations, as seen in Figure 2.1. They are different
from the leptons because they can interact via the strong force and form bound states, like
the proton. There are three generations and each contains two particles, making six different
flavors in total (u, d, s, c, t, b). The first generation contains lighter quarks, up (u) and
down (d), the only quarks known to form stable bound states (like the proton). The second
generation contains strange (s) and charm (c) quarks, and the third contains the heaviest
quarks, bottom (b) and top (t), which are sometimes also called beauty and truth. The first
three (u, d, s) are typically called light quarks. The charm quark is sometimes included
in this category as well, but for the purposes of this document will either be considered
separately or considered to be a heavy quark along with the bottom quark. The top quark
is by far the heaviest and that is a distinguishing characteristic of this quark. It is also
special because it will decay to other particles before it hadronizes (unlike the other quarks)
preserving “bare quark” information in its decay products. This is because its decay time is
0.5 × 10−24 s [18], which is shorter than the hadronization time scale. This scale, Λ−1 ,
QCD
corresponds roughly to 10−23 s [24]. Other quarks survive longer than this timescale and will
7

hadronize instead of decay, which means they produce a bound state of mesons or baryons.
Mesons are combinations of quarks and anti-quarks, while baryons are combinations of three
quarks.

2.1.3

Force Carriers

The other major particle category contains the force carriers, or gauge bosons. One of these is
the gluon (g), particularly involved in strong interactions and can also self-interact. Photons
(γ) are the force carriers of the electromagnetic interaction, but are not usually involved
in the single-top interactions. The other mediators are bosons associated with electroweak
interactions, the Z and W . Both are relatively heavy (80 to 90 GeV) compared to the other
particles at this scale, and are about half as heavy as the top quark. Additionally, it has been
postulated that there is a Higgs boson and a Higgs field which gives mass to the particles in
the standard model. However, at the time of publication this has not been observed, so we
will not go into detail about it here.

2.2

Particle Properties and |Vtb|

The standard model particles have very different characteristics, including a variety of charges
and masses. Anti-particles are designated with a bar over the top of their symbol and have
the negative of the normal particle’s charge. A particle’s charge is given as a fraction of the
elementary charge, e = 1.6 × 10−19 Coulomb. The down, strange and bottom quark all
have -1/3 charge (bottom row of quarks in Figure 2.1) while the up, charm and top quarks
have +2/3 charge (top row of quarks in Figure 2.1). The electrons, muons, and taus have -1
charge while the neutrinos, gluon, photon, and Z boson have 0 charge. The W boson has ±1
8

charge. Additionally, particles also have a flavor, as discussed previously, and quarks have
a color charge. The color charge is much like the electric charge but related to the strong
interaction (hence its relation to quarks). The allowed meson and baryon bound states are
color singlets.
The particle masses vary over several orders of magnitude. The range of quark and
lepton masses (neutrinos are not pictured), are displayed in Figure 2.2. Notice that there
are three quarks with masses of 1 GeV or larger, the c, b, and t quarks. The top quark is
of particular interest in this document and we use the value 172.5 GeV, which is consistent

Mass [MeV]

Mass [MeV]

with the current Particle Data Group value [18].

105
104
103

105
104
103

102

102

10

10

1

1

e

µ

τ

u

Lepton

d

s

c

b

t
Quark

Figure 2.2: The standard model leptons (left) and quarks (right), by mass.

The gluon and W boson have the special properties that they can effectively change the
color and flavor of a quark, respectively, while the neutral Z boson forms a vertex with a
particle and its anti-particle. The Z-boson may decay to an electron and positron (or any
other pair of leptons, neutrinos, or quarks) but not to an electron and up quark, for instance.
A gluon may form a vertex with top and anti-top but not two tops. The t-channel single-top
9

process involves the W boson and thus flavor exchange. For example, a vertex involving a
W + may include a top and anti-bottom quark, but not two top quarks. The probability
that a W vertex could involve a top and a down or strange quark is nearly zero according to
the standard model, while the probability of top and bottom is nearly one. This is displayed
in the Cabibbo-Kobayashi-Maskawa (CKM) matrix [25, 26], which is close to a unit matrix
except for the light quark Vus and Vcd terms, which are off-diagonal elements with values
of about 0.2.
The CKM matrix describes how likely it is for a quark to change to a quark of another
flavor. Specifically, the probability is the relevant matrix entry squared multiplied by the
density of states. These are traditionally called Vqq ′ , where q is a quark and q ′ is a quark
with another flavor. More information about the values may be found in the PDG [18]. The
matrix element we will be particularly interested in, Vtb , may be indirectly measured with
¯
tt production, but directly observed with single-top production. The standard model value
is 1.
The single-top cross-section, related to the number of single-top events produced in the
collider, is derived from the square of the amplitude, M . The amplitude varies as follows in
the standard model, where γ terms are constant matrices, PL is 1/2(1 − γ 5 ), and ¯ and t
b
are field terms for the anti-bottom quark and top quark respectively:

M ∝ ¯ µ Vtb PL t
bγ

(2.1)

Thus, the cross-section is proportional to |Vtb |2 in the standard model. If we allow anomalous
couplings in this term above some new physics scale, the term Vtb may be rewritten as VL ,
where VL is just Vtb plus a factor that depends on the new physics scale [27].
10

The Lagrangian, allowing anomalous coupling terms, may be written as follows [27, 28].
Here PR is 1/2(1 + γ 5 ), MW is the W boson mass, the γ and σ terms are constant (Dirac
or Pauli) matrices, g is a coupling constant, qν is the W boson momentum four-vector, and
−
Wµ is the field term for the W boson:
g
g iσ µν qν
−
−
√ ¯ µ (VL PL + VR PR )tWµ − √ ¯
(gL PL + gR PR )tWµ + ...
LW tb =
bγ
b
2
2 MW

(2.2)

We will assume the anomalous couplings VR , gL and gR are 0 in this document and will
measure the value |VL | to see if it deviates from the standard model expectation. We will
also assume that there are no non-negligible contributions from Vts or Vtd when doing this
measurement.
Because the amplitude squared is proportional to the cross-section, by using both expected and observed cross-section and |VL | values, one may write:
σt,obs
|VL,obs |2 =
|V
|2
σt,sm L,sm

(2.3)

where σ is the cross-section, obs refers to the observed value and sm refers to the standard
model. In this way, one may directly find the |VL | value from a single-top observation. The
standard model expectation for VL,sm = Vtb is 1, so a value greater than 1 for |VL | would
indicate non-standard model couplings.

2.3

Overview of Physics Processes

Unfortunately, the LHC collisions do not just produce single-top events, nor are single-top
events extremely distinct or more common than the many other processes that are produced.
11

In this section we overview the single-top processes, other physics processes, and some of the
characteristics that will be considered in order to distinguish them.

2.3.1

Single-top and Other Processes

Feynman diagrams are a common way to visualize particle physics interactions and also
the equations that describe them. In these diagrams, time flows from left to right. The
leftmost particles are the initial particles (initial state) and the rightmost particles are the
final particles (final state). Figure 2.3 shows the Feynman diagrams for single-top processes.
There are three different production modes: t-channel, W t, and s-channel. W t is also
known as associated production and W t-channel. The t-channel production is a scattering
interaction while the s-channel production is an annihilation interaction. In this dissertation,
the signal channel is the t-channel mode and the other two are considered to be backgrounds.
Notice in each case there is exactly one top quark, the characteristic of single-top production. The top quark comes from an interaction mediated by a W boson except in the case
of W t production, where it is produced along with a W boson. The t-channel in particular
has two quarks in the initial state, a b-quark (or a gluon producing a b-quark, as is shown)
and generic q-quark. This q-quark is usually a valence quark, while the b-quark may come
from the sea of quarks in the proton or from a gluon. The final state involves the lone top
quark and another generic quark in the opposite flavor of the initial q-quark, which is often
energetic and forward (close to the beam line). It is also possible to have an extra jet in the
final state from a gluon in the initial state. Incidentally, in the previous section we noticed
the mass of the W boson is smaller than the top quark, but it is still possible for a W to
produce a top quark if it is a virtual W , in the s-channel diagram for example.
12

Although it is not shown in these diagrams, the top quark decays to a W and b-quark.
The W further decays to either a lepton and neutrino or two quarks. For this analysis, we
will focus on the lepton decay case.

q

q’

q

q’

W

W
b

t

b
b

g

b

q

W

t
t

b
g

W

t

g

t
t

b

W

q

b

Figure 2.3: Feynman diagrams for single-top production. The diagrams in the top row are
for the signal, t-channel single-top production. In the second row, diagrams on the left are
W t production and the diagram on the right is s-channel single-top production.
Figure 2.4 shows the diagrams for the other backgrounds for our single-top t-channel
¯
signal. These include multijets (also called QCD), W +jets, Z+jets, tt, and diboson (includes
W W , W Z, and ZZ), where jets are streams of particle decays and interactions stemming
¯
from the decay of quarks that have hadronized. Of these, only tt contains top quarks and
it contains two of them, rather than the one top quark that single-top t-channel contains.
13

Nevertheless, it is difficult to distinguish single-top t-channel from its backgrounds. This
is partly because the final states can appear to be quite similar, especially given that the
detector is not perfect at particle identification, and partly because of the smaller number
of expected signal events relative to background events.
Although the diagrams in Figures 2.3 and 2.4 are basic, straight-forward diagrams, it is
possible to have more complex diagrams with extra gluons in the initial or final state, or loops
of particle production (such as a gluon making two gluons which in turn recombine into one
gluon). These extra possibilities can be described in separate diagrams, and it is possible to
have diagrams from two different processes which have the same final state. In this case, the
diagrams are said to interfere and it is important to consider such things when generating
Monte Carlo (MC). For the signals and backgrounds considered in this analysis, there are two
¯
cases of interference in particular. The first is single-top W t production and tt production.
¯
W t is already very similar to tt except for a b-quark (a top quark decays to a W and a bquark). If a gluon in the W t initial state produces the incoming b-quark, it will also produce
¯
an outgoing ¯ making the final state look like tt. This does not have a large contribution
b,
to the analysis however, as this ¯
b-quark is generally low in pT (momentum transverse to the
beam direction, see Section 3.2.1). The pT requirement for jets (see Section 4.3) generally
removes this from consideration. However, the interference is accounted for when MC is
generated.
Another possibility involves the t-channel single-top signal. If the incoming quark is from
a gluon instead of a valence quark, the gluon produces the incoming quark plus an extra
quark for the final state. The new final state contains two light quarks, t, and a possible
b. This is the same final state discussed in the last paragraph, if the W decays to two light
14

g

t

q

q
g

q

g

g

t

q’

g

u

q

W
q
g

q

g

g

u

q’

Z

q

W

q’

Z

¯
Figure 2.4: Feynman diagrams for backgrounds to single-top production. The tt is the
diagram on the top left, W +jets is the top central diagram and multijet production is the
top right diagram. The final two diagrams are the smallest backgrounds, Z+jets on the
bottom left and diboson on the bottom right.
15

quarks instead of a lepton and neutrino in the case of W t, and for one of the top quarks in
¯
the case of tt. However, the extra particles from the gluons often having low pT (thus not
satisfying the jet definition), so this scenario does not impact the analysis.

2.3.2

Cross-section

The cross-section for a process reflects how often we expect a collision to produce that
particular process. It is often useful to think of it in terms of the number of events produced:

N = σL

(2.4)

where N is the number of events, σ is the process cross-section and L is the integrated
luminosity (explained in Section 3.1), which represents the number of collisions.
The cross-section may include additional factors like k-factors or branching ratios. The
k-factors are corrective fractions which change a cross-section from a leading order to next-toleading order value, for example. A leading order (LO) cross-section is a theory calculation
involving just basic diagrams without loops or extra vertices. Next-to-leading order (NLO)
includes an additional level of complexity of loops and vertices, making it a longer, more
difficult calculation. With each step up in completeness, the calculation becomes more
technically difficult, so we do not have exact theoretical cross-sections for our processes.
Branching ratios (BR) are fractions to change the total cross-section for a complete
process to a partial cross-section. For instance, in the t-channel diagram, the final state
involves a top quark, which decays to a b-quark and a W . This W may decay either to two
more quarks, like up and down quarks, or to a lepton and neutrino. For reasons discussed in
Section 6, we require exactly one lepton in our selection and only generate Monte Carlo for
16

final states including a lepton. Thus, the cross-section that we actually normalize the MC
to is the fraction of the total cross-section that involves a single lepton in the final state.
The probability for the W to decay to a lepton and neutrino is a branching ratio that is
multiplied with the cross-section.
The cross-sections used in this analysis for the signals and backgrounds are listed in
Table 2.2 for 7 TeV collisions, including k-factors (if applicable) and branching ratios. They
are given in the standard units of picobarns (pb), where a barn is 10−28 m2 . The W +jets is
separated here by flavor in some cases. A special procedure is applied to separate the W +jets
into light and heavy flavors later in the analysis based on the truth-level hadron type, in a
way that avoids double-counting events. Truth level refers to Monte Carlo information about
the particle generated before applying detector effects (see Chapter 4). The division is into
light (u, d, s), c, and heavy (c¯ and b¯ for the jets (the processes may also have additional
c
b)
light jets). The k-factors used here are 1.20 for W +jets in general (except W +cjets, which
¯
uses 1.52), 1.25 for Z+jets and 1.12 for tt.
Measuring t-channel single-top production is the focus of this analysis but we would
like to compare the measurement with an expected cross-section value. For this we use the
cross-sections given in Table 2.1 [1, 2, 3], and the branching ratios from the PDG, with
values of 10.75% for W → eνe , 10.57% for W → µνµ , and 11.25% for W → τ ντ [18]. The
cross-sections contain both top and anti-top contributions, and we expect these particle and
anti-particle contributions to be different for processes that have valence quarks in the initial
state. The LHC collides two protons, each of which contains two up and one down quarks,
leading to an excess of positively charged quarks. For the t-channel, which usually has a
valence quark in the initial state, the standard model cross-section is 41.9 pb due to events
17

¯
containing t quarks and 22.7 pb from events containing t quarks.
Process
t-channel
Wt
s-channel

Cross-section [pb]
64.57 + 2.71 - 2.01
15.74 + 1.06 - 1.08
4.63 + 0.19 - 0.17

Table 2.1: (N)NLO cross-sections for single-top processes [1, 2, 3]

It is also interesting to note that the signal cross-section and background cross-sections
are different by many orders of magnitude, as seen in Table 2.2. This means that many, many
events have to be identified correctly and rejected in order to try to pick out our needle in
this immense haystack.
Most of these cross-sections listed are fairly well known, partly because they are so
much larger (relatively), and large statistics samples have been available for some time at
long running experiments (like the Tevatron experiments) with relatively low systematic
uncertainties. However, lower cross-section processes such as our signal have only recently
been observed and the cross-sections are not necessarily well measured. The goal of this
analysis is to provide a cross-section measurement of the t-channel process and to see if it
agrees with the standard model prediction.

2.4

New Physics Possibilities

In recent years, there have been several indications that the standard model does not explain everything. Although the standard model has been very successful, observations in
astronomy have indicated the presence of dark matter [29] and dark energy [30] which are
not predicted by the standard model, and in proportions larger than the matter we know
18

Process
t-channel → eνe
t-channel → µνµ
t-channel → τ ντ
¯
tt (non-hadronic)
Wt
s-channel → eνe
s-channel → µνµ
s-channel → τ ντ
Z + 0 jet
Z + 1 jets
Z + 2 jets
Z + 3 jets
Z + 4 jets
Z + 5 jets
W + 0 jet
W + 1 jets
W + 2 jets
W + 3 jets
W + 4 jets
W + 5 jets
W + b¯ + 0 jet
b
W + b¯ + 1 jets
b
W + b¯ + 2 jets
b
¯ + 3 jets
W + bb
W + c¯ + 0 jet
c
W + c¯ + 1 jets
c
W + c¯ + 2 jets
c
W + c¯ + 3 jets
c
W + c + 0 jet
W + c + 1 jets
W + c + 2 jets
W + c + 3 jets
W + c + 4 jets
WW
WZ
ZZ

Cross-section [pb]
6.9
6.8
7.3
90
16
0.50
0.49
0.52
835
168
51
14
4
1
8,300
1,600
460
120
31
8
57
43
21
8
153
126
62
20
980
312
77
17
4
17
6
1

Table 2.2: Cross-sections for various processes including branching ratios and k-factors.
Values shown for one lepton decay (ex. electron) in the case of Z+jets and W +jets processes
¯
and leptonic decays only for tt. The diboson sample is filtered to require at least one electron
or muon with pT > 10 GeV. Single-top s-channel and t-channel list different lepton decays
for the W separately to show the branching ratios used.
19

of (standard model particles) [31]. Additionally, the very small neutrino masses are not
explained in the standard model [32]. Several theories have been suggested to account for
these observations, but none of the proposed new particles have been shown to exist. It
is importation to check the standard model with detailed experimental measurements, to
confirm the standard model and perhaps gain information about new physics if deviations
are discovered.
Single-top t-channel production, a standard model process, is interesting because it is
still new and not fully examined. Although it has been found to exist, we are only now accumulating enough events to do precision measurements of the cross-section and kinematics. If
the cross-section or t-channel kinematics are not consistent with the standard model, it may
indicate new physics. It is possible that there could be a flavor changing (like the W ) neutral
current (neutral like the Z) in the process for instance, that would change the W tb vertex.
It is also possible there could be a fourth generation of quarks, which would again cause the
CKM matrix Vtb value to deviate the standard model value. Detailed measurements of the
single-top production could provide direct evidence of these phenomena.
In this document, we take the first step, which is to measure the t-channel single-top crosssection and compare it to the standard model value. We do this by applying a small number
of kinematic requirements to the events, to provide a straight-forward measurement. This
is the first cut-based analysis with this level of precision on the single-top t-channel crosssection. It is also possible to use more sophisticated statistical methods to do a measurement
of this signal, and the usefulness of this approach is explored in Appendix B.

20

Chapter 3
ATLAS and the LHC
In order to study the single-top t-channel cross-section, we must first collect information
from these rare events. The top quark is very massive and requires a large amount of energy
to produce events containing it. To do this, we generate high energy particles in beams and
collide them together in an underground ring. Here, we can collect most of the information
about the particle tracks and energies and also produce a large number of these collisions.
This last point is crucial for low cross-section processes like the signal in this analysis.

3.1

The Large Hadron Collider

The Large Hadron Collider [33], or LHC, is the particle collider in question, a proton-proton
collider located on the border of Switzerland and France, near Geneva, Switzerland. It is
26.7 km in circumference, or 5.3 miles in diameter, and the beams collide with a center-ofmass energy of 7 TeV during normal data taking. This is half of the design center-of-mass
energy (14 TeV) and is what is used for the data in this analysis. The first 7 TeV collisions
occurred in March of 2010, and this document considers data taken in the first half of 2011.
21

The LHC is the main ring, which reuses the former LEP tunnel, and there are several
other rings that boost the beam up to its injection energy of 450 GeV. First, though there
is the proton source, where hydrogen gas is separated into protons and electrons. It is also
possible to collide lead in the LHC and in this case a different source is used, but for our
purposes we will focus on the standard proton-proton collisions. The protons are formed into
bunches and trains of bunches, and pass through the first part of the accelerator complex, a
linear accelerator called the LINAC2. After this the protons go through circular accelerators
to boost the beam energy, the Proton Synchrotron Booster (PSB), Proton Synchrotron (PS),
and Super Proton Synchrotron (SPS) systems, before being injected into the LHC.
Within one bunch there are about 100 billion protons, not all of which actually collide
or collide to produce interesting events. Each bunch is spaced apart by 50 ns and the
number of bunches in the ring has been increasing steadily as data taking has progressed,
up to about 1000. The bunching of the protons incidentally allows some space for one
collision’s particles to decay or leave the detector before the next set of particles collide.
The reason these bunches are put so close together and contain so many particles is related
to getting enough data to find the single-top t-channel production we are looking for. The
instantaneous luminosity [34], which reflects how many events are produced, is determined
by various accelerator settings:

L =

fr n1 n2 nb γr F (θ, σ)
4πǫn β ∗

(3.1)

Here fr is the frequency the protons go around the main LHC ring (approximately the
speed of light, c, divided by 27 km), n1 and n2 are the number of protons per bunch, nb is
the number of bunches in each beam, ǫn is the normalized emittance (related to the deviation
22

of particles from the ideal beam and thus also beam lifetime), and β ∗ is related to the beam
focus at the interaction point. The combination ǫn β ∗ is the overall beam cross-section at the
collision point. Here, the β ∗ is 1.5 m and the emittances are on the order of µm, 4 × 10−6
m [35]. The γr is the relativistic γ, which is just the beam energy (3.5 TeV per beam) divided
by the proton mass (about 1 GeV/c2 ), about 3.5 × 103 . Finally, the F (θ, σ) is a geometrical
luminosity reduction factor related to the crossing angle and the density distribution of
protons in a bunch, and is about 0.84 [36]. The peak instantaneous luminosity varies day by
day (it will fall off as a data collection run goes on), but is approximately 1 × 1033 cm−2 s−1
for the time period in question. Following the equation, and putting in approximate values,
we can get a similar number:

L =

104 s−1 · 1011 · 1011 · 103 · 3.5 × 103 · 0.84
= 4 × 1032 cm−2 s−1
−4 cm · 1.5 × 102 cm
4π · 4 × 10

(3.2)

With such tight beam focus and so many protons, it is possible to have more than one
collision per bunch crossing. On average, for the data we consider here, there are about six
interactions per crossing. The impact of the change in β ∗ for the data used for this analysis
and the following data can be seen in Figure 3.1. The decrease in β ∗ approximately doubled
the number of events per crossing in later data sets. The lower number of interactions
per crossing is an advantage of the data set used in this document. Most of these extra
interactions are not interesting, but it is possible that the events could mix in a way that
confuses the event identification. Studies are done to check that the analysis is not biased
by these “pile-up” effects.
What is typically quoted is not the instantaneous luminosity but the integrated luminosity
(luminosity for a given period of time). This is usually expressed in units like pb−1 (a barn is
23

Recorded Luminosity [pb-1 ]

104

ATLAS Online 2011, s=7 TeV

103

∫ Ldt=5.2 fb

-1

β * = 1.0 m, <µ> = 11.6
β * = 1.5 m, <µ> = 6.3

102
10
1
10-1
10-2
10-3
0

2

4

6

8

10 12 14 16 18 20 22 24

Mean Number of Interactions per Crossing

Figure 3.1: Average number of interactions per crossing for the 2011 ATLAS data set for
different values of β ∗ used by the LHC. The β ∗ = 1.5 m data set was used for the analysis
in this document [4]. ATLAS Experiment c 2011 CERN.

10−28 m2 ), which means this can be easily multiplied by a cross-section in pb to determine
the number of events expected, as seen in Section 2.3.2. For this analysis, we are considering
1035.27 pb−1 , or 1.04 fb−1 .
However, even after all of these events are produced, nothing can be measured without
a detector to collect the relevant information about the collision. The information provided
is not a snapshot of the interaction we are interested in like the Feynman diagrams in
Section 2.3.1, but rather the final, relatively stable particles that come out of it which
actually reach the detector. There are four different detectors located around the LHC ring
at different points where the beams cross to produce collisions, and this analysis uses data
from the ATLAS detector.
24

3.2

The ATLAS Detector

The ATLAS (A Toroidal LHC ApparatuS) detector [5], shown in Figure 3.2 is a multipurpose
detector designed to detect many different processes. It is a very large detector, the largest
constructed by volume, and is about 25 meters (or 82 feet) high. It consists of several
different detector components designed to detect the various particles that travel through it.
In general, these include b-quarks, lighter quarks, electrons, and muons (as well as photons,
but these don’t appear in our final state). The quarks hadronize and form “jets” of particles
which are actually detected in the detector.

3.2.1

Detector Variables and Geometry

There is certain information that is determined in the detector itself: energy, timing and
particle track information. The layout of the detector is with the z-axis along the beamline.
The y-axis points up vertically from the detector and the x-axis is the remaining direction,
pointing towards the center of the LHC ring. The φ direction is the angle measured in the x
and y plane, starting from the positive x-axis, and the θ direction is measured in the y and
z plane, starting from the positive z-axis.
The θ angle is generally not used as such but transformed into a quantity called pseudorapidity (η):

η = −ln(tan(θ/2))

(3.3)

This quantity is 0 if the particle heads out of the interaction perpendicular to the beam
(θ = 90◦ ) and is about 4.5 close to the beamline (θ = 1◦ ), at the limit of the detector.
25

Figure 3.2: Cut away view of the ATLAS detector [5], ATLAS Experiment c 2008 CERN.
26

Pseudorapidity (η)

Figure 3.2.1 shows values of η for various values of θ.

5
4
3
2
1
0
0 10 20 30 40 50 60 70 80 90
Theta (θ)

Figure 3.3: Graphic showing absolute values of η for various values of θ.

It is also common to use the quantity ∆R as a measure of separation. We define this as:

∆R2 = ∆η 2 + ∆φ2

(3.4)

In this chapter, R refers to the radial direction in a cylindrical coordinate system. Additionally, the term transverse in this document (denoted by a subscript T) means the combination
of the x and y directions, which is perpendicular to the beam direction along the z-axis. For
instance, pT is the transverse particle momenta,
27

p2 + p2 .
X
Y

3.2.2

The Inner Detector

The inner detector has the finest positional resolution of the various sub-detectors. The fine
resolution is particularly important for identifying and reconstructing hadronized b-quarks,
or b-jets, which will be discussed in more detail in Section 4.3.1. The primary purpose of
the inner detector is tracking. This is the closest detector to the beam pipe in the central
region and covers a region of |η| < 2.5.
There are three major sections: Pixel, SemiConductor Tracker (SCT), and Transition
Radiation Tracker (TRT). The Pixel is the innermost section and has an initial layer called
the B-layer. The closeness of this layer to the interaction is limited by the beam pipe itself,
which is about 6 cm in diameter. This section of the detector is composed of small squares
of silicon (pixels) and has very good positional resolution, 10 µm in R-φ space and 115 µm
in z. As charged particles hit the silicon, ionization electrons flow to anodes and a signal is
created. There are three pixel layers circling the barrel region and an additional three layers
on each side. The next section is the SCT. It is very similar to the pixel section but has
microstrips of silicon about 6 cm long rather than pixels. It has four layers of back-to-back
strips giving a possible 8 hits per track. The resolution is still good although not quite as
precise as the pixel region particularly in the z direction (17 µm in R-φ space and 580 µm
in z).
Finally there is the TRT which is basically a two part detector. It consists of “straw
tubes” which are tubes filled with Xenon gas and a wire down the middle. Each tube is 4
mm in diameter and 37 cm long in the endcap region or 144 cm long in the barrel region.
Around these tubes are various materials with different dielectric constants. When particles,
especially very high energy, low-mass particles like electrons pass through these different
28

materials, transition radiation is emitted (related to the particle’s γr value, E/m, so electrons
will radiate more than low energy, high mass particles) [37]. These photons hit the Xenonfilled tubes and create ions which, because of a potential difference between the tube and the
wire in the center, drift towards the wire and cause a signal. This is particularly useful in
helping with electron identification, especially for |η| < 2.0. The position resolution in this
section isn’t as good as the pixel or SCT detectors, but there are still about 300,000 straws
over a large area, and particles will have more “hits” in the TRT straws than the previous
detector sections, assisting with particle track reconstruction. The TRT only provides R-φ
information and can resolve to 130 µm per straw. However, each track has approximately
36 hits in this region, compared to 3 or 8 in the other two inner detector regions.

3.2.3

The EM Calorimeter

The electro-magnetic (EM) calorimeter is particularly intended to pick out the tracks and
energy of electrons and photons, which tend to stop in this region. It is composed of layers
of lead with steel and liquid argon (LAr), starting with an initial LAr layer called the
presampler which gathers information about showers that may have occurred in previous
detector material. Through the rest of the calorimeter, the electrons will interact with layers
of lead, each of which are about 1 to 2 mm thick, depending on the detector region. There
are three major sections of the EM calorimeter, and most electrons of high enough energy for
physics analyses like this one are deposited in the central region. This region has 0.025x0.025
resolution in η − φ space. The first region helps with rejection of photons or pions and the
last region helps collect energy from very energetic electrons. More energetic electrons will
make showers in more of the lead layers. The showers themselves are detected via creation
29

of ions in the LAr. Photons are also detected in this region and are distinguished from
electrons by the lack of a track in the inner detector. There are two levels of coverage in this
detector, the central region, |η| < 1.5 and the two-wheel endcap region, 1.4 < |η| < 3.2. The
resolution is worst in the forward region of this detector, 2.5 < |η| < 3.2, and this analysis
will not consider electrons from this region. The design energy resolution in this detector
σE
√
( E ) is 10% .
E
It should be noted that there is one particular region of the detector between the barrel
and endcap in the EM calorimeter, 1.37 < |η| < 1.52, where there is excessive extra material
between the inner detector and the EM calorimeter [38]. This makes it difficult to properly
reconstruct the energy of electrons that are detected, and of course they may deposit most
of their energy in this region and never make it into the rest of the detector at all. This is
sometimes referred to as the ”crack” region and electrons from this region are not considered
in the analysis.

3.2.4

The Hadronic and Forward Calorimeters

The hadronic calorimeter is where the hadronic showers from hadronized quark decays (jets)
tend to reach and eventually stop. Here we complete the track and energy information for
jets. The portion of the jets that hit the calorimeter are actually composed of various light
particles, commonly including particles such as pions and kaons (which have masses of about
140 MeV and 500 MeV, respectively). This part of the detector is special because it contains
not only a central and barrel region, but also a forward region which is next to the beam
pipe (as is the inner detector). Each of the regions have some overlap with each other to
avoid lining up too many detector transition regions with each other (where extra material
30

is present and resolution is not as good). Extra material can cause extra interactions that
may not be well modeled and particles could be missed, so it is important to minimize this.
The central region (|η| < 1.7) contains scintillating tiles and steel, and is known as the tile
calorimeter. The hadrons interact with the layers of steel and the showering particles create
photons when they hit the scintillating tiles. These photons are then collected by photomultipliers, which turn the photons into an electrical signal. The barrel region (1.5 < |η| < 3.2)
contains the hadronic end-cap calorimeters (HEC), which uses LAr and is essentially an
extension of the EM calorimeter but with copper plates. There are three layers in the barrel
and four in the endcap, with a resolution of about 0.1x0.1 in η − φ space for |η| < 2.5 and
0.2x0.2 otherwise in the endcap region. The design energy resolution in the central and
√
barrel regions is 50% .
E
The forward region (3.1 < |η| < 4.9) has special forward calorimeters right next to the
beam pipe and thus has a different configuration to handle the larger amounts of radiation.
Here, copper has tube-shaped holes formed in it with each hole containing a tungsten rod
and LAr between the two. The particles shower in the copper and the ions form in the
LAr and travel towards the rod. This region is especially important for the t-channel singletop searches as an energetic forward jet is a distinguishing characteristic between it and its
√
backgrounds. The design energy resolution in the central and barrel regions is 100% .
E

3.2.5

The Muon Spectrometer

Finally there is the muon system, primarily intended to detect muons, which tend to travel
farther through the detector than other particles (except neutrinos, which interact so weakly
that it is difficult to detect them). This is related to the mass of the muon, which is about
31

106 MeV (much larger than the electron, at 0.5 MeV), and its decay time, which is much
longer than the particles like pions and kaons in jets. The longer decay time allows it to
reach the outer regions of the detector (cτ is 659 m) and its larger mass prevents it from
showering too much earlier in the detector. Thus, we can have a special detector for muons,
in the outermost portion of the detector, to determine information about the direction and
momenta of the muons.

There are four major components of the muon system. Two components are dedicated
to detecting the muon track and the other two are dedicated to reporting the presence of a
muon (triggering) and giving additional position information. In each case, one component is
in the barrel region and the other in the endcap region. The Monitored Drift Tubes (MDT)
are primarily responsible for track determination over the full |η| < 2.7 region, except for
the inner section of the muon detector forward region (2.0 < |η| < 2.7), where Cathode Strip
Chambers (CSC) are used. The general principle is similar in both cases. There is a gas filling
drift tubes or between plates, and a charged particle creates ions which drift towards a wire.
The resolution of the MDT is about 35 µm in the z direction, while the CSC has a resolution
of about 40 µm in the plane orthogonal to φ and 5 mm in the φ (non-bending) direction. The
triggering portions are the Resistive Plate Chambers (RPC) and Thin Gap Chambers (TGC)
in the central (|η| < 1.05) and endcap (1.05 < |η| < 2.4) regions, respectively. The first is
composed of sets of plates (no wires) that the ionized particles travel between. The second
contains many wires between plates, like the CSC, but the wires are arranged differently to
favor a faster response time. These extra triggering systems are needed because the response
time of the main systems is too long to allow triggering of a high pT muon associated with
some events, and also to provide information about the muon track in an additional (φ)
32

direction. The RPC has a resolution of 10 mm in both the z and φ directions while the TGC
has a resolution of 2 to 6 mm in z and 3 to 7 mm in φ.

3.2.6

Magnets

It should be mentioned that one of the primary methods of measuring the momenta of
charged particles is by measuring the curvature of their tracks in a magnetic field. Magnetic
fields also help to distinguish charged and neutral particles (whose tracks have no curvature
due to a magnetic field), aiding in particle identification. Magnetic fields are created by
two different sets of magnets in the ATLAS detector. The first set is a 2 Tesla solenoid
magnet system located between the inner detector and the EM calorimeter which provides
a magnetic field for the inner detector. In addition to providing a strong field the magnet
coil and related structure must not be too thick or dense, as the particles are intended to
pass through this magnet layer relatively unimpeded. The second set consists of large toroid
magnets (about 0.5 to 1 T within the muon detector) surrounding the muon system, in
both the barrel and endcap regions. The tendency of a particle to curve in a magnetic field
indicates that it is charged, but the degree of curvature also gives information about the
momentum of the particle. This can be seen from the equating the Lorentz and Centripetal
force equations, giving:

F = Bqv = γmv 2 /r → γmv = p = qBr → p ∝ r

(3.5)

where B is the magnetic field, q is the particle charge, v is particle velocity, r is the radius
of curvature, γ is the relativistic gamma and p is the momentum. From this we can see
that particles with more momentum have a larger radius of curvature, meaning that the
33

tracks will curve less (be straighter) in the detector. Additionally, particles with a large γr
value will have straighter tracks. Particles that are not charged will not curve due to the
magnetic field (or leave a track). Thus, these magnets are essential for particle identification
and measurements.

3.2.7

The Trigger and Data Collection

Finally, there is the Trigger and Data AcQuisition system (TDAQ) [39]. Although not
strictly part of the ATLAS detector itself, per se, this system is essential to data analyses.
The LHC produces collisions at such a high rate that it is impossible to store all of the
collected data for analysis. Most of the data, however, are glancing or low energy collisions
that are not the events we are looking for in studies of processes such as single-top. It is
possible to reject many of these events immediately, using hardware triggers. There are then
two other trigger levels which spend increasing amounts of time determining if an event is
worth saving or not before the data are finally recorded for use in analyses.
The three different trigger levels are called level 1 (L1), level 2 (L2) and event filter (EF).
At each level, more information is considered to determine if an event should be kept or
rejected. This is important as computer storage space would rapidly run out if all events
were kept. Most events are “common” events involving low energy jets. We want to be sure
that we collect enough of the less common high energy events (like the single-top events we
are looking for) so we reject many of these less interesting events.
The L1 trigger is hardware only and rejects events very quickly (less than 2 CPU µs per
event) and in large number, with a maximum rate of 75 kHz [39, 38] although in practice
the rate may be half this value. The other two triggers are software based. The L1 trigger
34

essentially just looks for high transverse energy objects in the event, but the L2 trigger
considers the regions of interest (RoIs) containing these objects and can consider full detector
information in these regions. The rate after the L2 decision is about 3 kHz and it takes
about 50 CPU ms per event to make a decision to keep or reject the event at this level.
Finally the EF is the last level which looks at the whole detector and uses standard analysis
reconstruction software to find the event information and make a decision. After this stage,
the event is permanently stored and disseminated to analysers. The overall event rate at
this level is about 200 to 600 Hz. It takes longer to determine whether to keep events at
this level, about 4 CPU seconds per event by design (as low as 0.4 CPU seconds per event
during data taking), but this is still quite fast.
There are many different types of triggers. In this analysis, we use single lepton triggers,
corresponding to the single leptons expected in the t-channel single-top final state. When the
data are processed, a low threshold trigger is initially applied, and higher threshold triggers
are applied later at the analysis level. This application of the low threshold triggers divides
the data into different analysis streams. In this document we use the Muon and Egamma
(electron) streams for the main analysis. There is also another main physics stream, the
JetTauEtMiss stream, which is used in this analysis for the multijets background estimate.

3.2.8

Data Quality

In some cases the detector may have a component temporarily fail or go offline, and it may
not be possible to reconstruct certain particles well. In this case, events taken during these
times are rejected due to data quality issues. This rejection is done “offline”, meaning it
is performed after the initial low threshold triggers are applied, and removes data events
35

from the analysis by applying a “good runs list” (GRL) selection as the first selection on
the data sample. This is because some analyses do not use the full detector, so even if some
of the data for a muon analysis for instance are not collected correctly because of technical
problems with the muon spectrometer, an analysis only using the inner detector information
can still use the data. On the other hand, an analysis such as this one, which uses nearly
the full detector range, would not be able to use such data.
One exception to this GRL selection is the so-called “LAr hole” issue, which was a
problem with the front end electronics for the LAr calorimeter that created a “hole” in the
detector data collection. This problem persisted for a few months before being fixed and was
present for all but the first 165 pb−1 of the data set used in this analysis, meaning about
85% of the data has the potential to be affected. In this case an additional event selection
is applied to the data to account for this issue, removing only events where the particle
reconstruction is affected by this hole (rather than removing all of the events, which would
have been the standard GRL selection procedure for an analysis like this one). In the end,
only about 10% of data events are actually removed from the analysis due to this issue.

36

Chapter 4
Particle Reconstruction
The data collected by the ATLAS detector are not particularly easy to interpret at first
glance. The data begin as energy deposits and tracks while the theory consists of simulated
hadronized quarks, leptons and neutrinos (this is referred to as truth level MC). Truth level
MC information is largely unused in this analysis. Instead, the two sets, data and MC, are
processed to reconstruct the event and, in the case of MC, include detector information like
extra material or overlapping tracks affecting particle reconstruction. Event reconstruction is
applied to form particles and reconstruct the event, so at this level there are quantities such
miss (missing transverse energy) rather than neutrinos, and jets rather than quarks.
as ET
We will call this stage of processing (the final stage before analysis) the reconstruction or
detector level. At this point, the two sets, data and MC, should be equivalent (for instance,
miss distributions should be the same between the two if the data are perfectly modeled by
ET
the MC). In the following sections, we will give the definitions for a muon, electron, neutrino,
or jet at the reconstruction level. We will also include criteria that require particles to be
separated and well reconstructed.
37

4.1

Electrons

Electrons appear to be narrow curving cones of energy in the detector. The narrow curving
track, with a shorter trail of energy depositions through the detector than a muon, is its
primary distinguishing feature. There are electrons that can occur in the detector from
sources other than being directly produced in the main collision however, including electrons
inside of jets and electrons from photon interactions. It is also possible to mis-identify narrow
jets as electrons, or photons as electrons. In this analysis, we apply several criteria when
identifying if a certain energy deposit and associated tracks are really an electron from the
primary collision.
In the ATLAS experiment, there are three different initial electron selections which can be
used in different analyses. These are referred to as loose, medium, and tight, where medium
includes loose as well as extra medium requirements, and tight includes both medium and
loose as well as extra tight requirements [38]. The more selections that are applied, the more
confidence we have that the particle identified as an electron is really an electron, although
some real electrons which happen to fail these requirements are also removed (making it
less efficient). For this analysis, we prefer to be sure that the particle is what we have
identified it as (high purity), so we require the tight selection. Overall, this selection includes
requirements to ensure that the energy deposits are narrow and where we expect them to
be for an electron (the EM calorimeter), to reduce jets in particular being mis-identified as
electrons, and that a track is well matched to this deposit and inner detector deposits, to
reduce photon conversions being mis-identified as electrons.
The requirements for tight electrons are given elsewhere [38], but we repeat them here
for completeness. The loose selection requires the electron |η| < 2.47, low leakage of energy
38

depositions into the hadronic calorimeter, and includes a requirement on energy deposits in
the middle of the EM calorimeter, where most electron energy deposits would be expected to
be. The shower width is examined in this layer as well. The medium selection has additional
criteria related to the shower width using the first EM calorimeter layer and the deviation in
the energies of the largest and second largest deposits in this layer. There are requirements
related to the track, that there is at least 1 hit in the pixel portion of the inner detector, at
least 7 hits from both the pixel and SCT, and that the track’s transverse impact parameter
(the shortest distance from the track to the primary interaction vertex), |d0 |, is less than
5 mm. The final medium requirement is related to track and cluster matching, requiring
the distance in |η| between the cluster in the initial EM layer and the determined track to
be less than 0.01. The final set of selections to make the electron tight include additional
cluster and track matching requirements: that the distance in |φ| between the cluster in the
middle EM layer and the determined track be less than 0.02, a requirement on the cluster
energy divided by the track momentum, and tightens the |η| distance requirement applied
for medium electrons from 0.01 to 0.005. The |d0 | requirement is also tightened to be less
than 1 mm. The TRT portion of the inner detector is used, introducing requirements on
the total number of TRT hits and considering the ratio of high threshold hits to total hits
in the TRT. Finally, there are requirements to reduce photon conversions. The number of
B-layer hits (the first pixel detector layer) must be at least one and electron candidates that
are matched to reconstructed photon conversions are rejected.

We further require electrons to have a transverse momentum (pT ) of at least 20 GeV.
Electrons must also be isolated, meaning they are not near other particles. The isolation
requirement is specifically optimized for single-top analyses and requires etcone30/ET < 0.15
39

and ptcone30/ET < 0.10. The variables etcone30 and ptcone30 refer to the amount of
transverse energy deposited or track momentum in a cone around the electron track(s) with
a R of 0.3, where ∆R =

∆η 2 + ∆φ2 < 0.3. Electrons must also have |η| < 2.47, and

exclude the region 1.37 < |η| < 1.52 due to detector limitations. Additionally, if electrons
fall within the LAr hole, then they are not considered to be electrons.

4.2

Muons

Muons are primarily distinguished by their relatively long lifetimes and long, curved tracks
which reach into the muon calorimeter section of the detector. Muons are required to satisfy
several strict quality requirements. As with electrons, the muons have several categories
for an initial identification definition. In this case, the categories refer to different muon
reconstruction algorithms. The one used here is the combined muon [40, 41] algorithm,
which considers both inner detector and muon spectrometer tracks, which are reconstructed
separately. A combined fit is performed on the tracks from the two detectors to form a final
muon track. If a combined track cannot be formed, the particle is not considered to be a
muon. Of the different algorithms, this is the one that has the highest purity.
There are a few track quality requirements used to define a muon which are related to
inner detector information, including at least one B-layer hit, at least two pixel hits, and
SCT and TRT hit and quality requirements. These are a bit detailed, and are given here for
completeness. We require the flag expectBLayerHit to be false or the number of BLayer hits
> 0, meaning there must be a hit in the B-layer unless the track passes through a dead area
of the detector. A muon must have the number of pixel hits plus the number of crossed dead
pixel sensors ≥ 2, the number of SCT hits plus the number of crossed dead SCT sensors
40

≥ 6, and the number of pixel holes plus the number of SCT holes ≤ 2. Holes are where a
module did not respond as expected, even though modules elsewhere along the track did.
Finally, there is a complex requirement on the number of TRT hits divided by the number
of outliers related to the quality of the track fit, where outliers are hits that deviate from
the track. We require, where n is the number of TRT hits plus the number of TRT outliers,
n ≥ 6 and the number of TRT outliers divided by n to be < 0.9 for |η| < 1.9. Then we
also require the number of TRT outliers divided by n to be < 0.9 if n ≥ 6 for |η| ≥ 1.9. In
this last case, if n < 6, the event will pass, unlike the first case. These requirements help to
ensure a high quality inner detector track is matched to the muon spectrometer track.
The isolation requirement is the same as the electron isolation requirement, namely that
etcone30/ET < 0.15 and ptcone30/ET < 0.10. The muons we select are specifically not
allowed to overlap in position with jets, meaning any muon candidate within ∆R of 0.4 of
a jet is not considered. For this purpose, we consider all jets with pT above 20 GeV and
include jets that overlap with electrons. Additionally muons must have pT > 20 GeV and
|η| < 2.5.

4.3

Quarks and Jets

Perhaps the most complex reconstructed objects in the detector are jets. Jets are hadronized
quark decays, showers of many particles that tend to be absorbed in the hadronic calorimeter.
Because they are basically sprays of particles, it is possible for them to overlap and be in
odd shapes. In order to work with these, we need to understand which energy deposits
correspond to which jets.
The method used to form jets in this analysis is an algorithm called the anti-kt algo41

rithm [42]. There are two major jet algorithm types, cone and clustering algorithms, where
anti-kt is a clustering algorithm that forms jets that happen to have very cone-like shapes.
A clustering algorithm is a bottom-up algorithm that combines individual tracks together
to form a jet, while a cone algorithm is a top-down algorithm which forms a cone for the jet
and considers deposits within that cone. For this algorithm, the area in η − φ space is πR2 .
This is the area containing energy deposits associated to one particular jet, assuming that
there are no other high pT (hard) objects within a distance 2R. For this analysis we use a
cone size R of 0.4. If there is another hard jet, the harder jet will have a cone shape and
the lower pT (soft) jet will have a crescent shape. The anti-kt algorithm is used because not
only is it reasonably fast, but the jets are grouped using the highest pT energy deposits first
and then looking at surrounding objects, meaning that random low energy deposits will not
change the jet shape. This means it is infrared safe because it avoids potential divergences
from an infinite number of very soft, low energy jets. Also, each deposit and track is assigned
to some jet. There is no splitting and merging of overlapping jets, so it doesn’t matter if a
jet is split into two parallel (collinear) particles, making it collinear safe.
We use jets called AntiKt4TopoEMJets, where Topo refers to topological clusters [43, 44].
This is an algorithm that clusters energy deposits together for the jet, by starting with an
energetic deposit with a signal to noise ratio greater than 4, and adding neighboring deposits
that have a signal to noise ratio greater than 2. AntiKt refers to the jet algorithm, and EM
refers to the initial energy correction applied to the jets (see Section 5.2.5).
We have additional quality requirements. We remove any jets that have been reconstructed with corrected energy that is negative and thus are not physical (this is a very
small effect). Any jet candidates that overlap with electrons with ∆R < 0.2 are not consid42

ered. Further, we require jets to have pT > 25 GeV and |η| < 4.5. Notice that this is a much
more forward requirement than that of the leptons. The calorimeters allow information this
far forward in the detector and it is particularly important information for our analysis.

4.3.1

b-tagging

There are two subsets of jets that are used frequently in this analysis, tagged and untagged.
Jets that are b-tagged (tagged) are required to have a high probability of being a hadronized
b-quark. The remaining jets are referred to as untagged. Additionally, jets must have
|η| < 2.5 to be b-tagged because of the inner detector range. This means all jets with |η|
outside of this range are considered untagged.

4.3.1.1

How b-quarks are Identified

The bottom quark is an unusual particle. It is heavy and travels a long distance, relatively,
from its creation before it forms a jet (b-jet). The lifetime of the b-quark is about τ =
1 × 10−12 seconds. We can determine the distance it should travel, on average, by assuming
an energy of about 40 GeV. Because E = γmc2 and d = γcτ , where τ is the lifetime, m is
the mass (about 4 GeV/c2 ) and E is the energy, we can write, where c is the speed of light
(c = 3 × 108 m/s):
d=

E
40
· 3 × 108 m/s · 1 × 10−12 s = 0.003 m
cτ ≈
2
4
mc

(4.1)

This means that the b-quarks travel about 3 mm from the main interaction point before
forming a jet.
Tracks from the inner detector can be reconstructed and traced back inside the beam pipe
43

(where there is, of course, no detector). These tracks will then intersect within the beam
pipe, which has a diameter of about 6 cm. Most intersect in a primary vertex, the place the
proton-proton collision occurred. However, some may intersect in other places, secondary
vertices, where a b-hadron has formed a jet (see Figure 4.1). Of course, as there are multiple
proton-proton collisions producing pile-up events, and just more particles in general, it can
be difficult to really distinguish which tracks go where, and to which vertex. This is why
the inner detector resolution is so very important and also the reconstruction algorithms to
determine these vertices. Because of the importance of the inner detector, b-tagged jets are
only defined within its range, |η| < 2.5.

Figure 4.1: Event display for a b-jet, with the secondary vertex shown in the dashed box
and primary vertex shown as a round ball [6], ATLAS Experiment c 2011 CERN
44

The b-tagger is just a distribution related to the likelihood of a jet coming from a b, and
a jet is b-tagged based on whether the b-tagger value for that jet is above or below a certain
threshold, called an operating point. A jet is considered to be mis-tagged if the jet was
not really from a b-hadron but was still b-tagged. Different operating points have different
levels of performance. There are two major ways to determine b-tagger performance, the
b-tagging efficiency and the mis-tagging efficiency. These two measures are proportional, so
a high b-tagging efficiency sample will have high mis-tagging efficiency. This means that if
the b-tagging efficiency is high, most of the jets that are really b-hadrons will be b-tagged,
but there will also be a relatively high proportion of jets that were not really b-hadrons that
were nevertheless b-tagged as well. Incorrectly b-tagging jets that do not originate from a
b-hadron is sometimes also discussed in terms of a rejection factor, which is the inverse of
the mis-tagging efficiency.
In our case, the final state has both a b-jet and a (typically) light quark jet. The large
backgrounds in this analysis before b-tagging are backgrounds with light jets in the final
state, while the signal has both a light and b-jet. Therefore, while we remove some of our
signal by having a lower b-tagging efficiency, we prefer to remove proportionally more of
our background by choosing an operating point with a low mis-tagging efficiency. Even
though fewer jets are b-tagged, we have more confidence that the ones we do b-tag are really
b-hadrons than if we had chosen a higher b-tagging efficiency.
The b-tagger used in this analysis is the JetFitterCombNN b-tagger [45]. This is a combination of two b-taggers called JetFitter and IP3D. The JetFitter algorithm uses a Kalman
filter [46] to determine the path along which b and c hadrons (from decays inside the b-jet)
and the primary vertex lie, and this determines a track for the b-jet. Additional discrimina45

tion based on the secondary vertex and its uncertainty is done using a likelihood method.
The IP3D b-tagger uses the impact parameter information in all three dimensions with a
likelihood technique to discriminate between the b-jets and lighter jets. An impact parameter is the shortest distance from the primary vertex (interaction point) to a track. The
transverse impact parameter is a common quantity known as d0 , and IP3D uses both transverse and longitudinal (z0 ) impact parameter information. The JetFitterCombNN forms a
neural network based on information from these two algorithms. The output of the neural
network forms the JetFitterCombNN b-tagger.

4.3.1.2

Impact of Different Operation Points on the Analysis

For this analysis, we choose the JetFitterCombNN b-tagger with a threshold of 2.4, so if the
JetFitterCombNN value is > 2.4 the jet is b-tagged. This gives a 57% b-tagging efficiency, but
a very high light quark rejection of about 1000 [45] (or a mis-tagging efficiency of about 0.1%).
This is the lowest b-tagging efficiency (and lowest mis-tagging efficiency) operating point
approved for use. In Figures 4.2 and 4.3, the effect on the yields of using different b-tagging
operating points can be seen, where the chosen operating point is shown with a vertical line.
The yields for each process are given for a particular threshold for the JetFitterCombNN btagging variable, as well as a scaled version of the signal divided by the background. Both of
these are rough indications of signal separation and analysis performance (but note that they
don’t include systematic uncertainties). In general it is clear that while the t-channel yields
go up for a looser (lower) operating point, the backgrounds also increase, at a greater rate.
The separation appears to be better for higher thresholds where the mis-tagging efficiency
is lower. Although we lose some of our overall event yield, the background is reduced at
a greater rate than the signal is reduced. For this analysis, we use the highest threshold
46

available, 2.4.

4.4

Taus

Thus far, tau leptons have not been discussed because we do not specifically reconstruct or
select for taus in this analysis, although of course this is a lepton that could be involved in
the W decay from the top quark. The reason for this is the short tau decay time and the
nature of its decay particles. Unlike the other two leptons, electrons and muons, taus do not
travel very far into the detector before decaying (it has a lifetime of about 3 × 10−13 s and
a mass of about 1.8 GeV [18]). Taus may decay into quarks, at which point they look like
jets (it is theoretically possible to identify a tau from decay particle information, as we do
for b-jets, but that is not currently done). It is also possible for the tau to decay to one of the
other two lepton types, plus neutrinos (this happens about 40% of the time). In this case,
we incidentally select for these when we select for a muon or electron in our event. However,
we don’t specifically select or reconstruct a tau. The MC and data both have taus in them
and the same selection (and lack of special reconstruction) is applied in both cases, so this
is consistent.

4.5

Neutrinos and Missing Energy

Neutrinos interact weakly (and not very often). Thus, we do not try to detect the neutrinos
but instead use momentum conservation to determine the missing transverse energy, or
miss
ET , which corresponds to the neutrino’s pT (or sum of the neutrino pT values). If there
miss value. Information about
is more than one neutrino, of course, there is still just one ET
47

Candidate Events / 0.1

105

∫ L dt = 1.04 fb-1

2 jets 1 tag

104

s = 7 TeV

103
102
10
1
10-1
-2

0

2

4
6
8
JetFitterCombNN

Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
S/B*1000
Figure 4.2: Distribution of the 2 jet yields for the signal (t-channel) and its backgrounds,
given a selection on the JetFitterCombNN b-tagging variable at the given x-axis value (1
b-tag). Selections at higher x-axis values have lower b-tagging efficiencies but higher mistagging efficiencies. The black vertical line shows the threshold used in the analysis.

48

Candidate Events / 0.1

105

∫ L dt = 1.04 fb-1

3 jets 1 tag

104

s = 7 TeV

103
102
10
1
10-1
-2

0

2

4
6
8
JetFitterCombNN

Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
S/B*1000
Figure 4.3: Distribution of the 3 jet yields for the signal (t-channel) and its backgrounds,
given a selection on the JetFitterCombNN b-tagging variable at the given x-axis value (1
b-tag). Selections at higher x-axis values have lower b-tagging efficiencies but higher mistagging efficiencies. The black vertical line shows the threshold used in the analysis.

49

the momentum in the z direction is not preserved as there is no information collected inside
of the beam pipe. We can’t determine how much momentum is missing in that direction from
particles that may have traveled only in the z direction and missed the detector. We do have
information everywhere else though, so we are able to determine the missing momentum in
the x and y directions.
miss for ATLAS [47] is calculated from the sum of the calorimeter energy deposits
The ET
associated with reconstructed particles (includes jets, electrons, photons, and tau decays as
well as other deposits) and the energy from reconstructed muons in the x and y directions.
The two portions of the calorimeter energy deposits in the “other” category are called soft
jets, jets with pT below 20 GeV but above 7 GeV (too low to be considered jets in this
analysis) and cell out deposits, low energy deposits too low to be classified as soft jets or
other physics objects. When all of these contributions are summed, because the initial
collision is in the z direction with no momentum in the x or y directions, we expect the sum
miss
to be 0. The deviation from 0 gives the ET .
For this analysis, we will want to use the momentum information in the longitudinal or
z direction, so it is reconstructed from information about the W boson. The single lepton
miss (which we expect comes from one neutrino in our selected events) correspond
and ET
to a single W boson. The mass of the W is well known, and we take it to be 80.42 GeV,
consistent with the current Particle Data Group value [18]. From this information, we can
reconstruct the neutrino momentum in the z direction, using the following equation and
taking the neutrino and lepton masses to be zero:

2
P µ Pµ = MW
50

(4.2)

Here, P is the four-momentum of the lepton and neutrino combination, and MW is the W
mass.
After some manipulation, the equation can be rewritten as:

2 2
2
2 2
le νpT − (A + B)2 + (le − lpz )νpz + 2(A + B)lpz νpz = 0

(4.3)

2
MW
where A = 2 and B = lpx νpx + lpy νpy . Here, ν is the neutrino and l is the lepton where
2
2
2
le is the lepton energy, lpz is the lepton longitudinal momentum and lpT = lpx + lpy is the
miss
lepton transverse momentum. The quantity νpT is just ET . This is a quadratic equation
which can be solved for νpz . In the solution, it is possible to have two results, and in this
case we take the smaller of the two values. It is possible to have a negative discriminant
2 2
2 2
miss is primarily used
(1 + (νpT lpz ) < νpT le ) and in that case a 0 value is taken. The ET
in the analysis until the final cut-based selections are applied and we make use of the νpz
information to reconstruct the top quark.

51

Chapter 5

Monte Carlo Simulation and
Corrections

The Monte Carlo (MC) which simulates events produced by the proton-proton collisions does
not simply appear from equations, but instead must be produced and corrected using computer algorithms. There are two steps to this process, a generator that produces the general
event with quarks, leptons and neutrinos, and then a showering algorithm that adds extra
jets and gluons to these “simple” processes made by the generator so they resemble more
closely what we see in the detector, where higher-ordered processes are produced. Additionally, after considering the effects of the detector and producing what is called reconstruction
level MC from the truth level MC (which does not include detector effects), there are still
corrections to be made to the particle energies and the MC events in general to better match
the data. In this chapter we discuss the MC production and these additional MC corrections.
52

5.1

MC Generator and Showering

The simulation of MC requires a few processing steps. The first is a MC generator which reproduces the basic Feynman diagrams and the second is a showerer, which adds on additional
particles. In practice it isn’t quite so clear-cut. There can be some overlap between what
the showerer and the generator do, and diagram overlap removal procedures are applied in
this case. There may also be some unsimulated feynman diagrams depending on the process
and choice of showering algorithm or generator.
For this analysis we use Pythia [48] for parton showering in the single-top processes and
Herwig [49] with Jimmy [50] for the showering for all other processes. The generators are
more varied. For our signal we use AcerMC [51], which uses a procedure to reproduce an
extra, soft b-quark from a incoming gluon more correctly than alternative generators [52].
¯
The tt process is generated using the MC@NLO [53] generator, which includes more diagrams than a standard leading-order generator. The W +jets and Z+jets processes use
Alpgen [54], while diboson simulations use Herwig. The parton density functions (PDFs)
describe the structure of the proton and give the probability of having certain quarks or
gluons from the proton with a given proton momentum fraction for some energy scale. The
pdfs used here are from CTEQ6L1 [55] for Alpgen processes, and CTEQ66 [55] for the
MC@NLO process. The single-top AcerMC plus Pythia and Herwig diboson samples
use the LO* PDF MRST2007lomod [56, 57]. Generators and showering algorithms are updated frequently as they are tuned to better match the data. There is some uncertainty
related to our measurement because we know these probably don’t precisely match our data.
However, studies from other experimental data, such as from the Tevatron experiments, have
produced generators and showering algorithms that match up well with LHC data, and the
53

agreement will be discussed in Chapter 8.
Finally, it should be noted that the final simulation of the particles going through the
material of the ATLAS detector is done with separate programs [58] based on GEANT4
software [59]. This stage of processing accounts for the specific configuration of the ATLAS
detector, including regions where there may be more or less material. This stage also introduces simulation of the resolution in different portions of the detector. The events are then
reconstructed in the same way as data collected by ATLAS. Additionally, the MC used in
this analysis has the ATLAS tag of MC10b. It has three simulated bunch trains with 225
ns separation between the trains. Each train has 36 filled bunches with 50 ns separation
between bunches, the same separation as the data. These simulation conditions assist the
reproduction of pile-up effects in the Monte Carlo.

5.2

Monte Carlo Weighting and Corrections

When the Monte Carlo (MC) is produced, the quantities of generated events are set to
ensure that there are enough events to allow a sufficient variety of kinematics (and make
the statistical uncertainty low). However, these quantities are not the same as those seen
in data; there are often more MC events than data events. In order to compare the MC to
the data sample, the MC must be weighted so that the proportions of the different processes
are as we expect and the overall normalization is correct. Here we describe how the event
weighting is done, and which weights and corrections are applied.
54

5.2.1

Theoretical cross-section and luminosity weight

The first and perhaps most important weight normalizes each process to its theoretical crosssection and also the whole MC sample to the number of events expected for the amount of
data we have (the integrated luminosity). The weight multiplied onto each MC event is
formed as:
XS · BR · K · L
NM C

(5.1)

where XS · BR · K is the cross-section times branching ratio times k-factor discussed in Section 2.3.2, L is the integrated luminosity (1035.27 pb−1 ) and NM C is the number of Monte
Carlo events. The numerator is simply the number of expected events from Equation 2.4,
with the cross-section written out with corrections. The values for XS · BR · K are given in
Table 2.2.
The denominator is the number of MC events, as stated. However, it is important
that this include any weights that can affect the overall number of events before analysis
selections. These include the pile-up weight, discussed next, and negative weights associated
with MC generators. Certain MC generators, particularly NLO top-quark process generators
¯
like MC@NLO (tt) or AcerMC (single-top production) give some events negative weights
during generation related to interference effects when including NLO processes. Thus, this
weight is applied when determining the NM C value as well as later in the analysis.

5.2.2

Pile-up weight

The other weight applied to the NM C value (and all MC events) is the pile-up weight,
which is related to the number of primary vertices. This is a weight which adjusts the MC
to represent the events one expects under certain (data-like) pile-up conditions. The pile-up
55

conditions may change after a large sample of MC is generated, so this allows more flexibility.
The difference between the NM C in the full MC sample with and without this pile-up weight
is typically about 1%, so the effect on NM C is minimal.
The weight itself ranges in value from about 0 to 5, where many events are given weight
0 because they are simulated with pile-up conditions exceeding the current data conditions.
This of course has an effect on the MC statistical uncertainty, as the MC statistics are
effectively reduced in this case.

5.2.3

Lepton scale factor

The lepton scale factor is a weight used to adjust the MC so that the lepton efficiencies
match those found in the data. Scale factors are discrete numbers applied to the MC which
may have some dependency on pT or η. There are different scale factors related to the
trigger, reconstruction and identification for each lepton type. These scale factors are all
approximately 1 [38, 40, 60] and have a minimal impact on the analysis.

5.2.4

Mis-tagging and b-tagging scale factor

Like the lepton scale factors, the b-tagging and mis-tagging efficiencies we see in data are
not exactly the same as MC, so we apply a scale factor to correct the MC. This scale factor
is also typically close to 1 [45, 61]. However, the uncertainties on the b-tagging scale factor
are larger than the others for this analysis, so the b-tagging scale factor has an increased
level of importance. It would be possible to eliminate this scale factor and uncertainty if
b-tagging were not used in the analysis, but the signal separation is not sufficient to do this
with the current data total. For more details on b-tagging and mis-tagging efficiencies in
56

this analysis, see Section 4.3.1.

5.2.5

Energy corrections in the analysis

The energies of different particles are not necessarily quite the same in MC as they are in
data. Although some corrections are applied to the events before they reach analysers, there
is some fine-tuning done at the analysis level. We can smear or scale the particle energy,
where smearing involves changing the particle energy using random numbers from some
distribution, typically a Gaussian. This may be done as an uncertainty on the analysis, as
is the case with jets, or it may be applied to the nominal sample, as is the case for leptons.
In the case of the leptons, the corrections are chosen to have a better match between the
Z mass peak and width in the data and MC. The electrons have two instances of energy
corrections [38]. The first is a scaling done in the data to correct the energy of the electrons.
This sort of correction is usually done before the analysis level, as for jets, but in this case it
is done afterwards. The second is a smearing, done in MC, to adjust the width of the Z peak
to what we see in data. For the muons, scaling and smearing are both applied to the MC
only. In this case, because tracks are used from the inner detector and muon spectrometer
to form the full muon track, there are separate corrections on the tracks in each region [62].
Jet energies are corrected in two stages from what is actually measured in the detector
to what we have in the MC simulation. The first correction is to the EM scale, the main
correction to the detected energy, based on test beam and cosmic ray studies. The second
correction is a jet energy scale (JES) correction [43, 63], an additional calibration based on
the jet pT and η. It includes corrections for losses due to dead material, noise and other
measurement issues, or leakage energy from particles depositing energy outside the hadronic
57

calorimeter. The jet energy is corrected for pile-up effects and the jet direction is adjusted
to go through at the primary vertex for the jet rather than the detector center (which is the
default). The jets are called EM-JES calibrated jets.
The jet energy resolution (JER) corrections are done in a separate iteration of the analysis
and the difference from the nominal sample is taken as an uncertainty [64, 65]. The JER
adjustment affects the jet energy by adjusting the value according to a Gaussian distribution,
where the Gaussian width depends on the jet pT and η value. There are two major techniques
to determine the jet energy resolution, a di-jet balance method and a bi-sector method. These
methods each respectively look at the deviation between two jets with similar expected
pT values or the projection of the sum of two jet’s momenta in a plane transverse to the
beam axis. The function used to adjust the jet energy in this analysis is based on the results
of these two techniques.

58

Chapter 6
Preselection
In Section 2.3.2 the cross-sections for the signal and background processes were given. It is
clear that without selections to reduce the background events relative to the signal events,
single-top t-channel cannot be distinguished. The haystack is large, and our needles are
buried and hard to see. The preselection selects events that have single-top t-channel-like
kinematic characteristics.
To see how these selections are chosen, we examine the t-channel final state, shown in
detail in Figure 6.1. The figure shows that there is at least one b-tagged jet and at least two
jets overall (the b-quark from the initial gluon is not always present or detected), with one
miss
lepton and one neutrino (ET ) from the decay of the W . The scenario where a W decays
to quarks is not selected for, as that final state contains only jets and is very difficult to
distinguish from the large cross-section multijets background. The multijets cross-section is
so large that even requiring one lepton, despite the low lepton fake rate in this analysis, still
results in a fairly large number of multijets events selected.
Requiring a t-channel final state incidentally helps to reduce the backgrounds, in addition
59

q

q’

W
b

t
g

b

W
l
b

ν

Figure 6.1: Feynman diagram for t-channel single-top production, showing the final state
after the top quark decay. The other t-channel diagram is the same as this one, except
without the gluon in the initial state and thus without the ¯
b-quark in the final state.
to choosing events that look like our signal. Rejecting events with less than 2 or more than
¯
3 jets helps to reduce W +jets and tt, respectively, as these processes tend to have fewer or
more jets than the signal.
The preselection used in this analysis in detail is given below. The selection without the
b-tagged jet number requirement is called the pretag selection:
• The event must have a good quality primary vertex (has at least 5 tracks)
• Exactly one, triggered lepton (muon or electron), matched to a reconstructed lepton
object
• The leptons must have pT > 25 GeV and muons must also have pT < 150 GeV
miss > 25 GeV
• There must be ET
• Two or three jets, with a one jet selection used for a sideband region
• The jets must not be bad
60

• LAr quality requirements related to the LAr hole must be met
• Data events with LAr bursts (noise) are removed
miss
• Triangular cut of ET + WT > 60 GeV
• Exactly one of the jets must be b-tagged
The primary vertex requirement reduces contamination in events with extra pile-up interactions (often multijets), where a different vertex might be confused for the one we are
interested in. The lepton requirement helps to reduce multijets events, which do not have
a real lepton. The trigger requirement specifically requires the EF mu18 trigger for the one
muon selection and EF e20 medium trigger for the one electron selection. The trigger matching ensures that the lepton in the analysis matches with a trigger-level object. This selection
has a small effect on the analysis. Due to an issue with the MC, the muon trigger matching
was not applied for the muon channel (although the trigger itself was still applied). The
pT requirement for the leptons is 25 GeV, to be sufficiently away from the trigger thresholds
of 18 and 20 GeV, to reduce the related uncertainty. The upper pT threshold is applied due
to low statistics when determining the muon scale factors in this region (the impact on the
miss selection has the same threshold as
analysis from this selection is very small). The ET
the lepton selection and helps to reduce the multijets background. The pT thresholds for
the particles in general help to reduce the multijets and W +jets backgrounds, which often
have lower pT particles.
The analysis requires 2 or 3 jets to select a t-channel-like final state. The events must
satisfy several selections to remove events which contain so-called bad jets. These are jets
that arise due to cosmic rays, detector problems, or beam issues and the whole event is
61

removed if it includes a bad jet.
For completeness, the definition of bad jets, which can cause an event to be rejected,
is as follows [66, 67, 43]. There is a bad jet if the energy fraction in the hadronic end-cap
calorimeter (HEC) is > 0.5 and the fraction of energy corresponding to HEC cells with
a cell Q-factor (related to the energy pulse shape measured versus expected) greater than
4000 is > 0.5 (corresponds to HEC spikes and hardware issues). The event is rejected if
the jet’s energy fraction in the electromagnetic calorimeter is > 0.95, the fraction of energy
corresponding to LAr cells with a cell Q-factor greater than 4000 is > 0.8, and |η| < 2.8 for
the jet (EM calorimeter noise issues). Finally, the event is rejected if the jet timing is > 25
ns (indicates out-of-time jets, from a cosmic ray for instance). The timing is the deviation
of the event time from the time of energy deposition for the detector cells related to the jet,
weighted by their energy squared.
Of the remaining four selections, there are two selections related to the LAr. The first
removes events where jet reconstruction is affected by the LAr hole. The second removes
events with noise bursts related to the LAr. Finally, we apply a triangular cut which reduces
the multijets background and, last, we require one jet to be b-tagged.

62

Chapter 7
Modeling the Signal and the
Backgrounds
In order to study single-top t-channel production and its backgrounds, we need to model
these processes accurately. The Monte Carlo (MC) techniques that were used in this analysis
to simulate data were discussed in Chapter 5 and are used for the three single-top production
¯
modes, tt, Z+jets and diboson modeling. Here, we discuss the data-based estimates we use
for the multijets normalization and kinematic shapes, as well as the W +jets normalization
and flavor composition.

7.1

Multijets Estimation

Multijets (sometimes colloquially referred to as QCD) are difficult to simulate in quantities
necessary to be useful in analyses. This is a process with a very large cross-section and a
very, very small proportion of events left after selections are applied. It just isn’t feasible to
generate MC for this background.
63

We do, however, have a lot of multijets in the data, in our off-signal region. We can
make use of this to select a relatively pure sample of multijets events which is used for
both kinematic shapes and to determine the normalization (i.e. how many multijets events
are actually in the preselection sample). There are several ways to form such a region.
For instance, one could require the leptons to not be tight or not be isolated, keep the
other selections and cuts the same, and end up with an orthogonal multijets sample. This
particular method, however, suffers from too much contamination from W +jets events.
The method chosen for this analysis is the jet-electron method. In this method, the usual
electron trigger is replaced by a jet trigger. Correspondingly the data stream is replaced
by the JetTauEtmiss stream (the main analysis uses muon and electron streams). The
triggered jet must also have a high EM fraction, so most of the energy is deposited in the
EM calorimeter, and at least 4 tracks, to avoid including photon conversions. All other
selections and cuts are unchanged from the preselection. This sample is used to determine
the kinematic shapes. Because of the low statistics due to increasing trigger thresholds
as the data taking has progressed, the shapes before the b-tagging selection are used for
distributions after b-tagging as well. There is no lepton charge information associated with
the jets we are subsituting for electrons, so positive charges are applied randomly to half of
the jets and negative charges are assigned to the others.
miss disThe overall normalization is found by fitting to a kinematic distribution. The ET
tribution is usually used, although the transverse W mass has been used as a cross-check
and to help determine the uncertainty on our multijets estimate, which is 50%. The yields
are given in Table 7.1. The yields are determined separately for the µ and e channels but
are combined for the analysis done in this document, which does not distinguish between
64

lepton types.
Pretag events
Jet bin
e channel
µ channel
1-jet
24000 ± 12000 12000 ± 6000
2-jet
15000 ± 7500 6800 ± 3400
3-jet
6000 ± 3000
1700 ± 850

Tagged
e channel
320 ± 160
710 ± 355
580 ± 290

events
µ channel
290 ± 145
440 ± 220
270 ± 135

Table 7.1: Estimate of multijets yields for the pretag and preselection samples for different
number of jet selections, separated by lepton type.

7.2

W +jets Estimation

The W +jets process is a large background for this analysis after preselection and the heavy
flavor fractions are not especially well understood [68, 69, 70]. For this reason, we use the
data to determine the overall W +jets normalization as well as the normalization of the
separate quark flavor contributions. These are W +light jets, W + c+jets, W + c¯+jets and
c
W + b¯
b+jets. The last two are combined together for the purposes of this normalization.
¯
The method used here was first developed during the ATLAS tt redisovery [71], although
not used due to low statistics, and has been used in each data-based single-top analysis
note [72, 14, 15] in 2011. The general idea is to form a series of equations involving off-signal
regions which can then be solved for scale factors to adjust the W +jets MC yields to what
we expect based on the data. There are two contributions. One is the scaling of the MC
W +jets sample so that the total W +jets yield matches the data in an off-signal region. The
second is the scaling of the W +jets MC sample by flavor to match the flavor fractions in
data in off-signal regions. The scaling depends on the number of jets and the W +jets MC
flavor, which is based on what type of truth level quarks the W +jets MC event is associated
65

with: light (lq), c, c¯ or b¯ We assume that the data yield minus the multijets estimate and
c
b.
¯
the non-W +jets MC yield (single-top, tt, diboson, and Z+jets) is the W +jets yield in data.
First, the overall W +jets normalization is determined as a function of the number of
jets in the event using the sample before b-tagging is required, the pretag sample. The scale
factor is determined as:
data
NW +jets
MC
NW +jets

=

MC
N data − Nmultijets − Nnon−W +jets
MC
NW +jets

(7.1)

MC
where N data is the data yield, Nmultijets is the number of multijets events, Nnon−W +jets
MC
is the yield for MC processes which are not W +jets, and NW +jets is the W +jets yield.
The overall normalization scale factors are given in Table 7.2.
W +1jet
0.966 ± 0.001

W +2jets
0.914 ± 0.002

W +3jets
0.879 ± 0.004

Table 7.2: Scale factors for the overall normalization factor used to normalize MC to data
for W +jets. The uncertainties are statistical only.

The normalization of the individual flavor scale factors involves additional equations
corresponding to separate off-signal (sideband) regions. We use three different regions for
this: 2 jets pretag, 1 jet 1 b-tag, and 2 jets 1 b-tag. This last region contains some of the
final analysis events, so these events are removed before doing the estimate of the W +jets
flavor fractions.
We solve a series of equations for the flavor fractions, Fb¯ , Fc2 , and Flq2 , where Fc¯2
c
b2
is not listed because Fc¯2 and Fb¯ are assumed to be the same (one scale factor for both
c
b2
processes). These flavor fractions we solve for are all estimated for the 2 jet pretag selection
66

and will be propagated later on into other regions. For example, Fc2 is:
pretag
Nc2
Fc2 =
pretag
NW +jets2

(7.2)

where N is the number of events and the letters refer to the different flavors (c is c quarks).
M
W +jets2 refers to all 2 jet W +jets events. Thus, Fc2 C is the yield of MC W +jets events
with both a truth c quark and 2 jets, divided by the total MC W +jets yield with 2 jets. The
data
quantity Fc2 is what we will determine using off-signal regions, and is the total W + cjet
events in data divided by the total W +jets events in data.
The set of equations (Equations 7.3, 7.4, and 7.5) to determine the flavor fractions are
written as follows. The equations state that the total data minus W +jets backgrounds
(i.e. data-based W +jets) is the same as the sum of the MC W +jet samples separated by
flavor. In these equations, the superscripts p and t for the N quantities mean pretag and
b-tagged samples. The N ’s are yields from the data minus the non-W +jets MC (single-top,
¯
tt, diboson, and Z+jets) and multijets estimate. All other quantities use MC pretag values
except the b-tagging probabilities P , which use both MC b-tag and pretag information.
Specific definitions of quantities follow these equations:

p
p
N2 =N2 · (Fb¯ + kc¯tob¯ · Fb¯ + Fc2 + Flq2 )
b2
c b
b2

(7.3)

p
t
N1 =N1 · (Pb¯ · kb¯
b1
b2to1 · Fb¯ + kc¯tob¯ · Pb¯ · kb¯
b2
c b
b1
b2to1 · Fb¯
b2

(7.4)

+ Pc1 · kc2to1 · Fc2 + Plq1 · klq2to1 · Flq2 )
p
t
N2 =N2 · (Pb¯ · Fb¯ + kc¯tob¯ · Pb¯ · Fb¯ + Pc2 · Fc2 + Plq2 · Flq2 )
b2
b2
c b
b2
b2

(7.5)

In the equations above, Equations 7.3, 7.4, and 7.5, the P ’s are the b-tagging probability
67

where the number of jets and jet flavor are specified by subscripts. They are used to convert
the pretag sample flavor fractions (F ) we are solving for to b-tagged flavor fractions. The
MC and data P values are assumed to be the same (b-tagging scale factors are applied, see
Section 5.2.4), and we use the MC yields to determine the N ’s which form the P quantities.
For instance,

N t¯
Pb¯ = bb1
b1 N p
b¯
b1

(7.6)

The k’s in the equations are the ratio of yields in different number-of-jet bins or, in one
case (kc¯tob¯), the flavor, and are always determined using the pretag sample. They are
c b
conversion factors between jet bins or flavors. As with the P values, we use the MC yields
to calculate the k quantities, which are taken to be the same in data. For example,
p
N¯
bb1
kb¯
b2to1 = N p
b¯
b2

p
Nc¯1
and kb¯ c = pc
btoc¯ N
b¯
b1

(7.7)

Finally, as previously mentioned, the N ’s in the equation represent the number of data
minus non-W +jets MC and multijets events for the given bin, using p for pretag, t for 1
b-tag, 1 for the 1 jet bin and 2 for the 2 jet bin. Note that the N ’s are the only data-based
quantities in the flavor fraction determination.
Thus, there are three equations, Equations 7.3, 7.4, and 7.5, and three unknown F values,
meaning a solution is found with simple algebra. These F ’s are then propagated into other
number of jet bins. When these values are combined with the overall W +jets normalization
factors discussed earlier and given in Table 7.2, the final W +jets scale factors for this analysis
are obtained (WSF). The equation used to form the scale factors for the two jet bin (which
doesn’t involve extra propagation) is given below in Equation 7.8. The F/F portion is the
68

flavor fraction scaling and the N/N portion at the end of the equation is the overall W +jets
normalization from Equation 7.1. All quantities are pretag:
data
data
Fc,2 · NW jets,2
WSFc,2 =
M
MC
Fc,2C · NW jets,2

(7.8)

To find the scale factors in other bins, the three jet bin in particular, we use the following
formula, shown here for the 3 jet W c scale factor, where all quantities are pretag:
data
data
Fc,2 · NW jets,3
WSFc,3 =
M
M
MC
Fc,2C · (N M C + Nc¯,3 + Nc,3C · WSFc,2 + N M C )
c
lq,3
b¯
b,3

(7.9)

The final scale factor (WSF) values are shown in Table 7.3 for the various number of jet
bins and W +jets flavor types. These are the values used to adjust the W +jets normalization
in the analysis. The systematic uncertainties considered here are discussed in the W +jets
portion of Section 10.1.
Jet Bin

WSFb¯
b
W +1jet 1.361±0.090±1.066
W +2jet 1.252±0.090±0.864
W +3jet 1.182±0.090±0.854

WSFlq

WSFc

0.908±0.004±0.270
0.835±0.004±0.230
0.788±0.004±0.369

1.273±0.040±0.449
1.172±0.004±0.302
1.106±0.004±0.443

Table 7.3: Correction factor WSF for each W +jets flavor for the muon and electron samples
combined, with statistical (first) and systematic (second) uncertainties.

69

Chapter 8
Event Yields and Discriminating
Variables
In the full data set, it is impossible to distinguish the signal from the immense background.
To make an accurate measurement of the cross-section, we need to apply more selections that
will reduce the background and isolate the single-top t-channel signal. In this chapter we discuss the yields after the preselection and the effect of the b-tagging preselection requirement.
We will also outline the variables considered to achieve additional signal discrimination and
demonstrate the agreement between data and MC using the preselection with and without
the b-tagging requirement.

8.1

Event Yields

After applying the preselection, data-based normalization and models for multijets and
W +jets, as well as additional event corrections, we obtain the initial analysis yields which
may be compared to data. The pretag yields by process are as given in Table 8.1 and the
70

yields after preselection (i.e. including b-tagging) are given in Table 8.2. The signal divided
by background (S/B) is only about 0.1 after the preselection, but improved by about a factor
of 10 from the pretag yields, showing the importance of the b-tagging selection. The yields
are given in the different analysis channels which will be considered in Section 9.1, based on
the number of jets and charge of the lepton.
2 Jets
Lepton + Lepton t-channel
1230
678
¯
tt, Other top
1730
1680
W +light jets
102000
64800
W +heavy flavor jets
35400
30800
Z+jets, Diboson
10200
9580
Multijets
11430
10540
TOTAL Exp
162000
118000
S/B
0.01
0.01
DATA
162148
117010

3 Jets
Lepton + Lepton 816
455
3510
3510
26600
16000
10800
8920
3560
3500
3750
3890
49000
36300
0.02
0.01
46830
34925

Table 8.1: Event yields for the two-jets and three-jets tag positive and negative lepton
charge channels after the preselection, except for the b-tagging selection. The multijets and
W +jets backgrounds are normalized to the data, all other samples are normalized to theory
cross-sections. Lepton types (muon and electron) are combined.

8.2

Discriminating Variables

Because the signal divided by the background is only 0.1 after applying the preselection, we
would like to apply more selections that will reduce the background and isolate the singletop t-channel signal. Approximately 80 variables examined in the analysis. We consider
the pT and η of all of the reconstructed particles, as well as differences in the η, φ and R
quantities. For example, we consider the |∆η(b, ju )|, the ∆η between the leading untagged
jet and the b-tagged jet. We also consider the cosines of angles between various particles, as
71

2 Jets
Lepton + Lepton t-channel
611
327
¯
tt, Other top
805
781
W +light jets
544
308
W +heavy flavor jets
3100
2630
Z+jets, Diboson
175
150
Multijets
586
557
TOTAL Exp
5820
4750
S/B
0.12
0.07
DATA
5912
4701

3 Jets
Lepton + Lepton 399
221
1720
1720
183
154
1350
1020
92
83
418
430
4160
3630
0.11
0.06
4016
3491

Table 8.2: Event yields for the two-jets and three-jets tag positive and negative lepton charge
channels after the preselection. The multijets and W +jets backgrounds are normalized to
the data, all other samples are normalized to theory cross-sections. Lepton types (muon and
electron) are combined.

well as the invariant mass of various particle combinations, including all of the jets in the
event (m(AllJets)) and the b-quark, lepton and neutrino (m(lνb)). This last quantity is the
reconstructed top quark mass in processes with top quarks decaying leptonically, assuming
the decay products are correctly identified (note that we use the reconstructed neutrino z
momentum for this, see Section 4.5). We also consider the transverse mass of the W , the
sum of the momenta of various particles (H), and the sum of the pT of all the particles in
the event (HT ). Finally, we use the number of jets, the number of b-tagged jets, and the
charge of the lepton to define analysis channels. The lepton type, muon or electron, is not
used for this purpose.
The variables used in this analysis are shown in Figures 8.1 to 8.4, demonstrating good
agreement between the data and the signal plus background model. The first set of figures
shows the distributions after applying the preselection requirements except b-tagging (pretag)
for 2 jets (Figure 8.1) and for 3 jets (Figure 8.2). This first set includes a band showing the
jet energy scale uncertainty. In these figures and others, “other top” refers to the s-channel
72

and W t single-top contributions. The W +jets heavy flavor includes W c, W c¯, and W b¯
c
b+jets
Figures 8.3 and 8.4 show the same distributions after the requirement of exactly one
b-tagged jet in the event for 2 or 3 jet samples.

73

Events / 0.25

Events / 25 GeV

2 jets Pretag

∫ L dt = 1.04 fb-1
s = 7 TeV

60000

40000

s = 7 TeV

30000

10000

Data/Pred.

0
1.5
1
0.5
100

200

300

400
500
m(lνj) [GeV]

×103
100

Events / 0.30

Data/Pred.

∫ L dt = 1.04 fb-1

2 jets Pretag

20000

20000

Events / 30 GeV

40000

∫ L dt = 1.04 fb-1
s = 7 TeV
2 jets Pretag

50

0
1.5
1
0.5
0

1

2

2 jets Pretag

40000

3

4
|η(j )|
2

∫ L dt = 1.04 fb-1
s = 7 TeV

30000
20000

0

Data/Pred.

Data/Pred.

10000

1.5
1
0.5
0

200

400

600
HT [GeV]

0
1.5
1
0.5
0

2

4

6
|∆η(j , j )|

1 2

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
JES Uncertainty Band
Figure 8.1: Discriminating variables for the pretag sample (no b-tagging) for 2 jet events.
Hatched bands show the jet energy scale uncertainty. The last bin contains the sum of
the events in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. Pred. refers to the predicted signal plus background model.
74

Events / 0.25

Events / 25 GeV

3 jets Pretag

∫ L dt = 1.04 fb-1

15000

s = 7 TeV

10000

5000

Data/Pred.

0
1.5
1
0.5
100

200

3 jets Pretag

300

400
500
m(lνj) [GeV]

Events / 56 GeV

Data/Pred.

s = 7 TeV

10000

5000

Events / 30 GeV

∫ L dt = 1.04 fb-1

3 jets Pretag

∫ L dt = 1.04 fb-1
s = 7 TeV

20000
15000
10000

0
1.5
1
0.5
0

1

2

3

4
|η(j )|
2

∫ L dt = 1.04 fb-1

3 jets Pretag

s = 7 TeV

20000

10000

0

Data/Pred.

Data/Pred.

5000

1.5
1
0.5
0

200

400

600
HT [GeV]

0
1.5
1
0.5
0

200

400

600
800
m(j j j )[GeV]

12 3

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
JES Uncertainty Band
Figure 8.2: Discriminating variables for the pretag sample (no b-tagging) for 3 jet events.
Hatched bands show the jet energy scale uncertainty. The last bin contains the sum of
the events in that bin or higher. Other top refers to the s-channel and W t single-top
contributions. Pred. refers to the predicted signal plus background model.
75

Events / 0.25

Events / 20 GeV

∫ L dt = 1.04 fb-1

2000 2 jets 1 tag

s = 7 TeV

1500

1500

∫ L dt = 1.04 fb-1

2 jets 1 tag

s = 7 TeV

1000

1000
500
500

3000

100

200

2 jets 1 tag

0
0

300 400 500
m(lνb) [GeV]
Events / 0.30

Events / 30 GeV

0
0

∫ L dt = 1.04 fb-1
s = 7 TeV

2000

1000

0
0

1500

1

2

2 jets 1 tag

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

1000
500

200

400

600
HT[GeV]

0
0

2

4

6
|∆η(b, j )|
u

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 8.3: Discriminating variables for the preselection sample (with b-tagging) for 2 jet
events. The last bin contains the sum of the events in that bin or higher. Other top refers
to the s-channel and W t single-top contributions.

76

Events / 0.25

Events / 20 GeV

1500

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

1000

∫ L dt = 1.04 fb-1

3 jets 1 tag

1000

s = 7 TeV

500
500

100

200

3 jets 1 tag

0
0

300 400 500
m(lνb) [GeV]
Events / 56 GeV

Events / 30 GeV

0
0

∫ L dt = 1.04 fb-1
s = 7 TeV

1000

1

2

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1

2000 3 jets 1 tag

s = 7 TeV

1500
1000

500

500
0
0

200

400

600
HT[GeV]

0
0

200

400

600
800
m(j j j )[GeV]
12 3

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 8.4: Discriminating variables for the preselection sample (with b-tagging) for 3 jet
events. The last bin contains the sum of the events in that bin or higher. Other top refers
to the s-channel and W t single-top contributions.

77

Chapter 9
The Cut-Based Analysis
The separation of the t-channel single-top signal from its backgrounds is performed with a
cut-based analysis. This analysis type typically requires a limited number of selections. One
advantage of a cut-based analysis is that it is relatively easy to interpret. In this chapter,
we discuss the kinematic regions (channels) chosen for this analysis as well as the selections
and how they were determined.

9.1

Analysis Channels

The analysis channels are chosen to be orthogonal (non-overlapping) kinematic regions. We
choose quantities for this that are discrete, specifically the jet number and lepton charge.
The background composition depends on the number of jets in the event. The W +jets and
¯
multijets backgrounds tend to have lower numbers of jets in the event while the tt background
usually has four jets (although of course can also have less or more based on the W decay,
gluon radiation variations, jet and lepton pT thresholds, and jet reconstruction inefficiencies).
The t-channel single-top diagram has 2 or possibly 3 jets, so it is natural to look in these
78

channels.
We also consider the lepton charge when defining analysis channels. The LHC collides
protons with protons and because protons are composed of two up and one down valence
quarks, there is an excess of positively charged up valence quarks. This translates into an
excess of positively charged leptons in the case of t-channel single-top, which usually has a
valence quark in the initial state. Processes like W +jets also have some charge asymmetry,
¯
but others like tt form primarily from gluons in the initial state and do not. Thus, this
channel separation helps to reduce the background in the positively charged lepton channel
and changes the background composition.

9.2

Analysis Method

Performing the cut-based analysis includes determining the choice of selections to be applied
to each analysis channel. Each channel has its selections optimized separately, although
sometimes the final selections are the same for certain channels.

9.2.1

Selection Optimization

The optimization to determine the analysis selections for a given channel uses a significance
criterion. This has not been used to determine a significance of the result, only to optimize
the selections. The analysis itself is a cross-section measurement analysis, so one might
expect that a cross-section criterion would be used in the optimization. However, expected
cross-sections were calculated for several cut sequences and the ones with the lowest crosssection uncertainties also tended to have the lowest significance estimates. Additionally, this
criterion allows an early check of the expected significance level, which we would prefer to
79

be above 5 sigma for various channel combinations.

The significance criterion used includes the background uncertainties, and the calculation
is very fast, which is important given the number of variables and selection thresholds that
are considered. The method is a binomial significance method, also called Zbi [73]. This
S
method is chosen over other common criteria, such as √ , because it is a real significance and
B
includes systematic uncertainties. The way it is implemented in this analysis is as suggested
in the Zbi documentation [73], where δb is the background systematic uncertainty, Nb is
the background yield and Non is the signal plus background yield. These three parameters
are the only inputs, so signal yield uncertainties are not included. The value pbi is the
probability, written in the form of “the” incomplete beta function [74] (Bincomp ), as used
in the analysis. The significance is Zbi and written in terms of the error functions Ef f :
Nb
δ2
b
Nof f = τ ∗ Nb
τ =

1
pbi = Bincomp (
, Non , Nof f + 1)
1+τ
√
2Ef f −1 (1 − 2pbi )
Zbi =

Several important background uncertainties are included for the purposes of the optimization.
Included systematic uncertainties, discussed in Section 10.1, are jet energy scale, b-tagging
scale factor, mis-tagging scale factor, MC statistical, multijets background normalization,
W +jets background normalization and flavor composition, and theoretical cross-section uncertainties.
80

The optimization of the selections themselves is done in an iterative way. For a particular
variable, the significance is evaluated for about 300 different possible thresholds over the
variable range. For each histogram bin, an integral is taken in both the left and right
directions, the equivalent of a selection that is less than or greater than the threshold.
The two significance options (less than and greater than) are stored in two corresponding
histograms at that bin location. When all thresholds for a variable have been evaluated,
the maximum significance for each case for the variable in question is reported. After all
the variables we are interested in are considered, the variable with the largest significance
(and its associated threshold) is chosen. This selection is applied to the sample and the
process is repeated to choose successive selections. Figure 9.1 shows these histograms for
an example variable (the reconstructed top mass). The curve is relatively smooth and the
choice of threshold is noted. The threshold peak is relatively broad, so small changes to the
MC do not significantly impact the cut selection.

Additionally, selection sequences are considered that include the second best variable as
the first selection, or other high significance variables for this or other selections. This is
because it is possible that the best selection and threshold from the first round may be a very
harsh selection. After this selection, the statistics might be too low for further selections
to improve the significance (considering the impact on the statistical uncertainties). On the
other hand, a different sequence, starting with a weaker cut but involving two other cuts,
could, as a sequence, give a better uncertainty than the first sequence (one selection) did.
Still, it should be noted that even with this variation, not all possible cut sequences are tested
and the method is biased towards selection sequences that start with strongly discriminating
variables and cut thresholds.
81

Significance

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

50

100

150

200

250

300

350

m(lν b) [GeV]

Significance (var < X)
Significance (var > X)

Figure 9.1: Distribution of the significance (y-axis) for the reconstructed top mass, for the
2 jet channel after preselection. The vertical lines show the optimal cut thresholds for the
two selections shown (less than and greater than some reconstructed top mass value) and
the arrows indicate the region that is kept after the selection is applied.

82

Because the method includes uncertainties (including MC statistical uncertainty) and
involves integrals from a given bin to the end of a range, it is relatively insensitive to random
fluctuations. Additionally, the thresholds are rounded. There is no particular reason that a
selection on the reconstructed top mass of greater than 192.75 GeV, for example, should be
much better than a selection at 190 GeV. This then acts as a check on the selections reported
by the automated method and gives a more realistic view of the detector resolution.

9.2.2

b-tagging Threshold and Cut-Based Selections

As discussed in Section 4.3.1, the b-tagging threshold choice can have a large impact on the
analysis. Although the impact of different operating points on analysis preselection yields
was shown in that section, we can also evaluate the impact later in the analysis. Here, the
selection optimization is repeated for three different b-tagging operating points. The best
significance (for some associated threshold) for each variable is given, where each y-axis entry
corresponds to some variable i. Figure 9.2 shows this for the 3 jets channel with positively
charged leptons, preselection only, and then preselection plus one of two strong selections
on the reconstructed top mass or untagged jet η. In all three cases, the higher operating
point is favored (as used in this analysis). This was not necessarily expected; it could have
been that a looser operating point might have been paired with a tighter threshold for some
variable to give a higher significance than a tighter operating point. However, we can see
that this is not the case.
83

Variables

Variables

40

3 jets

35
30

40
35

25

20

15

15

10

10

5

m(lνb)>210 GeV

25

20

5

0
0
Variables

3 jets

30

1

2

3

4

40

0
0

5
6
7
Significance

1

2

3

4

5

6
7
8
Significance

3 jets
|η(j )|>2.0

35

u

30
25

JFNN 0.35

20
15

JFNN 2.0

10

JFNN 2.4

5
0
0

1

2

3

4

5
6
7
Significance

Figure 9.2: Distribution of the significance (x-axis) for various variables (each y-axis entry
is a separate variable), given a JetFitterCombNN b-tagging operating point, denoted by
different marker shapes. The plots are all for the 3 jets, positively charged lepton channel.
The top left plot is preselection only, the top right is preselection plus a requirement that
the reconstructed top mass be less than 210 GeV, and the bottom plot is preselection plus
a requirement that the |η| of the highest pT untagged jet be greater than 2.0. The 2.4
operating point is used in the analysis.

84

9.3

Selection Choices

For this analysis, the optimal variables and selection thresholds consist of four different
selections, where the last selection is different between the channels depending on jet number.
¯
This is due to the much larger tt background in the 3 jet channel, which is better rejected by
a different selection. There is no difference in selection for this analysis based on the lepton
charge, although it is not unreasonable that some difference in selection could happen based
on lepton charge in a future analysis, because of the different background composition.
The selections in common for all channels are: |η(ju )| > 2.0, 150 GeV < m(lνb) <
190 GeV, and HT > 210 GeV. The 2 jet selection also requires |∆η(b, ju )| > 1.0 and the 3
jet selection requires m(j1 j2 j3 ) > 450 GeV. In the case of the three jet channel, the untagged
light jet is taken to be the highest pT untagged jet in the final state. Figures 9.3 and 9.4
show the separation given by these variables after the requirement of exactly one b-tagged
jet in the event for 2 or 3 jet samples.
These selections have some physical justification. The first selection makes use of the
untagged jet. Because the t-channel initial state usually contains a valence quark, the untagged jet in the final state is often energetic and close to the beam line, much more often
than for the background processes. Thus, we require the untagged jet to be forward (close to
the beam line, so a large |η| value). The second selection simply requires the reconstructed
top mass to be close to the expected value. The single-top t-channel process only has one
top quark so the decay products are the reconstructed W boson and the b-tagged jet. In
the case of the backgrounds, there either is no top quark, or there are too many and the
correct decay products may not be matched together during the top reconstruction. Thus,
this selection also is a powerful discriminator. The third common selection requires the sum
85

Event Fraction / 0.25

s = 7 TeV

0.2
0.1
0
0

Event Fraction / 30 GeV

∫ L dt = 1.04 fb-1

2 jets 1 tag

100

200

2 jets 1 tag

300

∫ L dt = 1.04 fb-1
s = 7 TeV

0.4

0.2

0
0

200

400

∫ L dt = 1.04 fb-1

0.15 2 jets 1 tag

s = 7 TeV

0.1

0.05

0
0

400
500
m(lνb) [GeV]

1

2

3

4

5
|η(j )|

u

Event Fraction / 0.30

Event Fraction / 20 GeV

0.3

0.2

2 jets 1 tag

∫ L dt = 1.04 fb-1
s = 7 TeV

0.15
0.1
0.05

600
HT[GeV]

0
0

2

4

6
|∆η(b, j )|

u

Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 9.3: Discriminating variables for the preselection sample (with b-tagging) for 2 jet
events normalized to unit area. The last bin contains the sum of the events in that bin or
higher. Other top refers to the s-channel and W t single-top contributions.

86

Event Fraction / 0.25

s = 7 TeV

0.2

0.1

0
0

Event Fraction / 30 GeV

∫ L dt = 1.04 fb-1

3 jets 1 tag

0.4

100

200

3 jets 1 tag

300

∫ L dt = 1.04 fb-1
s = 7 TeV

0.3
0.2
0.1
0
0

200

0.15

400

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

0.1
0.05
0
0

400
500
m(lνb) [GeV]

1

2

3

4

5
|η(j )|

u

Event Fraction / 56 GeV

Event Fraction / 20 GeV

0.3

0.3

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

0.2
0.1

600
HT[GeV]

0
0

200

400

600
800
m(j j j )[GeV]

12 3

Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 9.4: Discriminating variables for the preselection sample (with b-tagging) for 3 jet
events normalized to unit area. The last bin contains the sum of the events in that bin or
higher. Other top refers to the s-channel and W t single-top contributions.

87

of the transverse momenta of the final state particles to be large, which helps to reject lower
pT W +jets or multijets events.
The final selection is different for the different jet channels. In the 2 jet channel, we
require the b-tagged jet (associated with the top) and the untagged jet to be separated in
|η|. This helps to reject backgrounds where both jets may have come from a gluon or from
a top quark decay, and are more likely to be close together than the jets in a t-channel
event. In the 3 jet channel, we require the invariant mass of the system of three jets to be
¯
large. This is a particularly good discriminator against tt events, where these three jets may
have all come from a top quark, for instance. In the t-channel single-top signal, we expect
the untagged jet to be energetic and separated from the b-jet, leading to a potentially large
invariant mass.
The individual channel compositions after all cuts are shown in Figure 9.5 and distributions after all selections except the one on the variable pictured are shown in Figure 9.6 for
the 2 jet selection and Figure 9.7 for the 3 jet selection. In all three cases, the t-channel
cross-section is normalized to the observed result formed using all four channels, as discussed
in Section 10.2.1.3.
Table 9.1 shows the number of events after all cut-based analysis selections for the positive
and negative lepton charge and number of jet channels. The t-channel yield is the standard
model expectation in this table. All analysis systematic uncertainties are included in the
reported yields. The individual uncertainty contributions are discussed in Section 10.1.
Although we do not split the events by the lepton type when making analysis channels
and determining the result, it is possible to investigate what the proportion of the different
leptons is in this analysis. There is no particular dependency on the lepton type inherent
88

Events

300 1 tag
250

∫ L dt = 1.04 fb-1
ATLAS Data
Single-top t-channel

s = 7 TeV

200

tt, Other top
W+heavy flavor

150
100

W+light jets

50
0

Z+jets, Diboson
2 Jets + 2 Jets - 3 Jets + 3 Jets -

Multijets

Lepton Charge and Jet Number

Figure 9.5: Distribution of the lepton charge after the full cut-based selection for 2 jets and
3 jets. These are the four primary analysis channels. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels. Other top
refers to the s-channel and W t single-top contributions.
this analysis and we would expect the number of electrons and muons to be roughly equal.
The leptons in the analysis come from W boson decays, and the probability of a decay to a
muon versus an electron is the same (see branching ratios in Section 2.3.2). To determine
these numbers we use all of the analysis channels combined (plus and minus charge, two
and three jets) after the cut-based selections, where the t-channel single-top contribution is
normalized to the observed cross-section determined using all four channels, and the multijets
and W +jets contributions determined using the data-based normalizations. The expected
number of events with muons is 204 and there are 182 corresponding data events observed.
For the electron selection, there are 181 events expected and 204 events observed in data.
These numbers are very similar and demonstrate the roughly one to one ratio of muons and
electrons in this analysis. The deviation of the electron yield from muon yield is about 10%,
which is well within the uncertainties for this analysis. The systematic uncertainty on the
total expected yield by channel is given in Table 9.1 and is about 15 to 20%, while the data
statistical uncertainty is about 7 to 8%.

89

Events / 0.25

Events / 20 GeV

∫ L dt = 1.04 fb-1

200 2 jets 1 tag

s = 7 TeV

150

80

s = 7 TeV

60

100

40

50

20
100

200

300 2 jets 1 tag

0
0

300 400 500
m(lνb) [GeV]
Events / 0.30

0
0
Events / 30 GeV

∫ L dt = 1.04 fb-1

2 jets 1 tag

∫ L dt = 1.04 fb-1
s = 7 TeV

200

1

2

2 jets 1 tag

40

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

20
100
0
0

200

400

600
HT[GeV]

0
0

2

4

6
|∆η(b, j )|
u

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 9.6: Discriminating variables for 2 jet events after applying all cut based cuts except
for the cut on the variable shown. The t-channel single-top contribution is normalized to the
observed cross-section determined using all four channels. Other top refers to the s-channel
and W t single-top contributions. The last bin contains the sum of the events in that bin or
higher.

90

Events / 0.25

Events / 20 GeV

80

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

60
40

100

200

3 jets 1 tag

300

s = 7 TeV

20

∫ L dt = 1.04 fb-1
s = 7 TeV

20

0
0

400
500
m(lνb) [GeV]

1

2

3

4

5
|η(j )|

u

Events / 56 GeV

Events / 30 GeV

30

10

20
0
0

∫ L dt = 1.04 fb-1

3 jets 1 tag

∫ L dt = 1.04 fb-1

80 3 jets 1 tag

s = 7 TeV

60
40

10
20

0
0

200

400

600
HT[GeV]

0
0

200

400

600
800
m(j j j )[GeV]

12 3

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets
Figure 9.7: Discriminating variables for 3 jet events after applying all cut based cuts except
for the cut on the variable shown. The t-channel single-top contribution is normalized to the
observed cross-section determined using all four channels. Other top refers to the s-channel
and W t single-top contributions. The last bin contains the sum of the events in that bin or
higher.

91

Cut-based 2 Jets
Lepton +
Lepton t-channel
85.2 ± 28.6 39.4 ± 12.8
¯
tt, Other top
14.0 ± 6.4 12.8 ± 4.2
W +light jets
3.3 ± 1.9
2.0 ± 1.2
W +heavy flavor jets 39.1 ± 10.6 27.1 ± 7.5
Z+jets, Diboson
1.1 ± 0.8
1.0 ± 0.8
Multijets
0.2 ± 0.2
0.3 ± 0.3
TOTAL Exp
142.9 ± 31.2 82.6 ± 15.5
S/B
1.5
0.9
DATA
193
101

Cut-based 3 Jets
Lepton +
Lepton 33.6 ± 7.0
14.6 ± 6.2
10.5 ± 4.2
10.7 ± 7.9
0.8 ± 1.3
0.3 ± 0.3
8.7 ± 6.0
3.4 ± 3.1
0.3 ± 0.2
0.2 ± 0.3
1.5 ± 1.1
3.1 ± 2.0
55.5 ± 10.2 32.2 ± 10.68
1.6
1.0
53
39

Table 9.1: Event yields for the two-jets and three-jets tag positive and negative leptoncharge channels after the cut-based selection. The multijets and W +jets backgrounds are
normalized to the data, all other samples are normalized to theory cross-sections (including
single-top t-channel). Uncertainties shown are systematic uncertainties. Other top refers to
the s-channel and W t single-top contributions.

92

Chapter 10
The Measurements
The purpose of this dissertation is to measure the single-top t-channel cross-section. In
previous chapters we have modeled the signal and backgrounds, and reduced the backgrounds
yields relative to the signal, first in an initial preselection and then again using cut-based
selections. In this chapter, we evaluate the signal cross-section after applying these selections
and discuss the uncertainties related to this measurement. We also estimate the value of the
CKM matrix element |Vtb |.

10.1

Systematic Uncertainties

Before we can determine the cross-section, we need to evaluate the uncertainties on the
quantities which go into the calculation. The cross-section is related to the number of
events that are observed for some given amount of proton-proton interactions, as stated in
Section 2.3.2. If more events are observed than expected, the cross-section is higher than the
expected value. Uncertainties on the measurement are important here, as deviations from
the expected cross-section may well be due to systematic uncertainties. In this section, we
93

discuss the systematic uncertainties on the measurement.
There are several sources of systematic uncertainties relevant to this analysis.

We

overview them by category and then give some information about their impact on the signal
and background yields. Most of the uncertainties are related to how well the MC reproduces
the data. For additional information on most of the scale factors, corrections, and MC itself,
see Chapter 5.
b-tagging: There is an uncertainty associated with the b-tagging and mis-tagging scale
factors, which relate the efficiencies measured in data to those in MC. The mis-tagging
scale factor uncertainty is small for this analysis, but the b-tagging efficiency scale factor
uncertainty can be large. There is also a c-tagging efficiency uncertainty, which for this
analysis is assumed to be twice that of the b-tagging efficiency uncertainty. This is considered
fully correlated with the uncertainty in b-tagging efficiency and is included in the reported
b-tagging efficiency scale factor uncertainty. This is a large uncertainty for this analysis,
with variations of around 10% on the signal and background yields.
Leptons: There are uncertainties on the lepton scale factors, which relate the trigger,
identification, and reconstruction scale factors in data to MC, and also uncertainties on the
lepton energy scale and resolution, which are related to smearing the lepton energy, described
in Section 5.2.5. For this study there was an issue with the MC related to the muon trigger
matching. This caused us not to apply trigger matching for the muon channel (although the
trigger itself was still applied). An uncertainty of 1.5% was added to account for this. These
uncertainties overall are typically < 5% for the different analysis processes.
Jets: There are three uncertainties associated with jets: the jet energy scale (JES), jet
energy resolution (JER) and jet reconstruction (jetreco). The JES uncertainty [43, 63] is
94

related to the energy calibration. For example, we may not have perfectly simulated the
dead material or leakage when adjusting the energy and there is some uncertainty related to
this. JES includes a few different components, including a pile-up and b-JES contribution.
The pile-up is a special correction to account for pile-up conditions during 2011 data taking
and the effect on jet energies. The b-JES factor is a separate correction for jets which have
a truth b-quark assignment. It considers b-quark fragmentation, material and calorimeter
response separately for these jets. There is also some consideration of flavor composition
uncertainty (gluon fraction distribution), which has a different distribution for each of the
top samples and a flat distribution for other processes. The distance to other jets is also
considered and jets that are close to one another have an additional uncertainty. Overall,
this JES uncertainty (after including W +jets scale factor correlations) is largest for the light
quark W +jets events, which are removed effectively by analysis cuts. The impact is around
¯
10% for tt and a few percent for the signal in the largest signal channel, 2 jets with a positive
lepton charge.
The other two jet related uncertainties generally have an impact of a few percent for
the different processes. JER uncertainty is evaluated by smearing the jet energy (this is
not done in the nominal sample, unlike for leptons, as discussed in Section 5.2.5). The
jet reconstruction evaluates how sensitive the analysis is to a missed jet. This is done by
randomly dropping jets from the event based on jet kinematics.
Theoretical cross-section: There are several processes for which we do not have databased normalization estimates. In most cases, the contribution of these processes to the
¯
final yield is small. In the case of tt, we have performed a cross-check (see Appendix A)
and found the estimated normalization is consistent with the theoretical value, which has a
95

smaller uncertainty. We use a 10% uncertainty for the single-top s-channel and W t processes,
5% for diboson processes, 60% uncertainty for Z+jets and the cross-section variation is
¯
taken to be 164.57+11.4 pb for the tt process [71, 75]. In this analysis we combine certain
−15.7
processes together when reporting yields and results. When this is done, uncertainties such
as the theoretical cross-section uncertainty are based on the proportion of each process in
the combined sample (rather than taking the largest uncertainty, for instance).
Multijets: There is an uncertainty on the multijets normalization, discussed in Section 7.1. This is determined by re-estimating the normalization by fitting a different variable
(W transverse mass). We use 50% for this uncertainty.
W +jets: There are uncertainties on the W +jets scale factors discussed in Section 7.2.
These include b-tagging scale factor, mis-tagging scale factor, JES, cross-section, and data
statistical uncertainties. Many of these uncertainties are correlated with the uncertainties
in the t-channel single-top cross-section measurement. This means that the behavior of the
JES uncertainty for the W +jets scale factor estimate and W +jets yield JES uncertainty are
related to each other.
To properly include these correlations, we re-estimate the W +jets scale factors for each
uncertainty scenario and then apply the appropriate scale factor when estimating the W +jets
yield uncertainty. We assume that the JES upward shift scenario, for example, is the “real”
scenario and do all of the estimations such as we would for the nominal sample, using JES
upwardly shifted numbers instead of nominal numbers. Then, to find the total JES upwardly
shifted uncertainty, we compare the final yield (with the JES shifted scale factors applied to
the JES shifted sample) to the nominal sample (with the nominal scale factors applied to
the nominal sample).
96

The JES, b-tagging scale factor and mis-tagging scale factor uncertainties always include
these correlation effects. The theoretical cross-section uncertainties and multijets normalization uncertainties for the W +jets scale factors are also correlated, but because they are not
correlated with W +jets yield uncertainties, they are listed separately when uncertainties are
given by processes (and are given in this way to the statistical tool). The correlations are
included in the final cross-section measurement. It should be noted that a 100% uncertainty
is used for the single-top cross-section uncertainties for the W +jets scale factors estimate.
Finally, the statistical uncertainties are considered separately and are referred to as W +jets
normalization uncertainties. These are ≤ 5%.
There is another uncertainty associated with the W +jets normalization, related to the
propagation of the scale factors from the 2 jet bin to other bins. This is a 25% uncertainty
for a movement to the 3 jet bin. This is referred to as the W +3 jet bin normalization
uncertainty.
One additional uncertainty related to the W +jets is an uncertainty on the simulated
shape. To evaluate this, two Alpgen [54, 76] parameters are varied and the uncertainties
from these two variations are added in quadrature. These parameters are the minimum
Alpgen pT to consider a parton a hard (high pT ) parton (ptjmin) and the function which
gives the factorization scale for the pdf (iqopt).
MC statistical: There is an uncertainty associated with the number of simulated MC
events. If not enough events are generated, there may not be a sufficient range of kinematics
to accurately represent the data. The uncertainty is evaluated as the square root of the sum
of the squares of the event weights and can range as high as 98% after all cut-based analysis
selections.
97

LAr hole: There is some uncertainty on the removal of events affected by the LAr hole,
discussed in Section 3.2.8. The uncertainty is a ±1 sigma variation of the jet pT threshold
for jets considered as potentially being in the dead region and typically has a < 5% effect
on the signal and background yields.
miss related uncertainties [47] for this analysis. The first
Missing ET : There are two ET
miss pile-up uncertainty) and the second is due to energy scale and
is due to pile-up effects (ET
miss uncertainty), including cell out contribution uncertainties
energy resolution effects (ET
(energy deposits not associated with jets, electrons, τ ’s or photons) and soft jet uncertainties
(related to objects that have a pT too low to be considered a jet). The pile-up uncertainty
portion is a 10% variation. Both uncertainties typically range from 1 − 10%.
ISR/FSR: There is some uncertainty on the simulation of initial and final state radiation.
These are extra particles perhaps formed by gluons producing extra radiation (jets) in the
initial or final state portion of the Feynman diagram. Extra jets, if the pT is high enough,
could move events from the 2 jet channel to the 3 jet channel and thus affect the analysis.
Radiation can also potentially reduce the jet energy for a given jet enough to make the jet
fall below the pT theshold to be considered as such or impact pT related event selections.
This uncertainty is evaluated by changing certain parameters when producing the MC to
¯
increase or decrease the parton shower activity, and is evaluated separately for the tt and
single-top processes. Special AcerMC samples showered with Pythia are used for all the
top processes. For this analysis, we vary the ISR and FSR simultaneously (which produces
a larger variation than varying them separately for the largest signal channel, 2 jets with
positive leptons). This is one of the largest uncertainties, with variations of around 10 − 30%
depending on the process.
98

PDF: The uncertainty of the parton distribution function is evaluated by finding the
variation from changing the PDF in the preselection sample from the one used in this analysis
(see Section 5.1), to CTEQ66 [55] and MSTW2008nnlo68cl [57, 77]. This uncertainty
ranges from 1% to 8% depending on the process.
Generator and Shower: The MC generator or showering programs may not exactly
match the data. To evaluate these uncertainties, an alternative generator or showering
¯
program is used and the deviation determined. This is done for the tt and the singletop processes. For the t-channel single-top process, MCFM [78] is used to determine the
deviation of the signal acceptance from the nominal (with AcerMC) to be 7%. For the
other processes, the generator uncertainties are determined after cut-based selections as
¯
usual, using MC@NLO versus Herwig for tt and AcerMC versus MC@NLO for the
s-channel and W t single-top processes. The shower uncertainties for the single-top processes
¯
are determined using AcerMC plus Pythia versus AcerMc plus Herwig. The tt shower
uncertainties are found by comparing yields from Powheg [79, 80] plus Pythia and Powheg
plus Herwig. These uncertainties are all symmetrized, so the deviation between the nominal
and the alternate program is divided in half, where one half is taken as the up shift and the
other is taken as the down shift. These are some of the larger uncertainties in the analysis,
with variations around 10 − 15% depending on the process.
η reweighting: The shape of the η distribution of the forward jet is not especially wellmodeled. We adjust the MC to match the data in a pretag sample for this distribution and
then evaluate the difference between using this and using the nominal sample after all of
the analysis selections. This uncertainty is a one-sided uncertainty (there is only a positive
shift, no negative shift). The uncertainty is about 5 − 10% depending on the process.
99

Luminosity: The luminosity estimate has some uncertainty associated with it. The
luminosity estimate is done with dedicated luminosity estimate runs. The uncertainty is
3.7% [34] for the data used in this analysis.
The individual uncertainties that are used to find the total cross-section uncertainties
are given in Table 10.1, Table 10.2, Table 10.3, and Table 10.4 by process, where each table
gives the values for a different analysis channel. These are the values which are used in the
statistical tool (see Section 10.2.1) to determine the cross-section. In certain cases, processes
have very high MC statistical uncertainties after all cut-based selections, especially in the 3
jet channels. This can cause some large estimates for other uncertainties as well. Although
the actual uncertainties may not be as high as we estimate, we keep the large values to be
conservative.

10.1.1

Effect of Pile-up

For this study, there are on average about 6 interactions per crossing (primary vertices),
and it is possible that extra events could cause problems at the reconstruction level when
identifying the primary vertex or reconstructing jets. To determine the impact of pile-up on
this analysis, the MC was divided into two samples based on the number of primary vertices
in the event, where high pile-up is considered to be ≥ 6 primary vertices and low pile-up
is considered to be < 6 primary vertices. The sample is divided before any selections and
then normalized to the expected yields in both cases. The analysis is repeated using each
sample, and we find that the cross-section shifts by 6% versus nominal when using the high
pile-up sample and 4% versus nominal when using the low pile-up sample. This is within the
statistical uncertainty of the analysis and also within the MC statistical uncertainty, which
100

Uncertainties(%)
Jet energy scale
Jet energy resolution
Jet reconstruction
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Generator single-top
¯
Generator tt
Shower
ISR/FSR
PDF
Luminosity
miss
ET

¯
t-channel tt, W t, s W +light W +heavy Z,Dib.
-3
-11
-19
-1
33
-1
7
28
-9
-9
±4
±1
±4
<1
<1
±2
<1
±1
12
9
7
-3
15
-12
-9
-10
3
-15
<1
<1
24
-4
5
<1
<1
-23
4
-5
±3
±3
±2
±1
±1
±4
±7
±1
±1
±11
±12
-15
32
27
39
±3
±8
±1
±4
±4
±4

Multijets
-

LAr
η reweighting
W shape
W jj norm
W c, c¯, b¯ norm
c b
W 3 jet norm
Multijets
¯
tt XS
single-top XS
Z+jets XS
Diboson XS
MC Statistics

-1

-5

-5

-1

-

<1
miss pile-up
ET

-1

1

-16

<1

<1

-

-2

-1

-5

-5

-1

-

<1
1
-1
5
-

1
1
-1
2
-

-16
<1
<1
<1
<1
<1

-2
<1
-1
4
<1
-

<1
<1
<1
9
-

-

-

-

-

-

-

±4

±5
±2
±6

±3
±1
±4
±6
<1
±34

±5

±41
±2
±47

±50
±100

±9
±5
±17
±2
<1
±12

Table 10.1: Percent systematic uncertainties for the 2 jet plus channel. Here, XS means
cross-section, Z means Z+jets, and Dib. means diboson. Norm refers to normalization, s
indicates single-top s-channel. If two values are given, the top value is the upshift and the
bottom value is the downshift.
101

Uncertainties(%)
Jet energy scale
Jet energy resolution
Jet reconstruction
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Generator single-top
¯
Generator tt
Shower
ISR/FSR
PDF
Luminosity
miss
ET

¯
t-channel tt, W t, s
<1
-7
-4
9
±3
±1
<1
<1
12
9
-12
-9
<1
<1
<1
<1
±3
±3
±2
<1
±7
<1
±9
±14
±5
-14
-16
24
25
±3
±8
±4
±4

LAr
η reweighting
W shape
W jj norm
W c, c¯, b¯ norm
c b
W 3 jet norm
Multijets
¯
tt XS
single-top XS
Z+jets XS
Diboson XS
MC Statistics

<1

<1
miss pile-up
ET

-4

W +light W +heavy Z, Dib.
-22
3
-1
-19
-11
-20
±30
±1
±2
±2
9
2
4
-12
-3
-4
23
-3
21
-22
3
-21
±3
±5
±1
±4

Multijets
-

-7

-13

<1

-

2

<1

2

1

-

-3

<1

-7

-11

<1

-

<1
<1
-1
4
-

2
1
-1
2
-

<1
<1
-1
4
±3
<1

2
<1
-3
4
±2
-

<1
<1
<1
4
-

-

-

-

-

-

-

±6

±6
±2
±6

±3
±1
±4
±6
<1
±45

±4

±40
±2
±55

±50
±100

±6
±1
±5
±2
<1
±15

Table 10.2: Percent systematic uncertainties by process for the 2 jet minus channel. Here,
XS means cross-section, Z means Z+jets, and Dib. means diboson. Norm refers to normalization, s indicates single-top s-channel. If two values are given, the top value is the upshift
and the bottom value is the downshift.
102

Uncertainties(%)
Jet energy scale
Jet energy resolution
Jet reconstruction
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Generator single-top
¯
Generator tt
Shower
ISR/FSR
PDF
Luminosity
miss
ET

¯
t-channel tt, W t, s
4
-8
-10
16
<1
<1
±1
<1
9
7
-9
-8
<1
<1
<1
<1
±3
±3
±1
±1
±7
<1
±22
±7
±8
-5
4
-1
22
±3
±8
±4
±4

LAr
η reweighting
W shape
W jj norm
W c, c¯, b¯ norm
c b
W 3 jet norm
Multijets
¯
tt XS
single-top XS
Z+jets XS
Diboson XS
MC Statistics

-1

3
miss pile-up
ET

-1

W +light W +heavy Z, Dib.
18
37
-32
-17
17
-40
±10
±2
±2
±3
2
-7
11
-4
9
-11
33
-4
1
-32
3
-1
±2
±9
±1
±4

Multijets
-

-98

5

<1

-

-2

<1

-3

<1

-

1

<1

-98

5

<1

-

1
<1
-2
6
-

-2
2
-1
4
-

-5
<1
<1
7
±1
-

<1
<1
<1
5
-

-

-

-

<1
<1
-2
4
±2
±1

-

-

±7

±7
<1
±6

±25
±6
±3
±2
±7
<1
±70

±5

±25
±15
±14
±38
±3
<1
±23

±40
±2
±67

±50
±48

-

Table 10.3: Percent systematic uncertainties by process for the 3 jet plus channel. Here,
XS means cross-section, Z means Z+jets, and Dib. means diboson. Norm refers to normalization, s indicates single-top s-channel. If two values are given, the top value is the upshift
and the bottom value is the downshift.
103

Uncertainties(%)
Jet energy scale
Jet energy resolution
Jet reconstruction
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Generator single-top
¯
Generator tt
Shower
ISR/FSR
PDF
Luminosity
miss
ET

¯
t-channel tt, W t, s
7
-6
-21
14
±1
±6
<1
±1
9
6
-9
-8
<1
<1
<1
<1
±3
±3
±3
±2
±7
<1
±30
±10
±50
29
40
30
22
±3
±8
±4
±4

LAr
η reweighting
W shape
W jj norm
W c, c¯, b¯ norm
c b
W 3 jet norm
Multijets
¯
tt XS
single-top XS
Z+jets XS
Diboson XS
MC Statistics

<1

-4
miss pile-up
ET

-4

W +light W +heavy Z, Dib.
-39
73
<1
-26
24
55
±12
±2
±1
±10
6
-3
18
-7
3
-18
16
-4
<1
-16
4
<1
±98
±17
<1
±4

Multijets
-

<1

<1

<1

-

<1

<1

<1

<1

-

-4

-1

<1

-1

<1

-

-3
<1
-1
5
-

-1
1
-2
5
-

<1
<1
<1
4
±1
-

<1
<1
<1
5
-

-

-

-

<1
<1
<1
6
±3
±1

-

-

±11

±6
<1
±6

±25
±6
±3
±2
±7
<1
±66

±5

±25
±12
±10
±26
±3
<1
±35

±60
<1
±98

±50
±39

-

Table 10.4: Percent systematic uncertainties by process for the 3 jet minus channel. In
this table, XS means cross-section, Z means Z+jets, and Dib. means diboson. Norm refers
to normalization, s indicates single-top s-channel. If two values are given, the top value is
the upshift and the bottom value is the downshift.
104

increases when the sample is halved. Based on this study, we consider the analysis to be
insensitive to pile-up effects.

10.2

Results

In this section we discuss the technique used to determine the observed cross-section and
the |Vtb | value. We discuss five different results, involving different combinations of the
four channels considered based on the number of jets and lepton charge: 2 jets with a
positively charged lepton, 2 jets with a negatively charged lepton, 3 jets with a positively
charged lepton, 3 jets with a negatively charged lepton. These combinations are 2 jets, 3 jets,
plus (positively charged lepton), minus (negatively charged lepton), and all four channels
combined. The measurement from the combination of the four channels leads to the primary
analysis result.

10.2.1

Cross-section Calculation

As mentioned earlier, the cross-section is related to the number of observed events. However, multiple analysis channels and a variety of uncertainties make the calculation more
complicated that simply subtracting the expected background yield from the data and finding the deviation of this value from the expected signal yield. Also, because the number of
data events observed is determined after making selections for the signal, we multiply the
expected signal yield by the signal acceptance, making both background and signal uncertainties part of the equation. The cross-section calculation is performed using a statistical
tool called BILL (Binned Log Likelihood Fitter) [81], used previously for a neural network
single-top analysis [15].
105

The cross-section is determined via a maximum likelihood fit of the signal and background
model to the data, allowing yields to float by different amounts constrained by a Gaussian
term. Scale factors (β) are determined for each process, where these scale factors are the
ones that give the best fit to the data, for all channels considered. The data-based W +jets
and multijets estimates are not allowed to vary, while the other non-signal processes may
float within their theoretical cross-section uncertainties. The signal yield has no restrictions.
The fit is based on a product of Poisson likelihoods for each channel which is multiplied by
the product of the Gaussian constraints for all the backgrounds. The Gaussian distributions
account for our prior knowledge of the backgrounds, and have a width of the theoretical
uncertainty variation ( 0 for data-based backgrounds, the theoretical uncertainty for other
backgrounds).
Because this analysis is a cut-and-count type of analysis, each channel has a distribution
which is just one bin, each measurement uses 2 or 4 channels, and the fit itself is very
straight-forward. The results of the fit are given in Table 10.5, where these values are scale
factors to be multiplied onto the expected yields to get the observed yields. These factors are
the output from the BILL tool. Because the data-based backgrounds have a β value defined
to be 1, and the other backgrounds have low theoretical uncertainties, the only β values that
are not approximately 1 are those for the signal. The t-channel β value is multiplied by the
expected cross-section to obtain the observed cross-section.
This tool uses a frequentist method to determine the cross-section uncertainties, meaning
many (100,000) different pseudo-experiments are generated based on the input yield and
uncertainties. In this way, all the various possibilities within uncertainties are explored and
a distribution reflecting the probability of all possible outcomes is created, where the RMS
106

Channels
All Channels
2 Jets
3 Jets
Plus Charge
Minus Charge

¯
t-channel tt,
1.4184
1.5543
1.0544
1.4006
1.4653

Other top W +light W +heavy Z, Dib.
0.9936
1.00000
1.00000
1.0083
0.9985
1.00000
1.00000
0.9974
1.0079
1.00000
1.00000
1.0015
0.9917
1.00000
1.00000
1.0065
1.0000
1.00000
1.00000
1.0001

Multijets
1.0000
1.0000
1.0000
1.0000
1.0000

Table 10.5: The fit values by process and channel. The 2 or 3 jet channels include both
lepton charges, and the lepton charge channels include both 2 and 3 jet events. All channels
is the combination of plus and minus lepton charge events with 2 and 3 jets. Dib. means
diboson and Z means Z+jets.

reflects the overall combined uncertainty of the measurement. The number of events in each
pseudo-experiment is determined via a Poisson distribution with a mean of the expected
yield and the uncertainties are varied by Gaussian distributed random numbers. There is
also a factor related specifically to the theoretical uncertainties of the backgrounds, as was
the case for the fit to determine the β values, but again this has a small impact on the result.

The results are displayed in Figure 10.1, where the total cross-section uncertainty is derived from the mean and the RMS of the distribution. For the observed uncertainty, the
yields are scaled by the fit values, so β is now 1. The deviation of the mean from 1 is
the bias (representing the asymmetry of the uncertainties), and this is added in quadrature
with the RMS to give one side of the uncertainty, while the RMS alone (0 bias assumption) gives the other uncertainty shift. In other words, the uncertainty is the

RMS2 or

(1 − mean)2 + RMS2 . For the example in Figure 10.1, which uses observed yields for all
four channels and includes all of the uncertainties, the RMS is 0.284 and the mean is 1.133,
giving uncertainties of +31% and -28%.
107

Ensembles

4000

∫ L dt = 1.04 fb-1

3500

s = 7 TeV
All Channels, 1 tag

3000
2500
2000
1500
1000
500
0
0

0.5

1

1.5

2

2.5

β

Figure 10.1: Pseudo-experiment distribution used for the final cross-section uncertainty determination. This distribution is for the observed cross-section uncertainty, for all channels
combined. The β value is the fit for a given pseudo-experiment with yields scaled by the
values in Table 10.5, and the uncertainty is determined from the distribution RMS and
deviation of the mean from 1.
10.2.1.1

Two and Three jet Single Top Quark t-channel Production

We can combine the four separate channels into sets of 2 jets and 3 jets (lepton charges are
combined). When this is done we find a cross-section of σt = 100+9 (stat)+32 (syst) =
−9
−31
100+33 pb for 2 jets, where the expected cross-section is σt = 65+23 pb, and σt =
−32
−23
68+13 (stat)+28 (syst) = 68+30 pb for 3 jets, where the expected cross-section is σt =
−13
−22
−25
65+30 pb. Both results are consistent with the standard model value within about one
−24
standard deviation and consistent with each other within uncertainties.

10.2.1.2

Positively and Negatively Charged Single Top Quark t-channel Production

One can also combine the four channels into a positive and negative lepton charge sample.
Because the top quark decays to a W boson and b-quark (and then the W boson decays to
108

a lepton and a neutrino) without hadronizing, the charge information from the top quark
is preserved in the lepton. Therefore, the positively charged lepton channel measurement
corresponds to a measurement of the positively charged top quark portion of the t-channel
single-top cross-section. There is a separate theoretical prediction for the top and antitop portions of the cross-section, given in Section 2.3.2. The results of this measurement are
σ + = 59+6 (stat)+17 (syst) = 59+18 pb for top (positive lepton charge), where the expected
−6
−16
−16
t
cross-section is σ + = 42+14 pb. The measurement is σ − = 33+5 (stat)+12 (syst) =
−13
−5
−11
t
t
33+13 pb for anti-top (negative lepton charge), where the expected cross-section is σ − =
−12
t
23+10 pb.
−10
10.2.1.3

Combined t-channel Production Cross-section Result

Finally, all four channels can be combined to give a total cross-section result. The observed
t-channel single-top cross-section is σt = 92+7 (stat)+28 (syst) = 92+29 pb, where σt =
−7
−25
−26
65+22 pb is expected. This is consistent with the standard model and within about one
−20
standard deviation of the theoretical single-top t-channel cross-section.
Table 10.6 shows a breakdown of the systematic uncertainties and their contribution
to the expected cross-section measurement for the combination of all four channels and
Table 10.7 shows the same but for the observed result. The data statistical uncertainty is
much lower than the systematic uncertainties, meaning that this cross-section measurement
is dominated by systematic uncertainties. The largest uncertainties for this analysis are
ISR/FSR, shower/generator, and b-tagging uncertainties.
The ISR/FSR uncertainty may decrease in future analyses as this is studied further and
the level of variation required is better understood. The b-tagging uncertainty will also likely
improve in future analyses as more data are collected and the b-tagging efficiencies and scale
109

factors are better estimated. The shower/generator uncertainty is unlikely to change very
much until shower/generator programs are updated. On the other hand, the MC statistical
uncertainty will become more of an issue in future analyses. As the data statistics increase,
the number of MC events that must be generated increases. This means that the MC
statistical uncertainty will increase in future analyses unless they are altered to use looser
selections or faster MC generation methods.
Source
Data statistics
MC statistics
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Jet energy scale
Jet energy resolution
Jet reconstruction
W shape
W jj normalization
W c, c¯, b¯ normalization
c b
W 3 jet normalization
η reweighting
miss
ET
miss pile-up
ET
LAr
PDF
Generator
Shower
ISR/FSR
Theory cross-section
Multijets
Luminosity
Total Systematics
Total

∆σ/σ (%)
+10/-10
+6/-6
+13/-13
+1/-1
+3/-3
+1/-1
+2/-3
+2/-2
+1/-1
+1/-1
+1/-1
+2/-2
+2/-2
+8/-5
+1/-2
+1/-2
+1/-1
+5/-5
+8/-8
+12/-11
+21/-19
+7/-7
+3/-3
+5/-5
+33/-29
+34/-31

Table 10.6: Systematic uncertainties for the expected t-channel cross-section measurement,
where the final line includes all systematic uncertainties and the data statistical uncertainty.

110

Source
Data statistics
MC statistics
b-tagging scale factor
Mistag scale factor
Lepton scale factor
Lepton efficiencies
Jet energy scale
Jet energy resolution
Jet reconstruction
W shape
W jj normalization
W c, c¯, b¯ normalization
c b
W 3 jet normalization
η reweighting
miss
ET
miss pile-up
ET
LAr
PDF
Generator
Shower
ISR/FSR
Theory cross-section
Multijets
Luminosity
Total Systematics
Total

∆σ/σ (%)
+8/-8
+4/-4
+12/-12
+1/-1
+3/-3
+2/-2
+2/-3
+2/-2
+1/-1
+1/-1
+1/-1
+2/-2
+2/-2
+7/-5
+1/-2
+1/-1
+1/-1
+4/-4
+7/-7
+11/-11
+19/-18
+5/-5
+2/-2
+4/-4
+30/-27
+31/-28

Table 10.7: Systematic uncertainties for the observed t-channel cross-section measurement,
where the final line includes all systematic uncertainties and the data statistical uncertainty.

111

10.2.2

Estimate of |Vtb |

As discussed in Section 2.2, the CKM matrix element |Vtb | can be directly estimated from
t-channel single-top production using the ratio of the observed and predicted cross-sections.
We again use the notation where VL is Vtb plus (potentially) a factor that depends on the
new physics scale [27]. We may write (based on Equation 2.3), where σ is the cross-section,
obs refers to the observed value and sm refers to the standard model prediction:
σobs
|V
|
σsm L,sm

|VL,obs | =

(10.1)

or, with |VL,sm | = |Vtb | = 1 from the standard model we obtain,
σobs
σsm

|VL,obs | =

(10.2)

Performing the calculation to propagate the uncertainties gives

δV L,obs =

VL,obs
2

δ
δsm 2
)
( obs )2 + (
σobs
σsm

(10.3)

where δ refers to the uncertainty. Thus, we obtain a value of |VL,obs | = 1.19+0.20 for
−0.18
the four channel combination. In this case we used 10% for the theoretical cross-section
uncertainty [71]. This result is consistent with the standard model value of 1.0 (and thus
being simply the standard model |Vtb |) within two standard deviations.
It is also possible to determine a lower 95% confidence level limit on the |Vtb | value,
assuming a standard model upper value of 1. We form a Gaussian with a mean of 1.42
(the measured divided by standard model cross-section) and use the uncertainty given for
112

the combined result. We integrate from 1 towards 0, taking the limit to be the point where
95% of the curve has been integrated. With this standard model assumption, we obtain
|Vtb | > 0.67 at the 95% confidence level.

10.2.3

Comment on Significance

It is fairly straightforward to determine a significance using a frequentist tool like BILL.
One simply determines the likelihood of a background-only hypothesis fluctuating to imitate
the signal hypothesis, and we do this by evaluating many pseudo-experiments. Pseudoexperiments are generated as described in Section 10.2.1. The calculation is done by determining the value −2ln(Q), the test statistic (also known as the log-likelihood ratio or LLR).
A fit is done for a given ensemble to determine how likely it is that the ensemble satisfies
the background only (HB ) or signal plus background (HSB ) hypotheses. The ratio of the
probabilities is the Q in the LLR value:

Q=

p(HSB )
p(HB )

(10.4)

The expected significance is determined from the number of background-only pseudoexperiments that have a LLR value that is greater than the mean of the pseudo-experiments
which assume a signal plus background (standard model) hypothesis. This is done by finding
the mean of the signal plus background LLR distribution and finding how many background
only ensembles have LLR values above this mean, compared to the total number of background only ensembles. In this way, the probability of the background fluctuating to look
like the signal, and thus the significance, can be determined.
The difficulty with this method is that around and especially above the 5 sigma signifi113

cance level (the level at which observation is typically claimed in high energy physics), the
number of pseudo-experiments needed can become very large (10 million to 100 million or
more). For this dissertation, the result has been shown to be above 5 sigma previously [14, 15]
with less data and larger systematic uncertainties, so we do not repeat this for the main result. We do demonstrate the individual expected results for two channels below 5 sigma,
the 3 jet and negative charge channels. In high energy physics, discovery requires a 5 sigma
significance, or a p-value (probability) of the background fluctuating to look like signal of
0.0000006. Evidence requires 3 sigma significance, or a p-value of 0.003.
The LLR distributions for the three jet and negative charge channels are shown in Figure 10.2. About 800000 pseudo-data sets were created in each case. For the three jet channel,
the expected significance is 3.8 sigma with a p-value of background fluctuating to look like a
standard model signal of 8 × 10−5 . For the minus charge channel, the expected significance
is 4.1 sigma with a p-value of background fluctuating to look like a standard model signal of
2 × 10−5 .

114

Background Only
Signal and Background

Figure 10.2: Distribution used to determine the expected significance for the 3 jet channel
(all lepton charges are allowed) and negative charge channel (2 and 3 jets allowed). The
two curves are ensembles with and without the assumption of a standard model signal. The
vertical line shows the mean of the standard model signal and background distribution.
115

Chapter 11
Conclusions and Implications for
Future Work
In this dissertation we have discussed the estimate of the t-channel single-top cross-section
using ATLAS data. The ATLAS detector is a multi-purpose detector located at the LHC
at CERN and 1.04 fb−1 of data from the 2011 data taking run was used, with a 7 TeV
center-of-mass energy. The data were processed to assign energy and tracks to reconstructed
particles like those in a Monte Carlo simulation. Selections were applied to both the data
and MC to reduce the signal and background ratio to a more reasonable level of about 0.1.
At this point, a cut-based analysis was performed, where four additional selections for four
orthogonal channels based on jet number and lepton charge were chosen and applied. A fit
and frequentist technique was then used to determine the cross-section and its uncertainty.
Separate measurements of the top and anti-top cross-section were performed, giving observed
results of σ + = 59+18 pb for top (positive lepton charge) and σ − = 33+13 pb for anti-top
−16
−12
t
t
(negative lepton charge). The final result included all four channels and was σt = 92+29 pb,
−26
116

where σt = 65+22 pb was expected. Additionally, we found |VL,obs | = 1.19+0.20 for the
−20
−0.18
four channel combination and, assuming a standard model upper limit of 1 on this value,
we determined a lower-bound 95% confidence level limit of |Vtb | > 0.67. These are the first
measurements of t-channel production with ATLAS data, in particular the cross-sections
separated by charge, and follow from initial studies released in 2011 [72, 14, 15].

Future studies will likely benefit from additional channels beyond the four used here
and perhaps tighter selection thresholds, made possible by additional data. For instance
¯
one could examine the 4 jet bin. It is heavily contaminated with tt events, but it may be
possible to remove enough of these events to be worthwhile. Additionally, it is possible to
have a 3 jet event with 2 jets b-tagged and this is another possible kinematic region, though
¯
again heavily contaminated with tt background. In this study, the three jet bin was used,
¯
which also suffers from a large tt background. The invariant mass of all three jets was a
very effective selection for removing a large portion of this background while still retaining
a reasonable amount of signal events. Future analyses may want to consider selections using
the invariant mass of all jets except the jet that best reconstructs the top mass (using a
lepton and neutrino) for the four jet and the 3 jet 2 b-tag bin. The remaining jets used in
the invariant mass are likely from the decay of the second top quark. With these invariant
mass selections, in addition to selections related to the reconstructed top mass and untagged
jet |η|, it may be possible to perform an analysis to measure single-top t-channel in these
regions, with S/B ratios of 0.5 or more in these channels, with these types of selections, as
demonstrated in Appendix C. Additional channels will improve the analysis as more events
can be included. Furthermore, such selections make it possible to study the kinematics of
the second b-quark from the gluon in events from the 3 jet 2 b-tag bin, which can improve
117

event generation.
Although modern particle physics is more difficult than smashing stones together, it is
nevertheless rewarding, as new information about the universe we live in is discerned from
these studies. We know so much about the physical universe in this modern era and yet
there is still much to be done and to learn. In this case, we have made a new measurement
of a standard model process only recently observed. Future studies will likely reduce these
uncertainties and extract new information about properties of the top quark. It is a very
exciting time to contribute to the understanding of single-top production, as we just start
to scratch the surface of what can be done with studies of this process.

118

Appendices

119

Appendix A
Data Based Cross-check of
¯
tt Background
In the main text we have discussed the data-based estimation of the multijets and W +jets
¯
background processes. There is another large background, tt, where the theoretical crosssection is used for the normalization in the analysis. It is also possible to do a data-based
estimate of this background. In this section, we review one way to do this estimate. The
¯
tt estimate discussed here is not used in the analysis described in the main text, but instead
is a cross-check of the value used (1.0) and its uncertainty.
¯
To determine the tt background, we define orthogonal off-signal regions (as we did for the
W +jets estimate). All preselection requirements except for the number of jets and b-tagged
jets selections are applied. We also require the t-channel yield to be < 6% of the total, and
apply as few selections as possible beyond the preselection (with different numbers of jets
¯
and b-tagged jets). Two tt dominated selections are defined as the number of jets equal to
4 or more with 1 b-tagged jet, and the 2 b-tagged jets selection with at least 2 jets. Both of
120

these regions are also discussed as potential signal regions in Section C, so if this is done,
the regions used for signal determination would need to be removed, just as the 2 jet signal
kinematic region was removed from the W +jets estimate. Additionally, the 3 jet region is
considered but this region has a relatively large (∼ 8%) portion of t-channel single-top events
¯
(hence its use as a signal channel) relative to the other tt determination regions. In this case,
an additional selection must be introduced to control the amount of t-channel and to exclude
the signal region. Here, we choose to require the reconstructed top mass to be > 210 GeV.
¯
This isolates tt events and removes single-top events, which are more likely to have the bquark, lepton, and missing energy associated with a top quark all correctly identified and
¯
thus an invariant mass of these particles closer to the top quark mass value. The tt events
where the selected b-quark, lepton, and missing energy are not correctly identified tend to
have a larger invariant mass (the two top quarks are typically back-to-back, so particles
selected from both top quarks are likely to have a higher invariant mass).
We also select channels based on the event having a muon or electron as the selected
lepton. Thus we have six different channels in total, which are each of the following selections
with a muon selection or electron selection:

* 2 b-tagged jets, at least 2 jets

* 1 b-tagged jet, at least 4 jets

* 1 b-tagged jet, exactly 3 jets, m(lνb) > 210 GeV

These channels are all orthogonal to each other. We can consider each result from these
six channels as a separate experiment and combine them. First, we calculate a scale factor.
121

This is defined as:
SFt¯ =
t

Data − MC(not t¯)
t
MC(t¯)
t

(A.1)

¯
If the data and the Monte Carlo were to agree exactly, then the tt SF woult be 1.0. To
find the combined statistical uncertainty for the channels, we follow the method discussed
by Lyons [82, 83]. The statistical uncertainty is written as δ, where the square of this value
is the variance (δ 2 ). The combination is found as follows, using i for the different channels:

1
=
2
δtot

1
2
δi

(A.2)

The scale factors themselves are also combined for the different channels as discussed by
Lyons. We weight each channel by the inverse of the statistical uncertainty squared. The
combination of scale factors is done as follows, where SF is the scale factor. Notice the
denominator is just

1 from Equation A.2:
δtot

SFtot =

SFi
2
δi
1
2
δi

(A.3)

To determine the systematic uncertainties for each channel, the SF is estimated using
MC values shifted due to a given uncertainty. For a given systematic uncertainty scenario,
the systematic-shifted SF are combined for each of the channels as in the nominal sample,
again using the same statistical uncertainty as a weight as in Equation A.3. The deviation between the combined nominal SF and the combined uncertainty-shifted SF is then the
uncertainty for the combination due to the systematic in question. By determining the combined systematic uncertainties this way, correlations between the channels can be properly
122

included. Finally, all of the systematic uncertainties and the data statistical uncertainty are
added in quadrature to obtain the overall uncertainty. The systematic uncertainties which
are considered are the b-tagging scale factor, mis-tagging scale factor, and jet energy scale.
Other systematic uncertainties are neglected for the purposes of this cross-check.
The multijets estimate for these channels is done using the values from Section 7.1 and
knowledge of the proportion of jets in the 2 b-tagged jet region versus the 1 b-tagged jet
region and the proportion of jets in the 4 or more jet region versus the 3 jet region. The 3
jet multijets estimate is adjusted by these proportions to obtain the estimate for the new off
signal regions. The multijets estimate from the 3 jet bin is thus propagated into the other
¯
regions considered for the tt scale factor estimate by assuming that the multijets number
¯
of jets and b-tagged jets distributions are correct. For the 3 jet tt region, which makes
a selection on the reconstructed top mass, this same selection is simply applied to the 3
miss distribution are performed for the tt scale
¯
jets multijets sample. No new fits to the ET
factor estimate. These values are approximate and the uncertainty related to propagating
the multijets yield into different bins is neglected for this cross-check. The values are given
in Table A.1.
The W +jets estimate for these channels uses the data-based 3 jet bin heavy flavor fractions from Section 7.2 for the 1 b-tagged jet, exactly 3 jets, m(lνb) > 210 GeV channel. This
is because there is a selection used for this channel which impacts W +jets events differently
depending on quark flavor. For the other two channels, we use the W +jets data-based normalizations appropriate for the number of jets in question, including a normalization of 0.75
for the 4 jets channel. The heavy flavor fractions do not have an impact on the scale factor
determination for these two channels, as there are no selections beyond preselection applied.
123

Table A.1 gives the W +jets yields for the six channels, as well as yields for other processes.
Electron
≥2j,2b 3j,1b,m(lνb) ≥4j,1b
¯
tt
2190
591
3300
t-channel
146
48.9
207
W +light jets
9.6
44.0
72.6
W +heavy flavor jets
168
408
403
Multijets
36.6
78.4
303
Other
102
100
250
TOTAL Exp
2650
1270
4540
DATA
3179
1242
4615

Muon
≥2j,2b 3j,1b,m(lνb) ≥4j,1b
2270
579
3430
159
54
233
12.5
78.4
80.0
173
448
475
18.7
35.7
144
111
94.0
215
2740
1290
4580
3389
1297
4773

¯
Table A.1: Event yield for the various tt normalization estimate channels. The multijets and
W +jets backgrounds are normalized to the data, all other samples are normalized to theory
cross-sections (including single-top t-channel). Other refers to Z+jets, dibosons, s-channel
single-top and W t single-top contributions.

The scale factors and their uncertainties for each of the six channels plus the combinations of channels by lepton type, and then all channels, can be seen in Figure A.1. The
statistical uncertainties are quite small. Again, only the b-tagging scale factor, mis-tagging
scale factor, jet energy scale and data statistical uncertainties are included in this crosscheck. The electron and muon channel combinations give very similar values, SFe = 1.10 ±
0.02(stat)+0.23 (syst) = 1.10+0.23 and SFµ = 1.13 ± 0.02(stat)+0.23 (syst) = 1.13+0.23
−0.14
−0.14
−0.15
−0.15
respectively. The final result from the combination of all six channels is SF = 1.12 ±
0.01(stat)+0.23 (syst) = 1.12+0.23 . This is consistent with a scale factor of 1.0 and the
−0.15
−0.15
¯
uncertainty on the result is larger than the tt theoretical cross-section uncertainty used in

the main text (approximately 10%, see Section 10.1). From this cross-check, it is clear that
¯
the tt estimate used in the t-channel single-top analysis is consistent with the data.
Future analyses will want to include additional uncertainties such as ISR/FSR, shower
and generator uncertainties, as well as others used in the single-top t-channel cross-section
124

estimate. However, including these uncertainties in the current study would not change the
conclusion. As more data are taken, the uncertainties will likely become better understood
and have lower values than in this study. The data statistical uncertainty is already quite
low in this study, but the b-tagging scale factor uncertainty in particular is 14% for the
six channel combination, the dominant systematic uncertainty. If this uncertainty could be
reduced, it would have a significant impact on the precision of this scale factor estimate.

125

tt Scale Factor

2.5

∫ L dt = 1.04 fb-1

2

s = 7 TeV

1.5
1
0.5
0>=2j

eV >=4j b, >=2j 0GeV b, >=4j ctron Muon
le All
1
2b, )>210G 1b,
2 )>21
All E
lνb
(lνb
(
j, m
3j, m
b, 3
1b,
1

All

Channel

Electron
Muon
Combined
(stat+sys)
¯
Figure A.1: Scale factors for tt production using six separate channels, the combination of
electron channels, the combination of muon channels, and the combination of all six channels.
Statistical uncertainties are given by colored portions of the black lines unless the statistical
uncertainties are so small as to be covered by the marker itself. The black line shows the data
statistical, b-tagging scale factor, mis-tagging scale factor, and jet energy scale uncertainties
combined. Other uncertainties are neglected in this cross-check.

126

Appendix B
Multivariate Analysis
Although this document has focused on a simple, cut-based analysis approach, there are more
advanced analysis options. These include multivariate techniques such as boosted decision
trees. Multivariate techniques use computer algorithms to determine several dimensions of
selection sequences, making use of events which both pass or fail individual selections. The
result is an output related to the probability of an event being signal or background. In this
chapter we review the boosted decision tree technique and then suggest options for future
analyses using the variables from the main document and an additional set of variables. As
this section is intended as suggestions for future work and another viewpoint of the t-channel
single-top analysis, only the large uncertainties from the cut-based analysis are recalculated.

B.1

Boosted Decision Tree Overview

The boosted decision tree (BDT) [84] method has traditionally been used in single-top analyses [10, 11, 13] and this method is used here, as provided in a statistical package called
StatPatternRecognition [85]. A boosted decision tree is based on a collection of decision
127

trees, and an example of one tree is pictured in Figure B.1. A decision tree is a cut-flow
diagram, where selections are applied that eventually result in sets (leaves) of mostly signal
or mostly background events. These final sets of events are the leaves or terminal nodes of
the tree (each selection has an associated node that is not necessarily terminal). When a
decision tree is applied to a new event, if this event passes background-like selections it is
probably background, whereas if it passes signal-like selections it is probably signal. The
ultimate output of the multivariate classifier indicates how likely it is that an event is background or signal. One can then take a simple cut on the classifier output, to select for high
signal probability, or do a fitting technique to determine how much signal is present in the
data.

Figure B.1: A pictorial representation of a single decision tree, where A and C are variables
values, X and Y are selection thresholds. The node is designated as S for signal and B for
background. The S and B circles are the final nodes, or leaves, in the tree.

The tree itself is formed using an optimization criterion to determine which variable
128

to use for each selection (or node split) and what threshold to take. The goal of such a
criterion is to optimize the signal and background separation. For this study we use the
default optimization criterion, which is the Gini index. This is the purity times 1 minus
the purity, p(1-p). The purity is the signal events divided by all of the events considered in
that node, so if a node would have only signal events, the purity would be 1, giving a Gini
index of 0. If there are only background events, the purity is 0, and the Gini index is again
0. The goal of the splitting is to obtain nodes that are background or signal dominated,
so nodes are optimized to obtain a Gini index of 0 (or close to 0). Unlike the cut-based
analysis in Section 9.2.1, systematic uncertainties cannot be considered when determining
each individual selection of a tree.

The “boosted” portion of the name boosted decision tree refers to an algorithm which
reweights events based on whether or not they were mis-classified as signal and background in
the previous tree. These weights then affect how the performance is evaluated in the training
of the next tree. The boosting algorithm used in this study is called ǫ-boost [85, 84]. This
particular algorithm increases the weights of incorrectly classified events by a factor of e2ǫ .
The ǫ value may be set to different values, but here we use the default value of 0.01. In
the end, the various trees are all averaged to give a final boosted tree. The classifiers for
each tree, the functions which are averaged, are formed by minimizing what is called a
quadratic loss criterion. This is the average of the square of the difference between the true
and predicted classifications for all events.
129

B.1.1

Classifier Formation and Parameter Optimization

When forming a classifier, three different MC samples are formed by taking the modulus of
the event number and are called training, validation, and yield. The yield sample is only
used for the final BDT result. The training sample is used to form various classifiers and the
validation sample is used to evaluate if some particular classifier is the one we desire. The
one exception to this sample division in this study is the multijets process. The statistics
are quite low for this sample, so it is divided in half to form a training and yield sample,
again using the modulus of the event number. Additionally, because of limitations in the
statistical package, negatively weighted events cannot be used during the training phase
when the classifier is generated. There are such events in most of the MC samples for the
various top-quark processes. However, the proportion of negatively weighted events is low
(about 7% in the training sample for the signal). Even if this did have some effect, it would
simply result in a less than optimally trained classifier, not a biased result, because the
sample used for the result includes both negative and positively weighted events.
It is possible to train different combinations of channels: each channel separately, the
number of jet channels separately (but with both lepton charges allowed), and all four
channels combined. For this study we use two BDT’s for the final result, each with a
different number of jets (2 or 3). When samples are split in this way, the classifiers can
take advantage of the different kinematics in each number of jets channel. However, the
MC statistics will be lower after splitting the sample, potentially causing the kinematics and
events to be unevenly distributed. A multivariate classifier can be particularly sensitive to
this, especially if a tight cut on the classifier is taken, as we do here. This is one reason why
we do not further divide this sample into additional kinematic regions and combine several
130

classifiers for the final result.
There are several different classifier settings to choose from when forming a BDT. In this
study, we vary the number of decision trees the BDT uses and the minimum number of events
in the leaves for each tree. We use the default settings for other parameters, including the
type of boost (ǫ-boost with ǫ of 0.01), the per event loss (quadratic), and the optimization
criterion (Gini index), discussed at the beginning of Section B.1. The number of variables
considered is another parameter of the BDT and we consider several different combinations
of variables.
Many different trees are generated using the training sample with a variety of classifier
settings. We choose the trained BDT classifier and cut threshold for that classifier by using
a criterion that includes systematic uncertainties, as we do in the main text in Section 9.2.1.
In this case, we found a few classifiers that had consistent distributions in the training
and validation samples and were continuous. We then determine which of these would
give the best expected result, based on the significance calculated using validation sample
information. Multijets are not considered during the significance calculation.
It is possible to overtrain a BDT during the generation of the classifier, which means it is
too tuned to the particular MC sample’s kinematics subtleties, like being trained on noise.
Overtraining results in a BDT that is sub-optimal, which we would like to avoid, but doesn’t
invalidate the analysis. The χ2 [82] and Kolmogorov-Smirnov (KS) [86] tests are used to
check the training and validation sample agreements. Classifiers are chosen which have good
agreement (> 5%). Additionally, because the validation sample is used to determine the
BDT settings and threshold, it is also possible to be sensitive to this sample’s particular
distributions. We save a yield sample for the cross-section calculation to ensure that such a
131

sensitivity won’t impact the final result.

B.1.2

Cut-based Analysis Variables

Because this dissertation focuses on a cut-based analysis, it is interesting to consider what
would happen if we train BDTs using only the variables from the cut based analysis. For this,
we use all four variables considered in Section 9.3 for each number of jet channel, as well as
lepton charge for a total of five variables in each channel. The variables used for both channels
miss
are: sum of the transverse momenta of all jets, lepton, and ET ; leading untagged jet η;
top quark mass reconstructed using the b-tagged jet, lepton, and reconstructed neutrino;
and lepton charge. Additionally, ∆η between the b-tagged jet and leading untagged jet is
used for the 2 jet selection and the invariant mass of all jets is used for the 3 jet selection.
For the 2 jet selection, the classifier parameters and cut threshold are: 250 trees, 1500
events minimum per leaf, and 0.74 cut threshold. For the 3 jet selection, these are: 150 trees,
1250 events minimum per leaf, and 0.41 cut threshold. The BDT classifier distribution before
and after the selection for each channel is shown in Figure B.2, normalized to the observed
t-channel cross-section. The variable distributions after this cut threshold for each channel
are given in Figures B.3 and B.4 for the 2 and 3 jet selections respectively, also normalized to
the observed t-channel cross-section. Notice that after the selections, the kinematic regions
chosen for the distributions look similar to those in Figures 9.6 and 9.7, particularly the
reconstructed top mass, leading untagged jet η and the invariant mass of all of the jets.
Overall the agreement is fairly good between data and MC in these plots, keeping in mind
the lower MC statistics from splitting the MC into thirds and also the somewhat large
systematic uncertainties.
132

Events

Events

104

∫ L dt = 1.04 fb-1
s = 7 TeV

103

40

∫ L dt = 1.04 fb-1

30

2 jets 1 tag

s = 7 TeV
2 jets 1 tag

20

102

10
10
0.2

0.4

3 jets 1 tag

103

0
0

0.6
0.8
1
BDT Classifier
Events

Events

0

∫ L dt = 1.04 fb-1
s = 7 TeV

60

40

0.2

0.4

0.6
0.8
1
BDT Classifier

∫ L dt = 1.04 fb-1
s = 7 TeV
3 jets 1 tag

2

10

20
10
0

0.2

0.4

0
0

0.6
0.8
1
BDT Classifier

0.2

0.4

0.6
0.8
1
BDT Classifier

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets

Figure B.2: BDT classifier distributions for the 2 jet (top) and 3 jet (bottom) selections,
formed using cut-based analysis variables. The left column is before the selection on the BDT
classifier in a log scale, and the right column is after. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels. Other top
refers to the s-channel and W t single-top contributions.

133

The yields after the selections on the BDT thresholds are given in Table B.1. Overall
the yields are a little lower than the cut-based analysis (see Section 9.3). The signal to
background ratios are much higher in the 2 jet channel but a little lower or the same in the
3 jet channel. This indicates that the BDT for the 2 jet selection in particular has better
separating power between signal and background than the cut-based analysis cuts.
BDT 5 Variables 2 Jets
Lepton +
Lepton t-channel
27.7
7.6
¯, Other top
tt
2.2
1.0
W +light jets
0.8
< 0.1
W +heavy flavor jets
7.5
2.0
Z+jets, Diboson
< 0.1
< 0.1
Multijets
0.3
< 0.1
TOTAL Exp
38.5
10.7
S/B
2.6
2.4
DATA
60
16

BDT 5 Variables 3 Jets
Lepton +
Lepton 56.9
12.8
25.9
6.9
4.4
< 0.1
23.6
4.5
1.1
< 0.1
7.8
< 0.1
119.7
24.2
0.9
1.1
115
24

Table B.1: Event yield for the 2 jet and 3 jet 1 b-tag positive and negative lepton-charge
channels after the selection on the BDT formed using the cut-based analysis variables. The
multijets and W +jets backgrounds are normalized to the data; all other samples are normalized to theory cross-sections. The t-channel single-top contribution is normalized to the
observed cross-section determined using all four channels. Other top refers to the s-channel
and W t single-top contributions.

The cross-section is also calculated for the BDT distributions. The 2 and 3 jet channels
are split into negative and positive lepton charge channels, after selecting the desired region
of the BDT classifier, and the combination is calculated using all four channels. The crosssection calculation uses the systematic shifts and statistical methods from the cut-based
analysis (Section 10.1) except in the cases of the largest systematic uncertainties, which are
estimated using the shifts in the yields of the BDT classifier distributions after the selection
on it. The systematic uncertainties that are re-estimated are the statistical, b-tagging scale
factor, mis-tagging scale factor, jet energy scale, generator, parton shower, and ISR/FSR
134

uncertainties. The MC statistical uncertainty is not changed here, but we might expect it to
be about 1.7 times as large as in the cut-based analysis, if the proportion of events from the
different processes is relatively unchanged. This is because the MC event weights increase
√
by a factor of 3 and there are 1/3 as many events, giving a factor of 3 multiplied with
the square root of the sum of the squares of the weights of the events (the MC statistical
uncertainty). The expected cross-section uncertainties which are re-estimated and the total
uncertainties using both re-estimated and cut-based analysis values are given in Table B.2.

The uncertainties are generally comparable with the cut-based analysis except for the
ISR/FSR uncertainty, which is much larger. This may be due to the ISR/FSR uncertainty
not being considered during the optimization of the classifier with the validation sample,
leading to the selection of events that happen to have a larger uncertainty. This is something
that could be added to the classifier optimization in a future study. Additionally, the jet
energy scale uncertainty is higher and the b-tagging scale factor uncertainty is lower versus
the cut-based analysis, reflecting some differences in the selected events in the BDT compared
with the cut-based analysis. If we use the cut-based ISR/FSR uncertainty value, assuming
the BDT analysis could be improved to reduce this uncertainty, the expected cross-section
and its uncertainty would be σt = 65+21 pb, compared to σt = 65+22 pb from the cut-based
−19
−20
analysis in Section 10.2.1.3. The expected cross-section uncertainty with the re-estimated
ISR/FSR is σt = 65+34 pb. The observed cross-section value is σt = 82.9+36 pb, which is
−26
−28
consistent with the cut-based analysis result within uncertainties.
135

Events / 0.25

Events / 20 GeV

60

∫ L dt = 1.04 fb-1

2 jets 1 tag

s = 7 TeV

40

∫ L dt = 1.04 fb-1
20
15

s = 7 TeV
2 jets 1 tag

10
20
5
100

200

80

∫ L dt = 1.04 fb-1

60

s = 7 TeV
2 jets 1 tag

40
20

Events / 0.30

0
-2

0
0

300 400 500
m(lνb) [GeV]
Events / 30 GeV

Events

0
0

40

1

2

2 jets 1 tag

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

30
20
10

-1

0

20

s = 7 TeV
2 jets 1 tag

200

400

600
HT[GeV]

∫ L dt = 1.04 fb-1

15

0
0

1
2
Lepton Charge

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor

10
5
0
0

W+light jets
Z+jets, Diboson
2

4

6
|∆η(b, j )|
u

Multijets

Figure B.3: Discriminating variables for the 2 jet selection after a selection on the BDT
classifier formed using cut-based analysis variables. The last bin contains the sum of the
events in that bin or higher. The t-channel single-top contribution is normalized to the
observed cross-section determined using all four channels. Other top refers to the s-channel
and W t single-top contributions.

136

Events / 0.25

Events / 20 GeV

100

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

30

20

∫ L dt = 1.04 fb-1
s = 7 TeV
3 jets 1 tag

50
10

100

200

∫ L dt = 1.04 fb-1
150

0
0

300 400 500
m(lνb) [GeV]
Events / 30 GeV

Events

0
0

s = 7 TeV
3 jets 1 tag

100

1

2

3 jets 1 tag

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

40

20
50

Events / 56 GeV

0
-2

-1

0

0
0

1
2
Lepton Charge

200

400

600
HT[GeV]

∫ L dt = 1.04 fb-1
40

s = 7 TeV
3 jets 1 tag

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor

20

W+light jets
0
0

Z+jets, Diboson
200

400

600
800
m(j j )[GeV]
12

Multijets

Figure B.4: Discriminating variables for the 3 jet selection after a selection on the BDT
classifier formed using cut-based analysis variables. The last bin contains the sum of the
events in that bin or higher. The t-channel single-top contribution is normalized to the
observed cross-section determined using all four channels. Other top refers to the s-channel
and W t single-top contributions.

137

Source
Expected statistics
b tagging scale factor
Mistag scale factor
Jet energy scale
Generator
Shower
ISR/FSR
Total Systematics
Total

∆σ/σ (%)
+13/-13
+6/-6
+1/-1
+7/-8
+7/-7
+14/-14
+40/-29
+50/-38
+52/-40

Table B.2: Systematic uncertainties for the expected t-channel cross-section measurement
for the BDT formed using cut-based analysis variables, where the final line includes all
systematic uncertainties and the statistical uncertainty of the data. Uncertainties that were
re-estimated versus the cut-based analysis (Section 10.2.1) are listed individually. Others
are not listed but are included in the totals.

B.1.3

Additional Variables

Of course, there is no reason to choose only the variables used for the cut based analysis
when generating the BDTs. Starting from these variables, we now consider many additional
variable combinations, using variables that were considered for the cut-based analysis but
not used (see Section 8). After many options are considered, BDT classifiers are chosen for
the 2 jet and 3 jet selections which happen to use the same variables. These BDT classifiers
are chosen to have a large significance in the validation sample, a relatively low number of
variables, and good agreement between the training and validation BDT distributions.
The best classifiers have ten variables, including the lepton charge variable. In addition
to the 6 variables considered in this analysis (listed in Section B.1.2), the following are used
for both jet number selection channels: η of the lepton; cosine of the angle between the
lepton and the untagged jet, both in the rest frame of the top quark reconstructed using the
leading b-tagged jet; W transverse mass; and ∆η between the b-tagged jet and the lepton.
138

Note that the ∆η between the b-tagged jet and leading untagged jet and the invariant mass
of all jets are now used for both the 2 and 3 jet selections, unlike in Section B.1.2. The
distributions of the additional variables with the preselection applied for the full MC set are
shown in Figure B.5 for the 2 jet selection and Figure B.6 for the 3 jet selection, showing
good agreement between the data and the MC. Figures B.7 and B.8 show the separation
given by these variables after the requirement of exactly one b-tagged jet in the event for 2
or 3 jet samples.
For the 2 jet selection, the classifier parameters and cut threshold are: 150 trees, 2500
events minimum per leaf, and 0.64 cut threshold. For the 3 jet selection, these are: 150 trees,
1500 events minimum per leaf, and 0.42 cut threshold. The BDT classifier distributions
before and after the selection for each channel are shown in Figure B.9, normalized to the
observed t-channel cross-section. The variable distributions after this cut threshold for each
channel are given in Figures B.10 and B.11 for the 2 jet selection, and Figures B.12 and B.13
for the 3 jet selection, with all normalized to the observed t-channel cross-section. Again,
notice that after the selections, the kinematic regions selected in the distributions look similar
to those in Figures 9.6 and Figures 9.7, particularly the reconstructed top mass, invariant
mass and leading untagged jet η distributions.
The yields after the selections on the BDT thresholds are given in Table B.3. The signal
to background ratios here are about the same as those from Section B.1.2 for the 3 jet bin
but are much improved for the 2 jet selection. This indicates that the extra variables have
particularly helped the signal versus background discrimination in the 2 jet bin.
The additional variables are used to try to improve the uncertainty on the cross-section
measurement versus the BDT formed with cut-based variables only. The extra information
139

Events / 0.10

Events / 0.25

∫ L dt = 1.04 fb-1

2 jets 1 tag

1500

s = 7 TeV

1000

200
1

2

3

0
-1

4
5
|∆η(b, l)|
Events / 10 GeV

Events / 0.25

0
0

∫ L dt = 1.04 fb-1

2 jets 1 tag

s = 7 TeV

500

Events / 56 GeV

0

s = 7 TeV

600
400

500

1000

∫ L dt = 1.04 fb-1

800 2 jets 1 tag

-2

-1

0

1

∫ L dt = 1.04 fb-1

2 jets 1 tag

s = 7 TeV

2000

1000

0
0

2
η(l)

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame
u

50

100
150
200
WT Mass [GeV]

∫ L dt = 1.04 fb-1

2 jets 1 tag

4000

ATLAS Data
Single-top t-channel

s = 7 TeV

tt, Other top
W+heavy flavor

2000

W+light jets
0
0

Z+jets, Diboson
200

400

600
800
m(j j )[GeV]
12

Multijets

Figure B.5: Discriminating variables for the 2 jet selection before any BDT classifier selection. The last bin contains the sum of the events in that bin or higher. Other top refers to
the s-channel and W t single-top contributions.

140

Events / 0.10

Events / 0.25

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

1000

500

2

3

s = 7 TeV

400

800

0
-1

4
5
|∆η(b, l)|

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

600

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame

u

Events / 10 GeV

Events / 0.25

1

400

∫ L dt = 1.04 fb-1

1500 3 jets 1 tag

s = 7 TeV

1000

500

200

Events / 0.30

∫ L dt = 1.04 fb-1

3 jets 1 tag

200

0
0

0

600

-2

-1

3 jets 1 tag

0

1

0
0

2
η(l)

50

100
150
200
WT Mass [GeV]

∫ L dt = 1.04 fb-1
ATLAS Data
Single-top t-channel

s = 7 TeV

1000

tt, Other top
W+heavy flavor

500

W+light jets
0
0

Z+jets, Diboson
2

4

6
|∆η(b, j )|
u

Multijets

Figure B.6: Discriminating variables for the 3 jet selection before any BDT classifier selection. The last bin contains the sum of the events in that bin or higher. Other top refers to
the s-channel and W t single-top contributions.

141

Event Fraction / 0.25

Event Fraction / 0.10

0.1
0.05
1

2

3

0.1

s = 7 TeV

0.05

0

0.6

-2

-1

0

1

s = 7 TeV

0.1

0.05

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame

u

∫ L dt = 1.04 fb-1

2 jets 1 tag

∫ L dt = 1.04 fb-1

2 jets 1 tag

0
-1

4
5
|∆η(b, l)|
Event Fraction / 10 GeV

Event Fraction / 0.25

s = 7 TeV

0.15

0
0

Event Fraction / 56 GeV

∫ L dt = 1.04 fb-1

0.2 2 jets 1 tag

s = 7 TeV

0.2

0.1

0
0

2
η(l)

∫ L dt = 1.04 fb-1

0.3 2 jets 1 tag

50

100

150
200
WT Mass [GeV]

∫ L dt = 1.04 fb-1

2 jets 1 tag

Single-top t-channel

s = 7 TeV

0.4

tt, Other top
W+heavy flavor

0.2

W+light jets
Z+jets, Diboson

0
0

200

400

600
800
m(j j )[GeV]

Multijets

12

Figure B.7: Discriminating variables for the 2 jet selection before any BDT classifier selection
normalized to unit area. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions.

142

Event Fraction / 0.25

Event Fraction / 0.10

0.1
0.05
1

2

3

s = 7 TeV

0.1

0.05

0

-2

-1

0.2 3 jets 1 tag

0

1

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

0.1

0.05

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame

u

∫ L dt = 1.04 fb-1

3 jets 1 tag

0.15

0
-1

4
5
|∆η(b, l)|
Event Fraction / 10 GeV

Event Fraction / 0.25

s = 7 TeV

0.15

0
0

Event Fraction / 0.30

∫ L dt = 1.04 fb-1

0.2 3 jets 1 tag

0.3

s = 7 TeV

0.2
0.1
0
0

2
η(l)

∫ L dt = 1.04 fb-1

3 jets 1 tag

50

100

150
200
WT Mass [GeV]

∫ L dt = 1.04 fb-1
Single-top t-channel

s = 7 TeV

0.15

tt, Other top
W+heavy flavor

0.1

W+light jets

0.05

Z+jets, Diboson
0
0

2

4

6
|∆η(b, j )|

Multijets

u

Figure B.8: Discriminating variables for the 3 jet selection before any BDT classifier selection
normalized to unit area. The last bin contains the sum of the events in that bin or higher.
Other top refers to the s-channel and W t single-top contributions.

143

Events

Events

2 jets 1 tag

∫ L dt = 1.04 fb-1
s = 7 TeV

103

60

2 jets 1 tag

∫ L dt = 1.04 fb-1
s = 7 TeV

40
102
20
10
0.2

0.4

3 jets 1 tag

103

0
0

0.6
0.8
1
BDT Classifier
Events

Events

0

∫ L dt = 1.04 fb-1
s = 7 TeV

40

0.2

0.4

3 jets 1 tag

0.6
0.8
1
BDT Classifier

∫ L dt = 1.04 fb-1
s = 7 TeV

30
102

20

10

10

0

0.2

0.4

0
0

0.6
0.8
1
BDT Classifier

0.2

0.4

0.6
0.8
1
BDT Classifier

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor
W+light jets
Z+jets, Diboson
Multijets

Figure B.9: BDT classifier distributions for the 2 jet selection on the top line and the 3 jet
selection on the next line, for the BDT formed using ten analysis variables. The left figures
are before the selection on the BDT classifier, the right figures are after. Note that the
BDT distributions before selections are in a log scale. The t-channel single-top contribution
is normalized to the observed cross-section determined using all four channels. Other top
refers to the s-channel and W t single-top contributions.

144

BDT 10 Variables 2 Jets
Lepton +
Lepton t-channel
45.9
19.7
¯
tt, Other top
2.2
2.1
W +light jets
0.8
< 0.1
W +heavy flavor jets
9.7
6.5
Z+jets, Diboson
< 0.1
< 0.1
Multijets
1.9
1.6
TOTAL Exp
60.5
29.9
S/B
3.1
1.9
DATA
94
33

BDT 10 Variables 3 Jets
Lepton +
Lepton 46.0
16.7
16.6
7.5
2.4
< 0.1
25.4
8.3
0.3
0.6
3.6
< 0.1
94.3
33.1
0.9
1.0
82
38

Table B.3: Event yield for the 2 jet and 3 jet 1 b-tag positive and negative lepton-charge
channels after the selection on the BDT formed using ten analysis variables. The multijets
and W +jets backgrounds are normalized to the data; all other samples are normalized to
theory cross-sections. The t-channel single-top contribution is normalized to the observed
cross-section determined using all four channels. Other top refers to the s-channel and W t
single-top contributions.

should improve the signal and background separation, and may also help to improve the selection of low uncertainty kinematic regions. As in Section B.1.2, the 2 and 3 jet channels were
split into negative and positive lepton charge channels, after selecting the desired region of
the BDT classifier, and the combination was calculated using all four channels. The expected
cross-section uncertainties for the combination is given in Table B.4. Also, as in Section B.1.2,
only the statistical, b-tagging scale factor, mis-tagging scale factor, jet energy scale, generator, parton shower, and ISR/FSR uncertainties are re-estimated. Again, the ISR/FSR
uncertainty is very high here, and including this uncertainty in the BDT optimization might
improve the result in future studies. The other uncertainties are generally similar to the
cut-based result, although we again see that the b-tagging scale factor uncertainty is lower
than it was in the cut-based analysis from Section 10.2.1. The overall uncertainty is lower
than the BDT cross-section expectation using only cut-based analysis variables, indicating
the usefulness of the additional variables. The expected cross-section is σt = 65+30 pb,
−21
145

while combined result from the BDTs using only cut-based variables had an expected crosssection of σt = 65+34 pb. The observed cross-section value is σt = 83.8+34 pb, which has
−26
−25
a lower uncertainty than, and is consistent with, the value found from the BDTs using only
cut-based analysis variables. In particular the central value is very similar. This cross-section
is also consistent with the cut-based analyis value.
Source
Expected statistics
b tagging scale factor
Mistag scale factor
Jet energy scale
Generator
Shower
ISR/FSR
Total Systematics
Total

∆σ/σ (%)
+11/-11
+5/-5
+2/-2
+4/-4
+8/-8
+11/-10
+34/-24
+45/-30
+46/-32

Table B.4: Systematic uncertainties for the expected t-channel cross-section measurement
determined using the BDT created with ten analysis variables, where the final line includes all
systematic uncertainties and the statistical uncertainty of the data. Uncertainties that were
re-estimated versus the cut-based analysis (Section 10.2.1) are listed individually. Others
are not listed but are included in the totals.

146

Events / 0.25

Events / 20 GeV

80

∫ L dt = 1.04 fb-1

2 jets 1 tag

s = 7 TeV

60

s = 7 TeV
2 jets 1 tag

20

10

100

200

∫ L dt = 1.04 fb-1
100

s = 7 TeV
2 jets 1 tag

50

0
-2

-1

0
0

300 400 500
m(lνb) [GeV]
Events / 30 GeV

0
0
Events

∫ L dt = 1.04 fb-1

40
20

Events / 0.30

30

0

2

2 jets 1 tag

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

40

20

0
0

1
2
Lepton Charge

1

200

400

600
HT[GeV]

∫ L dt = 1.04 fb-1
20

s = 7 TeV
2 jets 1 tag

ATLAS Data
Single-top t-channel
tt, Other top
W+heavy flavor

10

W+light jets
0
0

Z+jets, Diboson
2

4

6
|∆η(b, j )|
u

Multijets

Figure B.10: Discriminating variables for the 2 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution is normalized
to the observed cross-section determined using all four channels. Other top refers to the
s-channel and W t single-top contributions.

147

2 jets 1 tag

Events / 0.25

Events / 56 GeV

40

∫ L dt = 1.04 fb-1
s = 7 TeV

30

s = 7 TeV

30

20

20

10

10

200

400

0
0

600
800
m(j j )[GeV]
12
Events / 0.25

0
0
Events / 0.10

∫ L dt = 1.04 fb-1

2 jets 1 tag

∫ L dt = 1.04 fb-1
20

s = 7 TeV
2 jets 1 tag

1

2

3

∫ L dt = 1.04 fb-1

2 jets 1 tag

20

4
5
|∆η(b, l)|

s = 7 TeV

15
10

10
5

Events / 10 GeV

0
-1
60

0

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame
u
2 jets 1 tag

-2

-1

0

1

2
η(l)

∫ L dt = 1.04 fb-1
s = 7 TeV

40

ATLAS Data
Single-top t-channel

20

tt, Other top
W+heavy flavor
W+light jets

0
0

Z+jets, Diboson
50

100
150
200
WT Mass [GeV]

Multijets

Figure B.11: Discriminating variables for the 2 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution is normalized
to the observed cross-section determined using all four channels. Other top refers to the
s-channel and W t single-top contributions.

148

Events / 0.25

Events / 20 GeV

80

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

60

30

3 jets 1 tag

∫ L dt = 1.04 fb-1
s = 7 TeV

20

40
10
20

150

100

200

0
0

300 400 500
m(lνb) [GeV]
Events / 30 GeV

Events

0
0

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

100

40

1

2

3 jets 1 tag

3

4

5
|η(j )|
u

∫ L dt = 1.04 fb-1
s = 7 TeV

30
20

50
10

Events / 0.30

0
-2

-1

0

3 jets 1 tag

0
0

1
2
Lepton Charge

400

600
HT[GeV]

∫ L dt = 1.04 fb-1
s = 7 TeV

30

200

ATLAS Data
Single-top t-channel

20

tt, Other top
W+heavy flavor

10

W+light jets

0
0

Z+jets, Diboson
2

4

6
|∆η(b, j )|
u

Multijets

Figure B.12: Discriminating variables for the 3 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution is normalized
to the observed cross-section determined using all four channels. Other top refers to the
s-channel and W t single-top contributions.

149

3 jets 1 tag

Events / 0.25

Events / 56 GeV

40

∫ L dt = 1.04 fb-1
s = 7 TeV

30

s = 7 TeV

20
10

30

200

400

3 jets 1 tag

0
0

600
800
m(j j )[GeV]
12
Events / 0.25

0
0
Events / 0.10

30

20
10

∫ L dt = 1.04 fb-1
s = 7 TeV

20

0
-1
60

1

2

3

4
5
|∆η(b, l)|

∫ L dt = 1.04 fb-1

3 jets 1 tag

s = 7 TeV

20

10

10

Events / 10 GeV

∫ L dt = 1.04 fb-1

3 jets 1 tag

0

-0.5
0
0.5
1
Cos(l, j ) in Top Rest Frame
u
3 jets 1 tag

-2

-1

0

1

2
η(l)

∫ L dt = 1.04 fb-1
s = 7 TeV

40

ATLAS Data
Single-top t-channel

20

tt, Other top
W+heavy flavor
W+light jets

0
0

Z+jets, Diboson
50

100
150
200
WT Mass [GeV]

Multijets

Figure B.13: Discriminating variables for the 3 jet selection. The figures are after the
selection on the BDT classifier formed using ten analysis variables. The last bin contains the
sum of the events in that bin or higher. The t-channel single-top contribution is normalized
to the observed cross-section determined using all four channels. Other top refers to the
s-channel and W t single-top contributions.

150

Appendix C
Alternative Analysis Channels
The main analysis in this document makes use of the 2 and 3 jet channels, split into positive
or negative lepton charge (see Section 9.1). However, there are other possibilities. For
¯
instance, the 4 jet bin, although the “natural” bin for tt production, could still be a useful
¯
channel if the tt can be successfully removed. Similarly the 3 jet bin, where 2 jets are b¯
tagged (unlike 1 b-tagged jet in the main analysis) is also dominated by tt production. If
¯
tt can be removed from this bin, we may be able to see our single-top signal. The event
yields for these two bins (split into lepton charge) after all preselection cuts including either
1 or 2 b-tagged jets, are shown in Table C.1. The signal divided by background (S/B) value
is also shown. No W +jets data-based normalization scale factors or multijets estimates are
included in any of the tables in this discussion. However, as the yields are dominated by
top processes, neither exclusion is expected to have a large effect on the conclusions of this
study.
The first two selections in the main analysis (Section 9.3) make use of differences between
the t-channel single-top production and its backgrounds, and we apply both of these selec151

4 Jets, 1 b-tagged
Lepton + Lepton t-channel
200
100
¯
tt, Other top
1800
1800
W +light jets
99
43
W +heavy flavor jets
400
310
Z+jets, Diboson
50
43
S/B
0.08
0.05

3 Jets, 2 b-tagged
Lepton + Lepton 72
46
560
550
0.2
0.2
73
45
4.9
2.7
0.11
0.08

Table C.1: Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and
negative lepton-charge channels after the preselection. The multijets are neglected and all
other samples are normalized to theory cross-sections.

tions here with a slight variation on the reconstructed top mass selection. The reasoning
is the same as before. The t-channel single-top production often has an energetic forward
¯
non-b jet, whereas tt tends to have more central jets. Also, the signal only has one top
¯
quark whereas tt has two. Due to reconstruction difficulties, the b associated with the top
decaying to leptons is not always correctly assigned when determining the reconstructed
¯
top mass for tt production, so a selection requiring a top mass near the expected value is
useful. Similarly, requiring the highest pT untagged jet to be forward is also helpful, just as
in the main analysis. The yields after requiring |η(ju )| > 2.0 and then after also requiring
m(lνb) < 190 GeV are shown in Tables C.2 and C.3 respectively. We use only the upper
top mass selection from the main analysis here because of the low multijets and W +jets
expected contribution (which is ignored for this discussion) in these bins.
Finally, we can also make use of the invariant mass of the jets. In the main analysis
¯
(Section 9.3), the 3 jet bin had a large tt component, and we used a selection involving the
¯
invariant mass of the jets to remove tt events. For the 4 jet bin, we propose requiring the
invariant mass of all jets except the best jet to be greater than 450 GeV. The best jet is the
miss
jet which, plus the lepton and ET , best produces the expected standard model top mass.
152

4 Jets, 1 b-tagged
Lepton + Lepton t-channel
74
33
¯, Other top
tt
240
230
W +light jets
24
5.4
W +heavy flavor jets
65
56
Z+jets, Diboson
7.1
7.6
S/B
0.22
0.11

3 Jets, 2 b-tagged
Lepton + Lepton 38
21
82
81
0.2
<0.1
14
6.3
0.5
0.5
0.40
0.24

Table C.2: Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and negative
lepton-charge channels after the preselection and |η(ju )| > 2.0. The multijets are neglected
and all other samples are normalized to theory cross-sections.

4 Jets, 1 b-tagged
Lepton + Lepton t-channel
50
22
¯
tt, Other top
120
120
W +light jets
16
2.4
W +heavy flavor jets
32
27
Z+jets, Diboson
3.9
3.6
S/B
0.29
0.14

3 Jets, 2 b-tagged
Lepton + Lepton 19
12
23.0
23.0
0.2
<0.1
6.6
3.2
0.4
<0.1
0.64
0.45

Table C.3: Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and negative
lepton-charge channels after the preselection, |η(ju )| > 2.0, and m(lνb) < 190 GeV. The
multijets are neglected and all other samples are normalized to theory cross-sections.

153

Thus, we are looking at the invariant mass of what should be the other top quark in the case
¯
of tt production, and the invariant mass should be close to that value. Single-top t-channel
can have a very energetic jet separated from the top quark decay products, leading to a
potentially very high invariant mass. These two effects give some separation, and we remove
events where the invariant mass is lower. Similarly for the 3 jet, 2 b-tagged jet selection, we
can look at this same invariant mass of all jets minus the best jet greater than 250 GeV.
This should give us the invariant mass of most of the jets from the other top quark in the
¯
case of tt production and so we again remove events where this invariant mass is lower to
¯
reduce tt contamination. Specifically we require m(AllJetsMinusBestJet) > 450 GeV for the
4 jet channel and m(AllJetsMinusBestJet) > 250 GeV for the 3 jet channel.
The yields after these two invariant mass selections are given in Table C.4. This table
¯
shows that the tt events are removed at a larger rate than the signal, improving the S/B
value from the previous tables. Most S/B values are over 0.5 and one is over 1.5. Of course,
the yields themselves are low, leading to larger statistical uncertainties. However, these
tables are normalized to the integrated luminosity used in the main analysis, 1.04 fb−1 .
Future analysis will use data sets of 5, 10, or more times this value, making these sorts of
tight selections more useful for those analyses. The use of the 4 jet 1 tag bin will allow
additional single-top events to be studied, improving the overall measurement. The 3 jet 2
tag channel is useful as an additional channel for more statistics and potential improvements
in the uncertainties from anti-correlation effects. However, this channel is also useful because
here we can study the extra b-quark from the gluon. This is not always well modeled by the
event generators (see Section 5.1) so studies of the kinematic properties of this particle in
data are important.

154

4 Jets, 1 b-tagged
Lepton + Lepton t-channel
27
12
¯, Other top
tt
29
31
W +light jets
1.8
0.6
W +heavy flavor jets
6.2
5.9
Z+jets, Diboson
1.2
2.0
S/B
0.71
0.30

3 Jets, 2 b-tagged
Lepton + Lepton 10
4.0
4.5
4.3
<0.1
<0.1
0.7
1.2
0.2
<0.1
1.89
0.74

Table C.4: Event yields for the 4 jets, one b-tag and 3 jets, 2 b-tags with positive and negative
lepton-charge channels after the preselection, |η(ju )| > 2.0, m(lνb) < 190 GeV, and either
m(AllJetsMinusBestJet) > 450 GeV for the 4 jet channel or m(AllJetsMinusBestJet) >
250 GeV for the 3 jet channel. The multijets are neglected and all other samples are normalized to theory cross-sections.

155

BIBLIOGRAPHY

156

BIBLIOGRAPHY

[1] N. Kidonakis, NNLL resummation for s-channel single top quark production, Phys.
Rev. D81 (2010) 054028, arXiv:1001.5034 [hep-ph].
[2] N. Kidonakis, Two-loop soft anomalous dimensions for single top quark associated
production with a W- or H-, Phys. Rev. D82 (2010) 054018, arXiv:1005.4451
[hep-ph].
[3] N. Kidonakis, Next-to-next-to-leading-order collinear and soft gluon corrections for
t-channel single top quark production, Phys. Rev. D83 (2011) 091503,
arXiv:1103.2792 [hep-ph].
[4] ATLAS Collaboration, G. Aad et al.,
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/LuminosityPublicResults, (2011) .
[5] ATLAS Collaboration, G. Aad et al., The ATLAS Experiment at the CERN Large
Hadron Collider , JINST 3 (2008) S08003.
[6] ATLAS Collaboration, G. Aad et al., Event Display, b-jet, Tech. Rep.
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/EventDisplayPublicResults, CERN,
Geneva, 2011.
[7] CDF Collaboration, F. Abe et al., Observation of top quark production in p¯ collisions
p
with the Collider Detector at Fermilab, Phys. Rev. Lett. 74 (1995) 2626.
[8] D0 Collaboration, S. Abachi et al., Observation of the top quark , Phys. Rev. Lett. 74
(1995) 2632–2637, arXiv:hep-ex/9503003.
157

[9] CDF and D0 Collaboration, Tevatron Electroweak Working Group, Combination of
CDF and D0 Measurements of the Single Top Production Cross Section,
arXiv:0908.2171 [hep-ex].
[10] D0 Collaboration, V. M. Abazov et al., Observation of Single Top-Quark Production,
Phys. Rev. Lett. 103 (2009) 092001, arXiv:0903.0850 [hep-ex].
[11] CDF Collaboration, T. Aaltonen et al., First Observation of Electroweak Single Top
Quark Production, Phys. Rev. Lett. 103 (2009) 092002, arXiv:0903.0885 [hep-ex].
[12] D0 Collaboration, V. M. Abazov et al., Model-independent measurement of t-channel
√
single top quark production in p¯ collisions at s = 1.96 TeV , Physics Letters B 705
p
(2011) no. 4, 313 – 319.
[13] CMS Collaboration, S. Chatrchyan et al., Measurement of the t-Channel Single Top
√
Quark Production Cross Section in pp Collisions at s = 7 TeV, Phys. Rev. Lett. 107
(2011) 091802.
[14] ATLAS Collaboration, G. Aad √ al., Observation of t-Channel Single Top-Quark
et
Production in pp Collisions at s = 7 TeV with the ATLAS detector ,
ATLAS-CONF-2011-088 (2011) .
[15] ATLAS Collaboration, G. Aad et al., Measurement of the t-channel Single Top-Quark
Production Cross Section in 0.70 fb-1 of pp Collisions at (s) = 7 TeV with the
ATLAS detector , ATLAS-CONF-2011-101 (2011) .
[16] D0 Collaboration, V. Abazov et al., √
Search for anomalous Wtb couplings in single top
quark production in p¯ collisions at s = 1.96 TeV , Physics Letters B 708 (2012)
p
no. 1-2, 21 – 26.
[17] CDF Collaboration, T. Aaltonen et al., Observation of single top quark production and
measurement of |Vtb | with CDF , Phys. Rev. D 82 (2010) 112005.
[18] K. Nakamura et al., (Particle Data Group), J. Phys. G 37 (2010) 075021.
[19] D0 Collaboration, V. M. Abazov et al., Precision Measurement of the Ratio
B(t → W b)/B(t → W q) and Extraction of Vtb , Phys. Rev. Lett. 107 (2011) 121802.
[20] CDF Collaboration, D. Acosta et al., Measurement of B(t → W b)/B(t → W q) at the
Collider Detector at Fermilab, Phys. Rev. Lett. 95 (2005) 102002.
158

[21] A. W. Hendry and D. B. Lichtenberg, The quark model , Reports on Progress in
Physics 41 (1978) no. 11, 1707.
[22] D. Griffiths, Introduction to Elementary Particles. Wiley-VCH Verlag GmbH & Co.
KGaA, Weinheim, 2004.
[23] F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern
Particle Physics. John Wiley & Sons, 1984.
[24] L. H. Orr and J. L. Rosner, Comparison of top quark hadronization and decay rates,
Physics Letters B 246 (1990) no. 1-2, 221 – 225.
[25] N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) .
[26] M. Kobayashi and T. Maskawa, CP-Violation in the Renormalizable Theory of Weak
Interaction, Prog. Theor. Phys. 49 (1973) .
[27] J. Aguilar-Saavedra, A minimal set of top anomalous couplings, Nuclear Physics B
812 (2009) no. 1-2, 181 – 204.
[28] G. L. Kane, G. A. Ladinsky, and C. P. Yuan, Using the top quark for testing
standard-model polarization and CP predictions, Phys. Rev. D 45 (1992) 124–141.
[29] G. Bertone, D. Hooper, and J. Silk, Particle dark matter: evidence, candidates and
constraints, Physics Reports 405 (2005) no. 5-6, 279 – 390.
[30] M. Kowalski et al., Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets, The Astrophysical Journal 686 (2008) no. 2, 749.
[31] N. Jarosik et al., Seven-year Wilkinson Microwave Anisotropy Probe (WMAP)
Observations: Sky Maps, Systematic Errors, and Basic Results, The Astrophysical
Journal Supplement Series 192 (2011) no. 2, 14.
[32] S. Bilenky et al., Absolute values of neutrino masses: status and prospects, Physics
Reports 379 (2003) no. 2, 69 – 148.
[33] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.
159

[34] √
ATLAS Collaboration, G. Aad et al., Luminosity Determination in pp Collisions at
s = 7 TeV using the ATLAS Detector in 2011 ,
http://cdsweb.cern.ch/record/1376384.
[35] V. Kain, B. Goddard, B. Holzer, J. Jowett, M. Meddahi, T. Mertens, and
F. Roncarolo, Transverse emittance preservation through the LHC cycle, Tech. Rep.
CERN-ATS-2011-056, CERN, Geneva, Sep, 2011.
[36] J.-P. Koutchouk and G. Sterbini, An Early Beam Separation Scheme for the LHC
Luminosity Upgrade, Proceedings of EPAC, Edinburgh, Scotland (2006) .
[37] Boris and Dolgoshein, Transition radiation detectors, Nuclear Instruments and
Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment 326 (1993) no. 3, 434 – 469.
[38] ATLAS Collaboration, G. Aad et al., Electron performance measurements with the
ATLAS detector using the 2010 LHC proton-proton collision data, arXiv:1110.3174
[hep-ex]. submitted to Eur. Phys. J. C.
[39] ATLAS Collaboration, G. Aad et al., Performance of the ATLAS Trigger System in
2010 , The European Physical Journal C - Particles and Fields 72 (2012) 1–61.
10.1140/epjc/s10052-011-1849-1.
[40] ATLAS Collaboration, G. Aad et al., Muon reconstruction efficiency in reprocessed
2010 LHC proton-proton collision data recorded with the ATLAS detector , Tech. Rep.
ATLAS-CONF-2011-063, CERN, Geneva, Apr, 2011.
[41] ATLAS Collaboration, G. Aad et al., Measurement of the
W − > lν and Z/gamma ∗ − > ll production cross sections in proton-proton collisions
√
at s = 7 TeV with the ATLAS detector , JHEP 1012 (2010) 060, arXiv:1010.2130
[hep-ex].
[42] M. Cacciari, G. P. Salam, and G. Soyez, The anti- k t jet clustering algorithm, Journal
of High Energy Physics 2008 (2008) no. 04, 063.
[43] ATLAS Collaboration, G. Aad et al., Jet energy measurement with the ATLAS
√
detector in proton-proton collisions at s = 7 TeV , arXiv:1112.6426 [hep-ex].
submitted to European Physical Journal C.
160

[44] W. Lampl et al., Calorimeter Clustering Algorithms: Description and Performance,
Tech. Rep. ATL-LARG-PUB-2008-002. ATL-COM-LARG-2008-003, CERN, Geneva,
Apr, 2008.
[45] ATLAS Collaboration, G. Aad et al., Commissioning of the ATLAS high-performance
b-tagging algorithms in the 7 TeV collision data, Tech. Rep. ATLAS-CONF-2011-102,
CERN, Geneva, Jul, 2011.
[46] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems,
Transactions of the ASME–Journal of Basic Engineering 82 (1960) no. Series D, 35–45.
[47] ATLAS Collaboration, G. Aad and others, Performance √ missing transverse
of
momentum reconstruction in proton-proton collisions at s = 7 TeV with ATLAS ,
The European Physical Journal C - Particles and Fields 72 (2012) 1–35.
10.1140/epjc/s10052-011-1844-6.
[48] T. Sjostrand, S. Mrenna, and P. Skands, PYTHIA Generator version 6.418 , JHEP 05
(2006) 026.
[49] G. Corcella et al., HERWIG 6.5: an event generator for Hadron Emission Reactions
With Interfering Gluons (including supersymmetric processes), JHEP 01 (2001) 010,
arXiv:hep-ph/0011363.
[50] J. M. Butterworth, J. R. Forshaw, and M. H. Seymour, Multiparton interactions in
photoproduction at HERA, Z. Phys. C 72 (1996) 637–646, arXiv:hep-ph/9601371.
[51] B. P. Kersevan and R. W. Elzbieta, The Monte Carlo Event Generator AcerMC
version 3.5 with interfaces to PYTHIA 6.4, HERWIG 6.5 and ARIADNE 4.1 ,
hep-ph/0405247 (2008) .
[52] B. P. Kersevan and I. Hinchliffe, A Consistent prescription for the production involving
massive quarks in hadron collisions, JHEP 0609 (2006) 033, arXiv:hep-ph/0603068
[hep-ph].
[53] S. Frixione, B. R. Webber, and P. Nason, MC@NLO Generator version 3.4 ,
hep-ph/0204244 and hep-ph/0305252 (2002) .
[54] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. D. Polosa, ALPGEN, a
generator for hard multiparton processes in hadronic collisions, JHEP 07 (2003) 001,
arXiv:hep-ph/0206293.
161

[55] J. Pumplin et al, New generation of parton distributions with uncertainties from global
QCD analysis, JHEP 07 (2002) 012, arXiv:hep-ph/0201195.
[56] A. Sherstnev and R. Thorne, Parton distributions for LO generators, The European
Physical Journal C - Particles and Fields 55 (2008) 553–575.
10.1140/epjc/s10052-008-0610-x.
[57] A. Martin, W. Stirling, R. Thorne, and G. Watt, Parton distributions for the LHC ,
The European Physical Journal C - Particles and Fields 63 (2009) 189–285.
10.1140/epjc/s10052-009-1072-5.
[58] ATLAS Collaboration, G. Aad and others, The ATLAS Simulation Infrastructure,
The European Physical Journal C - Particles and Fields 70 (2010) 823–874.
10.1140/epjc/s10052-010-1429-9.
[59] S. Agostinelli et al., Geant4- a simulation toolkit, Nuclear Instruments and Methods in
Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment 506 (2003) no. 3, 250 – 303.
[60] ATLAS Collaboration, G. Aad et al., A measurement of the ATLAS muon
reconstruction and trigger efficiency using J/psi decays, Tech. Rep.
ATLAS-CONF-2011-021, CERN, Geneva, Mar, 2011.
[61] ATLAS Collaboration, G. Aad et al., Calibrating the b-Tag Efficiency and Mistag Rate
in 35 pb−1 of Data with the ATLAS Detector , Tech. Rep. ATLAS-CONF-2011-089,
CERN, Geneva, Jun, 2011.
[62] ATLAS Collaboration, G. Aad et al., Muon Momentum Resolution in First Pass
Reconstruction of pp Collision Data Recorded by ATLAS in 2010 , Tech. Rep.
ATLAS-CONF-2011-046, CERN, Geneva, Mar, 2011.
[63] ATLAS Collaboration, G. Aad et al., Jet energy scale and its systematic uncertainty
√
in proton-proton collisions at s = 7 TeV in ATLAS 2010 data, Tech. Rep.
ATLAS-CONF-2011-032, CERN, Geneva, Mar, 2011.
[64] ATLAS Collaboration, G. Aad et al., Jet energy resolution and selection efficiency
relative to track jets from in-situ techniques with the ATLAS Detector Using
√
Proton-Proton Collisions at a Center of Mass Energy s = 7 TeV , Tech. Rep.
ATLAS-CONF-2010-054, CERN, Geneva, Jul, 2010.
162

[65] G. Romeo, A. Schwartzman, R. Piegaia, T. Carli, and R. Teuscher, Jet Energy
Resolution from In-situ Techniques with the ATLAS Detector Using Proton-Proton
√
Collisions at a Center of Mass Energy s = 7 TeV , Tech. Rep.
ATL-COM-PHYS-2011-240, CERN, Geneva, Mar, 2011.
[66] ATLAS Collaboration, G. Aad et al., Data-Quality Requirements and Event Cleaning
for Jets and Missing Transverse Energy Reconstruction with the ATLAS Detector in
√
Proton-Proton Collisions at a Center-of-Mass Energy of s = 7 TeV , Tech. Rep.
ATLAS-CONF-2010-038, CERN, Geneva, Jul, 2010.
[67] ATLAS Collaboration, G. Aad et al.,
https://twiki.cern.ch/twiki/bin/view/AtlasProtected/HowToCleanJets2011 , (2011) .
[68] CDF Collaboration, T. Aaltonen et al., First Measurement of the b-Jet Cross Section
√
in Events with a W Boson in pp Collisions at s = 1.96 TeV, Phys. Rev. Lett. 104
(2010) 131801.
[69] D0 Collaboration, V. Abazov et al., Measurement of the ratio of the p¯ → W + c-jet
p
cross section to the inclusive p¯ → W +jets cross section, Physics Letters B 666
p
(2008) no. 1, 23 – 30.
[70] ATLAS Collaboration, G. Aad et al., Measurement of the cross section for the
√
production of a W boson in association with b-jets in pp collisions at s = 7 TeV with
the ATLAS detector , Physics Letters B 707 (2012) no. 5, 418 – 437.
[71] ATLAS Collaboration, G. Aad et al., Measurement of the top quark-pair production
√
cross section with ATLAS in pp collisions at s = 7 TeV , The European Physical
Journal C - Particles and Fields 71 (2011) 1–36. 10.1140/epjc/s10052-011-1577-6.
[72] ATLAS Collaboration, G. Aad et al., Searches for Single Top-Quark Production with
√
the ATLAS Detector in pp Collisions at s = 7 TeV , Tech. Rep.
ATLAS-CONF-2011-027, CERN, Geneva, Mar, 2011.
[73] R. D. Cousins, J. T. Linnemann, and J. Tucker, Evaluation of three methods for
calculating statistical significance when incorporating a systematic uncertainty into a
test of the background-only hypothesis for a Poisson process, Nucl. Instrum. Methods
Phys. Res., A 595 (2008) 480.
[74] W. Press et al., Numerical Recipes in C, 2nd ed. Cambridge, 1992.
163

[75] M. Aliev et al., – HATHOR – HAdronic Top and Heavy quarks crOss section
calculatoR, arXiv/1007.1327.
[76] U. Felzmann, https://twiki.cern.ch/twiki/bin/view/Main/AlpgenFAQ, (2008) .
[77] A. Martin, W. Stirling, R. Thorne, and G. Watt, Uncertainties on αS in global PDF
analyses and implications for predicted hadronic cross sections, The European Physical
Journal C - Particles and Fields 64 (2009) 653–680. 10.1140/epjc/s10052-009-1164-2.
[78] J. M. Campbell and R. Ellis, MCFM for the Tevatron and the LHC , Nuclear Physics
B - Proceedings Supplements 205-206 (2010) no. 0, 10 – 15. Loops and Legs in
Quantum Field Theory, Proceedings of the 10th DESY Workshop on Elementary
Particle Theory.
[79] P. Nason, A new method for combining NLO QCD computations with parton shower
simulations, JHEP 11(2004)-040, hep-ph/0409146 (2004) .
[80] S. Frixione, P. Nason, et al., Positive weight next-to-leading-order Monte Carlo, JHEP
11(2007)-126 and JHEP 09(2007)111, hep-ph/07092092 and hep-ph/07073088 (2007) .
[81] W. Wagner. Private communication, 2011.
[82] L. Lyons, Statistics for nuclear and particle physicists. Cambridge University Press,
1986.
[83] L. Lyons, D. Gibaut, and P. Clifford, How to combine correlated estimates of a single
physical quantity, Nuclear Instruments and Methods in Physics Research Section A:
Accelerators, Spectrometers, Detectors and Associated Equipment 270 (1988) no. 1,
110 – 117.
[84] B. P. Roe et al., Boosted Decision Trees as an Alternative to Artificial Neural
Networks for Particle Identification, physics/0408124v2 (2004) .
[85] I. Narsky, StatPatternRecognition: A C++ Package for Statistical Analysis of High
Energy Physics Data, physics/0507143 (2005) .
[86] F. J. Massey, The Kolmogorov-Smirnov Test for Goodness of Fit, Journal of the
American Statistical Association 46 (1951) no. 253, 68–78.

164