SEARCH FOR THE STANDARD MODEL HIGGS BOSON
IN ASSOCIATION WITH A W BOSON AT D0
By
Savanna Marie Shaw

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics - Doctor of Philosophy
2013

ABSTRACT
SEARCH FOR THE STANDARD MODEL HIGGS BOSON
IN ASSOCIATION WITH A W BOSON AT D0
By
Savanna Marie Shaw
I present a search for the standard model Higgs boson, H, produced in association with a
W boson in data events containing a charged lepton (electron or muon), missing energy, and
two or three jets. The data analysed correspond to 9.7 fb−1 of integrated luminosity collected
at a center-of-momentum energy of

√

s = 1.96 TeV with the D0 detector at the Fermilab

Tevatron p¯ collider. This search uses algorithms to identify the signature of bottom quark
p
production and multivariate techniques to improve the purity of H → b¯ production. We
b
validate our methodology by measuring W Z and ZZ production with Z → b¯ and find
b
production rates consistent with the standard model prediction. For a Higgs boson mass
of 125 GeV, we determine a 95% C.L. upper limit on the production of a standard model
Higgs boson of 4.8 times the standard model Higgs boson production cross section, while the
expected limit is 4.7 times the standard model production cross section. I also present a novel
method for improving the energy resolution for charged particles within hadronic signatures.
This is achieved by replacing the calorimeter energy measurement for charged particles within
a hadronic signature with the tracking momentum measurement. This technique leads to a
∼ 20% improvement in the jet energy resolution, which yields a ∼ 7% improvement in the
reconstructed dijet mass width for H → b¯ events. The improved energy calculation leads to
b
a ∼ 5% improvement in our expected 95% C.L. upper limit on the Higgs boson production
cross section.

ACKNOWLEDGMENTS

There are many people to thank for their help throughout my education in physics. First and
foremost I would like to thank my thesis advisor, Professor Wade Fisher. Wade’s intelligence,
patience, and good humour made for a very enjoyable career as a graduate student. I will
be forever grateful for all his help and support over the years in everything from answering
physics questions, to helping debug code, to editing my thesis, to being the only American
I know who can actually make decent jokes about Canada.
An analysis as complex as the WH analysis presented in this thesis requires the hard work
of a team of people so I would also like to thank the members of the D0 WH analysis group
with whom I had the pleasure of working alongside for the past few years: Gregorio Bernardi,
Mike Cooke, Yuji Enari, Sebastien Greder, Ken Herner, Bob Hirosky, Emily Johnson, Dikai
ˇ
Li, Huong Nguyen, and Lidija Zivkovi´.
c
I would also like to thank Aurelio Juste for his supervision and collaboration of the jet
energy resolution studies presented in this thesis. This was a technically challenging project
that was never guaranteed to result in any sort of improvement, but Aurelio’s seemingly
never-ending supply of ideas and enthusiasm made it a very interesting and rewarding project
to work on.
Many thanks to the other graduate students and post-docs at D0 and at MSU for their
help both with questions relating to physics and questions more related to the peculiarities
of American culture.
Last, but certainly not least, I would like to thank my family. Without my parents, I
certainly would not be here (literally, and figuratively). I can not thank them enough for
their support and encouragement over the years. They really did believe that I could do
iii

anything I wanted, and as a result, I believed that too. I would also like to thank my little
sister for putting up with me for the entirety of her life, and never rubbing it in that she is
the far cooler one.
It’s impossible to to thank everyone who deserves my gratitude in such a small space,
and I have left numerous people out. To all of those who have helped me along the way who
aren’t listed, please accept my sincere gratitude for your help.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

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vii

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ix

KEY TO SYMBOLS AND ABBREVIATIONS . . . . . .

. . . . . . . . xxxii

Chapter 1 Introduction . . . . . . . . . .
1.1 Standard Model Particles . . . . . . . .
1.2 The Standard Model . . . . . . . . . .
1.2.1 QED . . . . . . . . . . . . . . .
1.2.2 QCD . . . . . . . . . . . . . . .
1.2.3 Electroweak Unification and the
1.2.4 Properties of the Higgs Boson .
1.3 Beyond the Standard Model . . . . . .

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Higgs Mechanism
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Chapter 2 Experimental Apparatus
2.1 The Tevatron . . . . . . . . . . .
2.2 The D0 Detector . . . . . . . . .
2.3 Data Acquisition . . . . . . . . .
2.4 Data Collection . . . . . . . . . .

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Chapter 3 Particle Identification and Reconstruction Algorithms
3.1 Charged Particle Tracks . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Primary Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Electrons and Photons . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Missing Transverse Energy . . . . . . . . . . . . . . . . . . . . . . .
3.7 Bottom Quark Identification . . . . . . . . . . . . . . . . . . . . . .

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62

Chapter 6 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Analysis Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4 Event Simulation
Chapter 5 Statistical Analysis

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6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11

Multijet Background Estimation . . . . .
Selection . . . . . . . . . . . . . . . . . .
b Tagging . . . . . . . . . . . . . . . . .
Multivariate Classification . . . . . . . .
Systematic Uncertainties . . . . . . . . .
Diboson (V Z) Production With Z → b¯
b
Upper Limits on Higgs Boson Production
D0 and Tevatron Higgs Boson Searches .
Future Studies of the Higgs Boson . . . .

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Chapter 7 Improvements to Jet Energy Resolution
7.1 Track-Cal Jet Algorithm . . . . . . . . . . . . . . .
7.2 Energy Resolution Improvement . . . . . . . . . . .
7.3 Improvement in Higgs Boson Analysis . . . . . . . .

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132

Chapter 8 Conclusion

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APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Appendix A Multijet MVA Input Distributions . . . . . . . . . . . . . . . . . . . 146
Appendix B Final BDT Input and Output Distributions . . . . . . . . . . . . . . 153
BIBLIOGRAPHY

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vi

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LIST OF TABLES

Table 1.1

The three generations of Fermions [1]. . . . . . . . . . . . . . . . . .

4

Table 1.2

The force carrying bosons [1]. . . . . . . . . . . . . . . . . . . . . . .

4

Table 6.1

The cross section times branching fraction for diboson and top-quark
simulated processes. . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

The cross section times branching fraction for W +jets simulated processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

The cross section times branching fraction for Z+jets simulated processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

Observed number of events in data and expected number of events
from each signal and background source (where V = W, Z) for events
with a muon and exactly two jets. The expected signal is quoted
at MH = 125 GeV. The total background uncertainty includes all
sources of systematic uncertainty added in quadrature. . . . . . . .

85

Observed number of events in data and expected number of events
from each signal and background source (where V = W, Z) for events
with an electron and exactly two jets. The expected signal is quoted
at MH = 125 GeV. The total background uncertainty includes all
sources of systematic uncertainty added in quadrature. . . . . . . .

85

Observed number of events in data and expected number of events
from each signal and background source (where V = W, Z) for events
with a muon and exactly three jets. The expected signal is quoted
at MH = 125 GeV. The total background uncertainty includes all
sources of systematic uncertainty added in quadrature. . . . . . . .

86

Observed number of events in data and expected number of events
from each signal and background source (where V = W, Z) for events
with an electron and exactly three jets. The expected signal is quoted
at MH = 125 GeV. The total background uncertainty includes all
sources of systematic uncertainty added in quadrature. . . . . . . .

86

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 6.7

vii

Table 6.8

Table 6.9

Table 6.10

Input variables for the MVAMJ (V H) discriminant, which was trained
using V H → ℓνb¯ events as a signal. Variables are ranked by their
b
importance in the BDT (which is based on how often they are used
in the training) [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

Table of input variables for the final signal discriminant. Variables
are ranked by their importance in the BDT (which is based on how
often they are used in the training) in the two tight b-tagged (2T),
two medium b-tagged (2M), two loose b-tagged (2L), and one tight
b-tagged (1T) categories [2]. . . . . . . . . . . . . . . . . . . . . . .

96

The expected and observed 95% C.L. limits, as a function of the Higgs
boson mass MH , presented as ratios of production cross section times
branching fraction to the SM prediction [2]. . . . . . . . . . . . . . . 113

viii

LIST OF FIGURES

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

For the interpretation of the references to colour in this and all other
figures, the reader is referred to the electronic version of this dissertation. A global fit to data from precision electroweak experiments
can place constraints on the W boson and top quark masses. Shown
here are the 68% and 95% contours from this fit including the Higgs
boson mass measurement in blue, and not including the Higgs boson
mass measurement in gray. The horizontal and vertical green bands
correspond to 1 standard deviation on the W boson and top quark
masses respectively. The diagonal lines show where different values
for the Higgs mass would appear in the W −top mass plane [3]. . . .

18

The masses of the top quark, W boson, and Higgs boson are related
through loop diagrams. . . . . . . . . . . . . . . . . . . . . . . . . .

18

95% confidence level upper limit on Higgs boson production cross section as a ratio to the Standard Model cross section from the ATLAS
experiment (top) [4] and the CMS experiment (bottom) [5]. Masses
up to 500 GeV are excluded, with the exception of a small window
of masses centred around 125 GeV. . . . . . . . . . . . . . . . . . .

19

The production cross section for the Higgs boson as a function of
Higgs boson mass at the Tevatron (where the center-of-momentum
√
energy, s, is 1.96 TeV). . . . . . . . . . . . . . . . . . . . . . . . .

21

Figure 1.5

The decay rates for the Higgs boson as a function of Higgs boson mass. 22

Figure 1.6

The Feynman diagrams for the most important Higgs boson production modes at the Tevatron: (a) gluon-gluon fusion, (b) associated
production of a Higgs boson with a pair of top quarks, and (c) vector
boson fusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

Figure 2.1

A schematic view of the accelerator chain at Fermilab. . . . . . . . .

25

Figure 2.2

A cross sectional view of the D0 detector, showing the tracking system
surrounded by the calorimeter and the muon detection system [6]. .

28

ix

Figure 2.3

A cross sectional view of the D0 tracking system. Closest to the
beampipe is the silicon microstrip tracker, surrounded by the central
fibre tracker. The tracking system is contained within a superconducting solenoid [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

Figure 2.4

A view of the SMT. . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

Figure 2.5

The layout of the CFT, showing the fibre layers. . . . . . . . . . . .

32

Figure 2.6

A diagram showing a cut away view of the D0 calorimeter. The
calorimeter is comprised of three pieces: a central calorimeter and two
end calorimeters. Each piece is made up of several layers of absorber
plates (made of Uranium or copper or steel) inserted in liquid argon.
These layers form the electromagnetic, the fine hadronic, and the
coarse hadronic calorimeters [6]. . . . . . . . . . . . . . . . . . . . .

33

A diagram of a calorimeter cell. Each cell consists of an absorber
plate, the liquid argon, and a plate to read out the charge. . . . . .

34

The calorimeter cells are arranged in towers along lines of constant
η, illustrated by the alternating shaded areas. . . . . . . . . . . . . .

35

A cross sectional view of the D0 preshower detectors located between
the solenoid and the calorimeters. The preshower detectors are comprised of interleaved scintillator strips with a wavelength shifting fibre
at the center [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

An exploded view of the arrangement of the drift tubes in the muon
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

A schematic view of the flow of data through the D0 trigger system [6]. 41

Figure 2.12

A schematic view of the relationship between the different trigger
components and the different detector subsystems [6]. . . . . . . . .

Figure 3.1

The HTF method for a single 1.5 GeV track with 5 hits. (a) Some
of the possible trajectories for a single hit in the x-y plane, (b) translation of a single hit into ρ − φ space, (c) multiple hits from the
same track form lines that intersect at a single point, and (d) the
intersection point as a peak in the ρ − φ histogram. . . . . . . . . .

x

43

48

Figure 3.2

The b-tagging efficiency (in black) and rate for light jets to be mistagged
(in red) as a function of the neural network output for jets with
pT > 30 GeV. The vertical blue lines indicate points on the neural
network output where the efficiencies in simulation have been corrected to match the efficiencies in data. . . . . . . . . . . . . . . . . 57

Figure 6.1

Example Feynman diagrams for processes we consider as backgrounds:
W +jets (top left), top quark pair production (top right), W Z production (bottom left), and multijet production (bottom right). . . .

68

Feynman diagrams for processes contributing to our Higgs boson signal: associated production of a Higgs with a W boson, with the Higgs
boson decaying to a pair of b-quarks (left); gg → H → W W (middle),
and associated production of a Higgs boson with a W boson, with
the Higgs boson decaying to a pair of W bosons (right). . . . . . . .

71

Reweighting functions to correct for mismodelling in the alpgen
V+jets MC for the second leading jet η (top left), leading jet η (top
right), W pT (middle left), ∆R(j1 , j2 ) (middle right), and lepton η
(bottom). The black points are the data with all non-V+jets backgrounds subtracted off. The black curves are the reweighting functions fit to the points, and the blue and red are the ±1 standard
deviations on the black curve. . . . . . . . . . . . . . . . . . . . . .

73

Example of the probability for a jet that passes the loose lepton identification requirements to pass the tight lepton isolation requirements
for the 15 < pT < 17 GeV range with 0.4 < min [∆φ(ET , jet)] < π
as a function of the electron η in the (a) CC and (b) EC. The solid
line is a fit to the data, and the dashed lines are the functions with
the parameters shifted up and down by their uncertainties. . . . . .

77

Example of the probability for a jet that passes the loose lepton identification requirements to pass the tight lepton isolation requirements
as a function of muon pT for (a) |η| < 1.0 and (b) 1.0 < |η| < 1.6,
with 0 < ∆φ(ET , µ) < 1. The solid line is a fit to the data, and
the dashed lines are the functions with the parameters shifted up and
down by their uncertainties. . . . . . . . . . . . . . . . . . . . . . .

78

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

xi

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 6.10

Figure 6.11

Figure 6.12

Figure 6.13

Figure 6.14

Muon trigger correction, derived from data to account for the gain
in efficiency when moving from single muon and muon+jets triggers
to inclusive triggers. The corrections are parametrized as a function
HT , shown for events with muon |η| < 1.0 with a) ET < 50 GeV and
b) ET ≥ 50 GeV. The black circles represent the correction when the
muon passes through the detector support region (−2 < φ < −1.2),
and the red triangles represent the correction in all other regions of
φ [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

The average b-jet identification output for events with two jets. We
define three categories containing two b-tagged jets based on this average output. The signal is shown for a Higgs boson mass of 125 GeV,
scaled by a factor of 50 [2]. . . . . . . . . . . . . . . . . . . . . . . .

84

Distributions for all selected events with two jets of (a) transverse
mass of the lepton-ET system, and (b) charged lepton pT . The signal
is multiplied by 1000. Overflow events are added to the last bin [2].

87

Distributions for all selected events with two jets of (a) leading jet
pT , and (b) second-leading jet pT . The signal is multiplied by 1000.
Overflow events are added to the last bin [2]. . . . . . . . . . . . .

88

Distributions for all selected events with two jets of (a) ET , and
(b) ∆R between the leading and second-leading jets. The signal is
multiplied by 1000. Overflow events are added to the last bin [2]. .

89

Invariant mass of the leading and second-leading jets in events with
two jets and (a) one tight b-tag, and (b) two loose b-tags. The signal
is multiplied by 200. Overflow events are added to the last bin [2]. .

90

Invariant mass of the leading and second-leading jets in events with
two jets and (a) two medium b-tags, and (b) two tight b-tags. The
signal is multiplied by 50. Overflow events are added to the last
bin [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

The output distribution for the Higgs boson signal vs multijet discriminant shown for all events containing exactly two jets. The signal
for MH = 125 GeV is scaled by a factor of 1000 [2]. . . . . . . . . .

94

Distributions of some of the most significant inputs to the final discriminant in events with exactly two jets: (a) pW /(pℓ + ET ), shown
T
T
for events with one tight b-tag; (b) max |∆η(ℓ, {j1 or j2 })|, shown for
events with two loose b-tags. The MH = 125 GeV signal is multiplied
by 200. Overflow events are added to the last bin [2]. . . . . . . . .

97

xii

Figure 6.15

Figure 6.16

Distributions of some of the most significant inputs to the final discriminant in events with exactly two jets: (a) q ℓ ×η ℓ , shown for events
with two medium b-tags; (b) (pT )V IS , shown for events with two
tight b-tags. The MH = 125 GeV signal is multiplied by 50. Overflow
events are added to the last bin [2]. . . . . . . . . . . . . . . . . . .

98

Distributions of some of the most significant inputs to the final discriminant in events with exactly three jets: (a) max |∆η(ℓ, {j1 or j2 })|,
shown for events with one tight b-tag; (b) q ℓ × η ℓ , shown for events
with two loose b-tags. The MH = 125 GeV signal is multiplied by
200. Overflow events are added to the last bin [2]. . . . . . . . . . .

99

Figure 6.17

Distributions of some of the most significant inputs to the final discriminant in events with exactly three jets: (a) aplanarity, shown for
events with two medium b-tags; (b) mℓνj2 , shown for events with two
tight b-tags. The MH = 125 GeV signal is multiplied by 50. Overflow
events are added to the last bin [2]. . . . . . . . . . . . . . . . . . . 100

Figure 6.18

Distributions of the final discriminant output, after the maximum
likelihood fit (described in Ch. ), in events with exactly two jets and:
(a) one tight b-tag, and (b) two loose b-tags. The MH = 125 GeV
signal is multiplied by 100 [2]. . . . . . . . . . . . . . . . . . . . . . 101

Figure 6.19

Distributions of the final discriminant output, after the maximum
likelihood fit (described in Ch. ), in events with exactly two jets and:
(a) two medium b-tags, and (b) two tight b-tags. The MH = 125 GeV
signal is multiplied by 20 [2]. . . . . . . . . . . . . . . . . . . . . . 102

Figure 6.20

Distributions of the final discriminant output, after the maximum
likelihood fit (described in Ch. ), in events with exactly three jets and:
(a) one tight b-tag, and (b) two loose b-tags. The MH = 125 GeV
signal is multiplied by 100 [2]. . . . . . . . . . . . . . . . . . . . . . 103

Figure 6.21

Distributions of the final discriminant output, after the maximum
likelihood fit (described in Ch. ), in events with exactly three jets and:
(a) two medium b-tags, and (b) two tight b-tags. The MH = 125 GeV
signal is multiplied by 20 [2]. . . . . . . . . . . . . . . . . . . . . . 104

Figure 6.22

The dijet mass shown for the expected diboson signal and backgroundsubtracted data after the maximum likelihood fit, summed over b-tag
channels. The error bars on data points represent the statistical uncertainty only. The post-fit systematic uncertainties are represented
by the solid lines. The signal expectation is shown scaled to the best
fit value [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

xiii

Figure 6.23

The final MVA discriminant output shown for the expected diboson signal and background-subtracted data rebinned as a function
of log(S/B), after the maximum likelihood fit, summed over b-tag
channels. The error bars on data points represent the statistical uncertainty only. The post-fit systematic uncertainties are represented
by the solid lines. The signal expectation is shown scaled to the best
fit value. The inset gives an expanded view of the high log(S/B)
region [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 6.24

The log likelihood ratio as a function of Higgs boson mass for the expected background only hypothesis (dashed black line), expected signal+background hypothesis (red dashed line), and data (solid black
line). The green and yellow bands represent, respectively, ± one and
two standard deviations on the background only hypothesis [2]. . . . 111

Figure 6.25

The upper 95% confidence level limit on the Higgs boson production
cross section times branching ratio as a ratio to the SM cross section
times branching ratio. The dashed line shows the expected limit, the
solid line shows the limit observed in data, and the green and yellow
bands show the ± 1 and 2 standard deviations on the expected limit [2].112

Figure 6.26

The LLR for the combined D0 Higgs boson searches (top) and the
combined Tevatron Higgs searches (bottom), showing the background
only expectation (the black dashed line), the signal+background expectation (red dashed line), the observed data (black solid line), and
the background plus a 125 GeV Higgs boson signal (blue dashed line).
The green and yellow bands are the ± 1 and 2 standard deviation on
the background only expectation [7, 8]. . . . . . . . . . . . . . . . . 114

Figure 6.27

The 95% C.L. limit as a function of Higgs boson mass for the combined D0 Higgs boson searches (top) and the combined Tevatron
Higgs boson searches (bottom), shown as a ratio the the SM cross
section. The black dashed line shows the expected limit, the solid
black line shows the observed limit, the blue dashed line shows the
limit expected if a Higgs boson with a mass of 125 GeV were present.
The green and yellow bands are the ± 1 and 2 standard deviation
on the expectation. Regions where the observed limit is below 1
(90 < MH < 101, 157 < MH < 178 GeV (D0), and 90 < MH < 108,
150 < MH < 182 GeV (Tevatron)), are regions of MH space that are
excluded at the 95% confidence level [7, 8]. . . . . . . . . . . . . . . 115

xiv

Figure 6.28

The probability for the background to fluctuate to the observed rate
in data as a function of Higgs boson mass for the D0 combination
(left) and the Tevatron combination (right). The black dashed line
shows the expectation, the solid black line shows the observed data,
the blue dashed line shows the expectation for a Higgs boson with
MH = 125 GeV. The green and yellow bands enclose the ± 1 and 2
s.d. fluctuations of the background [7, 8]. . . . . . . . . . . . . . . . 116

Figure 7.1

The fraction of energy deposited in various cones around a single pion
track for a pion energy of 10 GeV. 90% of the energy is contained
within a cone of ∆R = 0.15. . . . . . . . . . . . . . . . . . . . . . . 120

Figure 7.2

∆R=0.15 − P
[Etrack
track ∗ R(Ptrack )]/Ptrack for (a) 5 GeV simulated single
charged pion tracks, and (b) tracks within a jet with 4.5 < Ptrack <
5 GeV using simulated γ+jet events. The vertical lines indicate twice
the width of the charged pion distribution (σF ). . . . . . . . . . . . 123

Figure 7.3

The resolution for the track-cal jet energy + kCPS in the blue circles
and calorimeter jet energy + kCPS in the red crosses as a function of
kCPS , for a) |ηjet | < 0.4, and b) 0.4 < |ηjet | < 0.8. The pink solid
and green dashed lines show the track-cal jet energy and calorimeter
jet energy resolutions respectively for kcps = 0. . . . . . . . . . . . . 125

Figure 7.4

The resolution for the track-cal jet energy + kCPS in the blue circles
and calorimeter jet energy + kCPS in the red crosses as a function
of kCPS , for a) 0.8 < |ηjet | < 1.2, and b) 1.2 < |ηjet | < 1.6. The
pink solid and green dashed lines show the track-cal jet energy and
calorimeter jet energy resolutions respectively for kcps = 0. . . . . . 126

Figure 7.5

The ratio of the reconstructed jet pT to the true MC jet pT for jets
with 30 < pT < 40 GeV, and |η| < 0.4, for track-cal jets (in red) and
calorimeter jets (in black). The mean of this distribution is taken as
the calorimeter response. . . . . . . . . . . . . . . . . . . . . . . . . 127

Figure 7.6

The energy response for track-cal jets as a function of true MC pT for
various track multiplicities for a) |ηjet | < 0.4, and b) 0.4 < |ηjet | <
0.8. The response for calorimeter jets is also shown for comparison. . 128

Figure 7.7

The energy response for track-cal jets as a function of true MC pT
for various track multiplicities for a) 0.8 < |ηjet | < 1.2, and b)
1.2 < |ηjet | < 1.6. The response for calorimeter jets is also shown
for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

xv

Figure 7.8

The energy resolution for track-cal jets as a function of true MC pT
compared to the resolution for calorimeter jets for a) |ηjet | < 0.4,
and b) 0.4 < |ηjet | < 0.8. The bottom panels show the ratio of the
track-cal jet resolution to the calorimeter jet resolution. . . . . . . . 130

Figure 7.9

The energy resolution for track-cal jets as a function of true MC pT
compared to the resolution for calorimeter jets for a) 0.8 < |ηjet | <
1.2, and b) 1.2 < |ηjet | < 1.6. The bottom panels show the ratio of
the track-cal jet resolution to the calorimeter jet resolution. . . . . . 131

Figure 7.10

Distributions for all selected events with two jets of (a) transverse
mass of the lepton-ET system, and (b) charged lepton pT . The MH =
125 GeV signal is multiplied by 1000. Overflow events are added to
the last bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Figure 7.11

Distributions for all selected events with two jets of (a) leading jet
pT , and (b) second-leading jet pT . The MH = 125 GeV signal is
multiplied by 1000. Overflow events are added to the last bin. . . . 134

Figure 7.12

Distributions for all selected events with two jets of (a) ET , and (b)
∆R between the leading and second-leading jets. The MH = 125 GeV
signal is multiplied by 1000. Overflow events are added to the last bin. 135

Figure 7.13

Invariant mass of the leading and second-leading jets in events with
two jets and (a) one tight b-tag, and (b) two loose b-tags. The MH =
125 GeV signal is multiplied by 200. Overflow events are added to
the last bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Figure 7.14

Invariant mass of the leading and second-leading jets in events with
two jets and (a) two medium b-tags, and (b) two tight b-tags. The
MH = 125 GeV signal is multiplied by 50. Overflow events are added
to the last bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Figure 7.15

The dijet mass for track-cal jets (red) and calorimeter jets (black),
for the W H MH = 125 GeV signal (solid lines) and all backgrounds
(dashed lines) for events with exactly two jets and two tight b-tags.
All curves are normalized to have unit area. The mean and width
values quoted are determined by fitting the signal dijet mass peak
with a Gaussian distribution. The width of the signal peak is ∼ 7%
narrower for track-cal jets than for calorimeter jets. . . . . . . . . . 138

xvi

Figure 7.16

The dijet mass for track-cal jets (red) and calorimeter jets (black),
for W W events with exactly two jets and zero b-tags. The mean and
width values quoted are determined by fitting the signal dijet mass
peak with a Gaussian distribution. The width of the dijet mass peak
is ∼ 7% narrower for track-cal jets than for calorimeter jets. . . . . 139

Figure 7.17

The dijet mass shown for the expected diboson signal and backgroundsubtracted data rebinned, after the maximum likelihood fit, for events
with zero b-tagged jets (a) using calorimeter jets and (b) using trackcal jets. The error bars on data points represent the statistical uncertainty only. The post-fit systematic uncertainties are represented
by the solid lines. The diboson signal expectation is shown scaled to
the best fit value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Figure 7.18

The 95 % C.L. expected Higgs boson production cross section limit
(top), presented as a ratio to the SM cross section, for track-cal jets
(black dashed line), and calorimeter jets (black solid line). The green
and grey shaded areas represent the ±1 and 2 standard deviations on
the calorimeter jet expectation. The ratio of the expected 95% C.L.
limit for track-cal jets to calorimeter jets (bottom). . . . . . . . . . . 142

Figure A.1

Input variables to the multijet BDT shown for all events containing
two jets: (top left) η of the ET , (top right) the ET significance,
(bottom left) ∆η(ℓ, ν), and (bottom right) the twist of the ℓ − ν
system. The signal is shown for MH = 125 GeV multiplied by a
factor of 1000. Overflow events are added to the last bin. . . . . . . 147

Figure A.2

Input variables to the multijet BDT shown for all events containing
two jets: (top left) cos(θ) in the ℓν center-of-momentum frame, (top
right) the velocity of the dijet system, (bottom left) the mass asymmetry between the dijet and the ℓν system, and (bottom right) the
centrality of the ℓνjj system. The signal is shown for MH = 125 GeV
multiplied by a factor of 1000. Overflow events are added to the last
bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Figure A.3

Input variables to the multijet BDT shown for all events containing
two jets: (left) the magnitude of the vector sum of pT for all visible
particles, and (right) the maximum ∆η(ℓ, j). The signal is shown for
MH = 125 GeV multiplied by a factor of 1000. Overflow events are
added to the last bin. . . . . . . . . . . . . . . . . . . . . . . . . . . 149

xvii

Figure A.4

Input variables to the multijet BDT shown for all events containing
two jets: (top left) η of the ET , (top right) the ET significance, (bottom left) ∆η(ℓ, ν), and (bottom right) the twist of the ℓ − ν system.
The signal is shown for MH = 125 GeV. The signal is normalized to
the sum of the backgrounds. Overflow events are added to the last bin.150

Figure A.5

Input variables to the multijet BDT shown for all events containing
two jets: (top left) cos(θ) in the ℓν center-of-momentum frame, (top
right) the velocity of the dijet system, (bottom left) the mass asymmetry between the dijet and the ℓν system, and (bottom right) the
centrality of the ℓνjj system. The signal is shown for MH = 125 GeV.
The signal is normalized to the sum of the backgrounds. Overflow
events are added to the last bin. . . . . . . . . . . . . . . . . . . . . 151

Figure A.6

Input variables to the multijet BDT shown for all events containing
two jets: (left) the magnitude of the vector sum of pT for all visible
particles, and (right) the maximum ∆η(ℓ, j). The signal is shown
for MH = 125 GeV. The signal is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 152

Figure B.1

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is multiplied
by a factor of 200. Overflow events are added to the last bin. . . . . 154

Figure B.2

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag. The signal
is shown for MH = 125 GeV, and is multiplied by a factor of 200.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 155

Figure B.3

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag: (top left)
the mass asymmetry between the ℓν and dijet systems, (top right)
aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 200.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 156

Figure B.4

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is multiplied
by a factor of 200. Overflow events are added to the last bin. . . . . 157
xviii

Figure B.5

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag. The signal
is shown for MH = 125 GeV, and is multiplied by a factor of 200.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 158

Figure B.6

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag: (top left)
the mass asymmetry between the ℓν and dijet systems, (top right)
aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 200.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 159

Figure B.7

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag: (top
left) the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is multiplied
by a factor of 50. Overflow events are added to the last bin. . . . . . 160

Figure B.8

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag. The
signal is shown for MH = 125 GeV, and is multiplied by a factor of
50. Overflow events are added to the last bin. . . . . . . . . . . . . . 161

Figure B.9

Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag: (top left)
the multijet MVA output, (top right) cos(χ∗ ), (bottom left) cos(θ∗ ,
and (bottom right) the dijet transverse mass. The signal is shown for
MH = 125 GeV, and is multiplied by a factor of 50. Overflow events
are added to the last bin. . . . . . . . . . . . . . . . . . . . . . . . . 162

Figure B.10 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tags: the
magnitude of the vector pT sum for all visible particles. The signal
is shown for MH = 125 GeV, and is multiplied by a factor of 50.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 163
Figure B.11 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is multiplied
by a factor of 50. Overflow events are added to the last bin. . . . . . 164

xix

Figure B.12 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag. The signal
is shown for MH = 125 GeV, and is multiplied by a factor of 50.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 165
Figure B.13 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: (top left)
the multijet MVA output, (top right) cos(χ∗ ), (bottom left) cos(θ∗ ,
and (bottom right) the dijet transverse mass. The signal is shown for
MH = 125 GeV, and is multiplied by a factor of 50. Overflow events
are added to the last bin. . . . . . . . . . . . . . . . . . . . . . . . . 166
Figure B.14 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: the ratio of
the W pT to the sum of the lepton pT and ET . The signal is shown
for MH = 125 GeV, and is multiplied by a factor of 50. Overflow
events are added to the last bin. . . . . . . . . . . . . . . . . . . . . 167
Figure B.15 The final MVA output for events with two jets and one tight b-tag
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 168
Figure B.16 The final MVA output for events with two jets and one tight b-tag
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 169
Figure B.17 The final MVA output for events with two jets and one tight b-tag
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 170
Figure B.18 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 171
Figure B.19 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 172
Figure B.20 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 173
Figure B.21 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 174
xx

Figure B.22 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 175
Figure B.23 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 176
Figure B.24 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 177
Figure B.25 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 178
Figure B.26 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 179
Figure B.27 The final MVA output for events with two jets and two medium btags for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 180
Figure B.28 The final MVA output for events with two jets and two medium b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 181
Figure B.29 The final MVA output for events with two jets and two medium b-tags
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 182
Figure B.30 The final MVA output for events with three jets and two medium btags for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 183
Figure B.31 The final MVA output for events with three jets and two medium
b-tags for (top left) MH = 110 GeV, (top right) MH = 115 GeV,
(bottom left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . 184
Figure B.32 The final MVA output for events with three jets and two medium
b-tags for (top left) MH = 135 GeV, (top right) MH = 140 GeV,
(bottom left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . 185

xxi

Figure B.33 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 186
Figure B.34 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 187
Figure B.35 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 188
Figure B.36 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. . . . . . . 189
Figure B.37 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 130 GeV. . . . . . . 190
Figure B.38 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom
left) MH = 145 GeV, and (bottom right) MH = 150 GeV. . . . . . . 191
Figure B.39 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is normalized
to the sum of the backgrounds. Overflow events are added to the last
bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Figure B.40 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag. The signal
is shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 193
Figure B.41 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and one tight b-tag: (top left)
the mass asymmetry between the ℓν and dijet systems, (top right)
aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 194

xxii

Figure B.42 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is normalized
to the sum of the backgrounds. Overflow events are added to the last
bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Figure B.43 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag. The signal
is shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 196
Figure B.44 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two loose b-tag: (top left)
the mass asymmetry between the ℓν and dijet systems, (top right)
aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 197
Figure B.45 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag: (top
left) the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is normalized
to the sum of the backgrounds. Overflow events are added to the last
bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Figure B.46 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag. The
signal is shown for MH = 125 GeV, and is normalized to the sum of
the backgrounds. Overflow events are added to the last bin. . . . . . 199
Figure B.47 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tag: (top left)
the multijet MVA output, (top right) cos(χ∗ ), (bottom left) cos(θ∗ ,
and (bottom right) the dijet transverse mass. The signal is shown for
MH = 125 GeV, and is normalized to the sum of the backgrounds.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 200
Figure B.48 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two medium b-tags: the
magnitude of the vector pT sum for all visible particles. The signal
is shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 201
xxiii

Figure B.49 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: (top left)
the bid MVA output, (top right) the maximum ∆η(ℓ, j), (bottom
left) q ℓ ×η ℓ , and (bottom right) the minimum significance of the dijet
system. The signal is shown for MH = 125 GeV, and is normalized
to the sum of the backgrounds. Overflow events are added to the last
bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Figure B.50 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag. The signal
is shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin. . . . . . . . 203
Figure B.51 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: (top left)
the multijet MVA output, (top right) cos(χ∗ ), (bottom left) cos(θ∗ ,
and (bottom right) the dijet transverse mass. The signal is shown for
MH = 125 GeV, and is normalized to the sum of the backgrounds.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 204
Figure B.52 Input variables to the BDT trained to distinguish signal from all
backgrounds in events with two jets and two tight b-tag: the ratio of
the W pT to the sum of the lepton pT and ET . The signal is shown
for MH = 125 GeV, and is normalized to the sum of the backgrounds.
Overflow events are added to the last bin. . . . . . . . . . . . . . . . 205
Figure B.53 The final MVA output for events with two jets and one tight b-tag for
(top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 206
Figure B.54 The final MVA output for events with two jets and one tight b-tag
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 207
Figure B.55 The final MVA output for events with two jets and one tight b-tag
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 208
Figure B.56 The final MVA output for events with two jets and one tight b-tag
for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

xxiv

Figure B.57 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 210
Figure B.58 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 211
Figure B.59 The final MVA output for events with three jets and one tight b-tag
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 212
Figure B.60 The final MVA output for events with three jets and one tight btag for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Figure B.61 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 214
Figure B.62 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 215
Figure B.63 The final MVA output for events with two jets and two loose b-tags
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 216
Figure B.64 The final MVA output for events with two jets and two loose b-tags
for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Figure B.65 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 218

xxv

Figure B.66 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 219
Figure B.67 The final MVA output for events with three jets and two loose b-tags
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 220
Figure B.68 The final MVA output for events with three jets and two loose btags for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Figure B.69 The final MVA output for events with two jets and two medium btags for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 222
Figure B.70 The final MVA output for events with two jets and two medium b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 223
Figure B.71 The final MVA output for events with two jets and two medium b-tags
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 224
Figure B.72 The final MVA output for events with two jets and two medium btags for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Figure B.73 The final MVA output for events with three jets and two medium btags for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom
left) MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 226
Figure B.74 The final MVA output for events with three jets and two medium
b-tags for (top left) MH = 110 GeV, (top right) MH = 115 GeV,
(bottom left) MH = 120 GeV, and (bottom right) MH = 125 GeV.
The signal is normalized to the sum of the backgrounds. . . . . . . . 227

xxvi

Figure B.75 The final MVA output for events with three jets and two medium
b-tags for (top left) MH = 130 GeV, (top right) MH = 135 GeV,
(bottom left) MH = 140 GeV, and (bottom right) MH = 145 GeV.
The signal is normalized to the sum of the backgrounds. . . . . . . . 228
Figure B.76 The final MVA output for events with three jets and two medium
b-tags for MH = 150 GeV. The signal is normalized to the sum of
the backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Figure B.77 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 230
Figure B.78 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 231
Figure B.79 The final MVA output for events with two jets and two tight b-tags
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 232
Figure B.80 The final MVA output for events with two jets and two tight b-tags
for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Figure B.81 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left)
MH = 100 GeV, and (bottom right) MH = 105 GeV. The signal is
normalized to the sum of the backgrounds. . . . . . . . . . . . . . . 234
Figure B.82 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom
left) MH = 120 GeV, and (bottom right) MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 235
Figure B.83 The final MVA output for events with three jets and two tight b-tags
for (top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom
left) MH = 140 GeV, and (bottom right) MH = 145 GeV. The signal
is normalized to the sum of the backgrounds. . . . . . . . . . . . . . 236

xxvii

Figure B.84 The final MVA output for events with three jets and two tight btags for MH = 150 GeV. The signal is normalized to the sum of the
backgrounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

xxviii

KEY TO SYMBOLS AND
ABBREVIATIONS
η 2 + φ2

∆R

The distance in η-φ space, ∆R =

ℓ

Lepton, ℓ = e, µ

η

θ
Pseudorapidity, η = − ln(tan 2 )

γ

Photon

ET

Missing energy in the plane transverse to the beam line.

µ

Muon

ν

Neutrino

φ

The detector azimuthal angle.

τ

Tau

θ

The detector polar angle measured from the beam axis.

b

Bottom quark

c

Charm quark

CLS The ratio of the signal+background confidence level to the background-only confidence
CL
level, CLS = CL S
B

d

Down quark

e

Electron

g

Gluon

H0

The null (or background-only) hypothesis

H1

The null (or signal+background) hypothesis

HT

The sum over jet pT
xxix

ID

Identification

j1

Jet with the highest pT

j2

Jet with the second highest pT

MH

The mass of the Higgs boson

W
MT

Transverse mass of the reconstructed W boson

pT

Momentum in the plane transverse to the beam line.

s

Strange quark

t

Top quark

TµOR Logical OR of single-muon and muon+jets triggers
u

Up quark

V

Vector boson, V = W, Z

AA

Alternative Algorithm

BDT Boosted decision Tree
bid

Identification of mesons containing a b-quark

CC

Central Calorimeter

CFT Central Fibre Tracker
CL

Confidence Level

CPS Central Preshower Detector
EC

End Calorimeter

EM

Electromagnetic

FNAL Fermi National Accelerator Laboratory
FPS

Forward PreShower Detector

hf

Heavy Flavour: jets originating from heavy partons: b, c.

HTF Histogramming Track Finder
ICD

Inter-Cryostat Detector

ICR

Inter-Cryostat Region

JES

Jet Energy Scale
xxx

JESMU Jet Energy Scale for jets containing a muon from the decay of a B meson
JSSR Jet Smearing Shifting and Removal
L1

Trigger Level 1

L1Cal Level 1 Calorimeter Trigger
L1CalTrack Level 1 Calorimeter Track Trigger
L1CTT Level 1 Central Track Trigger
L1Mu Level 1 Muon Trigger
L1PS Level 1 Preshower Detector
L2

Trigger Level 2

L2Cal Level 2 Calorimeter Trigger
L2CTT Level 2 Central Track Trigger
L2Mu Level 2 Muon Trigger
L2PS Level 2 Preshower Trigger
L3

Trigger Level 3

Level 2 Silicon Track Trigger ,
lf

Light Flavour: jets originating from light partons: u, d, s, g.

LLR Log Likelihood Ratio
LO

Leading Order

MC

Monte-Carlo

MJ

Multijet

MVA Multivariate Analysis
NLO Next to Leading Order
PDF Parton Distribution Function
PDT Proportional Drift Tubes
PV

Primary Vertex

QCD Quantum Chromodynamics
QED Quantum Electrodynamics
xxxi

s. d.

Standard deviation

SM

Standard Model

SMT Silicon Microstrip Tracker

xxxii

Chapter 1
Introduction
Particle physics is the study of the most fundamental pieces of the universe. These fundamental pieces, or particles, and the interactions between them, in principle should be able
to describe all matter in the universe. It is impractical from a mathematical standpoint to
describe macroscopic systems of particles by their constituent single particles, so we limit the
discussion to systems of relatively few particles that interact over distances smaller than that
of an atomic nucleus. These particles, and their interactions are described in Chapter 1.1.
The standard model (SM) of particle physics is the quantum field theory that governs the
dynamics of the fundamental particles. The theoretical framework of the standard model
is described in Chapter 1.2.1-1.2.3. The standard model has been incredibly successful,
with many predictions experimentally verified. The discovery of the Z boson and the top
quark, and many other experimental results have agreed with the SM to high precision. As
successful as the SM has been, it is not complete. It does not include any explanation for
gravitational interactions, or the asymmetry between the amount of matter and anti-matter
in the universe, and also explains only the visible matter in the universe (which accounts for
only ∼ 5% of the total matter density of the universe). The relatively recent observation of
neutrino flavour oscillations is also at odds with the SM, as neutrinos in the SM are massless
and can therefore not oscillate.
The recent observation of the Higgs boson, which is responsible for generating the masses

1

of the gauge bosons as well as the fermions, is the last remaining prediction of the SM to be
experimentally verified, and is the main topic of this thesis. The current status of the Higgs
boson measurements discussed in Chapter 1.2.4.
In order to study the Higgs boson experimentally, we first need to be able to produce it.
This is done by colliding particles with high energies using sophisticated particle accelerators.
Observing the results of these high energy collisions with high precision requires intricate
detectors. The work described in this thesis was carried out at the Tevatron collider at
Fermilab, which collided protons and anti-protons at a center-of-momentum energy of 1.96
TeV. The D0 detector was used to collect the data analysed in this work. The Tevatron and
the D0 detector are described in Chapter 2.1 and 2.2 respectively. The particle identification
and reconstruction algorithms are described in Chapter . Following this, is a discussion of
event simulation in Chapter .
These different components are brought together in Chapter , where I describe how they
are used in the search for a Higgs boson produced in association with a W boson. This search
uses sophisticated multivariate techniques to maximize our sensitivity to the Higgs boson
signal while accepting as many potential signal events as possible. This search is mildly
sensitive to the Higgs boson signal, but greater sensitivity can be achieved by combining
this result with the other Higgs boson searches at the Tevatron in a combined search for the
Higgs boson. I discuss how this analysis fits into the more global D0 and Tevatron Higgs
boson picture in Chapter 6.10. Finally I discuss a method to improve the sensitivity for this
Higgs boson search by improving the jet energy resolution in Chapter .

2

1.1

Standard Model Particles

The standard model of particle physics combines special relativity and quantum mechanics into a theory framework that is used to describe the known fundamental particles and
the interactions between them (with the exception of gravity). The list of SM particles is
comprised of matter particles; leptons, quarks, and neutrinos; gauge bosons, which mediate
the interactions between particles; and the Higgs boson, which is a result of electroweak
symmetry breaking and is responsible for generating the masses of the massive gauge bosons
and matter particles. These particles are said to be fundamental as they do not contain any
known substructure.
Leptons and quarks are fermions. That is to say, they have an intrinsic angular momentum, known as spin, that is a half integer multiple of the reduced Plank constant, h. These
¯
fermions can be arranged into three generations containing one lepton, one neutrino, and
two quarks as shown in Table 1.1. Across generations, particles have the same quantum
numbers. For example, the leptons: electron (e), muon (µ), tau (τ ) all have the same charge
and spin, but the τ is more massive than the µ, which is more massive than the e.
The matter particles interact with each other through the exchange of force-carrying
particles corresponding to the electromagnetic, weak, and strong forces. These particles are
bosons, that is they are particles which have an intrinsic spin equal to integer multiples of
h, and are summarized in Table 1.2.
¯
All particles with electric charge interact electromagnetically through the exchange of a
photon, which is a massless particle with a spin of 1. Because the photon is massless, the
electromagnetic force has an infinite range. All fermions also interact via the weak force.
The weak force is mediated by the massive W ± and Z bosons. The masses of the weak

3

Table 1.1: The three generations of Fermions [1].
Fermion
Generation 1
Lepton
Electron (e)
Electric Charge
-1
Mass (MeV)
0.510998910±0.000000013
Neutrino
Electron (νe )
Electric Charge
0
Mass (MeV)
<2×10−6
Quark
up (u)
Electric Charge
2/3
+0.7
Mass (MeV)
2.3−0.5
Quark
down (d)
Electric Charge
−1/3
+0.5
Mass (MeV)
4.8−0.3

Generation 2
Muon (µ)
-1
105.658367±0.000004
Muon (νµ )
0
<0.19
charm (c)
2/3
1.275±0.025×103
strange (s)
−1/3
95±5

Generation 3
Tau (τ )
-1
1176.86±0.16
Tau (ντ )
0
<18.2
top (t)
2/3
173.07±0.89×103
bottom (b)
−1/3
4.18±0.03×103

Table 1.2: The force carrying bosons [1].
Particle

Force

Mass (GeV)

photon (γ) Electromagnetic
< 10−27
0
Z
Weak
91.1876±0.0021
±
W
Weak
80.399±0.023
gluon(g)
Strong
< O(10−3 )

bosons lead to a short interaction range (< 10−16 m). The strong force is mediated by the
massless gluon. Gluons are electrically neutral but carry colour charge and interact with
quarks (which also carry a colour charge). Because gluons themselves have a colour charge,
they can interact with themselves.
While the electromagnetic and weak interactions look quite different, they are actually
two aspects of the same interaction. The “weakness” of the weak interactions is due to the
limited interaction range rather than the inherent interaction strength. The masses of the

4

W and Z bosons, and thus the differences between electromagnetic and weak interaction
strengths, require an explanation. In the standard model, this is achieved through spontaneous electroweak symmetry breaking and the introduction of another boson called the
Higgs boson.

1.2

The Standard Model

The standard model combines quantum mechanics and special relativity into a theory framework to describe the interactions amongst the fundamental particles. In this framework
particles are interpreted as excitations of relativistic quantum fields. The behaviour of these
fields is described by the SM Lagrangian. This Lagrangian is a function of the fields, and is
described below [9, 10, 11].

1.2.1

QED

To describe the theory that governs the electromagnetic interactions, we will start with the
simple theory of a free electron. The Lagrangian for such a theory is:

¯
L = ψ iγ µ ∂µ − m ψ,

(1.1)

where ψ is a spinor field for the spin 1/2 electron of mass m, and γ µ are the Dirac matrices1 .
This Lagrangian is invariant under a global gauge transformation. That is, if we transform
1 The Dirac matrices are 4×4 matrices defined as: γ 0 =

where σi are the Pauli matrices

5

1 0
, γ i=1,2,3 =
0 1

0 σi
−σi 0

,

the phase of ψ globally:
ψ(x) → ψ(x) = e−iα ψ(x)

′

(1.2)

¯
¯ ′
¯
ψ(x) → ψ(x) = eiα ψ(x)

(1.3)

and

the Lagrangian remains unchanged. Now consider the Lagrangian under a local gauge transformation:
′

ψ(x) → ψ(x) = e−iα(x) ψ(x)

(1.4)

¯
¯
¯ ′
ψ(x) → ψ(x) = eiα(x) ψ(x)

(1.5)

and

¯
The ψmψ term in Eq. 1.1 is clearly invariant under a local gauge transformation, but
¯
the ψ∂µ ψ term is not. Thus, if we want our Lagrangian to be invariant under a local gauge
transformation, we require a gauge covariant derivative, Dµ to replace ∂µ such that:
′
¯
¯′
¯
ψ(x)Dµ ψ(x) → ψ (x)Dµ ψ (x) = ψ(x)Dµ ψ(x).

(1.6)

We can accomplish this by introducing a vector field Aµ (x) with coupling strength e and
write the covariant derivative as:

Dµ = ∂µ + ieAµ ,

with the requirement that Aµ transforms as:

6

(1.7)

′
1
Aµ → Aµ = Aµ + ∂µ α(x).
e

(1.8)

If we also introduce the field tensor to include the dynamics of the gauge field:

Fµν = ∂µ Aν − ∂ν Aµ ,

(1.9)

we can then write our gauge invariant Lagrangian as:

1
¯
L = ψ iγ µ Dµ − m ψ − Fµν F µν .
4

(1.10)

Alternatively, if we expand out the covariant derivative:

1
¯
¯
L = ψ iγ µ ∂µ − m ψ − eψγ µ ψAµ − Fµν F µν .
4

(1.11)

¯
From this we can clearly see three different pieces. The first piece, ψ iγ µ ∂µ − m ψ, is the
1
free electron Lagrangian we started with. The third part, 4 Fµν F µν describes the dynamics

¯
of the gauge field, Aµ . The second part, eψγ µ ψAµ , describes the interaction between the
spinor field ψ and the gauge field Aµ . We can identify Aµ as the field for the photon,
that interacts with our spinor field with strength e, which we can identify as the electric
charge. Note that there are no terms of the form Aµ Aµ . These terms would be photon mass
terms, but can not be included in our Lagrangian as they are not invariant under local gauge
transformations.

7

1.2.2

QCD

Quantum Chromodynamics (QCD) describes strong force interactions between quarks and
gluons. The QCD Lagrangian can be constructed in an analogous way to the QED Lagrangian by requiring invariance under SU(3) local gauge transformations of the form:

ψ → U ψ,

(1.12)

where U is a unitary 3 × 3 matrix. The QCD Lagrangian is given by:
L=

1
¯
ψ iγ µ Dµ − mj ψ − Ga Gµν ,
4 µν a
j

(1.13)

where j corresponds to one of the six quark flavours, and the index a is summed over the
eight colour degrees of freedom. Ga is the gluon field tensor, equivalent to Fµν in QED,
µν
and is given by:
a
a
b c
Ga = ∂µ Cν − ∂ν Cµ + gf abc Cµ Cν ,
µν

(1.14)

and the covariant derivative is:
a
Dµ = ∂µ + igs Cµ ta .

(1.15)

Here Cµ is the vector field of the gluons, and ta are the generators of the SU(3) gauge
group. The full QCD Lagrangian can be written in three pieces: a kinetic piece, Lkinetic ; a
quark-gluon interaction piece, Lquark−gluon ; and a gluon self-interaction piece Lgluon−gluon .
f lavours
1
a − ∂ Ca +
¯
Lkinetic = − ∂µ Cν
ψj iγ µ ∂µ − mj ψj
ν µ
4
j

8

(1.16)

f lavours

Lquark−gluon = −gs
Lgluon−gluon =

a¯
a
Cµ ψj γ µ Cµ ta ψj

(1.17)

j

gs abc
a
a
f
∂µ Cν − ∂ν Cµ
2

µ

ν
Cb Cc −

gs abc
µ ν d e
f fade Cb Cc Cµ Cν (1.18)
2

The gluon self interaction term comes from the gluons themselves carrying colour charge, and
does not have an equivalent in QED. There are a couple of properties of QCD that are not
obvious from the Lagrangian. The first is that quarks are confined to live within colour neutral hadrons (either as a colour-anticolour pair, or as a triplet of the three different colours).
From an experimental perspective, this has the implication that we don’t measure individual quarks within our detector, but rather composite particles called hadrons. The second
property is known as asymptotic freedom. At high energies, QCD becomes a perturbative
theory, and quarks and gluons behave as though they are free particles. The implication of
this is that we can treat the interaction of protons and anti-protons at high energy as an
interaction between a single quark or gluon from each proton and anti-proton.

1.2.3

Electroweak Unification and the Higgs Mechanism

The electromagnetic and weak forces are actually two facets of the same force. The unification of the two forces is completed within the SU (2)L × U (1)Y gauge group, with the
SU (2)L group representing weak isospin space and U (1)Y representing hypercharge space.
This representation is consistent with only left handed fermions being able to undergo flavour
i=1,2,3

changing weak interactions. The three gauge fields of SU (2)L are Wµ

with coupling g,

′

and the gauge field of U (1)Y is Bµν with coupling g . The kinetic term of the Lagrangian is
given by:
1 µν a
1
Lkinetic = − Wa Wµν − B µν Bµν ,
4
4
9

(1.19)

where
i
i
i
Wµν = ∂µ Wν − ∂ν Wµ + gǫijk Aj Ak ,
µ ν

(1.20)

Bµν = ∂µ Bν − ∂ν Bµ .

(1.21)

Since leptons have both right and left handed components but only left handed neutrinos
exist, it is natural to write the interactions with the gauge fields in two pieces. The first is a
purely right handed interaction with a singlet of a lepton field, R, that interacts only with
the Bµ field:
′Y
¯
Lsinglet = iRγ µ ∂µ + ig Bµ R.
2

(1.22)

The left handed lepton doublet of the lepton and neutrino fields:




 ν 





−
ℓ

L=

(1.23)

interacts with fields from both groups:

¯
Ldoublet = iLγ µ ∂µ + ig

′Y

2

Bµ + ig

σa a
W L.
2 µ

(1.24)

The physical fields that we observe for the photon, W ± , and Z can be written in terms
of these gauge fields and their couplings:

1
1
2
±
Wµ = √ Wµ ± Wµ
2

(1.25)

3
Zµ = − sin(θW )Bµ + cos(θW )Wµ

(1.26)

3
Aµ = cos(θW )Bµ + sin(θW )Wµ

(1.27)

10

(1.28)

where θW is the weak mixing angle (also called the Weinberg angle) which mixes the Bµ
3
and Wµ fields is defined as:

cos(θW ) =

g
′
g2 + g 2

.

(1.29)

One important thing to notice is that, so far, we haven’t included any mass terms for the
gauge bosons. However, we know from experimental observations that the W and Z bosons
do indeed have mass. Explicitly adding such terms to the Lagrangian would not preserve
local gauge invariance, so we require some mechanism to give the weak bosons mass. One
such method is to spontaneously break a symmetry. Electroweak spontaneous symmetry
breaking was proposed as a mechanism to include massive gauge bosons within the standard
model in 1964 by Higgs, Englert, Brout, Guralnik, Hagen, and Kibble [12, 13, 14], for which
Higgs and Englert were recently awarded the Nobel prize in physics [15].
To illustrate this phenomenon, consider the Lagrangian for a real scalar field, φ, in a
1
potential V (φ) = 1 µ2 φ2 + 4 λφ4 :
2

L=

2
1
1 2 2 1 4
µ φ + λφ .
∂µ φ −
2
2
4

(1.30)

If µ2 > 0, then the particle has a mass of µ and the fourth order self-interaction strength
of the field, φ, is λ. If we minimize the potential V (φ), we find that the ground state, or
vacuum, corresponds to φ = 0. We can also consider the case where µ2 < 0. In this case we
find that the ground state of the potential corresponds to φ = ±v, with v =

µ2 /λ. The

two ground states are completely equivalent, and when we choose one or the other as a point
to perturbatively expand about, we spontaneously break the symmetry. We will choose to

11

perturbatively expand our Lagrangian around the +v ground state, and will write the field
as φ(x) = v + η(x). Our Lagrangian can then be written in terms of v, η and λ:

′

L =

2
1
1
1
∂µ η − λv 2 η 2 − λvη 3 − λη 4 + λv 4 .
2
4
4

We can now see that we have a field η with a mass of

√

(1.31)

2λv. Ultimately, we would like

a massive gauge field, aµ , with charge, q. Luckily, our example can be easily taken a step
1
further by considering a locally gauge invariant complex scalar field, φ = 2 (φ1 + iφ2 ):

1
L = Dµ φ∗ Dµ φ − F µν Fµν − µ2 φ∗ φ − λ(φ∗ φ)2 ,
4

(1.32)

where:

Dµ

= ∂µ + iqaµ ,

Fµν = ∂µ aν − ∂ν aµ .

(1.33)
(1.34)

If we again consider the case where µ2 < 0, we see that the minimum is a circle in φ1 − φ2
space:
φ2 + φ2 = v 2 =
1
2

−µ2
λ

(1.35)

We can spontaneously break the symmetry and choose φ1 = v and φ2 = 0, and expand
around this minimum:
1
φ(x) = √ (v + η(x) + iǫ(x)),
2

12

(1.36)

and

′

L =

1
1
1
(∂µ η)2 + (∂µ ǫ)2 − F µν Fµν − v 2 λη 2 + q 2 v 2 aµ aµ − qvaµ ∂ µ ǫ.
2
4
2

(1.37)

Similar to the previous example, we can see that we have a scalar field η with mass
√

2λv. We also see that we have a massless scalar field, ǫ. Additionally, our gauge field, aµ ,

now has a mass of qv. The masslessness of the ǫ field comes from the process of breaking
the symmetry, and is somewhat intuitive. The potential in the tangential (ǫ) direction is
flat, which means there is no resistance to oscillations in the ǫ direction, which leads to a
massless field. Whenever we break a continuous symmetry spontaneously, we will end up
with a massless scalar field. We don’t observe such extra massless fields in nature, so how
should we interpret them? We can note that in the lowest order of ǫ, our complex scalar
field can be written as:

φ =
≃

1 (v + η + iǫ)
2

(1.38)

1 (v + η) eiǫ/v .
2

(1.39)

We can consider rewriting our Lagrangian, choosing a specific gauge, by expressing everything in terms of real fields h, θ, and aµ with:

φ →
aµ

1 (v + h) eiθ/v ,
2
1
→ aµ + qv ∂µ θ.

(1.40)
(1.41)

Here, θ is chosen in such a way that h is real. This choice of gauge renders our Lagrangian

13

independent of θ, so that the non-physical massless field that appeared from the spontaneous
symmetry breaking is now nowhere to be seen:

′′
1
1
1
1
1
L = (∂µ h2 ) − F µν Fµν − v 2 λh2 + q 2 v 2 aµ aµ − vλh3 − λh4 + q 2 aµ aµ h2 + vq 2 aµ aµ .
2
4
2
4
2

(1.42)
This is because the apparent extra degree of freedom of the massless field was actually just
the freedom to make a gauge choice. We are now left with a Lagrangian for two massive
fields: a massive gauge field aµ , and a massive scalar field h. This process is known as the
Higgs mechanism, and the field h is called the Higgs field.
We can now go even further, and apply this same procedure to a Lagrangian invariant
under SU (2)L ×U (1)Y transformations. In this case, we will need to couple to SU(2) doublets
with four degrees of freedom, so our field, Φ is now a doublet of complex scalar fields:

+ 
 φ

,

Φ=


0
φ


(1.43)

φ+ =

1 (φ + iφ ),
2
2 1

(1.44)

φ0 =

1 (φ + iφ ).
4
2 3

(1.45)

with

We again consider the µ2 < 0 case, and find the minimum of our potential. We choose

14

the minimum point to do our perturbative expansion around to be:

Φ=





1 0 


.



2
v

(1.46)

The choice of only allowing the neutral component to be non-zero is to conserve electric
charge. If we expand our Lagrangian about this minimum, we find that we get a massless
field, Aµ , corresponding to the photon, and two massive gauge bosons. In the end, we find:

MW

1
= 2 vg

(1.47)

MA

=0

(1.48)

′
1
MZ = 2 v g 2 + g 2

MW
MZ

(1.49)

= cos θW

(1.50)

We now have our weak bosons with non-zero masses, a massless photon, plus an additional
massive scalar boson, the Higgs boson. It is worth noting that the masses of the W and Z
bosons are predicted theoretically, however the Higgs boson mass is not. Also, our fermions
are still massless, as we could not simply add in an explicit mass term to our electroweak
Lagrangian and still preserve gauge invariance. The Higgs mechanism comes to the rescue
again. Let’s consider including the following term in our electroweak Lagrangian:




 φ+


¯L
¯
Lℓ = −ge (νℓ , ℓ) 


φ0





 ℓR + ℓ¯ φ− , φ0
R


15



 

 νℓ  

 

 .

 

ℓ

L

(1.51)

We, as before, break the symmetry spontaneously with:

φ=



1


2

0
v+h







(1.52)

so that out Lagrangian becomes:

¯
Lℓ = −mℓ ℓℓ −

mℓ ¯
ℓℓh,
v

(1.53)

where we have defined the lepton mass:

gℓ v
mℓ = √ .
2

(1.54)

Notice that the lepton masses are not predicted, as gℓ is not given.
Quark masses arise similarly from starting with the Lagrangian:


 φ+
ij
¯′ )L 
¯
Lq = −gd (ui , di 

φ0





¯
 −φ0


ij (u , d ) 
¯′ L 
 djR −gu ¯i i


φ−





 ujR +hermetian conjugate, (1.55)


where u and d correspond to up-type and down-type quarks respectively. After spontaneous
symmetry breaking this becomes:

¯
Lq = −mi di di 1 +
d

h
h
− m i ui ui 1 +
.
u¯
v
v

16

(1.56)

1.2.4

Properties of the Higgs Boson

While the Higgs boson was first predicted to exist about 50 years ago, we are only now
reaching the point where we can experimentally probe it. The standard model does not
predict the mass of this Higgs boson, so typically experiments look over a large range of
masses.
This mass range can be constrained experimentally by precision electroweak measurements and by direct searches for the Higgs boson. Indirect constraints on the Higgs boson
mass come from measuring precisely the mass of the W boson and top quark as shown in
Fig. 1.1 [3]. Diagrams such as those in Fig. 1.2 show how the W boson mass is related to
the top quark mass and the Higgs boson mass. Direct constraints have also been placed
on the Higgs boson mass. Searches for the Higgs boson at LEP constrain the Higgs boson mass to be greater than 114.4 GeV [16]. The Tevatron additionally excludes masses
150 < MH < 180 GeV [8].
In July 2012, the ATLAS and CMS experiments excluded masses up to about 500 GeV
with the exception of a narrow region centred on about 125 GeV [4, 5] as shown in Fig. 1.3. In
this narrow region, both experiments reported discovery2 of a new particle with a significance
of 5 standard deviations above the background-only expectation. At the same time the
Tevatron experiments reported evidence of a particle decaying to b-quarks with a significance
of three standard deviations above the background only expectation in the range of 115140 GeV [17].
For a given mass of the Higgs boson, the SM does predict the production cross section,
2 In particle physics, the words “evidence” and “discovery” have specific statistical mean-

ings. If the data are 3 standard deviations above the background-only expectation, that
corresponds to “evidence” of something new. If the data are 5 standard deviations above
the background-only expectation, that is referred to as a “discovery”.

17

Figure 1.1: For the interpretation of the references to colour in this and all other figures,
the reader is referred to the electronic version of this dissertation. A global fit to data
from precision electroweak experiments can place constraints on the W boson and top quark
masses. Shown here are the 68% and 95% contours from this fit including the Higgs boson
mass measurement in blue, and not including the Higgs boson mass measurement in gray.
The horizontal and vertical green bands correspond to 1 standard deviation on the W boson
and top quark masses respectively. The diagonal lines show where different values for the
Higgs mass would appear in the W −top mass plane [3].

Figure 1.2: The masses of the top quark, W boson, and Higgs boson are related through
loop diagrams.

18

95% CL Limit on σ/ σSM

10

ATLAS 2011
Obs.
Exp.
±1σ
± 2σ

2011 Data

∫ Ldt = 4.6-4.9 fb-1
s=7T
eV

1

10-1

CLs Limits
100 200 300

400

500

600
m H[GeV]

Figure 1.3: 95% confidence level upper limit on Higgs boson production cross section as a
ratio to the Standard Model cross section from the ATLAS experiment (top) [4] and the
CMS experiment (bottom) [5]. Masses up to 500 GeV are excluded, with the exception of a
small window of masses centred around 125 GeV.
19

and the decay rate for the Higgs boson into all allowed decay particles as is shown in Figs. 1.4
and 1.5 respectively. The dominant production mode for a Higgs boson at the Tevatron with
mass of MH = 125 GeV is through gluon-gluon fusion, followed by associated production of
the Higgs boson with a vector boson V = W, Z, fusion of two vector bosons, and production
of a Higgs boson produced in association with a pair of top quarks (see Fig. 1.6). The
dominant decay mode is into a pair of b quarks, followed by decay into W bosons. Searches
for gg → H → b¯ tend to be overwhelmed by jet production in hadron colliders. For this
b
reason, when searching for H → b¯ it is common to look for the Higgs boson produced in
b,
association with a W or Z boson, where the W or Z decays to leptons (which are produced
less frequently in a hadron collider, and are thus a unique signature relative to the background
of multijet production). This thesis focusses on the search for a Higgs boson produced in
association with a W boson, where the Higgs boson decays to b quarks, and the W boson
decays to a lepton, ℓ = µ, e and a neutrino.

1.3

Beyond the Standard Model

While the SM has been incredibly successful, it does have some shortcomings. It does not
explain dark matter or dark energy, or the asymmetry in the amount of matter over antimatter in the universe. It also does not include a description of gravity, or neutrino masses.
Additionally, there are two energy scales within the SM that are very different. The first is
the scale of electroweak symmetry breaking at ∼100 GeV. The second is the scale at which
the electroweak and strong forces would be unified, ∼ 1016 GeV. Typically, the unification
of electroweak and strong forces would mean that the Higgs boson mass would be on the
order of the second scale. To get the mass back down to the first energy scale, one needs

20

σ(pp→H+X) [fb]

10

–
pp→

3

Tevatron
H (N

NLO



–
pp
→W

LL Q

CD

H(



2

LO

+ NL

OE

NN

10

√s=1.96 TeV

+NN

QC

D+

W)

NL

OE

W)
–
pp→q

qH (N

10

–
pp→ –
ttH
(N

NLO Q

CD +

NLO E

W)

–

LO

pp→

QC

D)

ZH (

NNL

OQ

CD

+ NL

OE

W)

1
100

125

150

175

200

225

250

275

300

mH [GeV]

Figure 1.4: The production cross section for the Higgs boson √ a function of Higgs boson
as
mass at the Tevatron (where the center-of-momentum energy, s, is 1.96 TeV).

21

Figure 1.5: The decay rates for the Higgs boson as a function of Higgs boson mass.

Figure 1.6: The Feynman diagrams for the most important Higgs boson production modes
at the Tevatron: (a) gluon-gluon fusion, (b) associated production of a Higgs boson with a
pair of top quarks, and (c) vector boson fusion.
22

very finely tuned cancellations. Because the SM is not complete, there is motivation to look
for something beyond the SM. There are many theories positing mechanisms and particles
to address some of the SM’s shortcomings.
Supersymmetry theories propose that all SM particles have supersymmetric partner particles, where fermionic particles have a bosonic partner particle, and bosonic SM particles
have fermionic particles. These theories tend to contain multiple Higgs bosons, with one of
the Higgs bosons strongly resembling the SM Higgs boson. There are also theories that predict a Higgs boson that couples only to some particles and not others (a common example is
a Higgs boson that couples only to bosons with stronger bosonic couplings than are predicted
in the SM). Some theories do not include a Higgs boson at all. For example, technicolour
theories break electroweak symmetry and introduce the W and Z boson masses through new
gauge interactions. Since we have now observed the Higgs boson, these theories now contradict the observed data. Based on the current experimental results, the favoured theory for
mass generation is the Higgs mechanism, so I won’t discuss these additional theories further.

23

Chapter 2
Experimental Apparatus
In order to study the Higgs boson experimentally, one first needs to be able to produce and
detect its decay products. To do this we need a carefully controlled high energy environment
and the ability to measure such an environment. The Tevatron collider provided such an
environment by colliding protons with anti-protons at high energies. The proton and antiproton collisions occurred at two points along the ring, and a detector was built around each
of these collision points to detect the particles resulting from the collisions. Below, I will
describe the accelerator and the D0 detector, which was used to record the data used in this
thesis.

2.1

The Tevatron

The Tevatron [18] is the largest in a series of accelerators [19] located at the Fermi National Accelerator Laboratory (FNAL) complex in Batavia, Illinois, shown in Fig. 2.1. The
Tevatron is a circular synchrotron that collided protons and anti-protons with a centerof-momentum energy of 1.96 TeV at two locations around a ring with a radius of 1 km.
Multi-purpose detectors around each of these collision points measure properties of the particles resulting from the proton and anti-proton collisions. The running time of the Tevatron
can be split into different data collection epochs. Run I took place from 1992-1996, and Run
II from 2001-2011. Between Run I and Run II, upgrades to the accelerator made it possible
24

to run at higher center-of-momentum energies and at higher instantaneous luminosities. The
luminosity also increased over the course of Run II, and so Run II can also be divided into
different data taking epochs: Run IIa, Run IIb1, Run IIb2, Run IIb3, and Run IIb4.

Figure 2.1: A schematic view of the accelerator chain at Fermilab.

The colliding protons start as hydrogen gas. The gas enters a magnetron ion source
where the hydrogen is negatively ionized by a pulsed electric field. The H− ions then move
to the first stage of acceleration. A Cockroft-Walton electrostatic accelerator accomplishes
this initial acceleration, giving the H − ions 750 keV of kinetic energy. From the CockroftWalton accelerator, the ions go through a linear accelerator that accelerates the ions to 400
MeV. When the ions leave the linear accelerator, they pass through a carbon foil which strips

25

the electrons from the hydrogen ions leaving a beam of protons (H + ). The protons then
enter a circular synchrotron with a radius of 75 m, called the booster, which accelerates the
protons to 8 GeV and groups the protons into bunches.
The protons then travel to the main injector from the booster. The main injector is
another synchrotron that can accept both protons and anti-protons, accelerate them, change
the beam structure, and then send the beam towards multiple destinations. Protons can
either be injected into the Tevatron (after being accelerated to 150 GeV), or sent to the
anti-proton source (after accelerating the protons to 120 GeV). To create anti-protons, the
120 GeV proton beam from the main injector is collided with a nickel-iron-chromium alloy.
This results in a spray of particles; about one in one million of which are anti-protons with an
energy of about 8 GeV. The anti-protons are focussed into a beam and sent to the debuncher.
The debuncher reduces the momentum spread of the beam, before the anti-protons head to
the accumulator. The accumulator is a synchrotron that is used to store anti-protons until
the desired beam intensity is reached. Once the desired intensity of anti-protons is reached,
the anti-protons can be extracted into the main injector where they are accelerated to be
sent to the Tevatron.
Once in the Tevatron, the protons and anti-protons are each accelerated to 980 GeV, and
focused to collide at two points along the ring.

2.2

The D0 Detector

The D0 detector first started recording p¯ collisions during RunI of the Tevatron (1992p
1996). Between 1996 and 2001, the accelerators went through several upgrades. The main
injector and booster were built, the maximum center-of-momentum energy was increased

26

from 1.8 to 1.96 TeV, and the number of colliding bunches was increased from 6 to 36. The
D0 detector also went through significant upgrades to handle this new collision environment.
RunII of the Tevatron commenced in 2001 and continued through September 2011. The
data presented in this thesis are from RunII, so the RunII detector is described below.
The D0 detector is one of two general purpose detectors located at one of the two collision
points of the Tevatron [6], where protons and anti-protons collide once every 396 ns. The
detector has a cylindrical design with concentric sub-detectors centred on the collision point,
as shown in Fig. 2.2. Closest to the collision point is the tracking system which is enclosed
in a superconducting solenoid magnet which creates a 1.92 T magnetic field. Surrounding
this is a calorimeter, then the muon detection system, which includes a toroidal magnetic
field.
The coordinate system of the detector is defined as having positive z along the direction
of travel of the proton beam, and positive y pointing away from the center of the earth. The
distance perpendicular to the z-axis is labelled by r, and the polar and azimuthal angles
are labelled by θ and φ respectively. An useful quantity to consider is rapidity, Y, which is
invariant under Lorentz boosts along the z direction:

Y = tanh−1

v
,
c

(2.1)

where v is the speed of the particle, and c is the speed of light. The pseudo-rapidity, η, is
given by:
η = − ln tan

θ
2

=

|p| + pz
1
ln
2
|p| − pz

.

(2.2)

In the relativistic limit (E >> mc2 ), the pseudorapidity is approximately equal to the
rapidity. Values of η that are near 0 correspond to the central part of the D0 detector, and
27

Figure 2.2: A cross sectional view of the D0 detector, showing the tracking system surrounded
by the calorimeter and the muon detection system [6].

28

larger values of |η| correspond to the ends (or forward regions) of the detector. Distances
between objects are calculated in η-φ space using a distance:

∆R =

∆η 2 + ∆φ2 .

(2.3)

The trajectories of charged particles are measured using the Silicon Microstrip Tracker
(SMT) and the Central Fibre Tracker (CFT). The SMT is located directly outside of the
beam pipe, and has an inner radius of 2.7 cm and an outer radius of 10.5 cm. The CFT is
outside located of the SMT, and has an inner radius of 20 cm and an outer radius of 52 cm.
Surrounding both detectors is a 1.92 T superconducting solenoid magnet that is 2.7 m thick,
and has an inner (outer) radius of 1.1 (1.4) m. The tracking system is shown in Fig. 2.3.
The momentum of charged particles can be determined by measuring how much a particle
curves as it moves through the detectors within the magnetic field. The tracking system is
also used to determine the location of the primary interaction vertex (PV) with a resolution
of 35 µm, as well as positions of secondary decay vertices from particles that decay within
the tracking system.
The SMT is constructed from barrel and disk modules such that particle trajectories tend
to be perpendicular to the detector surface [20]. The modules are made up of a series of
silicon-doped wafers. A charged particle passing through the positive-negative (p-n) junction
creates electron-hole pairs. A voltage difference across the wafers causes the electrons to drift
to one side, where the charge is collected, digitized, and read out. The barrels measure 12
cm in length and are comprised of five layers of rectangular silicon wafers. Some of the
wafers are single sided, while some are double sided to determine the particle position in
the direction parallel to the strips. The double sided wafers have either a 2◦ or 90◦ angle

29

Figure 2.3: A cross sectional view of the D0 tracking system. Closest to the beampipe is
the silicon microstrip tracker, surrounded by the central fibre tracker. The tracking system
is contained within a superconducting solenoid [6].

30

Figure 2.4: A view of the SMT.
between the axial (parallel to the z axis), and the stereo sides. The single sided wafers are
all arranged axially. This allows positions to be measured in both the r − φ plane and the
r − z plane.
In addition to the barrels, there are also 12 disks, or F-disks to make measurements in
the r −z plane. The disks are comprised of wedge shaped double sided silicon modules. Each
barrel is capped by a disk, with additional disks farther out in z, to detect forward tracks.
The SMT system is shown in Fig. 2.4.
The CFT is made up of eight concentric layers of scintillating fibre. Each layer arranges
four fibres into an axial and stereo layer doublet, with the axial fibres oriented parallel to
the z axis, and the stereo fibres oriented at a 3◦ angle. Charged particles travelling through
the fibres excite the fibre core and photons are emitted with a wavelength of 340 nm. The
photons propagate down the internally reflective fibres, where they are read out by photon
counters which can detect a single photon. The layout of the CFT is illustrated in Fig. 2.5.
The calorimeter is used to measure the energy of photons, electrons, and hadrons, as well
as any imbalance in the transverse energy from which we infer the existence of neutrinos. The
calorimeter consists of absorber plates of either Uranium, copper, or steel inserted in liquid
argon, and is split into three pieces: the central calorimeter (CC), which covers |η| < 1; and
two end cap calorimeters (EC), which extend coverage to |η| ∼ 4, and is shown in Fig. 2.6.
31

Figure 2.5: The layout of the CFT, showing the fibre layers.
Each of these pieces is contained within a cryostat to maintain a temperature of 90 K.
A particle travelling through the calorimeter will interact either through the electromagnetic or nuclear forces with the absorber plates which will produce a spray of additional
particles. These particles then ionize the liquid argon. The resulting electrons are collected
and the magnitude of the charge is read out. The absorber plates, liquid argon, and the
charge read out constitute a “cell”, shown in Fig. 2.7. These cells are arranged such that their
boundaries are centred along lines of constant pseudorapidity. “Towers” of cells are defined
along such lines of pseudorapidity as illustrated in Fig. 2.8 with a size of η × φ = 0.1 × 0.1.
The innermost, or electromagnetic (EM), layers of the calorimeter are where most of
the electromagnetically interacting particles (such as electrons and photons) deposit most
of their energy through electromagnetic interactions. Particles are produced either through
pair production (γ → e+ e− ) or bremsstrahlung (e± → e± γ). The length of interest when
describing electromagnetic cascades is the radiation length, X0 . The radiation length is
the length over which the electron’s energy is reduced to 1/e of it’s original energy through
32

Figure 2.6: A diagram showing a cut away view of the D0 calorimeter. The calorimeter is
comprised of three pieces: a central calorimeter and two end calorimeters. Each piece is
made up of several layers of absorber plates (made of Uranium or copper or steel) inserted
in liquid argon. These layers form the electromagnetic, the fine hadronic, and the coarse
hadronic calorimeters [6].

33

Absorber Plate

Pad

Resistive Coat

G10 Insulator

Liquid Argon
Gap

Unit Cell
Figure 2.7: A diagram of a calorimeter cell. Each cell consists of an absorber plate, the
liquid argon, and a plate to read out the charge.
bremsstrahlung, or 7/9 of the mean free path for a photon to produce an electron-positron
pair. The EM layers of the calorimeter have a total depth of about 20 X0 .
Hadronic particles tend to deposit their energy deeper in the calorimeter, as they loose
energy through inelastic interactions with a nucleus in the absorber plates. The length
scale of interest here is the absorption length λ, which is the mean free path of a particle
before it inelastically interacts with a nucleus. The absorption length is generally larger than
the radiation length, so hadronic particles tend to deposit energy deeper in the calorimeter
than electromagnetic particles do (in uranium, the radiation length is 0.32 cm, while the
absorption length is 11.03 cm [1]). The EM layers of the calorimeter have an interaction
length of about 0.57 λ , and the hadronic layers of the calorimeter have an interaction length
of about 6 λ in the CC and up to about 10 λ in the EC. The D0 calorimeter is known as

34

Figure 2.8: The calorimeter cells are arranged in towers along lines of constant η, illustrated
by the alternating shaded areas.

35

a compensating calorimeter, which means that the ratio of the electromagnetic to hadronic
responses is approximately one. While this is true for the D0 detector, it depends on the
material used as an absorber, and is thus not true for a general calorimeter.
The cryostat walls between the central and end calorimeters lead to poor coverage by the
calorimeter for 0.8 < |η| < 1.4. To improve coverage in this inter-cryostat region (ICR), an
inter-cryostat detector (ICD) was added. The ICD is made up of two rings of scintillating
tiles mounted on the inner faces of the EC cryostats. The tiles increase coverage in the range
1.1 < |η| < 1.4.
Between the solenoid and the central calorimeter are the preshower detectors, shown in
Fig. 2.9. The central preshower detector (CPS) covers |η| < 1.3, while the forward preshower
detector (FPS) covers 1.5 < |η| < 2.5. The preshower detectors are designed to act as both
a tracking system and as calorimeters, and can be used to distinguish between photons and
pions. The detectors are made up of triangular scintillator strips interleaved together. At the
center of each strip is a wavelength shifting fibre that collects and transports the collected
light for readout. The CPS consists of a lead radiator that is approximately one radiation
length thick, and three triangular scintillator strips. The scintillator strips are arranged such
that there is one axial layer aligned with the z axis, and two stereo layers aligned at ±24◦ .
Each of the FPS detectors consist of two layers of scintillator strips with a lead-stainless-steel
absorber, that is two radiation lengths thick, in between.

36

Figure 2.9: A cross sectional view of the D0 preshower detectors located between the solenoid and the calorimeters. The
preshower detectors are comprised of interleaved scintillator strips with a wavelength shifting fibre at the center [6].

37

While the calorimeter absorbs the energy from most particles that travel through it, there
are some particles that pass through completely without depositing very much of their energy.
Neutrinos interact only through the weak force, and so the detector is mostly transparent
to neutrinos. High energy muons will also tend to pass through the detector. The muon’s
large mass relative to the electron and the fact that power radiated through bremsstrahlung
is inversely proportional to the mass of the particle to fourth power, means bremsstrahlung
tends to be suppressed. Since muons do not have colour charge, strong interactions with
the nuclei in the calorimeter do not happen. However, muons do deposit some energy in the
calorimeter through ionization. Typically the amount of energy a muon loses to ionization
is about 3 GeV, spread uniformly along its trajectory. Since muons are charged, they will
produce a track in the tracking system. While the track plus the small, collimated energy
deposit in the calorimeter is a unique signature, muon identification, and suppression of
pions mimicking a muon signature can be improved by the additional muon detectors [21].
The muon tracking system includes a 1.9 T toroidal magnetic field which points approximately along the φ direction. This causes the muon’s trajectory to curve to higher or
lower η, depending on the muon charge. To measure the deflection of the muon’s path in
this magnetic field, we look at track segments in layers both before and after the toroid.
There are four tracking layers before the toroid, which together are called layer A. After the
toroid are layer B and layer C, which have three tracking layers each. The tracking layers
are comprised of proportional drift tubes (PDTs) to measure the muon’s trajectory through
the trackers. A PDT consists of a thin wire in the center of a metal tube filled with an
ionizing gas, with the wire held at a large electric potential relative to the tube. When the
muon moves through the PDT, it ionizes the gas in the tube. The free electrons from the
ionization drift to the wire and produce an electrical pulse. The shape of the electrical pulse
38

can be used to determine the distance of closest approach to the axis of the tube, and the
time difference between when opposite ends of the tube receive the pulse can be used to
determine the longitudinal placement.
In the central region of the detector (|η| < 1.0), the PDTs have a cross section of
10×5.5 cm2 , and the gas composition is 84% argon, 8% methane, and 8% CF4 . The maximum electron drift time in the PDTs is 500 ns. In the forward regions (up to |η| ≈ 2), where
the particle density tends to be high, the drift tubes are rather smaller, with a cross section
of 9.4×9.4 mm2 . These so-called mini drift tubes have a drift time of about 60 ns, and the
ionizing gas is composed of 90% CF4 and 10% methane. The drift tubes in all regions are
aligned to be roughly parallel with the toroidal field. The arrangement of the muon drift
tubes is shown in Fig. 2.10

Figure 2.10: An exploded view of the arrangement of the drift tubes in the muon system.

Additionally, scintillator tiles are placed in the muon trackers to gain timing information.
39

Hits in the scintillator can be spatially matched to the PDTs to associate the muon track
with the appropriate collision. Without this timing information, there is ambiguity in the
bunch crossing to which the muon track corresponds, as the 500 ns drift time is larger than
the 396 ns bunch crossing time. The scintillator timing information can also be used to reject
non-collision muons occurring out-of-time with respect to the beam, such as those coming
from cosmic rays.

2.3

Data Acquisition

On average, 1.7 million beam bunches collide at the D0 detector every second. We can’t
feasibly record every bunch crossing. Even if we could record them all, the vast majority of
the collisions involve the partons within the protons and anti-protons scattering elastically.
These elastic collisions aren’t that interesting for analyses to consider. Instead we try to
record collisions containing an inelastic interaction. To select collisions of interest, we employ
a series of filters, or triggers [22]. D0 has three levels of triggers that, when combined, pass
about 100 events per second to be considered for analyses. Schematic views of the triggers
can be seen in Fig. 2.11 and 2.12.

40

Figure 2.11: A schematic view of the flow of data through the D0 trigger system [6].

41

The first trigger level, called Level 1 (L1), uses coarse information from the muon system,
the calorimeter, the preshower detectors, and the CFT. Approximately 2000 events per
second pass this first level. The incoming data are held in a buffer for 3.7 µs, so that the
subdetectors can provide the information needed for a decision on whether to have the data
move to the next trigger level. The Level 1 trigger is made up of several components: the L1
central track trigger (L1CTT), the L1 preshower trigger (L1PS), the L1 calorimeter trigger
(L1Cal), the L1 calorimeter track trigger (L1CalTrack), and the L1 muon trigger (L1Mu).
The L1CTT uses the axial layers of the CFT and CPS detectors to help reject fake tracks.
Hits from tracks in the axial layers of the CFT are matched to clusters in the axial layers
of the CPS, and this information is sent to the L1Mu and L1CalTrack systems. Thresholds
can be applied to clusters of energy found in the FPS detectors in the L1PS trigger. The
L1Cal triggers on estimates of the EM and hadronic energy in ∆η × ∆φ = 0.2 × 0.2 towers.
These towers can be used to reconstruct quantities such as the total transverse energy or the
number of towers above an energy threshold. The L1CalTrak trigger matches the positions
of tracks from the L1CTT trigger with the objects formed in the L1Cal trigger. Similarly,
the L1Mu trigger considers hits in the muon wire chambers and scintillation counters, and
integrates this with the information from the L1CTT triggers to find patterns consistent
with the passage of a muon.
The second level of triggering has an increased decision time of 100 µs. This allows for
more detailed information and more sophisticated algorithms to be used in the triggers. The
Level 2 (L2) trigger uses information correlated across different detector subsystems. In
addition to the CFT and preshower detectors used in L1, L2 also uses information from the
SMT. This allows the track list from L1 to be refined. The output event rate at L2 is about
half that of L1, 1000 events per second. The L2 trigger is comprised of the L2 silicon track
42

Figure 2.12: A schematic view of the relationship between the different trigger components
and the different detector subsystems [6].

43

trigger (L2STT) the L2 central track trigger (L2CTT), the L2 preshower trigger (L2PS),
the L2 calorimeter trigger (L2Cal), and the L2 muon trigger (L2Mu). The L2STT system
uses the SMT, which has a finer spatial resolution than the CFT, and refines the track list
found by the L1CTT trigger. This results in higher resolution track information, which in
turn results in higher resolution impact parameter measurements which allows us to identify
long lived particles. The L2CTT recalculates the tracks from the L1CTT triggers using
additional hit information. This information and the information from L2STT allow for track
isolation information to be calculated. The L2PS system identifies preshowers for electrons
and photons by looking for clusters with and without a L1CTT track match to clusters in the
preshower detectors respectively. The L2Cal system uses the towers constructed in L1Cal
and forms jets from groups of 5 × 5 towers. EM objects can also be calculated based on
towers in the EM layers of the calorimeter. An estimate of the ET can also be determined
from the vectorial sum of the calorimeter towers. The L2Mu trigger adds in more precise
timing and calibration information to the L1Mu information.
The third, and final, level of triggering is level 3 (L3). The L3 decision time is about one
second. The decisions are made based on algorithms that reconstruct physics objects with
almost as much sophistication as is done in analyses. Tracks are used to locate the primary
vertex, which also improves the calorimeter-based ET measurements. Secondary vertices can
also be identified, which means b-jet identification can be included in L3 triggers. Decisions
can be made on single objects, or on variables that combine several objects. Events pass the
L3 triggers at a rate of 100 events per second. The events that do make it past this final
trigger level are recorded for analysis.

44

2.4

Data Collection

Over approximately ten years of running, the Tevatron delivered a total of about 12 f b−1 of
luminosity to the D0 detector. The D0 detector collected 10.7 f b−1 of this (the detector is
not actively recording due to electronics latency or malfunctions for 100% of the collisions).
At the data analysis level, quality requirements are applied. For example, sometimes certain
components of the detector cease functioning temporarily. Events are not considered if any
part of the detector that is used in calculating particle identification was malfunctioning or
not operating. After data quality requirements, the analysis discussed in this thesis uses 9.7
f b−1 of data.

45

Chapter 3
Particle Identification and
Reconstruction Algorithms
Particles that travel through and interact with the detector leave behind energy deposits.
These different signatures are reconstructed by algorithms designed to identify elementary
particles.

3.1

Charged Particle Tracks

There are two algorithms used to reconstruct tracks for charged particles in the tracking
system: the histogrammming track finder (HTF), and the alternative algorithm (AA). The
HTF algorithm is designed to be more efficient at reconstructing tracks with high transverse momentum (pT ), in the forward η regions, and at high luminosities, whereas the AA
algorithm is designed to be more efficient at low pT .
The HTF method operates based on pattern recognition. A particle with charge, q, and
transverse momentum, pT , travelling through a magnetic field, B, will have a trajectory
curvature of:

ρ=

qB
.
pT

46

(3.1)

The trajectory of the particle through the detector is determined by the curvature, the
distance of closest approach, d0 , and the direction, φ. We are interested in tracks coming
from the interaction vertex, so we assume d0 ≈ 0. A series of paths can then be drawn from
the origin to a given hit with position (xi , yi ), which is transformed into (ρ, φ) space. Two
tracking hits correspond to a single point in (ρ, φ) space, but a single tracking hit corresponds
to a line as illustrated in Fig. 3.1. Different hits from the same track will produce multiple
lines (with different slopes) that intersect at a single point. Similarly, the (r, z) coordinate
is translated to the coordinate space of (z, dz/dr). From this a list of template hits is
produced separately for the SMT and CFT. The hits are passed through a Kalman filter.
The Kalman filter (or Kalman fit) is an iterative algorithm that is used to estimate unknown
variables using measurements of known variables over time. Each iteration of the Kalman
fit contains two steps. The first step estimates the unknown parameters (for example in the
case of tracks, these would be the curvature and direction) and their uncertainties based
on the current available information. Once the next measurement is taken, the estimates
are updated with the new information using a weighted average (with larger weights for
estimates with smaller uncertainties). The Kalman filter builds up a list of tracks based on
hits in the SMT, and the χ2 of the fit to track hits. These tracks are then extrapolated to
the CFT to build a complete track. Alternatively, the track can be started in the CFT, then
propagated to the SMT. The final list of tracks is the combination of the two approaches
with duplicate tracks merged.
The AA approach does not make the assumption that d0 is approximately zero, which
makes it the better choice for particles that have a large impact parameter, such as particles
that travel some distance through the tracker before decaying. The algorithm starts with
a seed track comprised of the three innermost hits in the SMT. The track is extrapolated
47

Figure 3.1: The HTF method for a single 1.5 GeV track with 5 hits. (a) Some of the possible
trajectories for a single hit in the x-y plane, (b) translation of a single hit into ρ − φ space,
(c) multiple hits from the same track form lines that intersect at a single point, and (d) the
intersection point as a peak in the ρ − φ histogram.
outwards, and additional hits are looked for in a narrow window around the extrapolation. If
no hit is found the layer is counted as a miss. If a is hit found, it is added to the track if the
fit χ2 increases by less than 16. If multiple hits are found, multiple track candidates arise.
The AA proceeds to move through all layers until it reaches the last layer, or until three
missed layers are encountered. The AA is also started with three hits in the CFT, with the
PV assumed as a fourth hit. The algorithm then proceeds iteratively inwards through the
detector. The final list is a combination of the SMT and CFT seeded tracks, with duplicate
48

tracks merged.
Neither the HTF nor the AA algorithm account for tracks losing energy to ionization
within the tracking system, or for the possibility of multiple scattering to change the track
direction. To deal with these effects, the tracks are run through a Kalman filter that fits a
more sophisticated track model to the hits for each track candidate. Placing an upper limit
on the χ2 from this fit helps cut down on the number of mis-reconstructed tracks.

3.2

Primary Vertices

At each beam crossing, it is possible to have multiple p¯ interactions. Usually only one
p
interaction results in an inelastic collision, in which we are interested. The interactions that
produce only elastic collisions are referred to as minimum bias interactions. The first step
to determining the primary vertex is to determine all vertices from a p¯ interaction. To do
p
this, tracks with pT > 0.5 GeV that have at least 2 hits in the SMT are clustered together
such that the distance in the z direction between a track and the cluster is less than 2 cm.
Kalman fits are performed to find the vertex for each cluster. If the fit χ2 per degree
of freedom is greater than 10, the track that contributes the most to the χ2 is removed
iteratively until χ2 /ndof < 10. These clusters then become a list of possible PV. Since we
generally expect tracks from a minimum bias interaction to have low pT , the probability for
a track to be from a minimum bias vertex can be constructed. The probabilities for tracks
to be from a minimum bias interaction can be combined to get a probability for each vertex
to be from a minimum bias interaction. The vertex that has the lowest probability of being
from a minimum bias interaction is selected as the PV.

49

3.3

Muons

Muons are identified using the tracking system, the calorimeter (through ionization), and the
outer muon system [23]. Tracks in the central tracking system are extrapolated outward to
the track segments in the muon system. A muon track will bend between layer A and layer
B of the muon system, due to the toroidal magnetic field. However tracks in layer B and
layer C will be collinear, so for muon identification layers B and C are considered as merged.
Muons that originate from semi-leptonic decays of b-quarks are also identified, through the
muon’s isolation. The isolation depends on the tracks near the muon, and the amount of
energy in the calorimeter near the muon, and can also be used to reject pions that mimic a
muon signature. Cosmic rays can be rejected by looking for scintillator hits that correspond
to the bunch crossing time plus the time of flight of the muon.

3.4

Electrons and Photons

The first step to identify electrons and photons is to form clusters of isolated energy deposits
in the calorimeter. Cells within ∆R = 0.2 of a seed cell make up these clusters. Next, we try
to identify a track matched to the cluster. If such a track is found, the cluster is assumed to
be an electron, otherwise it is assumed to be a photon. To differentiate between electrons
and hadronic particles, a Boosted Decision Tree (described in Ch. 6.6) is used to classify
distinct signatures of electrons and hadronic particles.

50

3.5

Jets

The quarks we see in our detector are coming from the decay of a particle (for example, a
higgs boson), or from a gluon splitting into a quark-antiquark pair. When moving through
the detector, the quarks start to move apart from each other. Because the colour potential
in the strong interaction grows as the quarks move away from each other, at some point the
potential energy will be larger than the energy required to produce a quark-antiquark pair
out of the vacuum. This process produces colour-neutral mesons and baryons. It is this
highly-collimated collection of particles, which are called jets, that is actually seen by the
detector. We associate this signature to the original quark.
Jet identification starts by building a tower out of calorimeter cells with energies above
a certain threshold. The towers are then formed into preclusters based on a simple cone
algorithm. The towers with pT > 0.5 GeV are ordered in a list from highest pT towers to
lowest. The first item of the list is considered as a precluster seed, and removed from the
list. The remaining objects in the list are processed and added to the precluster seed if
they are within ∆R = 0.3 of the seed. This continues until all objects in the list are part
of a precluster. From here, preclusters with pT > 1 GeV are used to seed protojets. The
protojets are constructed with a cone size of ∆R = 0.5 seeded by the preclusters separated
from the nearest protojet by at least ∆R = 0.25. The preclusters are iteratively added to
the protojets until the centroid of the prototjet changes by less than 0.001 when a precluster
is added to it, or until 50 iterations have occurred. Protojets with pT > 4 GeV are kept, and
to avoid double counting energy, protojets with greater than 50% of their preclusters shared
are merged, otherwise shared preclusters go to the closest protojet.
The jet energy that we measure with our detector is corrected to more accurately reflect

51

the total energy of the particles in the jet. This correction is called the jet energy scale
correction (JES), and it is comprised of several pieces to account for various inaccuracies in
the jet energy measurement [24]. The JES corrects both data and MC events according to:

Ejet =

Emeas − E0
,
Rjet Sjet

(3.2)

where Emeas is the raw jet energy measured with the detector. E0 is an offset energy
that compensates for uranium decay, energy from minimum bias interactions, energy from
previous bunch crossings, and noise in the electronics. The parameter Rjet is the calorimeter
energy response and is affected by the amount of energy deposited in the layers of the
detector before the calorimeter, or areas of the detector where there is no instrumentation,
and various non-linearities in the detector. The parameter Sjet corrects for showers that
have particles entering or leaving the jet cone.
The offset energy is measured in two parts. First the calorimeter response component
is measured by collecting data events at random and measuring the average energy. Effects
from additional interactions and energy from previous bunch crossings are measured by
taking a random sample of data events with an inelastic collision. The response Rjet and
Sjet are functions of where in the detector the jet is and the energy of the jet. The response
is measured using events where a photon and a jet are produced back to back. Because
we can use Z → ee events to obtain a precise calibration for the calorimeter response
to electromagnetic particles, the photon energy can be measured to high precision. Then
the fact that there should be no imbalance in transverse energy means that the jet energy
correction can be derived. The showering correction comes from MC studies which compare
the energy inside and outside cones of various radii. This is used to fit shower templates

52

to photon plus jet data to determine the ratio of energy inside the jet cone to the true
energy within the cone. Muons that are identified within the jet cone typically come from
semi-leptonic decays of B mesons where a neutrino carries off some of the energy. A separate
correction (JESMU) has been derived on jets containing muons to account for this.
Jet shifting, smearing, and removal (JSSR) allows jets in simulation to be recalibrated,
have their resolution smeared, and possibly discarded, in a consistent way to match behaviour
observed in data. This process has been calibrated using γ+jet and Z+jet events. First the
Z/γ

pT imbalance between the Z/γ and the jet is calculated in bins of pT
jet

:

Z/γ

p −p
∆S = T Z/γT
pT

.

(3.3)

To extract the shifting and smearing parameters of interest, a three step fitting procedure is
Z/γ

performed. The ∆S distribution is fit in different bins of pT

with the function:

jet
p −α
(∆S − ∆S )2  
 .
 T
−
√
× 1 + erf
f (∆S) = N × exp
σ2
2β










(3.4)

Here, the second term is a turn on term used to model the jet reconstruction threshold,
Z/γ

and is assumed to be independent of pT

. This term is fit simultaneously over all jet pT

bins, and thus fixes α and β, leaving the resolution, σ, and imbalance, < ∆S >, as free
Z/γ

parameters. Next, the resolutions are fit in each pT

bin, plotted as a function of pZ , and
T

fit according to:

σ(pT ) =

a2
b2
+ Z + c2 .
(pZ )2 pT
T

(3.5)

The a term describes instrumental effect, such as noise and multiple interaction within
53

the calorimeter. It is most important for low energy jets. The b term is a stochastic response
term. It describes fluctuations inherent in developing showers. The constant term describes
calibration errors, dead material in front of the calorimeter, and non-uniformities in the
calorimeter.
Finally, with the resolution fixed, the imbalance term is fit according to:

< ∆S >= A + B exp(−CpZ ) + D exp(−E(pZ )2 ).
T
T

(3.6)

Jets in simulation are smeared such that the resolution agrees with the data on average.
The energy level of the jets is then shifted to account for the differences in the mean, < ∆S >.

3.6

Missing Transverse Energy

Because we are colliding composite particles (protons and anti-protons), most of the particles
inside the protons do not contribute directly to the interaction, and end up travelling down
the beam pipe undetected. For this reason, we can not enforce momentum conservation in
the beam direction. However, we assume that the beam has zero momentum in the plane
transverse to the beam direction1 . This means that the total transverse energy resulting
from a collision should be zero. Neutrinos interact only weakly, and do not deposit energy
in the detector. We can infer their existence by looking for an imbalance in the transverse
energy. This missing transverse energy, or ET , is calculated as the negative of the sum of
1 Actually, not only do the protons and anti-protons in the beam have some momentum

in the plane transverse to the beam line, but the quarks and gluons inside the protons and
anti-protons also have non-zero transverse momentum. This transverse energy tends to be
small (a few GeV) compared to the energy of the particles in an event under consideration.

54

the energy deposited in the cells of the calorimeter:

x,y

ET x,y = −ET

cells

=−

i

x,y

Ei

(3.7)

The sum over calorimeter cells does not include the coarse hadronic calorimeter cells, as
these tend to be noisy and reduce the resolution of the measurement. Since the simulated
jet energy needs to be corrected to match data, these corrections must also be propagated to
the ET measurement. This is done by replacing the energy of the cells associated with a jet
by the corrected energy in the sum. Since muons leave very little energy in the calorimeter,
they mimic the signature of a neutrino from the point of view of the calorimeter. This means
that the muon energy is included in the above definition of ET . This is included at the final
data analysis level.

3.7

Bottom Quark Identification

Jets arising from a hadron containing a b-quark tend to have a relatively long lifetime of
∼ 10−12 s. This results in B hadrons travelling a few millimetres before they decay, leading
to a decay vertex that is displaced from the primary interaction vertex. This displaced
interaction vertex helps us identify, or tag, jets originating from a B hadron. The b-tagging
algorithm is based on a multivariate discriminant that uses information about tracks and
secondary vertices to distinguish jets containing b-quarks from those originating from c
quarks or light quarks (u, d, s) and gluons.
Before considering whether a jet is a b-jet or not, we first require that the jet is “taggable”.
This is a requirement that the jet must contain at least two tracks, each of which must have

55

at least one hit in the SMT. The determination of whether a jet contains a b-quark is done
in two steps using multivariate techniques. The first step uses six random forests [25] to
separate out jets containing b-quarks from jets not originating from b-quarks. One random
forest uses information about the track impact parameters, such as a the number of tracks
in a jet that pass various impact parameter thresholds, or the jet lifetime impact parameter,
which uses the impact parameters for all tracks in a jet to construct a probability that it
is a light jet. The other five random forests use information about the secondary vertex
such as the number of tracks associated with the secondary vertex, the distance of closest
approach of the secondary vertex to the primary vertex, and the maximum ∆R between
tracks. The outputs of these five random forests are combined using a neural network, which
helps exploit non-linear correlations between the random forests.
The b-tagging efficiency, and the rate for a light jet to be mistagged as a b-jet is measured
in data using a sample enriched in b-jets, and the MC efficiencies are corrected to match
the measured efficiencies. The efficiency and mistag rate depends on the jet pT and η, as
well as the value of the neural network output being considered. Figure 3.2 shows the btagging efficiency and mistag rates as a function of the neural network output for jets with
pT > 30 GeV. In the W H → ℓνb¯ analysis, the b-tag efficiency ranges from ∼ 50% to ∼ 80%,
b
and the mistag rate ranges from 0.15% to 11%.

56

1

T

0.2

0.8

0.15

0.6
0.1
0.4
0.05

0.2

10-2

10-1

Misidentification Rate

b-jet Efficiency

DØ, Simulation, p > 30 GeV, |η| < 1.1

MVA

Figure 3.2: The b-tagging efficiency (in black) and rate for light jets to be mistagged (in
red) as a function of the neural network output for jets with pT > 30 GeV. The vertical blue
lines indicate points on the neural network output where the efficiencies in simulation have
been corrected to match the efficiencies in data.

57

Chapter 4
Event Simulation
Since any given p¯ collision can produce a multitude of different particles, and those particles
p
can decay to stable particles, the final topology of an event can match the topology of several
processes. Differentiating between processes with the same topology is difficult, and will be
discussed in Ch. 6.6. Before we can even try to differentiate between different processes, we
must estimate the relative contribution from each process to our data. To do this, we simulate
possible outcomes for a p¯ collision and the detector response to the particles produced. This
p
is then compared to the data.
To simulate events, we use a monte-carlo (MC) random generator to expand the quantum
field theory equations perturbatively. The expansion, in principle, can be expanded to many
orders, but due to numerical or theoretical challenges it is usually cut off at leading order
(LO) or next-to-leading order (NLO). At D0, we usually calculate the LO terms to describe
an object’s kinematics, but use the NLO calculation to scale the cross section of a given
process or correct the kinematics.
There are a few effects to account for when performing the simulation. We need to
take into account that when the protons and anti-protons collide, it is really the constituent
quarks and gluons interacting, and these constituent particles carry some fraction of the
proton or anti-proton momentum. Additionally, we need to consider the possibility that
the interacting and/or resulting particles can radiate gluons or photons. We also need to

58

simulate the process of quarks forming hadrons (known as hadronization). Finally, we need
to simulate the passage of particles through our detector.
pythia [26] is a LO generator that is used widely in the field of high energy physics.
We use the CTEQ6L1 [27, 28] parton distribution function to model the quarks and gluons
contained in the incoming protons and anti-protons. Following the LO event simulation, we
use pythia to model the hadronization of quarks, and the radiation of low energy photons
or gluons from the incoming and final state particles. While pythia works well for modelling
low energy radiation, it does not model very well the radiation of high energy photons or
gluons. This higher energy radiation is handled well by a LO matrix element event generator
called alpgen [29]. alpgen calculates the LO term exactly, which gets the high energy
radiation correct. However, it doesn’t well describe the hadronization of quarks.
We can obtain the best of both worlds by using alpgen to provide final state partons,
which are then showered with pythia. In doing this, we may generate radiated jets with
pythia that are counted in the alpgen processing. To avoid double counting these jets, we
use the MLM matching scheme [30] to determine if there are jets corresponding to the original
final state partons from alpgen. When doing the showering with pythia, it is possible to
produce heavy-flavour jets, but these are also all ready accounted for by generating specific
heavy flavour samples using alpgen. To avoid double counting, in samples that should
contain only light jets, we veto events that have a b or c quark, and in samples that should
have only c quarks we veto events containing b quarks.
We use another LO matrix element event generator called singletop [31, 32] to simulate
single top events. It describes NLO distributions reasonably well, and also maintains a good
description of the spin correlations between the top quarks and resulting W boson.
When particles travel through the detector, they interact with the material inside of it,
59

as well as the magnetic fields from the solenoid and toroid. This needs to be simulated.
The simulation of the particles passing through the detector is done using the program
geant [33], which uses precise information about the geometry and composition of the
detector and magnetic fields to evolve the passage of particles through the detector. After
this, the electronic read out is also simulated to take into account electronic noise and known
inefficiencies. The final result is information in the same format as the data.
This simulation process is not perfect, and thus does not reproduce exactly the data.
Some of these differences are well known, and can be corrected for. Our simulation assumes only one proton interacting with one anti-proton in each event. In reality, with higher
luminosity events, we can have multiple interactions. To account for this, we overlay the
simulation with data events from randomly chosen minimum bias events from different instantaneous luminosities. In the simulation, the primary interaction location along the z axis
is assumed to be a Gaussian distribution. In data, the distribution is not quite Gaussian, so
the simulation is reweighted to match the distribution in data.
By looking at Z/γ ∗ events that decay to two leptons, the description of the Z boson pT
can be tested. It was found that at low Z boson pT , the simulation does not describe the
data well in either alpgen or pythia. A reweighting was derived such that simulated pT
spectrum matches that in data [34]. There is no measurement of the W boson pT to derive
an equivalent reweighting, so the W pT is corrected using the Z pT reweighting, adjusted
by the ratio of the W to Z differential cross sections at next-to-next-to-leading-order.
For each process that we simulate, we generate many thousands of events. We then must
normalize each process to the rates present in our data. Classically, if we have particles with
a density ρ, colliding with a speed v, the rate at which we expect a process with a cross

60

section σ to occur is given by:
Rclassical = vρσ.

(4.1)

We can express the analogous rate in quantum mechanics as:

RQM = L σǫ,

(4.2)

where L is the luminosity of the colliding beams, σ is the cross section for the process under
consideration, and ǫ is the detector efficiency. The cross section is calculated from theory,
and the luminosity and efficiency are both measured from data, giving us everything we need
to normalize our simulated samples.

61

Chapter 5
Statistical Analysis
To make any statistical statements about our data, we perform a statistical analysis as
is outlined below [35, 36, 37]. We are looking for events that have a small probability of
occurring (given the small cross section for Higgs boson production), but many chances
to occur (given the large number of collisions occurring at D0), so we can describe the
probability of observing d events given p predicted events by a Poisson distribution:

P (d, p) =

pd −p
e .
d!

(5.1)

We have two hypotheses we would like to compare: the null (or background-only) hypothesis
H0 , and the test (or signal+background) hypothesis H1 . The probabilities for each of these
hypotheses are then:

P (d|H0 )
P (d|H1 ) =

d
= b e−b ,
d!
(s+b)d −(s+b)
,
d! e

(5.2)
(5.3)

where b and s correspond to the number of predicted background and signal events respectively. To combine the two hypotheses into one metric to test the difference between the two

62

hypotheses, we form the log likelihood ratio:

LLR
LLR = 2

P (d|H )

= −2 ln P (d|H1 ) ,
0
Nc
i

Nb
sij − dij ln(1 +
j

(5.4)
sij
bij ) ,

(5.5)

where the sum over i is over the different categories (lepton flavour, number of jets, and
b-tag categories), and the sum over j is over the bins of the final MVA distribution. The
sums come about because the probability for multiple independent bins is the product of the
individual bin probabilities.
In reality, the predicted number of events in a given hypothesis is uncertain, and we
need to take into account systematic uncertainties on our predictions. This is done by
considering the various parameters that affect the predictions of H0 and H1 as described
in Sec. 6.7. Each of these parameters (referred to as nuisance parameters) has a range of
possible values around some central value, and are considered as Gaussian distribution with
the mean corresponding to the central value, and width corresponding to the uncertainty
size. Thus for each hypothesis, we allow the number of predicted events to vary within the
systematic uncertainties, and maximize the compatibility with our data. This is equivalent
to minimizing a χ2 :


′ 
Nc Nb
′
p(H)i  Nn
p(H) − d − d ln 
χ2 = −2 ln P (d|H, θ) = 2
+
R(H)2 .
ij
ij
ij
k
di
i j
k

(5.6)

′

Here, p(H)i is the predicted yields for a set of nuisance parameters, Nn , and R(H)k is the
deviation of the k th nuisance parameter from the central value in units of the Gaussian

63

probability distribution width, σk :
0
θ − θk
Rk = k
.
σk

(5.7)

Our log-likelihood ratio is then:

LLR

P (d|H ,θ )

= −2 ln P (d|H1 ,θ1 )
0 0

= χ2 (H0 )min − χ2 (H1 )min ,

(5.8)
(5.9)

where θ0 are the set of nuisance parameters that maximize the likelihood for H0 , and θ1 are
the set of nuisance parameters that maximize the likelihood for H1 .
From here, we want to be able to quantify any excess that we observe above our background only prediction. We do this by considering confidence levels and p-values. The
confidence level is a statement of how often the true value lies within a given interval. So
a confidence interval with confidence level of 1-α contains all values for which H0 is not rejected at a significance level α. The p-value is the probability that a hypothesis will fluctuate
resulting in the observed data. We can relate the confidence levels and p-values for the two
hypotheses by:

∞
CLB = 1 − P VB = x HS+B (LLR)dLLR
0

CLS+B

∞
= P VS+B = x HB (LLR)dLLR,
0

(5.10)
(5.11)

where x0 is the reference LLR (for example the data LLR). Since the LLR is a function of
the signal rate, the confidence level also must be a function of the signal rate.

64

In the absence of a significant signal, we want to set an upper limit on the signal
cross section. The most straight forward metric to do this would be to simply consider
CLS+B . However, this does not protect against against making false exclusion statements
from background-like fluctuations in our data. To prevent such false exclusions, we instead
consider:
CLS =

CLS+B
.
CLB

(5.12)

This allows us to exclude the signal-plus-background hypothesis at a confidence level of 1-α
when CLS < α. An upper limit on the cross cross section can be set (with a C.L. of 1 − α)
by determining how much we would need to scale up the signal rate by until CLS = α. If
the rate does not need to be scaled for CLS to reach α, then we can exclude the signal plus
background hypothesis at a confidence level of 1-α.

65

Chapter 6
Data Analysis
The goal of this research is to search for the Higgs boson. Since there are multiple production
mechanisms and decay modes for the Higgs boson, we first need to pick one production mode
and one decay mode to consider for our search. At the Tevatron, the Higgs boson has three
dominant production modes (Fig. 1.4): gluon-gluon fusion, and associated production with
either a W or a Z boson. The Higgs boson decays into different particles based on its mass
(Fig. 1.5). For a Higgs boson with a mass MH = 125 GeV, the dominant decay mode is to
a pair of bottom quarks, H → b¯ While the gluon-gluon fusion production mode is about
b.
an order of magnitude higher than associated production with a W or Z boson, the amount
of background events from the continuum of QCD b¯ production for gg → H → b¯ is far
b
b
too large compared to the Higgs boson production rate to make a search for gg → H → b¯
b
feasible. Instead, we search for a Higgs boson produced in association with a vector boson
(either a W or a Z), where the vector boson decays leptonically. Leptons are produced less
frequently than hadronic particles in a hadron collider, so by triggering on a lepton we can
greatly reduce the number of background event coming from multijet production. Presented
here is the search for a Higgs boson produced in association with a W boson, where the
Higgs boson decays to a pair b quarks, and the W decays to a lepton and a neutrino.

66

6.1

Analysis Strategy

Once we have decided on a final state topology in which to search for the Higgs boson,
we need to select events the events in data that match the topology of our expected final
state. Then we need to estimate the contribution to our data from various processes that
have the same final state topology as the Higgs boson signal. After we have selected the
data events for analysis and simulated the contributions from the different processes, we
try to distinguish our signal events from our background events. Since we are searching
for a Higgs boson that decays to a pair of bottom quarks, we categorize our events based
on b-tagging algorithms. We then distinguish signal and background using multivariate
techniques. Finally, we perform a statistical analysis to determine whether our data includes
the Higgs boson signal. To validate our search methodology, we perform a cross check by
measuring the cross section of V Z → ℓνb¯
b.

6.2

Monte Carlo Simulation

There are multiple processes that will produce the same final state topology as our W H →
ℓνbb signal. These processes include production of a W boson with jets, W +jets; production
of a Z boson with jets, Z+jets (where one of the leptons from the Z decay is not identified);
single-top quark and top quark pair production; diboson (W W, W Z, ZZ) production; and
multijet production. Example Feynman diagrams for the processes that we consider as
background for our Higgs boson search are shown in Fig. 6.1. Additionally, there are other
Higgs boson signals that result in a similar final state that are included in our signal sample:
ZH → ℓℓbb where one of the leptons is not reconstructed, gg → H → W W → ℓνjj,
gg → H → ZZ → ℓℓjj (where again one of the leptons is not reconstructed), and V H →
67

V W W → ℓνjjjj (where V = W, Z and we don’t reconstruct all four jets). Figure 6.2 shows
example Feynman diagrams for our signal processes. The multijet events are estimated
from data as is described in section 6.3. The other processes are simulated with MC event
generators. The signal and diboson samples are generated with pythia. The single top
samples are produced with singletop. The V+jets and top pair samples are generated
with alpgen and showered with pythia. The cross sections multiplied by the relevant
branching fractions for the simulated processes are given in Tables 6.1 to 6.3.

Figure 6.1: Example Feynman diagrams for processes we consider as backgrounds: W +jets
(top left), top quark pair production (top right), W Z production (bottom left), and multijet
production (bottom right).

In addition to the D0 common corrections described in the previous chapter, we derive
and apply some corrections for our simulated samples. Past studies have shown that alpgen
poorly reproduces certain kinematic distributions. To correct for this deficiency, we derive

68

Table 6.1: The cross section times branching fraction for diboson and top-quark simulated
processes.
MC Process
σ × B [pb]
WW
11.34
WZ
3.22
ZZ
1.20
¯
tt → bb + ℓ+ νℓ′− νℓ′
¯
0.4900
¯
tt → bb + ℓ+ νℓ′− νℓ′ +1-jet
¯
0.1980
¯
tt → bb + ℓ+ νℓ′− νℓ′ +2-jets
¯
0.0941
¯
tt → bb + 2j + ℓν
2.0340
¯ → bb + 2j + ℓν+1-jet
tt
0.8270
¯
tt → bb + 2j + ℓν+2-jets
0.4050
Single-top s-channel (tb → eνbb)
0.1050
Single-top s-channel (tb → µνbb)
0.1180
Single-top s-channel (tb → τ νbb)
0.1260
Single-top t-channel (tqb → eνbqb)
0.2520
Single-top t-channel (tqb → µνbqb)
0.2470
Single-top t-channel (tqb → τ νbqb)
0.2630

Table 6.2: The cross section times branching fraction for W +jets simulated processes.
MC Process
σ × B [pb]
W +1-jet, (W → ℓν) 1656.399
W +2-jets
388.983
W +3-jets
91.519
W +4-jets
20.920
W +5-jets
6.599
W bb, (W → ℓν)
17.828
W bb+1-jet
8.127
W bb+2-jets
2.971
W bb+3-jets
1.392
W cc, (W → ℓν)
45.684
W cc+1-jet
25.639
W cc+2-jets
10.463
W cc+3jets
5.08

69

Table 6.3: The cross section times branching fraction for Z+jets simulated processes.
Z+1-jet, (Z → ℓℓ), 15 < MZ < 75 GeV
50.6160
Z+2-jets, 15 < MZ < 75 GeV
12.3227
Z+3-jets, 15 < MZ < 75 GeV
3.4067
Z+1-jet, (Z → ℓℓ), 75 < MZ < 130 GeV
51.6103
Z+2-jets, 75 < MZ < 130 GeV
12.4390
Z+3-jets, 75 < MZ < 130 GeV
3.9607
Z+1-jet, (Z → ℓℓ),130 < MZ < 250 GeV
0.4700
Z+2-jets, 130 < MZ < 250 GeV
0.1229
Z+3-jets, 130 < MZ < 250 GeV
0.0418
Z+1-jet, (Z → ℓℓ), 250 < MZ < 1950 GeV 0.04472
Z+2-jets, 250 < MZ < 1950 GeV
0.0131
Z+3-jets, 250 < MZ < 1950 GeV
0.0048
Zbb, (Z → ℓℓ), 15 < MZ < 75 GeV
0.9853
Zbb+1-jet, 15 < MZ < 75 GeV
0.3810
Zbb+2-jets, 15 < MZ < 75 GeV
0.1497
Zbb, (Z → ℓℓ), 75 < MZ < 130 GeV
0.8050
Zbb+1-jet, 75 < MZ < 130 GeV
0.3643
Zbb+2-jets, 75 < MZ < 130 GeV
0.1969
Zbb, (Z → ℓℓ), 130 < MZ < 250 GeV
0.0066
Zbb+1-jet, 130 < MZ < 250 GeV
0.0034
Zbb+2-jets, 130 < MZ < 250 GeV
0.0018
Zbb, (Z → ℓℓ), 250 < MZ < 1960 GeV
0.0006
Zbb+1-jet, 250 < MZ < 1960 GeV
0.0003
Zbb+2-jets, 250 < MZ < 1960 GeV
0.0002
Zcc, (Z → ℓℓ), 15 < MZ < 75 GeV
8.6933
Zcc+1-jet, 15 < MZ < 75 GeV
2.1390
Zcc+2-jets, 15 < MZ < 75 GeV
0.7797
Zcc, (Z → ℓℓ), 75 < MZ < 130 GeV
1.9343
Zcc+1-jet, 75 < MZ < 130 GeV
1.0920
Zcc+2-jets, 75 < MZ < 130 GeV
0.6120
Zcc, (Z → ℓℓ), 130 < MZ < 250 GeV
0.0159
Zcc+1-jet, 130 < MZ < 250 GeV
0.0093
Zcc+2-jets, 130 < MZ < 250 GeV
0.0070
Zcc, (Z → ℓℓ), 250 < MZ < 1960 GeV
0.0013
Zcc+1-jet, 250 < MZ < 1960 GeV
0.0010
Zcc+2-jets, 250 < MZ < 1960 GeV
0.0005

70

Figure 6.2: Feynman diagrams for processes contributing to our Higgs boson signal: associated production of a Higgs with a W boson, with the Higgs boson decaying to a pair of
b-quarks (left); gg → H → W W (middle), and associated production of a Higgs boson with
a W boson, with the Higgs boson decaying to a pair of W bosons (right).

71

reweightings for our W /Z+jets samples. The reweightings are derived before the application
of b-tagging so that any possible signal contamination is very small. To improve the description of jet angles, we correct the η distributions for the two highest pT jets. The correction
has the form of a fourth-order polynomial, determined by fitting the ratio of V+jet events
in MC to data minus the non-V+jet backgrounds. The lepton η distribution is corrected
in W +jet events by a second-order polynomial. We also correct for an observed discrepancy between our data and simulation that is correlated between the W boson pT (pW ) and
T
∆R(j1 , j2 ). This two dimensional function is a product of a third-order polynomial in ∆R,
and an error function plus a Gaussian plus a constant in pW . The pW reweighting is applied
T
T
to W +jet events, and the ∆R correction is applied to both W and Z+jet events. Each
of these corrections is designed to alter the shape of the distributions, but preserve overall
normalizations. These reweighting functions can be seen in Fig. 6.3.

6.3

Multijet Background Estimation

When colliding protons and anti-protons, a large amount of the time the result will be
production of multiple jets. By considering events triggered by a lepton we can cut down on
this background. However it is possible for a jet to mimic a lepton signature in our detector
such that a jet is misidentified as a lepton. Mostly this occurs if most of the jet’s energy
upon hadronization goes into a single pion. The favoured decay mode for a charged pion is
π + → µ+ νµ , which will lead to a jet being misidentified as a muon. Neutral pions favour the
decay to a pair of photons, which can lead to a misidentified electron. It is also possible for
the jet to simply produce a shower shape similar to that expected for an electron so that we
would reconstruct an electron instead of a jet. The estimation of our multijet background

72

1.8
1.4

1.6
1.4

1.2

1.2
1

1
0.8

-2

2
1.8
1.6
1.4
1.2
1
0.8
0

-1

0.8

0
1
2
2ndLeading Jet η

-1

0

1
2
Leading Jet η

1.4
1.3
1.2
1.1
1
1

2

3

4

0.9
0

5
6
∆ R(j 1,j2)

20

40

60

80 100
WpT

Data-Non-V+Jets
Backgrounds
Reweighting Fit

1.4
1.2

Reweighting Fit +1 s.d.

1
0.8

-2

-2

-1

0

Reweighting Fit -1 s.d.

1
2
Lepton η

Figure 6.3: Reweighting functions to correct for mismodelling in the alpgen V+jets MC for
the second leading jet η (top left), leading jet η (top right), W pT (middle left), ∆R(j1 , j2 )
(middle right), and lepton η (bottom). The black points are the data with all non-V+jets
backgrounds subtracted off. The black curves are the reweighting functions fit to the points,
and the blue and red are the ±1 standard deviations on the black curve.

73

comes from data. We use the lepton isolation to define two orthogonal samples with similar
kinematic distributions. Events with a lepton that passes “loose” isolation requirements
are used to estimate the multijet contribution, and events with a lepton that passes “tight”
isolation requirements are used in the analysis sample. In multijet events, we expect that
usually the ET we measure to be from a mismeasurement instead of from a neutrino from
a W boson decay, so we use events with relatively low ET , 5 < ET < 15 GeV, to estimate
the multijet contribution. Then we weight the events so that we can properly estimate
the number of events contributing to our analysis sample. The template is created using
a modified version of the Matrix Method to reweight events in data. The matrix method
works by solving the following pair of equations for the number of real lepton and multijet
events:

NL

= Nℓ + NM J ,

NT = ǫℓ Nℓ + fj NM J ,

(6.1)
(6.2)

where NL/T are the number of events that pass loose/tight lepton isolation requirements,
Nℓ/M J is the number of real lepton/misidentified multijet events in the data sample with
the loose isolation requirements, ǫℓ is the efficiency for a real lepton that passes the loose
isolation requirements to subsequently pass the tight isolation requirements, and fj is the
efficiency for a jet that passes the loose isolation requirements to subsequently pass the tight
isolation requirements. Solving this system of equations for the number of multijet events in
the sample with tight isolation requirements:

T
NM J =

fj
(ǫ N − NT ).
ǫℓ − fj ℓ L
74

(6.3)

We can then weight each event in our templates by:

w=

fj
(ǫ − ΘT ),
ǫℓ − fj ℓ

(6.4)

where ΘT = 1 if the event satisfies tight isolation requirements, and 0 otherwise. The total
number of multijet events in the tight sample is then the sum of weights over all events that
pass the loose isolation requirements:

T
NM J =

NL

wi .

(6.5)

i=1

Since this method uses all events that pass the loose isolation requirements, events that
have a lepton that also passes the tight isolation requirements will contribute with a negative weight, and the multijet sample is not statistically independent from the data sample,
which could potentially result in correlated fluctuations. To avoid this, we employ a slightly
modified version of the matrix method where we consider only the events that pass the
loose lepton identification requirements, but fail the tight lepton identification requirements
(so-called loose-not-tight events). These events are weighted by:

Wi =

fj
.
1 − fj

(6.6)

This will result in a multijet prediction of:

T
NM J =

N L−n−T

Wi ,
i=1

where, N L−n−T is the number of events in the loose-not-tight sample.

75

(6.7)

The efficiencies for real leptons and jets misidentified as leptons depend on the event
kinematics. The real lepton efficiencies for electrons, ǫe , are parametrized as a function of
detector η, electron pT , and instantaneous luminosity. For muons, ǫµ is parametrized as
a function of muon pT . The efficiency rates are determined by studying Z → ℓℓ events.
The efficiency with which a jet is misidentified as a lepton, fj , is determined by studying
events with 5 < ET < 15 GeV by considering the ratio of loose to tight MC-subtracted
e
data events. For electrons, fj is parametrized as a function of electron pT , detector η, and
µ

min ∆φ(ET , jet). For muons, fj is parametrized as a function of muon pT , detector η, and
µ

e
∆φ(ET , µ). An example fj is shown in Fig. 6.4, and an example of fj is shown in Fig. 6.5.

6.4

Selection

Since we are trying to find a Higgs boson that decays to b-quarks, and a W that decays
leptonically, we want to look for exactly one high energy lepton (either an electron or muon),
a large amount of ET from the neutrino in the W decay, and two or three jets. We require
the lepton pT to be greater than 15 GeV to cut down on the number of multijet events
without cutting out too many signal events from our sample, since the pT of a lepton from
a W boson decay tends to be large compared to the misidentified leptons in the multijet
sample. The lepton η is required to be less than 2 for muons so that the muon passes
through the acceptance of the muon system. We require the electron to pass through either
the CC, |η| < 1.1, or the EC, 1.5 < |η| < 2.5. The ET is required to be greater than
15 GeV in electron events to ensure orthogonality with the sample in which we estimate
the multijet contribution to our data, and 20 GeV in muon events to further suppress the
multijet background. Since jets in our signal are coming from the decay of a Higgs, they

76

0.48
0.46
0.44
0.42
0.4
0.38
0.36
0

0.2

0.4

0.6

0.8

1

Lepton detector η

0.45
0.4
0.35
0.3
0.25
0.2
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5

Lepton detector η

Figure 6.4: Example of the probability for a jet that passes the loose lepton identification
requirements to pass the tight lepton isolation requirements for the 15 < pT < 17 GeV range
with 0.4 < min [∆φ(ET , jet)] < π as a function of the electron η in the (a) CC and (b) EC.
The solid line is a fit to the data, and the dashed lines are the functions with the parameters
shifted up and down by their uncertainties.

77

0.7
0.6
0.5
0.4
0.3
0.2

20 30 40 50 60 70 80 90 100

Lepton pT (GeV)

0.8
0.7
0.6
0.5
0.4
0.3
0.2

20 30 40 50 60 70 80 90 100

Lepton pT (GeV)

Figure 6.5: Example of the probability for a jet that passes the loose lepton identification
requirements to pass the tight lepton isolation requirements as a function of muon pT for
(a) |η| < 1.0 and (b) 1.0 < |η| < 1.6, with 0 < ∆φ(ET , µ) < 1. The solid line is a fit to the
data, and the dashed lines are the functions with the parameters shifted up and down by
their uncertainties.

78

will tend to have higher pT than jets coming from gluon splitting as the jets in our W b¯
b
background do. We therefore require that the jet pT be larger than 20 GeV. Since we are
looking for a charged lepton, and two charged jets (from the b-quarks from the Higgs boson
decay), we require that the event have a primary vertex with at least three associated tracks,
and that the z position be within the coverage of the SMT, |z| < 60 cm. We also require that
the primary vertex be matched to the interaction point by requiring that the radial distance
between the primary vertex and the interaction point be less than 1 cm. We also impose a
two dimensional requirement on the ET and transverse mass of the reconstructed W boson,
W
W
MT , such that MT > 40GeV − 0.5ET . This helps to reduce the multijet background,

since the lepton and neutrino in a multijet event tend to not come from a real W , the
transverse mass of the reconstructed W will tend to be low for these events. We have two
categories of leptons based on the lepton isolation. The leptons with a “loose” isolation are
used to estimate the multijet background as described above, and the leptons with a “tight”
isolation are used to perform the analysis. For electrons, the loose and tight isolation is
defined by different requirements on the electron ID MVA output. For muons, the loose
isolation requires that the lepton be outside of a reconstructed jet, ∆R(µ, jet) > 0.5. For
an isolated muon, we expect that most of the momentum from charged particles near the
muon should come from the muon itself. To account for this, the tight isolation additionally
requires that the ratio of the scalar sum of the pT of the tracks within ∆R = 0.5 of the muon
to the muon pT be less than 0.4. We also require that the ratio of the transverse energy
deposited in a hollow cone of 0.1 < ∆R < 0.4 around the muon to the muon pT must be
less than 0.12. This reduces the probability that a neutral particle has deposited energy in
the calorimeter near the muon.
The W /Z+jets cross sections have a large uncertainty, so we apply an additional scaling
79

factor to our W +jets and Z+jets samples based on a fit to data. The fit is done before
b-tagging by subtracting the non-V+jets MC (tt, single top, and diboson) from the data.
Then using the transverse mass of the W boson, the V+jets MC and multijet contributions
are simultaneously fit to the data, and overall scale factors are obtained. These fits are done
separately for electron and muon events, and separately for events with two jets and three
jets.
Events containing an electron are selected by a logical OR of triggers that require an
electromagnetic object. The efficiencies of the triggers measured in data are applied to the
MC simulation. These efficiencies are parametrized in electron η, φ, and pT . Depending on
the trigger, and the electron’s position within the detector, these efficiencies are 90 - 100%.
Events containing a muon are selected based on the logical OR of all available triggers,
except those that contain lifetime based requirements that are used for b-jet identification.
To determine the trigger efficiency in this inclusive trigger sample, we consider a subset of
triggers which are about 70% efficient where the simulation models the data well, based on
the logical OR of single muon and muon+jets triggers (TµOR ). By comparing the data in
this subset to that in the inclusive trigger sample, we can determine an inclusive trigger
correction for the MC trigger efficiency, Pcorr :

Pcorr =

(Ndata − NMJ )incl − (Ndata − NMJ )T
NMC

µOR

,

(6.8)

where the numerator is the difference (after subtracting off the multijet background component) between the number of data events in the inclusive and TµOR trigger samples, and the
denominator is the total number of MC events. The total trigger efficiency is estimated as
the efficiency in the TµOR sample + Pcorr , and is limited to be no more than 1.

80

The correction, Pcorr is derived as a function of the sum of jet pT , HT , and the ET , in bins
of muon η. The η bins are chosen based on different triggers dominating in different regions
of the detector. Single muon triggers dominate for |η| < 1.0, while muon+jets triggers are
dominant for |η| > 1.6. The intermediate region, 1.0 < |η| < 1.6, is a mixture of single
muon and muon+jets triggers. Detector supports allow only partial coverage of the muon
detector when the muon |η| < 1.6 and −2 < φ < −1.2. This support structure impacts
the trigger efficiency in these regions, so we derive separate corrections for events that pass
through the region where the supports are and events that do not encounter the support
region. Examples of these corrections can be seen in Fig. 6.6. This strategy results in a
trigger efficiency of ∼ 80 − 100%, depending on the HT and the muon’s position in the
detector.

6.5

b Tagging

Since we are looking for a Higgs boson that decays to b-quarks, we employ b-tagging to
categorize our candidate events based on the likelihood that the event contains either one or
two b-tagged jets, with one category for events with one b-tagged jet and three categories
for events with two b-tagged jets. The categories for events with two b-tagged jets are
chosen based on the MVA b-jet identification (bid) output shown in Fig. 6.7. We choose
the categories such that they each contain a different relative contribution of backgrounds,
and a different ratio of signal to background events. The category with one “tight” b-tagged
jet, requires that the bid MVA output is greater than 0.15. In Fig. 6.7, we see that below
a bid output of 0.35, the background is dominated by V +light jet (V +lf) and multijet
events with a small contribution from diboson (V V ) events, and above 0.55, the dominant

81

Pcorr

1.2
1

DØ, 9.7 fb-1
(a)

-2 < φ < -1.2
φ < -2, φ > -1.2
ET<50 GeV

0.8
0.6
0.4
0.2
0

50

100

150

200

250

300

Pcorr

HT (GeV)
1.6
DØ, 9.7 fb-1
1.4
(b)
1.2
1
0.8
0.6
0.4
0.2
0
50
100 150

-2 < φ < -1.2
φ < -2, φ > -1.2
ET≥50 GeV

200

250

300

HT (GeV)
Figure 6.6: Muon trigger correction, derived from data to account for the gain in efficiency
when moving from single muon and muon+jets triggers to inclusive triggers. The corrections
are parametrized as a function HT , shown for events with muon |η| < 1.0 with a) ET <
50 GeV and b) ET ≥ 50 GeV. The black circles represent the correction when the muon
passes through the detector support region (−2 < φ < −1.2), and the red triangles represent
the correction in all other regions of φ [2].

82

contribution is from V +heavy jet (V +hf) and top events. We also see that the signal is
peaking near 1 and also near 0.5. Thus, for events with two b-tagged events we define
three categories based on the average bid MVA output for the two jets: two “loose” b-tags
(0.02 < (bidj1 + bidj2 )/2 < 0.35), two “medium” b-tags (0.35 < (bidj1 + bidj2 )/2 < 0.55),
and two “tight” b-tags (0.55 < (bidj1 + bidj2 )/2). Events that fall into more than one b-tag
category, are considered in the most stringent tag category. For example, events that pass
the two tight b-tag requirements will also pass the two loose b-tag requirements, but are
only counted once, in the two tight b-tag category. The requirements for individual jets to
pass the loose (medium, tight) threshold, averaged over jet pT and η, have an identification
efficiency of 79% (57%, 47%), with a b-tagging misidentification rate of 11% (0.6%, 0.15%)
for light quark jets.
All events that pass our selection requirements discussed in Sec. 6.4 before being classified
into the different b-tagging categories make up our pretag sample. Figures 6.8 to 6.10 show
some selected distributions of various kinematic at the pretag level. We see that our expected
background events describe the data well. The reconstructed dijet mass is shown in Figs. 6.11
and 6.12 for the four different tag categories. From comparing the dijet mass in the different
b-tag categories, we can see that the ratio of the number of signal events to the number of
background events gets larger as we require stricter b-tag requirements, and also that the
relative background contributions changes as we look at the different b-tag categories. For
example the two tight b-tag category is dominated by top and V +heavy jet production,
whereas the two loose b-tag category has a larger contribution from V +light jet production.
The signal, data, and background yields are given in Tables 6.4 to 6.7 for events in the pretag
and all four tagging categories.

83

Events / 0.05

V(→lν)+2 jets, two tags
Data
1800 DØ, 9.7 fb -1
VV
Top

1600
1400

V+hf

1200

V+lf
Multijet

1000
800

Signal (× 50)

600

MH=125 GeV

400
200
0

0

0.2

0.4

0.6

j1

0.8

j2

1

(b +bID)/2
ID

Figure 6.7: The average b-jet identification output for events with two jets. We define three
categories containing two b-tagged jets based on this average output. The signal is shown
for a Higgs boson mass of 125 GeV, scaled by a factor of 50 [2].

84

Table 6.4: Observed number of events in data and expected number of events from each
signal and background source (where V = W, Z) for events with a muon and exactly two
jets. The expected signal is quoted at MH = 125 GeV. The total background uncertainty
includes all sources of systematic uncertainty added in quadrature.
Pretag 1 tight 2 loose 2 med. 2 tight
b-tag b-tags b-tags b-tags
¯
V H → ℓνbb
17.4
5.0
1.4
2.1
3.5
H → V V → ℓνjj
10.9
0.8
0.2
0.04
0
V H → V V V → ℓνjjjj
5.1
0.4
0.1
0.02
0
Diboson
2904
383
68.5
39.1
44.6
V + (g, u, d, s)-jets
78109
2645
807
60.9
5.5
¯ c)
V + (bb/c¯
13445
2531
486
341
335
¯
top (tt + single top)
3448
688
126
156
202
Multijet
28486
1560
367
121
87.6
Total background
expectation
126425
7813
1856
720
678
Total background
uncertainty
7576
835
177
87
85
Observed events
126811
7460
1870
656
544

Table 6.5: Observed number of events in data and expected number of events from each
signal and background source (where V = W, Z) for events with an electron and exactly two
jets. The expected signal is quoted at MH = 125 GeV. The total background uncertainty
includes all sources of systematic uncertainty added in quadrature.
Pretag 1 tight 2 loose 2 med. 2 tight
b-tag b-tags b-tags b-tags
¯
V H → ℓνbb
19.2
6.1
1.6
2.3
3.9
H → V V → ℓνjj
13.2
1.0
0.2
0.03
0
V H → V V V → ℓνjjjj
7.1
0.7
0.1
0.02
0.01
Diboson
2877
269
55.7
21.5
18.6
V + (g, u, d, s)-jets
89728
3121
892
63.6
6.4
¯ c)
V + (bb/c¯
13596
2595
480
338
343
¯ + single top)
top (tt
1932
703
137
184
252
Multijet
41986
2407
619
169
104
Total background
expectation
150158
9103
2187
779
727
Total background
uncertainty
7423
887
192
92
92
Observed events
150118
8946
2187
702
621

85

Table 6.6: Observed number of events in data and expected number of events from each
signal and background source (where V = W, Z) for events with a muon and exactly three
jets. The expected signal is quoted at MH = 125 GeV. The total background uncertainty
includes all sources of systematic uncertainty added in quadrature.
Pretag 1 tight 2 loose 2 med. 2 tight
b-tag b-tags b-tags b-tags
¯
V H → ℓνbb
4.1
1.0
0.4
0.5
0.8
H → V V → ℓνjj
4.4
0.4
0.1
0.03
0
V H → V V V → ℓνjjjj
2.9
0.3
0.1
0.02
0
Diboson
608
85.7
25.2
13.4
11.2
V + (g, u, d, s)-jets
10689
443
285
14.9
2.3
¯ c)
V + (bb/c¯
3577
682
228
135
109
¯
top (tt + single top)
1845
508
163
201
247
Multijet
4253
315
127
41.4
14.6
Total background
expectation
20983
2034
829
406
385
Total background
uncertainty
1360
205
73
41
40
Observed events
21297
2027
828
413
401

Table 6.7: Observed number of events in data and expected number of events from each
signal and background source (where V = W, Z) for events with an electron and exactly three
jets. The expected signal is quoted at MH = 125 GeV. The total background uncertainty
includes all sources of systematic uncertainty added in quadrature.
Pretag 1 tight 2 loose 2 med. 2 tight
b-tag b-tags b-tags b-tags
¯
V H → ℓνbb
4.4
1.1
0.5
0.5
0.8
H → V V → ℓνjj
4.5
0.4
0.1
0.04
0.01
V H → V V V → ℓνjjjj
3.4
0.4
0.2
0.02
0.01
Diboson
591
77.5
24.8
11.7
8.9
V + (g, u, d, s)-jets
9526
395
251
15.0
0.4
¯ c)
V + (bb/c¯
3240
639
204
124
104
¯ + single top)
top (tt
2979
609
198
235
274
Multijet
8197
629
259
75.6
57.2
Total background
expectation
24545
2351
937
461
445
Total background
uncertainty
1225
455
195
115
106
Observed events
24610
2251
987
466
396

86

Events / 3 GeV

V(→lν)+2 jets, pretag
60000 DØ, 9.7 fb -1
Data
VV
Top

(a)

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

20000

MH=125 GeV

10000
0

0

20

40

60

80

100 120

Events / 2.62 GeV

MW [GeV]
T
V(→lν)+2 jets, pretag
30000 DØ, 9.7 fb -1
Data
25000

VV
Top

(b)

20000

V+hf

15000

V+lf
Multijet
Signal (× 1000)

10000

MH=125 GeV

5000
0

20

40

60

80

100

120

Lepton pT [GeV]
Figure 6.8: Distributions for all selected events with two jets of (a) transverse mass of the
lepton-ET system, and (b) charged lepton pT . The signal is multiplied by 1000. Overflow
events are added to the last bin [2].
87

Events / 4.06 GeV

V(→lν)+2 jets, pretag
-1
Data
40000 DØ, 9.7 fb
VV
Top

(a)

35000
30000

V+hf

25000

V+lf
Multijet

20000

Signal (× 1000)

15000

MH=125 GeV

10000
5000
0
20

40

60

80 100 120 140

Leading jet p [GeV]
Events / 1.88 GeV

T

V(→lν)+2 jets, pretag
Data
DØ, 9.7 fb -1
60000
VV

(b)

Top

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

20000

MH=125 GeV

10000
0
20

30
nd

2

40

50

60

70

80

Leading jet p [GeV]
T

Figure 6.9: Distributions for all selected events with two jets of (a) leading jet pT , and (b)
second-leading jet pT . The signal is multiplied by 1000. Overflow events are added to the
last bin [2].
88

Events / 2.12 GeV

V(→lν)+2 jets, pretag
Data
25000 DØ, 9.7 fb -1
VV
Top

(a)
20000

V+hf
V+lf
Multijet

15000

Signal (× 1000)

10000

MH=125 GeV

5000
0

20 30 40 50 60 70 80 90 100

Events / 0.14

ET [GeV]
V(→lν)+2 jets, pretag
-1
Data
80000 DØ, 9.7 fb
70000

VV
Top

(b)

60000

V+hf

50000

V+lf
Multijet

40000

Signal (× 1000)

30000

MH=125 GeV

20000
10000
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

∆ R (j , j )
1 2

Figure 6.10: Distributions for all selected events with two jets of (a) ET , and (b) ∆R between
the leading and second-leading jets. The signal is multiplied by 1000. Overflow events are
added to the last bin [2].
89

Events / 20 GeV

V(→lν)+2 jets, one tight b-tag
-1
Data
5000 DØ, 9.7 fb
VV
Top

(a)
4000

V+hf
V+lf
Multijet

3000

Signal (× 200)

2000

MH=125 GeV

1000
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]

Events / 20 GeV

V(→lν)+2 jets, two loose b-tags
-1
Data
1200 DØ, 9.7 fb
VV
Top

(b)
1000

V+hf

800

V+lf
Multijet

600

Signal (× 200)
MH=125 GeV

400
200
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]
Figure 6.11: Invariant mass of the leading and second-leading jets in events with two jets
and (a) one tight b-tag, and (b) two loose b-tags. The signal is multiplied by 200. Overflow
events are added to the last bin [2].
90

Events / 20 GeV

V(→lν)+2 jets, two medium b-tags
Data
DØ, 9.7 fb -1
400
VV
Top

(a)

350
300

V+hf

250

V+lf
Multijet

200

Signal (× 50)

150

MH=125 GeV

100
50
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]

Events / 20 GeV

V(→lν)+2 jets, two tight b-tags
400 DØ, 9.7 fb -1
Data
VV
Top

(b)

350
300

V+hf

250

V+lf
Multijet

200

Signal (× 50)

150

MH=125 GeV

100
50
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]
Figure 6.12: Invariant mass of the leading and second-leading jets in events with two jets and
(a) two medium b-tags, and (b) two tight b-tags. The signal is multiplied by 50. Overflow
events are added to the last bin [2].
91

6.6

Multivariate Classification

We employ multivariate analysis (MVA) techniques to classify signal and background events.
We use a boosted decision tree [38, 39, 40, 41, 42] implemented in the tmva package [43]
both to distinguish our signal from our multijet background, to distinguish our signal from
all backgrounds .
The BDT is a form of a machine learning technique known as a decision tree. We start
with a list of variables that show good agreement between the simulation and the data, and
have some difference in the distribution between signal and at least one background process.
The decision tree uses these variables to create a series of yes/no splits on events that are
known to be classified as either signal or background. The splitting is done to maximally
separate signal from background, and stops when either a node contains events that are
pure signal or background, or when a minimum number of events in a node is reached.
Boosting involves building up a series of trees, where each tree is retrained, boosting the
weights for events that were misclassified in previous trainings. Our events are split into
three statistically independent subsamples for training, testing, and performing our final
statistical analysis. After the BDT is trained, it is applied to the testing sample to ensure
that our training does not pick up on statistical fluctuations in the training sample (known as
overtraining). Having an independent sample to perform our final statistical analysis helps
reduce the chance that optimizations performed on our training sample do not bias our final
result.
We train a BDT to distinguish our V H → V bb signal from our multijet background. The
variables used for the training were selected to exploit differences in the kinematics between
the multijet and signal events, are listed in Table 6.8, and are shown in Appendix A. This

92

BDT is trained using our pretag sample, so we have a large enough sample of multijet events
to perform the training. The output from this BDT is shown in Fig. 6.13, and is used as
an input to the final Higgs boson MVA which is used to distinguish our signal from all
background processes.
Table 6.8: Input variables for the MVAMJ (V H) discriminant, which was trained using V H →
ℓνb¯ events as a signal. Variables are ranked by their importance in the BDT (which is based
b
on how often they are used in the training) [2].
MVAMJ Input Variables Description
ην
Pseudorapidity of the missing ET vector
Sig
ET
ET significance, a measure of the consistency of the
observed ET with respect to zero ET , accounting for
the uncertainty in the calorimeter objects that contribute to ET
∆η(ℓ, ν)
Separation in η between the lepton and the reconstructed neutrino, |η ℓ − η ν |
TW →ℓν
Twist of the ℓν system = arctan(∆φ(ℓ, ν)/∆η(ℓ, ν))
cos θ(ℓ)ℓνCM
Cosine of the angle between the charged lepton and
the proton beam axis in the CM of ℓν system
V(j12 )
Velocity of the dijet system
Asym
m
Mass asymmetry between ℓν system and the dijet
system: (Mℓν − mj12 )/(Mℓν + mj12 )
C
Centrality is ( i pi )/( i |pi |), where i runs over ℓ
T
and all jets
ET
Missing transverse energy
V IS
pT
Magnitude of the vector sum of the pT of the visible
particles
max |∆η(ℓ, {j1 or j2 })|
Maximum ∆η between the charged lepton and the
leading or second leading jet
A final BDT is trained to distinguish signal from all backgrounds. This is done separately
in events with 2 jets, and events with three jets; each b-tagging category; and for muons and
electrons. Since the event kinematics for our signal depend on the mass of the Higss we are
considering, a separate BDT is trained for each possible Higgs boson mass between 90 and
150 GeV in steps of 5 GeV. The variables used to train these final BDTs are given in Table 6.9
(ranked by how often a given variable is used in the MVA), and examples of variables used
93

Events / 0.05

V(→lν)+2 jets, pretag
30000 DØ, 9.7 fb -1
Data
VV
Top

25000

V+hf

20000

V+lf
Multijet

15000

Signal (× 1000)

10000

MH=125 GeV

5000
0
-1

-0.6

-0.2

0.2

0.6

1

MVAMJ(VH)
Figure 6.13: The output distribution for the Higgs boson signal vs multijet discriminant
shown for all events containing exactly two jets. The signal for MH = 125 GeV is scaled by
a factor of 1000 [2].

94

in the training are shown for each jet and b-tag category in Fig. 6.14 to 6.17. One of the
most important variables used in the BDT is the dijet mass, as the signal is expected to
peak at the mass of the Higgs boson, and the backgrounds tend to peak at lower dijet mass
values. In the two tight and two medium b-tag categories, the output from the multijet
discriminant is also important in the BDT. While there are very few multijet events in these
b-tag categories, the other background processes tend to peak near zero in the multijet BDT
output. In the two loose and 1 b-tag categories, the bid MVA output distribution plays
a strong role. This is because in these b-tag categories, the dominant background is from
V +light jet production which tends to have lower bid output values than the H → b¯ signal
b
does. Figures 6.18 to 6.21 show the final MVA output for MH = 125 GeV. The additional
input variables and the BDT outputs for the other Higgs boson mass values are shown in
Appendix B. In all categories, we see the signal peaking near one, while the background
peaks near -1. We also observe that our data agrees well with our background prediction.
These distributions are used to perform our final statistical analysis as discussed in Ch. .

6.7

Systematic Uncertainties

We must account for sources of uncertainty in our analysis. This includes both statistical and
systematic uncertainties. The statistical uncertainties come from the number of data and MC
events we have available to describe kinematic distributions. The systematic uncertainties
are uncertainties resulting from object reconstruction and calibration and MC generation or
theory. To determine the systematic uncertainties on signals and backgrounds, we repeat
the full analysis with each source of uncertainty varied by ±1 standard deviation for the
parameter on which we are uncertain. We can divide the uncertainties into two categories:

95

Table 6.9: Table of input variables for the final signal discriminant. Variables are ranked by
their importance in the BDT (which is based on how often they are used in the training) in
the two tight b-tagged (2T), two medium b-tagged (2M), two loose b-tagged (2L), and one
tight b-tagged (1T) categories [2].
Variable
Description
2T 2M 2L 1T
MVAMJ (V H)
Output of the MVA trained to distinguish 1
1
¯ from the MJ background
W H → ℓνbb
mb1b2
The dijet invariant mass
2
4
3
1
W /(pℓ + E )
6
4
2
pT
The transverse momentum of the recon- 3
T
T
structed W divided by the sum of the transverse momentum of the lepton and the ET
j

12
bID

Averaged b-jet identification output for the
highest energy b-tagged jets
∗)
cos(χ
χ∗ = (ℓ, the direction of the W boson spin)
in ℓν system CM frame [44]
max|∆η(ℓ, j1 , j2 )|
Maximum ∆η between the charged lepton
and the leading or second leading jet
ℓ × ηℓ
q
Product of the lepton charge and its pseudorapidity
∆R(ℓ, j1 )
∆R between the charged lepton and the leading jet
min[SIG(j12 , {j1 , j2 })] Minimum SIG of the two leading jets de-

4

13

5

3

6

q ℓ × η j1

2

V(j12 )
cos(θ∗ )
mℓνj2
j

mT12
C
(pT )V IS

mAsym
A

j

pT2

Transverse mass of the two leading jets
Centrality is ( i pi )/( i |pi |), where i runs
T
over ℓ and all jets
Scalar sum of the pT of the visible particle
Mass asymmetry between ℓν system and the
dijet system: (Mℓν − mj12 )/(Mℓν + mj12 )
3λ3 /2 where λ3 is the smallest eigenvalue
of the normalized momentum tensor S αβ =
β
( i pα pi )/( i |pi |2 ) , where α, β = 1, 2, 3
i
correspond to the x, y, z momentum components, and i runs over selected objects.
96

4

11

2

3

7

2

6

6

8

5

9

15

9

5

10

7

11

9

11
12

12
10

7

11

13

16

12

13

14
15

14
8

8

10

16

9
5

8

10

12

13

7

j
pTi with

fined as pmin (j1 , j2 )∆R(j1 , j2 )/
T
i=1
respect to the dijet system. Based on the
pull variables described in [45]
Product of the the lepton charge and η of the
leading jet
Velocity of the dijet system
θ∗ = (W, u − type quark) in the Higgs CM
frame [44]
Invariant mass of the charged lepton, ET ,
and second leading jet system

pT of the second leading jet

1

Events / 0.05

V(→lν)+2 jets, one tight b-tag
4000 DØ, 9.7 fb -1
Data
VV
3500 (a)
Top

3000

V+hf

2500

V+lf
Multijet

2000

Signal (× 200)

1500

MH=125 GeV

1000
500
0

0

0.2

0.4

0.6

0.8

1

pW/(pl +ET)
T
Events / 0.2

T

V(→lν)+2 jets, two loose b-tags
Data
DØ, 9.7 fb -1
1000 (b)
VV
Top

800

V+hf

600

V+lf
Multijet
Signal (× 200)

400

MH=125 GeV

200
0

0 0.5 1 1.5 2 2.5 3 3.5 4

max(|∆ η (l, {j or j }|)
1

2

Figure 6.14: Distributions of some of the most significant inputs to the final discriminant in
events with exactly two jets: (a) pW /(pℓ + ET ), shown for events with one tight b-tag; (b)
T
T
max |∆η(ℓ, {j1 or j2 })|, shown for events with two loose b-tags. The MH = 125 GeV signal
is multiplied by 200. Overflow events are added to the last bin [2].
97

Events / 0.25

V(→lν)+2 jets, two medium b-tags
Data
DØ, 9.7 fb -1
500
VV

(a)

Top

400

V+hf

300

V+lf
Multijet
Signal (× 50)

200

MH=125 GeV

100
0
-2.5

-1.5

-0.5

0.5

1.5

2.5

Events / 12.5 GeV

ql × η l
V(→lν)+2 jets, two tight b-tags
Data
DØ, 9.7 fb -1
350
VV

(b)

Top

300

V+hf

250

V+lf
Multijet

200

Signal (× 50)

150

MH=125 GeV

100
50
0
50

100

150

200

Σ (pT)

VIS

250

300

[GeV]

Figure 6.15: Distributions of some of the most significant inputs to the final discriminant
in events with exactly two jets: (a) q ℓ × η ℓ , shown for events with two medium b-tags; (b)
(pT )V IS , shown for events with two tight b-tags. The MH = 125 GeV signal is multiplied
by 50. Overflow events are added to the last bin [2].
98

Events / 0.4

V(→lν)+3 jets, one tight b-tag
-1
Data
2200 DØ, 9.7 fb
2000
1800
1600
1400
1200
1000
800
600
400
200
0

VV
Top

(a)

V+hf
V+lf
Multijet
Signal (× 200)
MH=125 GeV

0 0.5 1 1.5 2 2.5 3 3.5 4

max(|∆ η (l, {j or j }|)
2

Events / 0.5

1

V(→lν)+3 jets, two loose b-tags
1200 DØ, 9.7 fb -1
Data
1000

VV
Top

(b)

V+hf

800
600

V+lf
Multijet

400

MH=125 GeV

Signal (× 200)

200
0
-2.5

-1.5

-0.5

0.5

1.5

2.5

ql × η l
Figure 6.16: Distributions of some of the most significant inputs to the final discriminant in
events with exactly three jets: (a) max |∆η(ℓ, {j1 or j2 })|, shown for events with one tight
b-tag; (b) q ℓ × η ℓ , shown for events with two loose b-tags. The MH = 125 GeV signal is
multiplied by 200. Overflow events are added to the last bin [2].
99

Events / 0.05

600

V(→lν)+3 jets, two medium b-tags
Data
DØ, 9.7 fb -1
VV
Top

(a)

500

V+hf

400

V+lf
Multijet

300

Signal (x50)

200

MH=125 GeV

100
0

0

0.1

0.2

0.3

0.4

0.5

Aplanarity

Events / 20 GeV

V(→lν)+3 jets, two tight b-tags
Data
400 DØ, 9.7 fb -1
350

VV
Top

(b)

300

V+hf

250

V+lf
Multijet

200

Signal (× 50)

150

MH=125 GeV

100
50
0
100

140

180

220

260

300

Mlν j [GeV]
2

Figure 6.17: Distributions of some of the most significant inputs to the final discriminant in
events with exactly three jets: (a) aplanarity, shown for events with two medium b-tags; (b)
mℓνj2 , shown for events with two tight b-tags. The MH = 125 GeV signal is multiplied by
50. Overflow events are added to the last bin [2].
100

Events / 0.08

V(→lν)+2 jets, one tight b-tag
5

10

DØ, 9.7 fb-1

Data

(a)

VV
Top
V+hf

4

10

V+lf
Multijet
Signal (× 100)

103

MH=125 GeV

102
-1

-0.6

-0.2

0.2

0.6

1

Events / 0.08

Final Discriminant
V(→lν)+2 jets, two loose b-tags

105

DØ, 9.7 fb-1

Data

(b)

VV
Top

104

V+hf
V+lf
Multijet

103

Signal (× 100)
MH=125 GeV

102

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure 6.18: Distributions of the final discriminant output, after the maximum likelihood
fit (described in Ch. ), in events with exactly two jets and: (a) one tight b-tag, and (b) two
loose b-tags. The MH = 125 GeV signal is multiplied by 100 [2].
101

Events / 0.08

V(→lν)+2 jets, two medium b-tags
10

Data

(a)

5

DØ, 9.7 fb-1

VV
Top

104

V+hf
V+lf
Multijet

3

10

Signal (× 20)

102

MH=125 GeV

10
1
-1

-0.6

-0.2

0.2

0.6

1

Events / 0.08

Final Discriminant
V(→lν)+2 jets, two tight b-tags
106
5

DØ, 9.7 fb-1

Data

(b)

VV
Top

10

V+hf

104

V+lf
Multijet

103

Signal (× 20)

102

MH=125 GeV

10
1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure 6.19: Distributions of the final discriminant output, after the maximum likelihood fit
(described in Ch. ), in events with exactly two jets and: (a) two medium b-tags, and (b) two
tight b-tags. The MH = 125 GeV signal is multiplied by 20 [2].
102

Events / 0.08

V(→lν)+3 jets, one tight b-tag
10

Data

(a)

5

DØ, 9.7 fb-1

VV
Top
V+hf

104

V+lf
Multijet
Signal (× 100)

103

MH=125 GeV

102

-1

-0.6

-0.2

0.2

0.6

1

Events / 0.08

Final Discriminant
V(→lν)+3 jets, two loose b-tags
105

DØ, 9.7 fb-1

Data

(b)

VV
Top

104

V+hf

103

V+lf
Multijet
Signal (× 100)
MH=125 GeV

102
10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure 6.20: Distributions of the final discriminant output, after the maximum likelihood fit
(described in Ch. ), in events with exactly three jets and: (a) one tight b-tag, and (b) two
loose b-tags. The MH = 125 GeV signal is multiplied by 100 [2].
103

Events / 0.08

V(→lν)+3 jets, two medium b-tags
106
5

10

DØ, 9.7 fb-1

Data

(a)

VV
Top
V+hf

104

V+lf
Multijet

103

Signal (× 20)
MH=125 GeV

102
10
1
-1

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1

Events / 0.08

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V(→lν)+3 jets, two tight b-tags
106
5

10

DØ, 9.7 fb-1

Data

(b)

VV
Top
V+hf

104

V+lf
Multijet

103

Signal (× 20)
MH=125 GeV

102
10
1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure 6.21: Distributions of the final discriminant output, after the maximum likelihood fit
(described in Ch. ), in events with exactly three jets and: (a) two medium b-tags, and (b)
two tight b-tags. The MH = 125 GeV signal is multiplied by 20 [2].
104

uncertainties that affect only the rate of a signal or background process, and/or uncertainties
that affect the shape of our MVA output distribution.
Uncertainties that affect only the rates of given processes:
• Theoretical uncertainties on the production cross sections times branching ratios of
¯
background processes: tt and single top quark production (7% [46, 47]), diboson production (6% [48]), V + lf production (6%), and V + hf production (20%, estimated
from mcfm [49, 50]).
• The parton distribution functions (PDF) used in MC generation affects signal and
background acceptances, so we include a 2% uncertainty to account for this.
• Since the V +jets experimental scaling factor for the three-jet channel is different from
unity, we apply an additional systematic uncertainty on the V +jets samples that is
uncorrelated across jet multiplicity and lepton flavour bins.
• Since there is some uncertainty in the measurement of the luminosity, we include an
uncertainty on the total integrated luminosity of 6.1% [51], which affects the expected
rates of signal and background processes.
• We include a 3% uncertainty on the efficiency of muon and electron identification, and
a 2% uncertainty on the efficiency of jet identification.
• We apply an uncertainty on our estimate of the multijet rate of 15% for electrons and
20% for muons. Since the multijet sample is statistically limited, the uncertainty on
the rate is determined by the number of events that end up in our final MVA in each jet
multiplicity and b-tag category. This is not correlated across b-tag categories, and thus
this uncertainty is uncorrelated across lepton, jet multiplicity, and b-tag categories.
105

Since we fit the multijet and V+jet background rates to data simultaneously, we include
an uncertainty on the V+jets rate that is anti-correlated with the multijet rate.
Uncertainties that affect the shape of our final MVA output include:
• The uncertainty on the jet taggability (∼ 3% per jet) comes from the difference between
the taggability scale factors being derived with one jet and being derived with two jets.
These scale factors should not depend on jet multiplicity, so the uncertainty is taken
to be large enough to cover this difference.
• The uncertainty on the b-tag efficiency is correlated between b- and c-jets, and not
correlated between light and heavy jets, so we include uncertainties on the b-tagging
efficiency by varying the heavy flavour tag rate functions up and down by one standard
deviation in samples containing heavy quark jets, and we vary the light quark tag rate
functions up and down by one standard deviation in samples devoid of heavy quark
jets. The size of these uncertainties is ∼ 2 − 3% per heavy quark jet, and ∼ 10% for
light quark jets.
• The trigger uncertainty in the muon channel is calculated as the difference between
applying a trigger correction calculated using the alpgen reweightings derived on the
TµOR trigger sample and applying the nominal trigger correction.
• The uncertainty on the jet energy scale is taken by shifting the JES parameters up and
down by one standard deviation.
• Similarly, the uncertainty on the jet energy resolution is taken by shifting the JSSR
parameters up and down by one standard deviation.

106

• We also include uncertainties on the alpgen MC generation from the MLM matching [29] applied to V +light-flavour events (≈ 0.5%), the alpgen renormalization and
factorization scales.
• Since we reweight our alpgen samples, we include separate uncertainties on each of
the five functions used to apply the reweighting. The adjusted functions are calculated
by shifting the parameter responsible for the largest shape variation of the fit by ±1
s.d. then calculating the remaining parameters for the function using the covariance
matrix obtained from the functional fit.
• The uncertainty on the shape of our multijet estimate is determined by relaxing the
ℓν
ℓν
requirement from Sec. 6.4 on MT to MT > 30 GeV − 0.5 × ET and repeating the

analysis with this selection in place. The positive and negative variations are taken to
be symmetric. As with the uncertainty on the multijet rate, we do not correlate the
multijet shape uncertainty across lepton, jet multiplicity, and b-tag categories.

6.8

Diboson (V Z) Production With Z → b¯
b

Since the SM processes V Z → V bb have the same final state as the Higgs boson signature in
this search, and also have a cross section small compared to the other background processes
(although still approximately 20 times larger than the W H production cross section), it is
a good candidate to use as a validation of our search methodology. The only change to
the analysis when performing this validation is to train the final MVA discriminant using
the W Z and ZZ processes in place of the Higgs boson as signal. Using the output of this
discriminant, we measure the the combined W Z and ZZ cross section by performing a
maximum likelihood fit to data as described in Ch. . We also perform the cross section
107

measurement using the dijet mass distribution, to verify the MVA procedure. The expected
significance of the measurement using the dijet mass distribution is 1.4 s.d. We measure a
cross section of 1.04 ± 0.39 (stat.) ± 0.28 (syst.) times the SM cross section of 4.4 ± 0.3 pb.
The expected significance of the measurement using the MVA output is 1.8 s.d., and we
measure a cross section of 0.50 ± 0.34 (stat.) ± 0.36 (syst.) times the expected SM cross
section. The dijet mass and MVA measurements are both consistent with each other, which
suggests that the MVA methodology is sound. Both values are also consistent with the
SM value, thus we have additional trust in our full analysis strategy when it is extended to
the Higgs boson search. Figures 6.22 and 6.23 shows the dijet mass and MVA discriminant
output for diboson events (W Z + ZZ) after subtracting the background from the data with
the V Z signal scaled to the best fit value. The MVA output distribution has been rebinned
as a function of log(S/B). We see that the background-subtracted-data agrees well with our
V Z prediction in both the MVA and dijet mass distributions.

6.9

Upper Limits on Higgs Boson Production

Once we have some distribution that distinguishes the signal from our expected background,
as we do for the MVAs described earlier, we want to be able to make some statistical
statement about our data (ie, we want to know how much our data resembles a model that
contains our signal). Since we do not see a significant excess in our data over our background
expectation, we set an upper limit on the W H production cross section at a confidence level
of 95% using the LLR as a test statistic as described in Ch. .
Typically in Higgs boson searches, the LLR is presented by displaying the LLR for each
of the two hypotheses and the data LLR value as a function of Higgs boson mass. The LLR

108

Events

200

DØ, 9.7 fb-1

150

Data-Background
VZ
±1 s.d. on Background

100
50
0
-50

-100

0

50 100 150 200 250 300 350 400

Dijet Mass (GeV)
Figure 6.22: The dijet mass shown for the expected diboson signal and backgroundsubtracted data after the maximum likelihood fit, summed over b-tag channels. The error
bars on data points represent the statistical uncertainty only. The post-fit systematic uncertainties are represented by the solid lines. The signal expectation is shown scaled to the
best fit value [2].

109

DØ, 9.7 fb-1

Data-background
VZ
±1 s.d. on background
20
10
0
-10
-20
-30

Events

Events

800
600
400
200
0
-200
-400
-600
-800

-1.45 -1.35 -1.25 -1.15 -1.05

log 10 (s/b)

-2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2

-1

log (s/b)
10

Figure 6.23: The final MVA discriminant output shown for the expected diboson signal
and background-subtracted data rebinned as a function of log(S/B), after the maximum
likelihood fit, summed over b-tag channels. The error bars on data points represent the
statistical uncertainty only. The post-fit systematic uncertainties are represented by the
solid lines. The signal expectation is shown scaled to the best fit value. The inset gives an
expanded view of the high log(S/B) region [2].

110

for the W H → ℓνb¯ search is shown in Fig. 6.24. We see that for a Higgs boson with a mass
b
less than 115 GeV, our observed LLR agrees more with the background-only prediction,
while for MH > 115 GeV, the LLR agrees with the signal+background prediction.

LLR

V( → lν)+2, 3 jets with 1 tight+2 b-tags
-1
LLRB ± 2 s.d
8 DØ, 9.7 fb
LLRB ± 1 s.d
LLRB
LLRS+B
LLROBS

6

4
2
0
-2
-4
90

100

110

120

130

140

150

MH (GeV)
Figure 6.24: The log likelihood ratio as a function of Higgs boson mass for the expected
background only hypothesis (dashed black line), expected signal+background hypothesis (red
dashed line), and data (solid black line). The green and yellow bands represent, respectively,
± one and two standard deviations on the background only hypothesis [2].
We calculate the 95% confidence level (α = 0.05), and present the upper limit on Higgs
boson production cross section times branching ratio for each Higgs boson mass point considered as a ratio to the SM Higgs boson production cross section times branching ratio for
the W H → ℓνb¯ search in Fig. 6.25 and Table 6.10. For a Higgs with MH = 125 GeV, we
b
set an observed (expected) limit of 4.8 (4.7) times the standard model cross section.

111

95% CL Limit / SM

V( → lν)+2, 3 jets with 1 tight+2 b-tags
10 DØ, 9.7 fb -1
Observed
3

Expected
Expected ± 1 s.d
Expected ± 2 s.d

102
10
1
90

Standard Model = 1.0

100

110

120

130

140

150

MH (GeV)
Figure 6.25: The upper 95% confidence level limit on the Higgs boson production cross
section times branching ratio as a ratio to the SM cross section times branching ratio. The
dashed line shows the expected limit, the solid line shows the limit observed in data, and the
green and yellow bands show the ± 1 and 2 standard deviations on the expected limit [2].

112

Table 6.10: The expected and observed 95% C.L. limits, as a function of the Higgs boson
mass MH , presented as ratios of production cross section times branching fraction to the
SM prediction [2].
MH (GeV) 90 95 100 105 110 115 120 125 130 135 140 145 150
Expected 1.8 1.9 2.2 2.5 2.9 3.4 3.8 4.7 5.8 7.9 11.1 16.7 20.8
Observed 1.6 1.3 2.2 2.0 2.1 2.9 3.4 4.8 6.6 10.1 13.6 18.8 18.5

6.10

D0 and Tevatron Higgs Boson Searches

While do not see a significant excess in data over the background only prediction in the
W H → ℓνb¯ search on its own, we combine all Higgs boson searches at D0, and also combine
b
the D0 results with those from CDF, to improve our statistical power. We combine all
searches for Higgs boson decaying to b¯ (which includes the search described in detail in this
b
thesis), W + W − , τ + τ − , and γγ. The LLR and cross section limits can be seen for the D0
Higgs boson combination, and for the full Tevatron (D0+CDF) Higgs boson combination
in Fig. 6.27. When we add together multiple channels which each see a small excess in
the data above the background prediction, we see a larger excess from MH ∼ 115 GeV to
MH ∼ 145 GeV.
We can quantify the excess we see in our data by asking what the probability is that our
background would fluctuate up to result in the data we observe. That is we can calculate the
background p-value. Figure 6.28 shows the p-values for the D0 and Tevatron Higgs boson
combinations as a function of Higgs boson mass. The p-value for the full Tevatron combination for MH = 125 GeV corresponds to a 3 standard deviation significance. Additionally, we
can measure the cross section time branching ratio for H → b¯ The full Tevatron H → b¯
b.
b
+0.69
combination results in a cross section of 1.59−0.72 times the SM cross section.

113

Log-Likelihood Ratio

LLRb ±1 s.d.

20

DØ, Lint ≤ 9.7 fb-1

LLRb ±2 s.d.

SM Higgs Combination

LLRb
LLRs+b

15

LLRObs
LLRM =125 GeV
H

10
5
0
-5

Log-Likelihood Ratio

100

120

140

160

180
200
MH (GeV)

LLRb ± 1 s.d.

30

Tevatron Run II, Lint ≤ 10 fb-1

LLRb ± 2 s.d.

SM Higgs Combination

LLRb
LLRs+b

20

LLRObs
LLRm =125 GeV/c2
H

10
0
-10
100

120

140

160

180
200
mH(GeV/c2)

Figure 6.26: The LLR for the combined D0 Higgs boson searches (top) and the combined
Tevatron Higgs searches (bottom), showing the background only expectation (the black
dashed line), the signal+background expectation (red dashed line), the observed data (black
solid line), and the background plus a 125 GeV Higgs boson signal (blue dashed line). The
green and yellow bands are the ± 1 and 2 standard deviation on the background only
expectation [7, 8].
114

95% CL Limit on σH / σSM

DØ, Lint ≤ 9.7 fb-1

Observed

SM Higgs Combination

Expected w/o Higgs
Expected w/M =125 GeV

10

H

Expected ±1 s.d.
Expected ±2 s.d.

1
DØ Exclusion
100

120

140

160

180

200

95% C.L. Limit/SM

MH (GeV)
10

Observed
Tevatron Run II, Lint ≤ 10 fb-1
Expected w/o Higgs
SM Higgs combination
Expected ± 1 s.d.
Expected ± 2 s.d.
Expected if mH=125 GeV/c2

1

SM=1

100

120

140

160

180
200
2
mH (GeV/c )

Figure 6.27: The 95% C.L. limit as a function of Higgs boson mass for the combined D0 Higgs
boson searches (top) and the combined Tevatron Higgs boson searches (bottom), shown as
a ratio the the SM cross section. The black dashed line shows the expected limit, the solid
black line shows the observed limit, the blue dashed line shows the limit expected if a Higgs
boson with a mass of 125 GeV were present. The green and yellow bands are the ± 1
and 2 standard deviation on the expectation. Regions where the observed limit is below 1
(90 < MH < 101, 157 < MH < 178 GeV (D0), and 90 < MH < 108, 150 < MH < 182 GeV
(Tevatron)), are regions of MH space that are excluded at the 95% confidence level [7, 8].
115

Background p-value

DØ, Lint ≤ 9.7 fb-1
10

1-CLb Observed
1-CLb Expected

SM Higgs Combination

1-CLb MH =125 GeV
Expected ±1 s.d.
Expected ±2 s.d.

1

1σ

10-1

2σ
-2

10

3σ

10-3
100

120

140

160

180

200

Background p-value

MH (GeV)
103

Tevatron Run II, Lint ≤ 10 fb-1

102

SM Higgs Combination

Observed
Expected w/ Higgs
Expected ± 1 s.d.

σH × 1.0 (m =125 GeV/c )
H
σH × 1.5 (m =125 GeV/c 2)
2

10

Expected ± 2 s.d.

H

1

1σ

10-1

2σ

-2

10

3σ

10-3
10-4

4σ

-5

10

100

120

140

160

180

200

mH (GeV/c2)
Figure 6.28: The probability for the background to fluctuate to the observed rate in data as
a function of Higgs boson mass for the D0 combination (left) and the Tevatron combination
(right). The black dashed line shows the expectation, the solid black line shows the observed
data, the blue dashed line shows the expectation for a Higgs boson with MH = 125 GeV.
The green and yellow bands enclose the ± 1 and 2 s.d. fluctuations of the background [7, 8].
116

6.11

Future Studies of the Higgs Boson

Now that the Higgs boson has been discovered, the next steps are to measure its properties
with high precision to determine if it really is the Higgs boson described in the standard
model. In addition to measuring the mass of the Higgs boson, it is important to measure
the strength with which the Higgs boson couples to all the different particles. Both the
LHC experiments and the Tevatron experiments have measured the coupling strength of the
Higgs to bosons and fermions [8, 52, 53], however, the precision of these measurements still
allows for many non-SM scenarios. Additionally, the Higgs boson in the standard model is
expected to have a spin of 0 and positive parity. So far results from ATLAS, CMS, and
D0 suggest that this is true, when comparing the standard model Higgs bosons to specific
alternative models [54, 55, 56, 57]. Future measurements of the Higgs boson properties will
improve our understanding of whether we are looking at the Higgs boson predicted by the
standard model, or if we are looking at a Higgs boson that is merely similar to the standard
model Higgs boson.

117

Chapter 7
Improvements to Jet Energy
Resolution
In searches for H → b¯ the variable that best discriminates between signal and background
b,
is the dijet invariant mass. The resolution of the dijet mass depends on the resolution with
which we can measure the energy of jets1 , and therefore an improvement to the jet energy
resolution would improve the dijet mass resolution. This improvement would increase the
sensitivity to the Higgs boson search discussed in this thesis. The resolution for the jet
energy, σ(E), as measured by the calorimeter is:

σ(E)
b
a
= √ ⊕ ⊕ c.
E
E E

(7.1)

√
The a/ E term is the stochastic response. It comes from fluctuations in shower development
within the calorimeter, which are due to individual jet fragmentation and fluctuations of
individual particles inside the jet shower. This is the dominant term for the jet energy
resolution over most of the range of jet energies used in physics analyses. The b/E term
describes the noise of the calorimeter measurement and is due to instrumental effects such
as electronic noise and the effects of multiple interactions. For low energy jets, this becomes
1 The dijet mass resolution is defined as the width of the resonant peak of the dijet mass

distribution. The energy resolution for individual jets is defined in Eq. 7.1.

118

the limiting factor in the resolution of the calorimeter. The constant term, c, describes errors
in calibration, non-uniformities in the calorimeter response, dead material, etc. This is the
limiting factors for high jet energies.
The tracking system can measure the momenta of individual charged particles that are
within a jet. At low energies, the tracking system provides a more precise momentum
measurement than the energy measurement of the calorimeter. If we use the track momentum
measurement instead of the calorimeter energy measurement for charged particles within a
jet, we can improve the jet energy measurement. From here forward in this text, jets that
use both the tracking system and the calorimeter to measure the jet energy will be called
“track-cal jets”, and jets that rely only on the calorimeter for the energy measurement will
be called “calorimeter jets”.

7.1

Track-Cal Jet Algorithm

The general idea behind track-cal jets is to replace the energy measurement from the
calorimeter for a charged particle with the momentum measurement from the tracking system, which has a better resolution. This is done by starting with the nominal calorimeter jet
energy measurement, then for each charged track in the jet we add in the momentum from
the track, and (to avoid double counting energy) subtract out the energy in the calorimeter
that is associated with the particle that made the track. We define the track-cal jet energy
as:
calo
Etrack−cal = Eraw +
tracks

∆R=0.15 ,
Ptrack − Etrack

(7.2)

calo
where Eraw is the nominal calorimeter jet energy, Ptrack is the track momentum, and
∆R=0.15 is the energy deposited in a cone of ∆R = 0.15 (where ∆R =
Etrack

119

∆η 2 + ∆φ2 )

around the charged track2 . The cone size used when subtracting the calorimeter energy near
the track was chosen based on studying single pion MC events. The cone size was chosen
to be large enough so that most of the energy from the track would be included, but small
enough to keep energy not coming from the track minimal. We found that a cone size of
∆R = 0.15 contained 90% of the track energy for single pion events on average, as can be
seen in Fig. 7.1.

Figure 7.1: The fraction of energy deposited in various cones around a single pion track for
a pion energy of 10 GeV. 90% of the energy is contained within a cone of ∆R = 0.15.

We want to make sure that the tracks we are considering for this calculation are coming
from real tracks (and not misreconstructed tracks) with a high resolution. To suppress tracks
arising from spurious signatures, we require that the the track mis-identification likelihood
2 Note that because the energy of the particles is much larger than the mass of the particles,

we can use energy and momentum interchangeably.

120

be larger than zero. To ensure that we select high resolution tracks, we require that the
track’s z position is within 0.5 cm of the PV, that the distance of closest approach of the
track in the radial direction is less than 0.05 cm, and that the significance of curvature of
the track (the ratio of the track pT to the resolution of the track pT ) is greater than 5.
In addition to selecting well measured tracks, we also need to carefully consider the
calorimeter energy we subtract from around the track. Of particular concern is the possibility
of having neutral particles overlapping with the track. If this happens, simply subtracting all
energy within the ∆R = 0.15 cone around the track is not correct, as we would be subtracting
energy that isn’t associated with the charged particle track. This is the limiting factor of the
track-cal jet correction, as it is impossible to tell how much of the energy deposited in the
calorimeter is coming from a charged particle vs a neutral one. The most practical solution
is to only modify the energy with the track momentum if we don’t think there is significant
energy from neutral particles deposited within the ∆R = 0.15 cone around the track. To
determine if there is significant energy coming from neutral particles, we first study single
pion events, where we have a jet containing a single charged track. Using these events, we
consider:
FSP =

∆R=0.15 − P
Etrack
track ∗ R(Ptrack )
,
Ptrack

(7.3)

where R(Ptrack ) is the average calorimeter response for a single pion, which depends on the
track momentum, and location of the pion in the detector. FSP should be zero if we are
replacing the calorimeter energy by the track momentum correctly on average. Therefore,
for a single charged track, we expect FSP to peak at zero, with a non-zero width due to
fluctuations in the jet formation and calorimeter energy measurement. If FSP is large and
negative, we consider that a sign that we misidentified a charged track. In this case we do not

121

want to apply the track-cal jet correction, as we would be overestimating the charged track
momentum. If FSP is large and positive, that is an indication that we are overestimating the
calorimeter energy associated with a charged track. We consider this a sign that there are
neutral particles depositing energy in the calorimeter near the charged particle track. We
calculate FSP in bins of Ptrack and jet η, and calculate the width of FSP , σF (Ptrack , ηrmjet ),
to use as a metric to determine if there is significant energy from neutral particles deposited
near the charged track. Then for each track within a jet we calculate:

|ftrack | =

∆R=0.15 − P
[Etrack
track ∗ R(Ptrack )]
< 2σF .
Ptrack

(7.4)

If |ftrack | < 2σF , the energy replacement is performed. Otherwise the energy replacement
is not performed (ie, the calorimeter energy measurement is used instead of the tracking
momentum measurement). Examples of FSP and ftrack are shown in Fig. 7.2 with vertical
lines indicating 2σF . This track-cal jet algorithm doesn’t perform well for jets with large
|η|, as the tracking resolution gets worse in this region, so we only apply this algorithm to
jets with |η| < 1.6.
We can also gain in the energy resolution by adding in the energy from the CPS detector,
multiplied by a calibration factor, kCPS , where kCPS was chosen to minimize the energy
resolution. This corrects for energy lost in dead material before the calorimeter (the solenoid,
cables, etc.). We found that adding kCPS × ECPS to the track-cal jet energy improved the
energy resolution when the jet |η| < 1.2, however, for 1.2 < |η| < 1.6, we found that
correcting the calorimeter energy by adding kCPS × ECPS to the calorimeter energy instead
of the track-cal energy resulted in a better jet energy resolution. Figures 7.3 and 7.4 show
the resolution as a function of kCPS for the different jet η regions. The full energy correction,

122

∆R=0.15 − P
Figure 7.2: [Etrack
track ∗ R(Ptrack )]/Ptrack for (a) 5 GeV simulated single charged
pion tracks, and (b) tracks within a jet with 4.5 < Ptrack < 5 GeV using simulated γ+jet
events. The vertical lines indicate twice the width of the charged pion distribution (σF ).

123

with optimal values of kCPS , is given by:

calo
Etrack−cal = Eraw +

∆R=0.15 + 18 ∗ E
CPS , if |ηjet | < 1.2,
tracks Ptrack − Etrack

(7.5)

Etrack−cal

calo
= Eraw + 13 ∗ ECPS , if 1.2 < |ηjet | < 1.6,

(7.6)

Etrack−cal

calo
= Eraw , if |ηjet | > 1.6.

(7.7)

7.2

Energy Resolution Improvement

Because the track-cal jets algorithm acts as a jet energy correction, the calorimeter response
used in the JES is not necessarily the same for track-cal jets as it is for calorimeter jets
as discussed in Ch. 3.5. Therefore, a response function was derived for track-cal jets using
photon+jet MC, by taking the ratio of the track-cal jet pT to the true MC pT in bins of the
true MC particle pT , number of tracks in the jet, and jet η. An example of this distribution
can be seen in Fig. 7.5 for jets with 30 < pT < 40 GeV and |η| < 0.4. The mean of these
distributions is then plotted as a function of MC particle pT in bins of the number of tracks,
and jet η, and fit with logarithmic functions.
These response functions are applied back to the photon+jet MC, and again the ratio of
the track-cal jet pT to the true MC pT is considered, with the RMS of these distributions
being the resolution. The response functions are shown in Fig. 7.6 and 7.7, and the resolution
is shown in Fig. 7.8 and 7.9. The jet energy resolution with track-cal jets is 20% better than
for calorimeter jets on average. For a typical jet from H → b¯ events with pT = 45 GeV and
b
|η| < 1.2, the improvement in the jet energy resolution is 25%.

124

σ(E)/E

0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15

DO Preliminary
(a)

CPS+Track-cal
Track-cal
CPS+Calorimeter
Calorimeter

5

10

15

20

25

σ(E)/E

kcps
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15

CPS+Track-cal

DO Preliminary

Track-cal

(b)

CPS+Calorimeter
Calorimeter

5

10

15

20

25

kcps
Figure 7.3: The resolution for the track-cal jet energy + kCPS in the blue circles and calorimeter jet energy + kCPS in the red crosses as a function of kCPS , for a) |ηjet | < 0.4, and b)
0.4 < |ηjet | < 0.8. The pink solid and green dashed lines show the track-cal jet energy and
calorimeter jet energy resolutions respectively for kcps = 0.

125

σ(E)/E

0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17

DO Preliminary
(a)

CPS+Track-cal
Track-cal
CPS+Calorimeter
Calorimeter

5

10

15

20

25

σ(E)/E

kcps
0.24
0.23
0.22
0.21
0.2
0.19
0.18

DO Preliminary
(b)

CPS+Track-cal
Track-cal
CPS+Calorimeter
Calorimeter

5

10

15

20

25

kcps
Figure 7.4: The resolution for the track-cal jet energy + kCPS in the blue circles and calorimeter jet energy + kCPS in the red crosses as a function of kCPS , for a) 0.8 < |ηjet | < 1.2, and
b) 1.2 < |ηjet | < 1.6. The pink solid and green dashed lines show the track-cal jet energy
and calorimeter jet energy resolutions respectively for kcps = 0.

126

Events

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

Calorimeter Jets
Track-Cal Jets

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

reconstructed pT/true pT
Figure 7.5: The ratio of the reconstructed jet pT to the true MC jet pT for jets with
30 < pT < 40 GeV, and |η| < 0.4, for track-cal jets (in red) and calorimeter jets (in black).
The mean of this distribution is taken as the calorimeter response.

127

Jet Energy Response

2

DØ Preliminary

(a)

1.8

Calorimeter
Track-cal, N tracks: 1

1.6

Track-cal, N tracks: 2

1.4

Track-cal, N tracks: 3

1.2

Track-cal, N tracks: 4

Track-cal, N tracks: 5
Track-cal, N tracks: 6
Track-cal, N tracks: 7
Track-cal, N tracks: 8
Track-cal, N tracks: 9
Track-cal, N tracks: >=10

1
0.8
0.6

20 40 60 80 100 120 140 160 180

Jet Energy Response

Jet pT (GeV)
2
1.8
1.6

DØ Preliminary

(b)
Calorimeter
Track-cal, N tracks: 1
Track-cal, N tracks: 2

1.4

Track-cal, N tracks: 3

1.2

Track-cal, N tracks: 4

Track-cal, N tracks: 5
Track-cal, N tracks: 6
Track-cal, N tracks: 7
Track-cal, N tracks: 8
Track-cal, N tracks: 9
Track-cal, N tracks: >=10

1
0.8
0.6
20

40

60

80 100 120 140 160

Jet pT (GeV)
Figure 7.6: The energy response for track-cal jets as a function of true MC pT for various
track multiplicities for a) |ηjet | < 0.4, and b) 0.4 < |ηjet | < 0.8. The response for calorimeter
jets is also shown for comparison.
128

Jet Energy Response

2
1.8
1.6

DØ Preliminary

(a)
Calorimeter
Track-cal, N tracks: 1
Track-cal, N tracks: 2

1.4

Track-cal, N tracks: 3

1.2

Track-cal, N tracks: 4

Track-cal, N tracks: 5
Track-cal, N tracks: 6
Track-cal, N tracks: 7
Track-cal, N tracks: 8
Track-cal, N tracks: 9
Track-cal, N tracks: >=10

1
0.8
0.6
20

40

60

80 100 120 140 160

Jet Energy Response

Jet pT (GeV)
2
1.8

DØ Preliminary

(b)

Calorimeter Jets

1.6

Track-cal Jets

1.4
1.2
1
0.8
0.6
20

40

60

80 100 120 140 160

Jet pT (GeV)
Figure 7.7: The energy response for track-cal jets as a function of true MC pT for various
track multiplicities for a) 0.8 < |ηjet | < 1.2, and b) 1.2 < |ηjet | < 1.6. The response for
calorimeter jets is also shown for comparison.
129

Energy Resolution

0.22
0.18
0.14
0.1
0.06
0.02

Ratio

1.2
1.1
1
0.9
0.8
0.7
0.6

(a) DØ Preliminary

Track-cal Jets
Calorimeter Jets

20

20

40

60

40

80

60

100

80

120

100

140

160

Jet pT (GeV)

120

Jet p (GeV)

Energy Resolution

0.22
0.18
0.14
0.1
0.06
0.02

Ratio

T

1.2
1.1
1
0.9
0.8
0.7
0.6

(b) DØ Preliminary

Track-cal Jets
Calorimeter Jets

20

20

40

40

60

80

60

100

80

120

100

140

160

Jet pT (GeV)

120

Jet p (GeV)
T

Figure 7.8: The energy resolution for track-cal jets as a function of true MC pT compared to
the resolution for calorimeter jets for a) |ηjet | < 0.4, and b) 0.4 < |ηjet | < 0.8. The bottom
panels show the ratio of the track-cal jet resolution to the calorimeter jet resolution.
130

Energy Resolution

0.25

Ratio

1.2
1.1
1
0.9
0.8
0.7
0.6

(a)

0.2
0.15

Track-cal Jets

DØ Preliminary

Calorimeter Jets

0.1
0.05
0

20

20

40

60

40

80

60

100

80

120

100

140

160

Jet pT (GeV)

120

Jet p (GeV)

Energy Resolution

0.22
0.18
0.14
0.1
0.06
0.02

Ratio

T

1.2
1.1
1
0.9
0.8
0.7
0.6

(b) DØ Preliminary

Track-cal Jets
Calorimeter Jets

20

20

40

40

60

80

60

100

80

120

100

140

160

Jet pT (GeV)

120

Jet p (GeV)
T

Figure 7.9: The energy resolution for track-cal jets as a function of true MC pT compared
to the resolution for calorimeter jets for a) 0.8 < |ηjet | < 1.2, and b) 1.2 < |ηjet | < 1.6. The
bottom panels show the ratio of the track-cal jet resolution to the calorimeter jet resolution.
131

7.3

Improvement in Higgs Boson Analysis

The track-cal jets correction is tested with the W H → ℓνb¯ search, described in the preceding
b
Chapter, to determine the impact on a resonant dijet signal and non resonant background
processes. The full analysis is repeated using track-cal jets instead of calorimeter jets. Figures 7.10 to 7.12 show kinematic distributions after our full selection with track-cal jets in
place of calorimeter jets. The reconstructed dijet mass is shown in Figs. 7.13 and 7.14 for the
four different b-tag categories. From these plots, we can see that our background prediction
matches our data well, when using track-cal jets instead of calorimeter jets. Figure 7.16
shows the dijet mass for calorimeter jets and track-cal jets overlayed for the signal and the
sum of backgrounds. The signal dijet mass peak for track-cal jets is ∼ 7% narrower than for
calorimeter jets.
We can also look at the improvement in events with jets originating from light quarks,
by considering diboson production, in events with zero b-tags. Figure 7.16 shows the dijet
mass for W W → ℓνq q events with zero b-tags, and Fig. 7.17 shows the dijet mass for V Z
¯
production in events with zero b-tags with the background subtracted from the data. The
reconstructed vector boson mass peak is ∼ 7% narrower when using track-cal jets compared
to using calorimeter jets.
To quantify the improvement to the W H → ℓνb¯ analysis, we look at the expected 95 %
b
C.L. upper limit on the Higgs boson production cross section, with and without the track-cal
jet correction. Figure 7.18 shows the expected limit as a ratio to the SM cross section with
and without using the track-cal jets as well as the ratio of using the track-cal jets to using
the calorimeter jets. We find that the expected limit improves by ∼ 5% when using track-cal
jets for MH = 125 GeV. In Fig. 7.15, we can see that there is a larger fraction of background

132

Events / 3.00 GeV

V(→lν)+2 jets, pretag
80000 DØ Preliminary, 9.7 fb -1 (a)
Data
70000
60000

VV
Top

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

20000

MH=125 GeV

10000
0

0

20

40

60

80

100 120

Events / 2.62 GeV

MW [GeV]
T
V(→lν)+2 jets, pretag
DØ Preliminary, 9.7 fb -1 (b)
30000
Data
25000

VV
Top

20000

V+hf

15000

V+lf
Multijet
Signal (× 1000)

10000

MH=125 GeV

5000
0

20

40

60

80

100

120

Lepton pT [GeV]
Figure 7.10: Distributions for all selected events with two jets of (a) transverse mass of the
lepton-ET system, and (b) charged lepton pT . The MH = 125 GeV signal is multiplied by
1000. Overflow events are added to the last bin.
133

Events / 4.06 GeV

V(→lν)+2 jets, pretag
DØ Preliminary, 9.7 fb -1 (a)
50000
Data
VV
Top

40000

V+hf

30000

V+lf
Multijet

20000

Signal (× 1000)
MH=125 GeV

10000
0
20

40

60

80 100 120 140

Leading jet p [GeV]
Events / 1.88 GeV

T

V(→lν)+2 jets, pretag
70000 DØ Preliminary, 9.7 fb -1 (b)
Data

60000

VV
Top

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

20000

MH=125 GeV

10000
0
20

30
nd

2

40

50

60

70

80

Leading jet p [GeV]
T

Figure 7.11: Distributions for all selected events with two jets of (a) leading jet pT , and (b)
second-leading jet pT . The MH = 125 GeV signal is multiplied by 1000. Overflow events
are added to the last bin.
134

Events / 2.12 GeV

V(→lν)+2 jets, pretag
DØ Preliminary, 9.7 fb -1 (a)
Data
25000
20000

VV
Top
V+hf

15000

V+lf
Multijet

10000

Signal (× 1000)

5000
0

MH=125 GeV

20 30 40 50 60 70 80 90 100

Events / 0.14

ET [GeV]
V(→lν)+2 jets, pretag
90000
DØ Preliminary, 9.7 fb -1 (b)
80000
Data
70000
60000
50000

VV
Top
V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

20000

MH=125 GeV

10000
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

∆ R (j , j )
1 2

Figure 7.12: Distributions for all selected events with two jets of (a) ET , and (b) ∆R
between the leading and second-leading jets. The MH = 125 GeV signal is multiplied by
1000. Overflow events are added to the last bin.
135

Events / 20.00 GeV

V(→lν)+2 jets, one tight b-tag
6000 DØ Preliminary, 9.7 fb -1
(a)

5000

Data
VV
Top

4000

V+hf

3000

V+lf
Multijet

2000

Signal (× 200)
MH=125 GeV

1000
0

0

50 100 150 200 250 300 350 400

Events / 20.00 GeV

Dijet mass [GeV]
V(→lν)+2 jets, two loose b-tags
1400
DØ Preliminary, 9.7 fb -1
Data
1200 (b)
VV
Top

1000
800

V+hf

600

V+lf
Multijet
Signal (× 200)

400

MH=125 GeV

200
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]
Figure 7.13: Invariant mass of the leading and second-leading jets in events with two jets
and (a) one tight b-tag, and (b) two loose b-tags. The MH = 125 GeV signal is multiplied
by 200. Overflow events are added to the last bin.
136

Events / 20.00 GeV

V(→lν)+2 jets, two medium b-tags
DØ Preliminary, 9.7 fb -1
450
Data
(a)
400
VV
350
Top
300
V+hf
250
V+lf
Multijet
200
Signal (× 50)
150
MH=125 GeV
100
50
0
0 50 100 150 200 250 300 350 400

Events / 20.00 GeV

Dijet mass [GeV]
V(→lν)+2 jets, two tight b-tags
-1
350 DØ Preliminary, 9.7 fb
(b)

300

Data
VV
Top

250

V+hf

200

V+lf
Multijet

150

Signal (× 50)

100

MH=125 GeV

50
0

0

50 100 150 200 250 300 350 400

Dijet mass [GeV]
Figure 7.14: Invariant mass of the leading and second-leading jets in events with two jets and
(a) two medium b-tags, and (b) two tight b-tags. The MH = 125 GeV signal is multiplied
by 50. Overflow events are added to the last bin.
137

2 Jets, 2 Tight b-tagged Jets
Track-Cal Jets Signal, M =125 GeV
H
Calorimeter Jets Signal, MH=125 GeV

0.12

Track-Cal Jets Background

0.1

Calorimeter Jets Background

0.08
0.06

Track-Cal Jets Signal:
Mean: 109, Width: 16.4

0.04

Calorimeter Jets Signal:
Mean: 109, Width: 17.6

0.02
0

0

50 100 150 200 250 300 350 400

Dijet Mass (GeV)
Figure 7.15: The dijet mass for track-cal jets (red) and calorimeter jets (black), for the
W H MH = 125 GeV signal (solid lines) and all backgrounds (dashed lines) for events with
exactly two jets and two tight b-tags. All curves are normalized to have unit area. The
mean and width values quoted are determined by fitting the signal dijet mass peak with a
Gaussian distribution. The width of the signal peak is ∼ 7% narrower for track-cal jets than
for calorimeter jets.

138

2 Jets, 0 b-tagged Jets

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

Track-Cal Jets WW
Calorimeter Jets WW

Track-Cal Jets WW:
Mean: 80.6, Width: 12.0
Calorimeter Jets WW:
Mean: 80.5, Width: 12.9

0

50 100 150 200 250 300 350 400

Dijet Mass (GeV)
Figure 7.16: The dijet mass for track-cal jets (red) and calorimeter jets (black), for W W
events with exactly two jets and zero b-tags. The mean and width values quoted are determined by fitting the signal dijet mass peak with a Gaussian distribution. The width of the
dijet mass peak is ∼ 7% narrower for track-cal jets than for calorimeter jets.

139

Events

800

(a)

600
400

DØ Preliminary, 9.7 fb-1
Data-Background
Fitted VZ
±1 s.d. on Background

200
0
-200
-400

0

50 100 150 200 250 300 350 400

Events

Dijet Mass (GeV)
800

(b)

600
400

DØ Preliminary, 9.7 fb-1
Data-Background
Fitted VZ
±1 s.d. on Background

200
0
-200
0

50 100 150 200 250 300 350 400

Dijet Mass (GeV)
Figure 7.17: The dijet mass shown for the expected diboson signal and backgroundsubtracted data rebinned, after the maximum likelihood fit, for events with zero b-tagged
jets (a) using calorimeter jets and (b) using track-cal jets. The error bars on data points represent the statistical uncertainty only. The post-fit systematic uncertainties are represented
by the solid lines. The diboson signal expectation is shown scaled to the best fit value.
140

events under the signal dijet mass peak for track-cal jets than for calorimeter jets. As the
Higgs boson mass increases, the signal dijet mass peak will move to larger values, farther
away from the background peak, resulting in a larger improvement for in the limit for larger
MH .

141

Comparison of Expected limits: WH → lν bb

95% CL Limit/SM

102

Expected Limit, Track-cal Jets
Expected Limit, Calorimeter Jets
Calorimeter Jets Expected ± 1σ
Calorimeter Jets Expected ± 2σ

10

1
100

110

120

130

140

150

MH [GeV]
Imrpovement (%)

Percent Improvement

11
10
9
8
7
6
5
4
3
2
1
100

110

120

130

140

150

MH [GeV]
Figure 7.18: The 95 % C.L. expected Higgs boson production cross section limit (top),
presented as a ratio to the SM cross section, for track-cal jets (black dashed line), and
calorimeter jets (black solid line). The green and grey shaded areas represent the ±1 and 2
standard deviations on the calorimeter jet expectation. The ratio of the expected 95% C.L.
limit for track-cal jets to calorimeter jets (bottom).
142

Chapter 8
Conclusion
I presented in this thesis the search for a Higgs boson produced in association with a W
boson where the W boson decays to a lepton and neutrino and the Higgs boson decays to a
pair of bottom quarks. Events were selected to match the W H → ℓνb¯ final state topology,
b
and sorted into categories based on the number and quality of jets coming from b-quarks.
Signal events were separated from background events using a Boosted Decision Tree machine
learning technique. To test the analysis methodology, we performed a measurement of the
V Z → V b¯ cross section, which has the same final state as our Higgs boson signal, and a
b
small cross section relative to our other background processes. By using the dijet invariant
mass, we measure a cross section of 4.6±1.5(stat.)±1.6(syst.) pb, and using the MVA output
we measure a cross section of 2.2±1.5(stat.)±1.6(syst.) pb. These values are consistent with
each other (within their uncertainties), which supports the validity of our MVA approach.
They are also consistent with the SM value of 4.4 ± 0.3 pb, which verifies that, with our
analysis strategy, we can measure processes with a small cross section relative to background
processes. Since the W H → ℓνb¯ search on its own does not see a significant excess in data
b
above the background prediction, we set an 95% C.L. limit on the production cross section
for Higgs boson masses between 90 and 150 GeV in steps of 5 GeV. For MH = 125 GeV we
expect (observe) a limit of 4.7 (4.8) times the SM cross section. This search was included in
the combined Tevatron Higgs boson search which measured an excess of data events with a

143

significance of 3 s.d. above the background only expectation, and a measured cross section
of 1.5 times the SM cross section. The sensitivity to H → b¯ strongly depends on the dijet
b
mass, and the resolution with which we can reconstruct the dijet mass. The dijet mass
resolution depends on the resolution with which we can determine the energy of jets. We
implemented a correction to the jet energy that replaces the calorimeter energy measurement
with the higher resolution tracking momentum measurement for charged particles within a
jet. This improves the accuracy of the jet energy measurement, and improves the energy
resolution by ∼ 20%, and the dijet mass resolution for our Higgs boson signal by ∼ 7%. This
translates to an improvement in our expected cross section limit for W H → ℓνb¯ of ∼ 5%.
b
The next several years of Higgs boson physics will be devoted to measuring its properties
to determine if we have found the standard model Higgs boson, or if we have found a Higgs
boson that simply looks like the standard model Higgs boson. While we can currently
measure many of the Higgs boson’s properties, such as its mass, its spin, and its couplings
to other particles; it will be important to improve the precision of these measurements to
truly understand the nature of this particle.

144

APPENDICES

145

Appendix A Multijet MVA Input
Distributions
Shown below in Figs. A.1 to A.3 are the variables used to train our BDT that discriminates
between signal and multijet events. Figures A.4 to A.6 show the same variables with the
total background and signal normalized to have the same area. The variables are described
in Table 6.8 in the main text.

146

Data

60000

VV
Top

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)

Events / 0.17

Events / 0.15

V(→lν)+2 jets, pretag

-2

-1

0

1

2

V+lf
Multijet

40000

Signal (× 1000)
MH =125 GeV

Data
VV
Top
V+hf
V+lf
Multijet

15000

Signal (× 1000)

0

1

2

3

4

Emiss
T

5

6

7

significance

V(→lν)+2 jets, pretag

Events / 0.05

Events / 0.10

50000

νη

20000

10000

V+hf

0

3

V(→lν)+2 jets, pretag

25000

60000

10000

0
-3

30000

VV
Top

20000

10000

35000

70000

30000

MH =125 GeV

20000

V(→lν)+2 jets, pretag
Data
80000

80
60
40

MH =125 GeV

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 1000)
MH =125 GeV

20
5000
0

0

0 0.5 1 1.5 2 2.5 3 3.5 4

W(→lν) ∆ η(lepton,ν)

0 0.2 0.4 0.6 0.8 1 1.2 1.4

W(→lν) Twist

Figure A.1: Input variables to the multijet BDT shown for all events containing two jets:
(top left) η of the ET , (top right) the ET significance, (bottom left) ∆η(ℓ, ν), and (bottom
right) the twist of the ℓ − ν system. The signal is shown for MH = 125 GeV multiplied by
a factor of 1000. Overflow events are added to the last bin.

147

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 1000)
MH =125 GeV

35000
30000
25000
20000
15000

V(→lν)+2 jets, pretag

Events / 0.14

Events / 0.03

V(→lν)+2 jets, pretag
40000
Data

Data

60000

VV
Top

50000

V+hf

40000

V+lf
Multijet

30000

Signal (× 1000)
MH =125 GeV

20000

10000
10000

5000
0

0

0 0.10.20.30.40.50.6 0.70.80.9 1

W(→lν) CM cosθ

VV
Top

40000

V+hf

30000

V+lf
Multijet
Signal (× 1000)

20000

6

7

8

30000
25000

Data
VV
Top
V+hf

20000

V+lf
Multijet

15000

Signal (× 1000)

10000

MH =125 GeV

10000
0
-0.8 -0.6 -0.4 -0.2 0

5

V(→lν)+2 jets, pretag

Events / 0.02

Events / 0.04

50000

4

Dijet Velocity

V(→lν)+2 jets, pretag
Data

3

MH =125 GeV

5000
0

0.2 0.4 0.6

W-Dijet Mass Assymetry

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

Figure A.2: Input variables to the multijet BDT shown for all events containing two jets:
(top left) cos(θ) in the ℓν center-of-momentum frame, (top right) the velocity of the dijet
system, (bottom left) the mass asymmetry between the dijet and the ℓν system, and (bottom
right) the centrality of the ℓνjj system. The signal is shown for MH = 125 GeV multiplied
by a factor of 1000. Overflow events are added to the last bin.

148

30000

VV
Top

25000

V(→lν)+2 jets, pretag

Events / 0.10

Events / 6.25 GeV

V(→lν)+2 jets, pretag
35000
Data

V+hf

20000

V+lf
Multijet

15000

Signal (× 1000)
MH =125 GeV

10000

35000
30000
25000
20000
15000
10000

5000
0
50

45000
40000

Data
VV
Top
V+hf
V+lf
Multijet
Signal (× 1000)
MH =125 GeV

5000
100

150

200

250

300

0

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

Visible sum pT

Figure A.3: Input variables to the multijet BDT shown for all events containing two jets:
(left) the magnitude of the vector sum of pT for all visible particles, and (right) the maximum
∆η(ℓ, j). The signal is shown for MH = 125 GeV multiplied by a factor of 1000. Overflow
events are added to the last bin.

149

60000

V(→lν)+2 jets, pretag

Events / 0.17

Events / 0.15

V(→lν)+2 jets, pretag
70000
Total Background
Signal

50000

MH =125 GeV

40000
30000

80000

Total Background

70000

Signal

60000

MH =125 GeV

50000
40000
30000

20000

20000

10000

10000
-2

-1

0

1

2

νη

V(→lν)+2 jets, pretag
35000
Total Background
30000
25000

0

3

Signal
MH =125 GeV

20000
15000

0

1

2

3

4

Emiss
T
Events / 0.05

Events / 0.10

0
-3

5

6

7

significance

V(→lν)+2 jets, pretag
40000
Total Background
35000

Signal

30000
25000

MH =125 GeV

20000
15000

10000

10000

5000

5000

0

0

0 0.5 1 1.5 2 2.5 3 3.5 4

W(→lν) ∆ η(lepton,ν)

0 0.2 0.4 0.6 0.8 1 1.2 1.4

W(→lν) Twist

Figure A.4: Input variables to the multijet BDT shown for all events containing two jets:
(top left) η of the ET , (top right) the ET significance, (bottom left) ∆η(ℓ, ν), and (bottom
right) the twist of the ℓ − ν system. The signal is shown for MH = 125 GeV. The signal is
normalized to the sum of the backgrounds. Overflow events are added to the last bin.

150

14000
12000
10000

Signal
MH =125 GeV

8000

V(→lν)+2 jets, pretag

Events / 0.14

Events / 0.03

V(→lν)+2 jets, pretag
16000
Total Background

Total Background

70000
MH =125 GeV

50000
40000

6000

30000

4000

20000

2000

10000

0

0

0 0.10.20.30.40.50.6 0.70.80.9 1

W(→lν) CM cosθ
V(→lν)+2 jets, pretag
70000

Total Background

60000
50000

Signal
MH =125 GeV

40000
30000

3

4

5

6

7

8

Dijet Velocity
V(→lν)+2 jets, pretag

Events / 0.02

Events / 0.04

Signal

60000

25000

Total Background
Signal

20000
MH =125 GeV

15000
10000

20000
5000

10000
0
-0.8 -0.6 -0.4 -0.2 0

0

0.2 0.4 0.6

W-Dijet Mass Assymetry

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

Figure A.5: Input variables to the multijet BDT shown for all events containing two jets:
(top left) cos(θ) in the ℓν center-of-momentum frame, (top right) the velocity of the dijet
system, (bottom left) the mass asymmetry between the dijet and the ℓν system, and (bottom
right) the centrality of the ℓνjj system. The signal is shown for MH = 125 GeV. The signal
is normalized to the sum of the backgrounds. Overflow events are added to the last bin.

151

Events / 0.10

Events / 6.25

V(→lν)+2 jets, pretag
Total Background

30000

Signal

25000

MH =125 GeV

20000
15000
10000
5000
0
50

100

150

200

250

300

V(→lν)+2 jets, pretag
20000
Total Background
18000
Signal
16000
14000
MH =125 GeV
12000
10000
8000
6000
4000
2000
0
0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

Visible sum pT

Figure A.6: Input variables to the multijet BDT shown for all events containing two jets:
(left) the magnitude of the vector sum of pT for all visible particles, and (right) the maximum
∆η(ℓ, j). The signal is shown for MH = 125 GeV. The signal is normalized to the sum of
the backgrounds. Overflow events are added to the last bin.

152

Appendix B Final BDT Input and
Output Distributions
Shown here are the input variables to the BDT trained to distinguish signal from all backgrounds in Figs. B.1 to B.14, and the output BDT distributions that were not included in the
text in Figs. B.15 to B.38. Additionally, the input variables and BDT output distributions
are shown with the signal and sum of backgrounds normalized to the same area in Figs. B.39
to B.84. The BDT input variables are described in Table 6.9 in the main text.

153

Events / 0.20

Events / 0.05

V(→lν)+2 jets, one tight b-tag
Data

12000

VV
Top

10000

V+hf

8000

V+lf
Multijet

6000

Signal (× 200)
MH =125 GeV

4000

5000
4000
3000
2000

0

0.2

0.4

0.6

0.8

0

1

2000

V(→lν)+2 jets, one tight b-tag

Events / 0.12

Events / 0.25

V(→lν)+2 jets, one tight b-tag
Data
5000

3000

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

b-id MVA BL

4000

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1000

2000
0

V(→lν)+2 jets, one tight b-tag
Data
6000

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

6000
5000
4000
3000
2000

1000

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1000

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

0

0 0.20.40.60.8 1 1.21.41.6 1.8 2

Dijet (1,2) Σ min.

Figure B.1: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and one tight b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is multiplied by a factor of
200. Overflow events are added to the last bin.

154

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

5000
4000
3000
2000

Events / 0.28

Events / 0.25

V(→lν)+2 jets, one tight b-tag

V(→lν)+2 jets, one tight b-tag
8000
Data
6000
5000
4000
3000
2000

1000

1000

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

lepton

q

V(→lν)+2 jets, one tight b-tag
4000
Data
VV
Top

3500
3000

V+hf

2500

V+lf
Multijet

2000

Signal (× 200)

1500

3

4

5

6

7

8

Dijet Velocity

1

Events / 0.04

Events / 10.00 GeV

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

7000

V(→lν)+2 jets, one tight b-tag
Data
4000
3500
3000
2500
2000
1500

MH =125 GeV

1000

1000

500

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

500

0
100

140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.2: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and one tight b-tag. The signal is shown for MH = 125 GeV, and is
multiplied by a factor of 200. Overflow events are added to the last bin.

155

V(→lν)+2 jets, one tight b-tag

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

6000
5000
4000
3000
2000

Events / 0.03

Events / 0.07

V(→lν)+2 jets, one tight b-tag

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

14000
12000
10000
8000
6000
4000

1000

2000

0
-0.8 -0.6 -0.4 -0.2 0

0

0.2 0.4 0.6

0

0.1

Events / 3.75 GeV

W-Dijet Mass Assymetry

0.2

0.3

0.4

0.5

Aplanarity

V(→lν)+2 jets, one tight b-tag
6000
Data
5000

VV
Top

4000

V+hf
V+lf
Multijet

3000

Signal (× 200)

2000

MH =125 GeV

1000
0
20
nd

2

30

40

50

60

70

80

Leading jet p (GeV/c)
T

Figure B.3: Input variables to the BDT trained to distinguish signal from all backgrounds in
events with two jets and one tight b-tag: (top left) the mass asymmetry between the ℓν and
dijet systems, (top right) aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 200. Overflow events are added
to the last bin.

156

Events / 0.05

Events / 0.05

V(→lν)+2 jets, two loose b-tags
Data

4000
3500

VV
Top

3000

V+hf

2500

V+lf
Multijet

2000

Signal (× 200)
MH =125 GeV

1500

V(→lν)+2 jets, two loose b-tags
-1
Data
1000 DØ, 9.7 fb
VV
Top

800

V+hf
V+lf
Multijet

600

Signal (× 200)

400

1000

MH =125 GeV

200

500
0

0

0.2

0.4

0.6

0.8

0

1

600
400

0.6

0.8

1

T

V(→lν)+2 jets, two loose b-tags

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

Events / 0.12

Events / 0.25

800

0.4

T

V(→lν)+2 jets, two loose b-tags

1000

0.2

W(→lν) p /W(→lν) sum p

b-id MVA BL
1200

0

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1400
1200
1000
800
600
400

200

200

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

0

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

Figure B.4: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two loose b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is multiplied by a factor of
200. Overflow events are added to the last bin.

157

V(→lν)+2 jets, two loose b-tags

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1200
1000
800
600
400

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two loose b-tags

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1600
1400
1200
1000
800
600
400

200

200

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

lepton

V(→lν)+2 jets, two loose b-tags
900

Data

800

VV
Top

700

V+hf

600
500

V+lf
Multijet

400

Signal (× 200)

300

4

5

6

7

8

Dijet Velocity

1

Events / 0.04

Events / 10.00 GeV

q

3

MH =125 GeV

V(→lν)+2 jets, two loose b-tags
Data
1000
800
600
400

200

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

200

100
0
100

140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.5: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two loose b-tag. The signal is shown for MH = 125 GeV, and is
multiplied by a factor of 200. Overflow events are added to the last bin.

158

V(→lν)+2 jets, two loose b-tags

Events / 0.03

Events / 0.07

V(→lν)+2 jets, two loose b-tags
1600
Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

1400
1200
1000
800
600

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 200)
MH =125 GeV

3500
3000
2500
2000
1500

400

1000

200

500

0
-0.8 -0.6 -0.4 -0.2 0

0

0.2 0.4 0.6

0

0.1

Events / 3.75 GeV

W-Dijet Mass Assymetry

0.2

0.3

0.4

0.5

Aplanarity

V(→lν)+2 jets, two loose b-tags
Data

1200

VV
Top

1000

V+hf

800

V+lf
Multijet

600

Signal (× 200)

400

MH =125 GeV

200
0
20
nd

2

30

40

50

60

70

80

Leading jet p (GeV/c)
T

Figure B.6: Input variables to the BDT trained to distinguish signal from all backgrounds in
events with two jets and two loose b-tag: (top left) the mass asymmetry between the ℓν and
dijet systems, (top right) aplanarity, and (bottom) the second leading jet pT . The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 200. Overflow events are added
to the last bin.

159

Events / 0.20

Events / 0.05

V(→lν)+2 jets, two medium b-tags
2000
Data
VV
1800
Top
1600
V+hf
1400
V+lf
1200
Multijet
1000
Signal (× 50)
800
MH =125 GeV
600
400
200
0
0
0.2
0.4
0.6
0.8
1

V(→lν)+2 jets, two medium b-tags
600
Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

500
400
300
200
100
0

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

V(→lν)+2 jets, two medium b-tags
Data
DØ, 9.7 fb -1
350
VV
Top

300

V+hf

250

V+lf
Multijet

200

Signal (× 50)

150

Events / 0.12

Events / 0.05

b-id MVA BL

400
300

100

50
0

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

500

200

MH =125 GeV

100

V(→lν)+2 jets, two medium b-tags
600
Data

0

0.2

0.4

0.6

0.8

W(→lν) p /W(→lν) sum p
T

0

1

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

T

Figure B.7: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tag: (top left) the bid MVA output, (top right)
the maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance
of the dijet system. The signal is shown for MH = 125 GeV, and is multiplied by a factor
of 50. Overflow events are added to the last bin.

160

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

500
400
300
200

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two medium b-tags

V(→lν)+2 jets, two medium b-tags
700
Data

500
400
300
200

100

100

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

lepton

q

V(→lν)+2 jets, two medium b-tags
Data

300

VV
Top

250

V+hf

200

V+lf
Multijet

150

Signal (× 50)

4

5

6

7

8

V(→lν)+2 jets, two medium b-tags
450
Data
400
350
300
250
200
150

MH =125 GeV

100

3

Dijet Velocity

1

Events / 0.04

Events / 10.00 GeV

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

600

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

100
50
0
100

50
140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.8: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tag. The signal is shown for MH = 125 GeV, and
is multiplied by a factor of 50. Overflow events are added to the last bin.

161

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

400
350
300
250
200
150

V(→lν)+2 jets, two medium b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two medium b-tags

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

300
250
200
150
100

100
50

50
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

-0.6

V(→lν)+2 jets, two medium b-tags
400
Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

350
300
250
200
150
100

0.6

1

V(→lν)+2 jets, two medium b-tags
Data

300

VV
Top

250

V+hf
V+lf
Multijet

200
150

Signal (× 50)

100

MH =125 GeV

50

50
0
-1

0.2

Spin Correlation 2
Events / 15.00 GeV

Events / 0.10

MVAMJ(VH)

-0.2

-0.6

-0.2

0.2

0.6

0

1

0

50

100 150 200 250 300

Dijet (1,2) m , GeV/c2

Spin Correlation 1

T

Figure B.9: Input variables to the BDT trained to distinguish signal from all backgrounds in
events with two jets and two medium b-tag: (top left) the multijet MVA output, (top right)
cos(χ∗ ), (bottom left) cos(θ∗ , and (bottom right) the dijet transverse mass. The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 50. Overflow events are added
to the last bin.

162

Events / 12.50 GeV

V(→lν)+2 jets, two medium b-tags
Data

250

VV
Top

200

V+hf
V+lf
Multijet

150

Signal (× 50)

100

MH =125 GeV

50
0
50

100

150

200

250

300

Visible sum pT
Figure B.10: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tags: the magnitude of the vector pT sum for all
visible particles. The signal is shown for MH = 125 GeV, and is multiplied by a factor of
50. Overflow events are added to the last bin.

163

Events / 0.20

Events / 0.05

V(→lν)+2 jets, two tight b-tags
Data
900
VV
800
Top

700

V+hf

600

V+lf
Multijet

500

Signal (× 50)
MH =125 GeV

400
300

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

500
400
300
200

200

100

100
0

V(→lν)+2 jets, two tight b-tags
600
Data

0

0.2

0.4

0.6

0.8

0

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

b-id MVA BL

V(→lν)+2 jets, two tight b-tags

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

450
400
350
300
250

Events / 0.12

Events / 0.25

V(→lν)+2 jets, two tight b-tags

200
150
100
50
0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

500
400
300
200
100
0

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

Figure B.11: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is multiplied by a factor of
50. Overflow events are added to the last bin.

164

V(→lν)+2 jets, two tight b-tags

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two tight b-tags
Data
500
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

400
300
200

500
400
300
200

100

100

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

lepton

q

V(→lν)+2 jets, two tight b-tags
Data

250

VV
Top

200

V+hf
V+lf
Multijet

150

Signal (× 50)

100

3

4

5

6

7

8

Dijet Velocity

1

Events / 0.04

Events / 10.00 GeV

Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

600

V(→lν)+2 jets, two tight b-tags
450
Data
400
350
300
250
200
150

MH =125 GeV

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

100

50

50
0
100

140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.12: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag. The signal is shown for MH = 125 GeV, and is
multiplied by a factor of 50. Overflow events are added to the last bin.

165

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two tight b-tags
500
Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

400
300
200

VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

250
200
150
100

100
0
-1

V(→lν)+2 jets, two tight b-tags
300
Data

50
-0.6

-0.2

0.2

0.6

0
-1

1

-0.6

MVAMJ(VH)
Data
VV
Top
Top
V+hf
V+lf
Multijet
Signal (× 50)
MH =125 GeV

300
250
200
150
100
50
0
-1

-0.6

-0.2

0.2

0.6

0.2

0.6

1

Spin Correlation 2
Events / 15.00 GeV

Events / 0.10

V(→lν)+2 jets, two tight b-tags

-0.2

V(→lν)+2 jets, two tight b-tags
Data

250
200

V+hf

150

V+lf
Multijet
Signal (× 50)

100

MH =125 GeV

50
0

1

VV
Top

0

50

100 150 200 250 300

Dijet (1,2) m , GeV/c2

Spin Correlation 1

T

Figure B.13: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: (top left) the multijet MVA output, (top right)
cos(χ∗ ), (bottom left) cos(θ∗ , and (bottom right) the dijet transverse mass. The signal is
shown for MH = 125 GeV, and is multiplied by a factor of 50. Overflow events are added
to the last bin.

166

Events / 0.05

V(→lν)+2 jets, two tight b-tags
Data
350 DØ, 9.7 fb -1
300

VV
Top

250

V+hf

200

V+lf
Multijet

150

Signal (× 50)
MH =125 GeV

100
50
0

0

0.2

0.4

0.6

0.8

W(→lν) p /W(→lν) sum p
T

1

T

Figure B.14: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: the ratio of the W pT to the sum of the lepton
pT and ET . The signal is shown for MH = 125 GeV, and is multiplied by a factor of 50.
Overflow events are added to the last bin.

167

V(→lν)+2 jets, one tight b-tag

108

Data

107

Events /Bin

Events /Bin

V(→lν)+2 jets, one tight b-tag
VV
Top
V+hf

106

V+lf
Multijet

5

10

Data

107

VV
Top
V+hf

106

V+lf
Multijet

5

10

Signal (× 100)

104

108

Signal (× 100)

4

10

MH =90 GeV

103

103

102

MH =95 GeV

102

-1

-0.6

-0.2

0.2

0.6

-1

1

-0.6

Data

107

VV
Top

Signal (× 100)

4

MH =100 GeV

10

1

Data

107

VV
Top

106

V+hf
V+lf
Multijet
Signal (× 100)
MH =105 GeV

103

103

102

102
-1

10

104

V+lf
Multijet

105

8

105

V+hf

106

0.6

V(→lν)+2 jets, one tight b-tag
Events /Bin

Events /Bin

V(→lν)+2 jets, one tight b-tag
10

0.2

Final Discriminant

Final Discriminant
8

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.15: The final MVA output for events with two jets and one tight b-tag for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

168

108

Data

107

V(→lν)+2 jets, one tight b-tag
Events /Bin

Events /Bin

V(→lν)+2 jets, one tight b-tag
VV
Top
V+hf

106

V+lf
Multijet

105

Data

107

VV
Top
V+hf

106

V+lf
Multijet

105

Signal (× 100)

104

108

Signal (× 100)

104

MH =110 GeV

103

103

102
-1

102
-1

MH =115 GeV

-0.6

-0.2

0.2

0.6

1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top

106

V+hf

10

MH =120 GeV

3

107

VV
Top

106

V+hf
V+lf
Multijet
Signal (× 100)
MH =130 GeV

103

10

102

102
10
-1

1

Data

104

Signal (× 100)

104

108

105

V+lf
Multijet

5

0.6

V(→lν)+2 jets, one tight b-tag

Data

107

0.2

Final Discriminant

V(→lν)+2 jets, one tight b-tag
108

-0.2

10
-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.16: The final MVA output for events with two jets and one tight b-tag for (top left)
MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and (bottom
right) MH = 130 GeV.

169

V(→lν)+2 jets, one tight b-tag
Events /Bin

Events /Bin

V(→lν)+2 jets, one tight b-tag
Data

108

VV
Top

107

V+hf

106

V+lf
Multijet

105

10

V+hf

106

V+lf
Multijet
Signal (× 100)

4

MH =135 GeV

10

VV
Top

7

105

Signal (× 100)

4

Data

108

MH =140 GeV

10

103

103

102

102

-1

-0.6

-0.2

0.2

0.6

1

-1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top

10

V+hf

106

V+lf
Multijet

105

0.6

Data

108

VV
Top

107

V+hf

106

V+lf
Multijet

Signal (× 100)

105

Signal (× 100)

MH =145 GeV

104

1

V(→lν)+2 jets, one tight b-tag

Data

7

0.2

Final Discriminant

V(→lν)+2 jets, one tight b-tag
108

-0.2

104

MH =150 GeV

103

103

102

102
-1

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.17: The final MVA output for events with two jets and one tight b-tag for (top left)
MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and (bottom
right) MH = 150 GeV.

170

V(→lν)+3 jets, one tight b-tag

Events /Bin

Events /Bin

V(→lν)+3 jets, one tight b-tag

108

Data

7

VV
Top

10

106

V+hf

5

V+lf
Multijet

10

104

102

VV
Top

106

V+hf

105

V+lf
Multijet
Signal (× 100)
MH =95 GeV

102

10
1
-1

10

103

MH =90 GeV

10

Data

7

104

Signal (× 100)

3

108

10
-0.6

-0.2

0.2

0.6

1

-1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top
V+hf

105

V+lf
Multijet

VV
Top

6

10

V+hf

105

V+lf
Multijet
Signal (× 100)

103

MH =100 GeV

MH =105 GeV

102

103

10

102
-1

1

Data

107

104

Signal (× 100)

104

0.6

V(→lν)+3 jets, one tight b-tag

Data

106

0.2

Final Discriminant

V(→lν)+3 jets, one tight b-tag
107

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.18: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

171

V(→lν)+3 jets, one tight b-tag
Events /Bin

Events /Bin

V(→lν)+3 jets, one tight b-tag
Data

107

VV
Top

106

V+hf

Data

107

VV
Top

6

10

V+hf

105

105

V+lf
Multijet

104

Signal (× 100)

104

Signal (× 100)

MH =110 GeV

103

MH =115 GeV

3

10

102

102
-1

V+lf
Multijet

-0.6

-0.2

0.2

0.6

10
-1

1

-0.6

Final Discriminant

V+hf

104

Events /Bin

Events /Bin

VV
Top

105

V+lf
Multijet

10

V+hf

105

V+lf
Multijet
Signal (× 100)

103

MH =130 GeV

2

10

10

10

1
-1

VV
Top

106

10

MH =120 GeV

102

1

Data

107

4

Signal (× 100)

3

0.6

V(→lν)+3 jets, one tight b-tag

Data

106

0.2

Final Discriminant

V(→lν)+3 jets, one tight b-tag
107

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.19: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

172

V(→lν)+3 jets, one tight b-tag
Events /Bin

Events /Bin

V(→lν)+3 jets, one tight b-tag
Data

107

VV
Top

6

10

V+hf
5

10

V+lf
Multijet

104

Signal (× 100)

103

MH =135 GeV

VV
Top

6

10

V+hf
5

10

V+lf
Multijet

104

Signal (× 100)
MH =140 GeV

103

102
10
-1

Data

107

102
-0.6

-0.2

0.2

0.6

10
-1

1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top
V+hf

5

10

Signal (× 100)
MH =145 GeV

103

VV
Top

6

10

V+hf

5

10

V+lf
Multijet
Signal (× 100)
MH =150 GeV

103
102

102
-1

1

Data

107

104

V+lf
Multijet

104

0.6

V(→lν)+3 jets, one tight b-tag

Data

106

0.2

Final Discriminant

V(→lν)+3 jets, one tight b-tag
107

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.20: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

173

8

10

V(→lν)+2 jets, two loose b-tags

Events /Bin

Events /Bin

V(→lν)+2 jets, two loose b-tags
Data

7

VV
Top

10

106

V+hf

105

V+lf
Multijet

104

VV
Top

10

106

V+hf

105

V+lf
Multijet
Signal (× 100)

103

MH =90 GeV

MH =95 GeV

2

2

10

10

10

10
1
-1

Data

7

104

Signal (× 100)

103

108

-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Final Discriminant
Events /Bin

Events /Bin

10

V+hf

105

V+lf
Multijet

104

Signal (× 100)

103

MH =100 GeV

1

Data

7

10

VV
Top

106

V+hf

105

V+lf
Multijet
Signal (× 100)
MH =105 GeV

103

102
10
-1

108

104

VV
Top

106

0.6

V(→lν)+2 jets, two loose b-tags

Data

7

0.2

Final Discriminant

V(→lν)+2 jets, two loose b-tags

108

-0.2

102
-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.21: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

174

V(→lν)+2 jets, two loose b-tags

Events /Bin

Events /Bin

V(→lν)+2 jets, two loose b-tags

108

Data

7

10

VV
Top

106

V+hf

105

V+lf
Multijet

10

106

V+hf

105

V+lf
Multijet
Signal (× 100)
MH =115 GeV

2

10

102
10
-1

VV
Top

10

103

MH =110 GeV

103

Data

7

104

Signal (× 100)

4

108

10
-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Data

10

VV
Top

106

V+hf

105

V+lf
Multijet

104

108

1

Data

7

VV
Top

10

106

V+hf

10

V+lf
Multijet

Signal (× 100)

104

Signal (× 100)

MH =120 GeV

103

103

MH =130 GeV

5

102

102
10
-1

0.6

V(→lν)+2 jets, two loose b-tags

Events /Bin

Events /Bin

V(→lν)+2 jets, two loose b-tags
7

0.2

Final Discriminant

Final Discriminant
108

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.22: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

175

V(→lν)+2 jets, two loose b-tags

Events /Bin

Events /Bin

V(→lν)+2 jets, two loose b-tags

108

Data

107

VV
Top

106

V+hf

105

V+lf
Multijet

Data

107

VV
Top

106

V+hf

105

Signal (× 100)

104

108

V+lf
Multijet
Signal (× 100)

104

MH =135 GeV

3

MH =140 GeV

3

10

10

102

102

-1

-0.6

-0.2

0.2

0.6

1

-1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top

106

V+hf

105

V+lf
Multijet

1

Data

7

VV
Top

10

106

V+hf

105

V+lf
Multijet
Signal (× 100)

3

10

MH =145 GeV

3

MH =150 GeV

2

10

10

10

102
-1

108

104

Signal (× 100)

104

0.6

V(→lν)+2 jets, two loose b-tags

Data

107

0.2

Final Discriminant

V(→lν)+2 jets, two loose b-tags

108

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.23: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

176

V(→lν)+3 jets, two loose b-tags

Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags

108

Data

107

VV
Top

106

V+hf

105

V+lf
Multijet

104
103

108

Data

7

VV
Top

10

106

V+hf

10

V+lf
Multijet

Signal (× 100)

104

Signal (× 100)

MH =90 GeV

103

MH =95 GeV

5

102

102

10

10

-1

-0.6

-0.2

0.2

0.6

-1

1

-0.6

Data
VV
Top

10

V+hf

5

V+lf
Multijet

10

0.6

1

V(→lν)+3 jets, two loose b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags

6

0.2

Final Discriminant

Final Discriminant

107

-0.2

Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

Signal (× 100)

104

Signal (× 100)

103

MH =100 GeV

103

MH =105 GeV

102

102
10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.24: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

177

V(→lν)+3 jets, two loose b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags
Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

10

V+hf

105

V+lf
Multijet
Signal (× 100)

103

MH =110 GeV

102

MH =115 GeV

102

10
1
-1

VV
Top

6

104

Signal (× 100)

103

Data

107

10
-0.6

-0.2

0.2

0.6

1

-1

-0.6

Data
VV
Top
V+hf

105

V+lf
Multijet

104
10

1

Data

106

VV
Top
V+hf

105

V+lf
Multijet

10

Signal (× 100)

103

MH =120 GeV

102

107

4

Signal (× 100)

3

0.6

V(→lν)+3 jets, two loose b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags
106

0.2

Final Discriminant

Final Discriminant

107

-0.2

MH =130 GeV

102

10
10

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.25: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

178

V(→lν)+3 jets, two loose b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags
Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

107

Data

106

VV
Top

105

V+hf
V+lf
Multijet

4

10

104

Signal (× 100)

103

MH =135 GeV

Signal (× 100)

103

MH =140 GeV

2

10
2

10

10
-1

10
-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Data
VV
Top

5

V+hf

4

V+lf
Multijet

3

Signal (× 100)

10
10
10

1

Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

MH =145 GeV

2

0.6

V(→lν)+3 jets, two loose b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two loose b-tags
106

0.2

Final Discriminant

Final Discriminant
107

-0.2

Signal (× 100)
MH =150 GeV

103

10

102

10
1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.26: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

179

V(→lν)+2 jets, two medium b-tags
Events /Bin

Events /Bin

V(→lν)+2 jets, two medium b-tags
Data

107

VV
Top

106
5

V+hf

4

V+lf
Multijet

10
10
10

VV
Top

6

10

V+hf

MH =90 GeV

105

V+lf
Multijet

104

Signal (× 20)

3

Data

107

Signal (× 20)

2

10

MH =95 GeV

103
102

10

1
-1

-0.6

-0.2

0.2

0.6

10
-1

1

-0.6

-0.2

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags
Events /Bin

Final Discriminant

V(→lν)+2 jets, two medium b-tags
Events /Bin

Final Discriminant
Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

107

Data

106

VV
Top
V+hf

105

V+lf
Multijet

104

Signal (× 20)

104

Signal (× 20)

103

MH =100 GeV

103

MH =105 GeV

102
10
-1

102

-0.6

-0.2

0.2

0.6

1

Final Discriminant

10
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.27: The final MVA output for events with two jets and two medium b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

180

V(→lν)+2 jets, two medium b-tags
Events /Bin

Events /Bin

V(→lν)+2 jets, two medium b-tags
Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

Data

106

VV
Top
V+hf

105

V+lf
Multijet

104

Signal (× 20)

Signal (× 20)

3

10

MH =110 GeV

103

107

MH =115 GeV

102

102

10
10
-1

-0.6

-0.2

0.2

0.6

-1

1

-0.6

-0.2

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags

107

Data

106

VV
Top

105

Events /Bin

Final Discriminant

V(→lν)+2 jets, two medium b-tags
Events /Bin

Final Discriminant

V+hf
V+lf
Multijet

4

10

106

VV
Top

105

V+hf
V+lf
Multijet

10

Signal (× 20)

103

MH =120 GeV

MH =130 GeV

2

2

10

10

10

10
1
-1

Data

4

Signal (× 20)

103

107

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.28: The final MVA output for events with two jets and two medium b-tags for
(top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

181

V(→lν)+2 jets, two medium b-tags

107

Data

106

Events /Bin

Events /Bin

V(→lν)+2 jets, two medium b-tags
VV
Top

5

10

V+hf

104

V+lf
Multijet

10

10

V+hf

105

V+lf
Multijet
Signal (× 20)

3

MH =135 GeV

102

VV
Top

6

104

Signal (× 20)

3

Data

107

MH =140 GeV

10

10

102

1

10

-1

-0.6

-0.2

0.2

0.6

-1

1

-0.6

-0.2

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags

107

Data

106

VV
Top

105

V+hf

104

Events /Bin

Final Discriminant

V(→lν)+2 jets, two medium b-tags
Events /Bin

Final Discriminant

V+lf
Multijet

10

105

V+hf
V+lf
Multijet
Signal (× 20)

103

MH =150 GeV

102

10

10

1
-1

VV
Top

10

MH =145 GeV

102

106

4

Signal (× 20)

3

Data

107

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.29: The final MVA output for events with two jets and two medium b-tags for
(top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

182

Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

V(→lν)+3 jets, two medium b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two medium b-tags

10

V+hf

105

V+lf
Multijet
Signal (× 20)

3

MH =90 GeV

10

VV
Top

6

104

Signal (× 20)

3

Data

107

MH =95 GeV

10

102

102

10

10

-1

-0.6

-0.2

0.2

0.6

1

-1

-0.6

-0.2

0.2

0.6

1

V(→lν)+3 jets, two medium b-tags

7

10

Data

106

VV
Top

105

Events /Bin

Final Discriminant

V(→lν)+3 jets, two medium b-tags
Events /Bin

Final Discriminant

V+hf
V+lf
Multijet

4

10

106

VV
Top
V+hf

105

V+lf
Multijet

10

Signal (× 20)

103

MH =100 GeV

MH =105 GeV

2

102

10

10

10
-1

Data

4

Signal (× 20)

103

107

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.30: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and
(bottom right) MH = 105 GeV.

183

7

10

Data

106

VV
Top

105

V+hf
V+lf
Multijet

4

10

V(→lν)+3 jets, two medium b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two medium b-tags

Data

106

VV
Top
V+hf

105

V+lf
Multijet

104

Signal (× 20)

103

107

MH =110 GeV

Signal (× 20)
MH =115 GeV

103

2

10

102

10
1
-1

-0.6

-0.2

0.2

0.6

10
-1

1

-0.6

-0.2

0.2

0.6

1

V(→lν)+3 jets, two medium b-tags

7

Events /Bin

Final Discriminant

V(→lν)+3 jets, two medium b-tags
Events /Bin

Final Discriminant
Data

10

VV
Top

Data
6

10

VV
Top

105

V+hf

104

V+lf
Multijet

Signal (× 20)

103

Signal (× 20)

MH =120 GeV

106

102

MH =130 GeV

V+hf

5

10

V+lf
Multijet

104
3

10

102

10

10

1

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.31: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

184

V(→lν)+3 jets, two medium b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two medium b-tags
Data

106

V+hf

104

V+lf
Multijet
Signal (× 20)

103

MH =135 GeV

2

VV
Top

105

V+hf

104

V+lf
Multijet
Signal (× 20)
MH =140 GeV

102

10

10

10
1
-1

10

103

VV
Top

105

Data
6

-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

-0.2

0.2

0.6

1

V(→lν)+3 jets, two medium b-tags
Events /Bin

Final Discriminant

V(→lν)+3 jets, two medium b-tags
Events /Bin

Final Discriminant
Data
6

105

V+hf

10

V+lf
Multijet

103

Signal (× 20)

102

MH =145 GeV

4

10

VV
Top

105

V+hf

104

VV
Top

10

Data
6

V+lf
Multijet
Signal (× 20)

103

MH =150 GeV

2

10

10
10
1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.32: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

185

V(→lν)+2 jets, two tight b-tags
Events /Bin

Events /Bin

V(→lν)+2 jets, two tight b-tags
Data

107

VV
Top

6

10

V+hf

5

10

V+lf
Multijet

104

Signal (× 20)

VV
Top

105

V+hf
V+lf
Multijet

10

Signal (× 20)

103

MH =95 GeV

102

102
10
-1

106

4

MH =90 GeV

103

Data

107

10
-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top

10

V+hf

105

V+lf
Multijet

104

V+hf

105

V+lf
Multijet
Signal (× 20)

103

MH =105 GeV

102

102

10

10
-1

VV
Top

106

10

MH =100 GeV

10

1

Data

107

4

Signal (× 20)

3

0.6

V(→lν)+2 jets, two tight b-tags

Data

6

0.2

Final Discriminant

V(→lν)+2 jets, two tight b-tags
107

-0.2

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.33: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

186

V(→lν)+2 jets, two tight b-tags
Events /Bin

Events /Bin

V(→lν)+2 jets, two tight b-tags
VV
Top

6

10

V+hf

105

V+lf
Multijet

104

Signal (× 20)

103

MH =110 GeV

Data

106

VV
Top

105

V+hf
V+lf
Multijet
Signal (× 20)

103

MH =115 GeV

102

102
10
-1

107

104

Data

107

10
-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Events /Bin

Events /Bin

V+hf
5

10

V+lf
Multijet

104

Signal (× 20)
MH =120 GeV

103

106

VV
Top

105

V+hf
V+lf
Multijet
Signal (× 20)
MH =130 GeV

102
10

102
10
-1

1

Data

103

VV
Top

107

104

Data

10

0.6

V(→lν)+2 jets, two tight b-tags

V(→lν)+2 jets, two tight b-tags

6

0.2

Final Discriminant

Final Discriminant

107

-0.2

1
-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.34: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

187

V(→lν)+2 jets, two tight b-tags
Events /Bin

Events /Bin

V(→lν)+2 jets, two tight b-tags
Data

107

VV
Top

106

V+hf

105

V+lf
Multijet

4

10

V+lf
Multijet
Signal (× 20)

103

MH =140 GeV

2

10

10

10
1
-1

V+hf

105
10

MH =135 GeV

2

VV
Top

106

4

Signal (× 20)

103

Data

107

10
-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Events /Bin

Events /Bin

Data
VV
Top

10

V+hf

105

V+lf
Multijet

104
10

1

Data

107

VV
Top

6

10

V+hf

105

V+lf
Multijet

104

Signal (× 20)

3

0.6

V(→lν)+2 jets, two tight b-tags

V(→lν)+2 jets, two tight b-tags

6

0.2

Final Discriminant

Final Discriminant

107

-0.2

Signal (× 20)

3

MH =145 GeV

MH =150 GeV

10

102

102

10

10

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.35: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

188

V(→lν)+3 jets, two tight b-tags
Events /Bin

Events /Bin

V(→lν)+3 jets, two tight b-tags
Data

107
106
105

V+hf

104

V+lf
Multijet
Signal (× 20)

103

Data

106

VV
Top

105

V+hf
V+lf
Multijet
Signal (× 20)

103

MH =90 GeV

102

107

104

VV
Top

MH =95 GeV

102

10

10

1

1

-1

-0.6

-0.2

0.2

0.6

1

-1

-0.6

Final Discriminant
Events /Bin

Events /Bin

V+hf
5

10

V+lf
Multijet

104

Signal (× 20)

103

MH =100 GeV

1

Data

106

VV
Top

105

V+hf
V+lf
Multijet
Signal (× 20)

103

MH =105 GeV

102

102
10
-1

107

104

VV
Top

10

0.6

V(→lν)+3 jets, two tight b-tags

Data

6

0.2

Final Discriminant

V(→lν)+3 jets, two tight b-tags
107

-0.2

10
1
-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.36: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV.

189

V(→lν)+3 jets, two tight b-tags

107

Data

106

Events /Bin

Events /Bin

V(→lν)+3 jets, two tight b-tags
VV
Top
V+hf

105

V+lf
Multijet

4

10

106

VV
Top
V+hf

105

V+lf
Multijet
Signal (× 20)

3

10

MH =110 GeV

102

MH =115 GeV

102

10
-1

Data

104

Signal (× 20)

103

107

10
-0.6

-0.2

0.2

0.6

-1

1

-0.6

0.6

Data

106

VV
Top

105

V+hf

104

V+lf
Multijet

Signal (× 20)

103

Signal (× 20)

MH =120 GeV

102

MH =130 GeV

Data

106

VV
Top

105

V+hf

104

Events /Bin

107

107

V+lf
Multijet

103
2

1

V(→lν)+3 jets, two tight b-tags

V(→lν)+3 jets, two tight b-tags
Events /Bin

0.2

Final Discriminant

Final Discriminant

10

10

10
1
-1

-0.2

1
-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.37: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 130 GeV.

190

7

10

Data

106

V(→lν)+3 jets, two tight b-tags

Events /Bin

Events /Bin

V(→lν)+3 jets, two tight b-tags
VV
Top

10

V+lf
Multijet

104

Signal (× 20)

3

MH =135 GeV

10

106

VV
Top

105

V+hf

104

V+lf
Multijet
Signal (× 20)
MH =140 GeV

102

102

10

10
-1

Data

103

V+hf

5

107

-0.6

-0.2

0.2

0.6

1
-1

1

-0.6

Final Discriminant
Events /Bin

Events /Bin

VV
Top

105

V+hf

104

V+lf
Multijet

10

1

Data

106

VV
Top

105

V+hf
V+lf
Multijet

10

Signal (× 20)

103

MH =145 GeV

102

107

4

Signal (× 20)

3

0.6

V(→lν)+3 jets, two tight b-tags

Data

106

0.2

Final Discriminant

V(→lν)+3 jets, two tight b-tags

107

-0.2

MH =150 GeV

102

10
10
1
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.38: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 135 GeV, (top right) MH = 140 GeV, (bottom left) MH = 145 GeV, and
(bottom right) MH = 150 GeV.

191

Events / 0.20

Events / 0.05

V(→lν)+2 jets, one tight b-tag
14000
Total Background

(a)

12000

Signal

10000

MH =125 GeV

8000
6000

V(→lν)+2 jets, one tight b-tag
2500 (b)
Total Background
Signal

2000

MH =125 GeV

1500
1000

4000
500

2000
0

0

0.2

0.4

0.6

0.8

0

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

b-id MVA BL

4000
3500
3000

(c)

V(→lν)+2 jets, one tight b-tag

Events / 0.12

Events / 0.25

V(→lν)+2 jets, one tight b-tag
Total Background
Signal
MH =125 GeV

2500
2000

(d)

5000

Total Background
Signal

4000
MH =125 GeV

3000
2000

1500
1000

1000

500
0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

0

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

Figure B.39: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and one tight b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is normalized to the sum of
the backgrounds. Overflow events are added to the last bin.

192

4000

(a)

V(→lν)+2 jets, one tight b-tag

Events / 0.28

Events / 0.25

V(→lν)+2 jets, one tight b-tag
Total Background

3500

Signal

3000

MH =125 GeV

2500
2000
1500

(b)

9000
8000
7000
6000
5000
4000

Signal
MH =125 GeV

3000
2000
1000

1000
500
0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

3

4

lepton

q

Total Background

3000

Signal

2500

6

7

8

V(→lν)+2 jets, one tight b-tag

Events / 0.04

Events / 10.00

(c)

5

Dijet Velocity

1

V(→lν)+2 jets, one tight b-tag
3500

Total Background

MH =125 GeV

2000
1500

(d)

Total Background

3000
Signal

2500
MH =125 GeV

2000
1500

1000

1000

500

500

0
100

140

180

220

260280300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.40: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and one tight b-tag. The signal is shown for MH = 125 GeV, and is
normalized to the sum of the backgrounds. Overflow events are added to the last bin.

193

7000
6000
5000

V(→lν)+2 jets, one tight b-tag

Events / 0.03

Events / 0.07

V(→lν)+2 jets, one tight b-tag
8000 (a)
Total Background
Signal
MH =125 GeV

4000

(b)

14000

Total Background

12000

Signal

10000

MH =125 GeV

8000
6000

3000
2000

4000

1000

2000

0
-0.8 -0.6 -0.4 -0.2 0

0

0.2 0.4 0.6

0

0.1

W-Dijet Mass Assymetry

0.2

0.3

0.4

0.5

Aplanarity

Events / 3.75

V(→lν)+2 jets, one tight b-tag

(c)

Total Background

5000
Signal

4000

MH =125 GeV

3000
2000
1000
0
20
nd

2

30

40

50

60

70

80

Leading jet p (GeV/c)
T

Figure B.41: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and one tight b-tag: (top left) the mass asymmetry between the ℓν
and dijet systems, (top right) aplanarity, and (bottom) the second leading jet pT . The signal
is shown for MH = 125 GeV, and is normalized to the sum of the backgrounds. Overflow
events are added to the last bin.

194

(a)

4000

Events / 0.05

Events / 0.05

V(→lν)+2 jets, two loose b-tags
4500
Total Background

3500

Signal

3000

MH =125 GeV

2500
2000

V(→lν)+2 jets, two loose b-tags
800
Total Background

(b)

700

Signal

600
MH =125 GeV

500
400

1500

300

1000

200

500

100

0

0

0.2

0.4

0.6

0.8

0

1

0

0.2

0.4

V(→lν)+2 jets, two loose b-tags
1000 (c)
Total Background

1

V(→lν)+2 jets, two loose b-tags

Events / 0.12

Events / 0.25

0.8

pW/(pl +ET)
T
T

b-id MVA BL

800

0.6

Signal
MH =125 GeV

600

(d)

1200

Total Background
Signal

1000

MH =125 GeV

800
600

400
400
200

200

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

0

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

Figure B.42: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two loose b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is normalized to the sum of
the backgrounds. Overflow events are added to the last bin.

195

1000

(a)

V(→lν)+2 jets, two loose b-tags

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two loose b-tags
Total Background
Signal

800

MH =125 GeV

600
400
200
0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

2000
1800
1600
1400
1200
1000
800
600
400
200
0

×jet η

(b)

Signal
MH =125 GeV

3

4

lepton

V(→lν)+2 jets, two loose b-tags
900

(c)

Total Background
Signal
MH =125 GeV

600

6

7

8

V(→lν)+2 jets, two loose b-tags

800
700

5

Dijet Velocity

1

Events / 0.04

Events / 10.00

q

Total Background

500
400

800
700
600

(d)

Total Background
Signal
MH =125 GeV

500
400

300

300

200

200

100

100

0
100

140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.43: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two loose b-tag. The signal is shown for MH = 125 GeV, and is
normalized to the sum of the backgrounds. Overflow events are added to the last bin.

196

(a)

Events / 0.03

Events / 0.07

V(→lν)+2 jets, two loose b-tags
Total Background

1800
Signal
1600
1400
MH =125 GeV
1200
1000
800
600
400
200
0
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

V(→lν)+2 jets, two loose b-tags
3500 (b)
Total Background
3000

Signal

2500

MH =125 GeV

2000
1500
1000
500
0

0

0.1

W-Dijet Mass Assymetry

0.2

0.3

0.4

0.5

Aplanarity

Events / 3.75

V(→lν)+2 jets, two loose b-tags

(c)

1200

Total Background
Signal

1000

MH =125 GeV

800
600
400
200
0
20
nd

2

30

40

50

60

70

80

Leading jet p (GeV/c)
T

Figure B.44: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two loose b-tag: (top left) the mass asymmetry between the ℓν
and dijet systems, (top right) aplanarity, and (bottom) the second leading jet pT . The signal
is shown for MH = 125 GeV, and is normalized to the sum of the backgrounds. Overflow
events are added to the last bin.

197

Events / 0.20

Events / 0.05

V(→lν)+2 jets, two medium b-tags
2000 (a)
Total Background
1800
Signal
1600
MH =125 GeV
1400
1200
1000
800
600
400
200
0
0
0.2
0.4
0.6
0.8
1

V(→lν)+2 jets, two medium b-tags
240 (b)
Total Background
220
200
Signal
180
MH =125 GeV
160
140
120
100
80
60
40
20
0
0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

b-id MVA BL
(c)

Events / 0.12

Events / 0.05

V(→lν)+2 jets, two medium b-tags
Total Background

250

Signal

200

MH =125 GeV

150

V(→lν)+2 jets, two medium b-tags
500

(d)

Total Background

400

Signal
MH =125 GeV

300
200

100
100

50
0

0

0.2

0.4

0.6

0.8

0

1

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

pW/(pl +ET)
T
T

Figure B.45: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tag: (top left) the bid MVA output, (top right)
the maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance
of the dijet system. The signal is shown for MH = 125 GeV, and is normalized to the sum
of the backgrounds. Overflow events are added to the last bin.

198

400
Signal

350

MH =125 GeV

300
250
200

V(→lν)+2 jets, two medium b-tags

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two medium b-tags
450 (a)
Total Background

Total Background

700

Signal

600

MH =125 GeV

500
400

150

300

100

200

50

100

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

lepton

V(→lν)+2 jets, two medium b-tags
300 (c)
Total Background
250

Signal

200

3

4

5

6

7

8

Dijet Velocity

1

MH =125 GeV

150

Events / 0.04

q
Events / 10.00

(b)

800

V(→lν)+2 jets, two medium b-tags
350 (d)
Total Background
300

Signal

250

MH =125 GeV

200
150

100

100

50
0
100

50
140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.46: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tag. The signal is shown for MH = 125 GeV, and
is normalized to the sum of the backgrounds. Overflow events are added to the last bin.

199

500

(a)

Total
Background
Signal

400

V(→lν)+2 jets, two medium b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two medium b-tags

MH =125 GeV

300

(b)

250

Signal

200
MH =125 GeV

150

200

100

100

50

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

-0.6

MVAMJ(VH)
(c)

Total Background
Signal

250

MH =125 GeV

200
150

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags

Events / 15.00

300

-0.2

Spin Correlation 2

V(→lν)+2 jets, two medium b-tags

Events / 0.10

Total Background

(d)

600

Total Background
Signal

500

MH =125 GeV

400
300

100

200

50

100

0
-1

-0.6

-0.2

0.2

0.6

0

1

0

50

100 150 200 250 300

Dijet (1,2) m , GeV/c2

Spin Correlation 1

T

Figure B.47: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tag: (top left) the multijet MVA output, (top
right) cos(χ∗ ), (bottom left) cos(θ∗ , and (bottom right) the dijet transverse mass. The signal
is shown for MH = 125 GeV, and is normalized to the sum of the backgrounds. Overflow
events are added to the last bin.

200

Events / 12.50

V(→lν)+2 jets, two medium b-tags
250
Total Background

Signal

200

MH =125 GeV

150
100
50
0
50

100

150

200

250

300

Visible sum pT
Figure B.48: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two medium b-tags: the magnitude of the vector pT sum for all
visible particles. The signal is shown for MH = 125 GeV, and is normalized to the sum of
the backgrounds. Overflow events are added to the last bin.

201

(a)

900

Events / 0.20

Events / 0.05

V(→lν)+2 jets, two tight b-tags
Total Background

800

Signal

700

MH =125 GeV

600
500
400

V(→lν)+2 jets, two tight b-tags
250

(b)

Total Background

200

Signal
MH =125 GeV

150
100

300
200

50

100
0

0

0.2

0.4

0.6

0.8

0

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Max. ∆ η(jet,Lepton)

V(→lν)+2 jets, two tight b-tags
400

(c)

Events / 0.12

Events / 0.25

b-id MVA BL
Total Background

350
300
250

Signal
MH =125 GeV

200
150

V(→lν)+2 jets, two tight b-tags
450 (d)
Total Background
400

Signal

350

MH =125 GeV

300
250
200
150

100

100

50

50

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

Lepton Q×η

0

0

0.4

0.8

1.2

1.6

2

Dijet (1,2) Σ min.

Figure B.49: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: (top left) the bid MVA output, (top right) the
maximum ∆η(ℓ, j), (bottom left) q ℓ × η ℓ , and (bottom right) the minimum significance of
the dijet system. The signal is shown for MH = 125 GeV, and is normalized to the sum of
the backgrounds. Overflow events are added to the last bin.

202

400

(a)

Events / 0.28

Events / 0.25

V(→lν)+2 jets, two tight b-tags
Total Background

350

Signal

300

MH =125 GeV

250
200

V(→lν)+2 jets, two tight b-tags
800 (b)
Total Background
700

Signal

600

MH =125 GeV

500
400

150

300

100

200

50

100

0
-2.5 -2 -1.5 -1-0.5 0 0.5 1 1.5 2 2.5

0

×jet η

3

4

lepton

V(→lν)+2 jets, two tight b-tags
250 (c)
Total Background

7

8

V(→lν)+2 jets, two tight b-tags

Signal

200

6

Dijet Velocity

1

Events / 0.04

Events / 10.00

q

5

MH =125 GeV

150

350

(d)

Total Background

300

Signal

250

MH =125 GeV

200
150

100

100
50
0
100

50
140

180

220

260

300

lνj mass, GeV/c

2

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Centrality

2

Figure B.50: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag. The signal is shown for MH = 125 GeV, and is
normalized to the sum of the backgrounds. Overflow events are added to the last bin.

203

500

Signal

400

V(→lν)+2 jets, two tight b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two tight b-tags
600 (a)
Total Background

MH =125 GeV

300

(b)

Total Background
Signal

200

MH =125 GeV

150
100

200
50

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

-0.6

MVAMJ(VH)
Total Background
Signal

200
MH =125 GeV

150
100

1

(d)

500

Total Background
Signal

400

MH =125 GeV

300
200
100

50
0
-1

0.6

V(→lν)+2 jets, two tight b-tags

Events / 15.00

Events / 0.10

(c)

0.2

Spin Correlation 2

V(→lν)+2 jets, two tight b-tags
250

-0.2

-0.6

-0.2

0.2

0.6

0

1

0

50

100 150 200 250 300

Dijet (1,2) m , GeV/c2

Spin Correlation 1

T

Figure B.51: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: (top left) the multijet MVA output, (top right)
cos(χ∗ ), (bottom left) cos(θ∗ , and (bottom right) the dijet transverse mass. The signal is
shown for MH = 125 GeV, and is normalized to the sum of the backgrounds. Overflow
events are added to the last bin.

204

Events / 0.05

V(→lν)+2 jets, two tight b-tags
Total Background

250

Signal

200
MH =125 GeV

150
100
50
0

0

0.2

0.4

0.6

0.8

1

pW/(pl +ET)
T
T
Figure B.52: Input variables to the BDT trained to distinguish signal from all backgrounds
in events with two jets and two tight b-tag: the ratio of the W pT to the sum of the lepton
pT and ET . The signal is shown for MH = 125 GeV, and is normalized to the sum of the
backgrounds. Overflow events are added to the last bin.

205

V(→lν)+2 jets, one tight b-tag

Events / 0.10

Events / 0.10

V(→lν)+2 jets, one tight b-tag
Total Background

5000

Signal

4000

MH=90 GeV

3000

Total Background

5000
4000

MH=95 GeV

3000

2000

2000

1000

1000

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+2 jets, one tight b-tag
5000
Signal
MH=100 GeV

3000
2000

0.2

0.6

1

Total Background

5000

Signal

4000

MH=105 GeV

3000
2000

1000
0
-1

-0.2

V(→lν)+2 jets, one tight b-tag

Total Background

4000

-0.6

Final Discriminant
Events / 0.10

Events / 0.10

Signal

1000

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.53: The final MVA output for events with two jets and one tight b-tag for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

206

V(→lν)+2 jets, one tight b-tag

Events / 0.10

Events / 0.10

V(→lν)+2 jets, one tight b-tag
Total Background

5000
Signal

4000

MH=110 GeV

3000

Signal

4000

MH=115 GeV

3000

2000

2000

1000

1000

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+2 jets, one tight b-tag
6000
Total Background
5000

Signal

4000

MH=120 GeV

3000

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.10

Events / 0.10

Total Background

5000

V(→lν)+2 jets, one tight b-tag
Total Background
6000
5000

Signal

4000

MH=125 GeV

3000

2000

2000

1000

1000

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.54: The final MVA output for events with two jets and one tight b-tag for (top left)
MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and (bottom
right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

207

V(→lν)+2 jets, one tight b-tag

Events / 0.10

Events / 0.10

V(→lν)+2 jets, one tight b-tag
Total Background

6000

Signal

5000

MH=130 GeV

4000
3000

Signal

5000

MH=135 GeV

4000
3000

2000

2000

1000

1000

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+2 jets, one tight b-tag
7000
Total Background

6000

Signal

5000

MH=140 GeV

4000
3000

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.10

Final Discriminant
Events / 0.10

Total Background

6000

V(→lν)+2 jets, one tight b-tag
7000

Total Background

6000

Signal

5000

MH=145 GeV

4000
3000

2000

2000

1000

1000

0
-1

-0.6

-0.2

0.2

0
-1

0.6

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.55: The final MVA output for events with two jets and one tight b-tag for (top left)
MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and (bottom
right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

208

Events / 0.10

V(→lν)+2 jets, one tight b-tag
7000

Total Background

6000

Signal

5000

MH=150 GeV

4000
3000
2000
1000
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.56: The final MVA output for events with two jets and one tight b-tag for MH =
150 GeV. The signal is normalized to the sum of the backgrounds.

209

3500

Total Background

3000

Signal

2500

Events / 0.20

Events / 0.20

V(→lν)+3 jets, one tight b-tag

MH=90 GeV

2000

V(→lν)+3 jets, one tight b-tag
Total Background
3500
3000

Signal

2500

MH=95 GeV

2000

1500

1500

1000

1000

500

500

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+3 jets, one tight b-tag
2000
Total Background
1800
Signal
1600
1400
MH=100 GeV
1200
1000
800
600
400
200
0
-1
-0.6 -0.2 0.2
0.6
1

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.20

Events / 0.20

Final Discriminant

-0.6

V(→lν)+3 jets, one tight b-tag
1800
Total Background
1600

Signal

1400

MH=105 GeV

1200
1000
800
600
400
200
0
-1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.57: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

210

Events / 0.20

Events / 0.20

V(→lν)+3 jets, one tight b-tag
Total Background

1800
1600

Signal

1400
1200

MH=110 GeV

1000
800

Total Background

1400

MH=115 GeV

1000
800

400
200
-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+3 jets, one tight b-tag
1600
Total Background
1400

Signal

1200
MH=120 GeV

1000
800

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.20

Events / 0.20

Signal

1200

600

600
400
200
0
-1

V(→lν)+3 jets, one tight b-tag
1600

600

V(→lν)+3 jets, one tight b-tag
1800

Total Background

1600
1400

Signal

1200

MH=125 GeV

1000
800
600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.58: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

211

1400

Events / 0.20

Events / 0.20

V(→lν)+3 jets, one tight b-tag
1600
Total Background
Signal

1200

MH=130 GeV

1000
800

V(→lν)+3 jets, one tight b-tag
1600

Total Background

1400

MH=135 GeV

1000
800

600

600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
Events / 0.20

Total Background

1400

Signal

1200

MH=140 GeV

1000
800

-0.6

-0.2

0.2

0.6

1

Final Discriminant

V(→lν)+3 jets, one tight b-tag

Events / 0.20

Signal

1200

V(→lν)+3 jets, one tight b-tag
1600
Total Background
1400

Signal

1200

MH=145 GeV

1000
800

600

600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.59: The final MVA output for events with three jets and one tight b-tag for (top
left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

212

Events / 0.20

V(→lν)+3 jets, one tight b-tag
Total Background

1400
Signal

1200

MH=150 GeV

1000
800
600
400
200
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.60: The final MVA output for events with three jets and one tight b-tag for
MH = 150 GeV. The signal is normalized to the sum of the backgrounds.

213

3000

Total Background

2500

V(→lν)+2 jets, two loose b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two loose b-tags

Signal
MH=90 GeV

2000
1500

Total Background

2500
2000

MH=95 GeV

1500

1000

1000

500

500

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+2 jets, two loose b-tags
2400
Total Background
2200
2000
Signal
1800
MH=100 GeV
1600
1400
1200
1000
800
600
400
200
0
-1
-0.6 -0.2 0.2
0.6
1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.10

Final Discriminant
Events / 0.10

Signal

V(→lν)+2 jets, two loose b-tags
2500
Total Background
Signal

2000

MH=105 GeV

1500
1000
500
0
-1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.61: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

214

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two loose b-tags
2400
Total Background
2200
2000
Signal
1800
MH=110 GeV
1600
1400
1200
1000
800
600
400
200
0
-1
-0.6 -0.2 0.2
0.6
1

MH=120 GeV

1500

500

-0.6

-0.2

0.2

0.6

-0.6

-0.2

0.2

0.6

1

Final Discriminant

1000

0
-1

1500

0
-1

Events / 0.10

Events / 0.10

Signal

2000

MH=115 GeV

500

V(→lν)+2 jets, two loose b-tags
Total Background

Signal

2000

1000

Final Discriminant
2500

V(→lν)+2 jets, two loose b-tags
2500
Total Background

1

Final Discriminant

V(→lν)+2 jets, two loose b-tags
2400
Total Background
2200
2000
Signal
1800
MH=125 GeV
1600
1400
1200
1000
800
600
400
200
0
-1
-0.6 -0.2 0.2
0.6
1

Final Discriminant

Figure B.62: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

215

V(→lν)+2 jets, two loose b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two loose b-tags
2400
Total Background
2200
2000
Signal
1800
MH=130 GeV
1600
1400
1200
1000
800
600
400
200
0
-1
-0.6 -0.2 0.2
0.6
1

Signal

2000
MH=135 GeV

1500
1000
500
0
-1

Signal

2000

-0.2

0.2

0.6

1

V(→lν)+2 jets, two loose b-tags

Total Background

2500

-0.6

Final Discriminant
Events / 0.10

Events / 0.10

Final Discriminant
V(→lν)+2 jets, two loose b-tags
3000

Total Background

2500

MH=140 GeV

1500

Total Background

2500
Signal

2000

MH=145 GeV

1500

1000

1000

500

500

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.63: The final MVA output for events with two jets and two loose b-tags for (top
left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

216

Events / 0.10

V(→lν)+2 jets, two loose b-tags
Total Background

3000
Signal

2500
MH=150 GeV

2000
1500
1000
500
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.64: The final MVA output for events with two jets and two loose b-tags for MH =
150 GeV. The signal is normalized to the sum of the backgrounds.

217

V(→lν)+3 jets, two loose b-tags

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two loose b-tags
Total Background

2500
Signal

2000

MH=90 GeV

1500

Signal

2000
MH=95 GeV

1500

1000

1000

500

500

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+3 jets, two loose b-tags
1400
Total Background
1200

-0.2

0.2

0.6

1

V(→lν)+3 jets, two loose b-tags

Signal

1000

-0.6

Final Discriminant
Events / 0.20

Events / 0.20

Total Background

2500

MH=100 GeV

800
600

Total Background

1200
Signal

1000

MH=105 GeV

800
600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.65: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

218

1400

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two loose b-tags
1600
Total Background
Signal

1200
MH=110 GeV

1000
800
600

1200
1000
800
600

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
Total Background

1200

Signal

1000

-0.2

0.2

0.6

1

V(→lν)+3 jets, two loose b-tags

Events / 0.20

1400

-0.6

Final Discriminant

V(→lν)+3 jets, two loose b-tags

Events / 0.20

MH=115 GeV

200

200

MH=120 GeV

800
600

1200

Total Background

1000

Signal
MH=125 GeV

800
600
400

400

200

200
0
-1

Signal

400

400

0
-1

V(→lν)+3 jets, two loose b-tags
1400
Total Background

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.66: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

219

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two loose b-tags
Total Background

1000

Signal

800

MH=130 GeV

600

V(→lν)+3 jets, two loose b-tags
1200
Total Background
1000

MH=135 GeV

800
600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+3 jets, two loose b-tags
900
Total Background
800
Signal

700
MH=140 GeV

600
500
400

-0.2

0.2

0.6

1

V(→lν)+3 jets, two loose b-tags
1200
Total Background
1000

Signal
MH=145 GeV

800
600
400

300
200

200

100
0
-1

-0.6

Final Discriminant
Events / 0.20

Events / 0.20

Signal

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.67: The final MVA output for events with three jets and two loose b-tags for (top
left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

220

Events / 0.20

V(→lν)+3 jets, two loose b-tags
Total Background

1000

Signal

800

MH=150 GeV

600
400
200
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.68: The final MVA output for events with three jets and two loose b-tags for
MH = 150 GeV. The signal is normalized to the sum of the backgrounds.

221

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two medium b-tags
Total Background

700
Signal

600

MH=90 GeV

500
400

V(→lν)+2 jets, two medium b-tags
700
Total Background
600

Signal

500

MH=95 GeV

400

300

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

700

Signal

600

Events / 0.10

Events / 0.10

Total Background

MH=100 GeV

500
400

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags
Total Background
700
600

Signal

500

MH=105 GeV

400
300

300

200

200

100

100
0
-1

-0.2

Final Discriminant

V(→lν)+2 jets, two medium b-tags
800

-0.6

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.69: The final MVA output for events with two jets and two medium b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

222

700

Total Background

600

Signal

500

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two medium b-tags

MH=110 GeV

400

V(→lν)+2 jets, two medium b-tags
Total Background
600
500

Signal

400

MH=115 GeV

300

300
200

200

100

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+2 jets, two medium b-tags
700
Total Background
600

Signal

500

MH=120 GeV

400
300

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags
Total Background

800
700

Signal

600

MH=125 GeV

500
400
300

200

200

100
0
-1

-0.2

Final Discriminant
Events / 0.10

Events / 0.10

Final Discriminant

-0.6

100
-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.70: The final MVA output for events with two jets and two medium b-tags for
(top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

223

Total Background

800
700

Signal

600

V(→lν)+2 jets, two medium b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two medium b-tags

MH=130 GeV

500
400

Total Background

800

Signal
MH=135 GeV

600
400

300
200

200

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+2 jets, two medium b-tags
Total Background
900
800

Signal

700
MH=140 GeV

600
500
400
200
100
-0.6

-0.2

0.2

0.6

0.2

0.6

1

V(→lν)+2 jets, two medium b-tags

300

0
-1

-0.2

Final Discriminant
Events / 0.10

Events / 0.10

Final Discriminant

-0.6

1

Final Discriminant

900
800
700
600
500
400
300
200
100
0
-1

Total Background
Signal
MH=145 GeV

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.71: The final MVA output for events with two jets and two medium b-tags for
(top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

224

Events / 0.10

V(→lν)+2 jets, two medium b-tags
Total Background

1000

Signal

800
MH=150 GeV

600
400
200
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.72: The final MVA output for events with two jets and two medium b-tags for
MH = 150 GeV. The signal is normalized to the sum of the backgrounds.

225

Total Background

1000

Signal

800

V(→lν)+3 jets, two medium b-tags

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two medium b-tags

MH=90 GeV

600

Signal

800

MH=95 GeV

600

400

400

200

200

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
Total Background

600

Signal

500

MH=100 GeV

400
300

0.2

0.6

1

Total Background

800
700

Signal

600

MH=105 GeV

500
400
300

200

200

100
0
-1

-0.2

V(→lν)+3 jets, two medium b-tags

Events / 0.20

700

-0.6

Final Discriminant

V(→lν)+3 jets, two medium b-tags

Events / 0.20

Total Background

1000

100
-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.73: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and
(bottom right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

226

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two medium b-tags
Total Background

600
Signal

500

MH=110 GeV

400
300

V(→lν)+3 jets, two medium b-tags
600
Total Background
500

Signal

400

MH=115 GeV

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+3 jets, two medium b-tags
700
Total Background
600

Signal

500

MH=120 GeV

400
300

-0.2

0.2

0.6

1

Final Discriminant
V(→lν)+3 jets, two medium b-tags

Events / 0.20

Events / 0.20

Final Discriminant

-0.6

Total Background

600

Signal

500

MH=125 GeV

400
300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.74: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

227

Total Background

500

Signal

400

V(→lν)+3 jets, two medium b-tags

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two medium b-tags

MH=130 GeV

300
200

450

Total Background

400
350

Signal
MH=135 GeV

300
250
200
150
100

100

50
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

Signal
MH=140 GeV

300

100

-0.6

-0.2

0.2

0.6

0.6

1

1

Final Discriminant

Total Background

450
400
350
300
250
200
150
100
50
0
-1

200

0
-1

0.2

V(→lν)+3 jets, two medium b-tags

Events / 0.20

Events / 0.20

400

-0.2

Final Discriminant

V(→lν)+3 jets, two medium b-tags
Total Background

-0.6

Signal
MH=145 GeV

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.75: The final MVA output for events with three jets and two medium b-tags for
(top left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

228

Events / 0.20

V(→lν)+3 jets, two medium b-tags
Total Background

400
350

Signal

300

MH=150 GeV

250
200
150
100
50
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.76: The final MVA output for events with three jets and two medium b-tags for
MH = 150 GeV. The signal is normalized to the sum of the backgrounds.

229

V(→lν)+2 jets, two tight b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two tight b-tags
Total Background
900
800
Signal

700
MH=90 GeV

600
500
400

700

Signal

600

MH=95 GeV

500
400

300

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+2 jets, two tight b-tags
Total Background
1000
Signal

800

MH=100 GeV

600

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Events / 0.10

Events / 0.10

Total Background

800

400

V(→lν)+2 jets, two tight b-tags
900
Total Background
800
Signal

700

MH=105 GeV

600
500
400
300
200

200

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.77: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

230

800

Total Background

700

V(→lν)+2 jets, two tight b-tags

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two tight b-tags

Signal

600

MH=110 GeV

500
400

Total Background

700
MH=115 GeV

500
400

300

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
V(→lν)+2 jets, two tight b-tags
900
Total Background
800

-0.2

0.2

0.6

1

V(→lν)+2 jets, two tight b-tags

Signal

700
MH=120 GeV

600

-0.6

Final Discriminant
Events / 0.10

Events / 0.10

Signal

600

500
400

Total Background

800
700

Signal

600

MH=125 GeV

500
400

300

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.78: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

231

800

Total Background

700

Events / 0.10

Events / 0.10

V(→lν)+2 jets, two tight b-tags

Signal

600

MH=130 GeV

500
400

V(→lν)+2 jets, two tight b-tags
1000

Total Background
Signal

800

MH=135 GeV

600
400

300
200

200

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

V(→lν)+2 jets, two tight b-tags
1000
Signal
MH=140 GeV

600
400

0.6

1

Total Background

1000
Signal

800

MH=145 GeV

600
400

200
0
-1

0.2

V(→lν)+2 jets, two tight b-tags

Total Background

800

-0.2

Final Discriminant
Events / 0.10

Events / 0.10

Final Discriminant

-0.6

200
-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.79: The final MVA output for events with two jets and two tight b-tags for (top
left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

232

Events / 0.10

V(→lν)+2 jets, two tight b-tags
1200
Total Background
1000

Signal
MH=150 GeV

800
600
400
200
0
-1

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.80: The final MVA output for events with two jets and two tight b-tags for MH =
150 GeV. The signal is normalized to the sum of the backgrounds.

233

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two tight b-tags
1000

Total Background
Signal

800

MH=90 GeV

600
400

V(→lν)+3 jets, two tight b-tags
900

Total Background

800
Signal

700

MH=95 GeV

600
500
400
300
200

200

100
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
Events / 0.20

Events / 0.20

Signal

600

0.2

0.6

1

V(→lν)+3 jets, two tight b-tags

Total Background

700

-0.2

Final Discriminant

V(→lν)+3 jets, two tight b-tags
800

-0.6

MH=100 GeV

500
400

800

Total Background

700

Signal

600

MH=105 GeV

500
400

300

300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.81: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 90 GeV, (top right) MH = 95 GeV, (bottom left) MH = 100 GeV, and (bottom
right) MH = 105 GeV. The signal is normalized to the sum of the backgrounds.

234

600

Signal

500

V(→lν)+3 jets, two tight b-tags

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two tight b-tags
700
Total Background

MH=110 GeV

400
300

Total Background

500

Signal

300

100

100
-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.4

0 0.2

0.6

1

Final Discriminant
V(→lν)+3 jets, two tight b-tags

Events / 0.20

V(→lν)+3 jets, two tight b-tags

Events / 0.20

MH=115 GeV

400

200

200

0
-1

600

Total Background

600
Signal

500
MH=120 GeV

400
300

600

Total Background

500

Signal
MH=125 GeV

400
300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.82: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 110 GeV, (top right) MH = 115 GeV, (bottom left) MH = 120 GeV, and
(bottom right) MH = 125 GeV. The signal is normalized to the sum of the backgrounds.

235

V(→lν)+3 jets, two tight b-tags

Events / 0.20

Events / 0.20

V(→lν)+3 jets, two tight b-tags
Total Background

500
Signal

400

MH=130 GeV

300

Total Background

500
Signal

400
300

200

200

100

100

0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant
Total Background

400

Events / 0.20

450

Signal

350

MH=140 GeV

300
250
200

-0.6

-0.2

0.2

0.6

1

Final Discriminant

V(→lν)+3 jets, two tight b-tags

Events / 0.20

MH=135 GeV

V(→lν)+3 jets, two tight b-tags
500
Total Background
Signal

400

MH=145 GeV

300
200

150
100

100

50
0
-1

-0.6

-0.2

0.2

0.6

0
-1

1

Final Discriminant

-0.6

-0.2

0.2

0.6

1

Final Discriminant

Figure B.83: The final MVA output for events with three jets and two tight b-tags for (top
left) MH = 130 GeV, (top right) MH = 135 GeV, (bottom left) MH = 140 GeV, and
(bottom right) MH = 145 GeV. The signal is normalized to the sum of the backgrounds.

236

Events / 0.20

V(→lν)+3 jets, two tight b-tags
450

Total Background

400
350
300
250

Signal

200
150
100
50
0
-1

MH=150 GeV

-0.6

-0.2

0.2

0.6

1

Final Discriminant
Figure B.84: The final MVA output for events with three jets and two tight b-tags for
MH = 150 GeV. The signal is normalized to the sum of the backgrounds.

237

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