SEARCH FOR HIGH-MASS DIELECTRON RESONANCES WITH THE ATLAS
DETECTOR
By
Sarah Heim

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

ABSTRACT
SEARCH FOR HIGH-MASS DIELECTRON RESONANCES WITH THE
ATLAS DETECTOR
By
Sarah Heim
This thesis describes a search for new heavy particles decaying into electron-positron pairs.
The search utilizes 1.08 fb−1 of proton-proton collisions at a center-of-mass energy of
√

s = 7 TeV, produced in 2011 by the Large Hadron Collider and recorded with the ATLAS

detector at the CERN laboratory in Switzerland. The reconstructed dielectron invariant
mass spectrum is compared to Standard Model expectations. Since no significant excess is
found, upper limits on the cross-section times branching ratio of Z ′ bosons and RandallSundrum gravitons are determined at the 95% confidence level using a Bayesian approach.
These limits are combined with limits obtained by a parallel analysis in the muon channel
′
and converted into lower limits on the masses of the Sequential Standard Model ZSSM boson (1.88 TeV), E6 Z ′ bosons (1.54 - 1.68 TeV), as well as the Randall-Sundrum graviton
¯
(1.67 TeV for k/MP l = 0.1).

To my parents, Gisela and Roland Heim.
And to my sister Julia.

iii

ACKNOWLEDGMENT

First of all, I want to thank my advisor Reinhard Schwienhorst who taught me how to do
high energy physics and who was always available to talk and answer questions with amazing
patience.
Thanks to Wojtek Fedorko for teaching me about likelihoods, pseudo-experiments, and
the proper way of searching for new physics.
Thanks to the rest of the MSU High Energy Physics group, especially to Jenny Holzbauer,
her accelerator husband Jeremiah, and James Koll for sharing their graduate student wisdom
with me and to Reiner Hauser whose knowledge about libraries, links and compilers saved
me hours of frustration. Not to forget Yuri Ermoline for helping me fix (among other things)
my bike, my laptop, and my glasses and Tom Rockwell, who kept the Tier3 alive.
Thanks to my committee, Professors Mahanti, Pope, Pratt, and Repko, for accepting
this job and a big thank you to Brenda Wenzlick and Debbie Barratt for helping me through
the bureaucratic jungle. I would have been quite desperate without you!
I also want to thank Bernd Stelzer and Oliver Stelzer-Chilton for sharing their statistical
and Z ′ knowledge with me and Ashutosh Kotwal for his theory insight.
Thanks to Simon Viel for being a great co-analyzer, co-convener, and co-hiker. Also to
Dan Hayden for great cooperation and the unskimmed 1 fb−1 cutflow.
I would also like to thank Amanda Smith for sharing her apartment, table, and cat with
me and for introducing me to American life.
And, of course, much love to Aaron Adair, who I thought of while writing this thesis.

iv

TABLE OF CONTENTS

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

viii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction

1

2 Standard Model of Particle Physics and beyond
2.1 Standard Model of Particle Physics . . . . . . . . . . . .
2.1.1 Symmetries and fields . . . . . . . . . . . . . . .
2.1.2 Lagrangian . . . . . . . . . . . . . . . . . . . . .
2.1.3 Feynman diagrams and cross-section calculations
2.1.4 Drell-Yan process . . . . . . . . . . . . . . . . . .
2.2 Beyond the Standard Model . . . . . . . . . . . . . . . .
2.2.1 Limitations of the Standard Model . . . . . . . .
2.2.2 Models predicting a dilepton resonance . . . . . .
2.2.3 Additional U(1) symmetries . . . . . . . . . . . .
2.2.4 Sequential Standard Model . . . . . . . . . . . . .
2.2.5 E6 model . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Randall-Sundrum graviton . . . . . . . . . . . . .
2.2.7 Previous limits . . . . . . . . . . . . . . . . . . .
3 Experimental setup
3.1 Large Hadron Collider . . . . . . .
3.1.1 Accelerator chain . . . . . .
3.1.2 LHC design . . . . . . . . .
3.1.3 LHC status 2011 . . . . . .
3.2 ATLAS detector . . . . . . . . . . .
3.2.1 Coordinate system . . . . .
3.2.2 Design . . . . . . . . . . . .
3.2.3 Inner Detector . . . . . . . .
3.2.4 Electromagnetic calorimeter
4 Electrons in the ATLAS detector
4.1 Z → ee event display . . . . . . .
4.2 Electron trigger . . . . . . . . . .
4.2.1 Level 1 Calorimeter trigger
4.2.2 High Level Trigger . . . .

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4.3
4.4
4.5
4.6

Electron reconstruction . . . . . . . . . . . .
Electron identification . . . . . . . . . . . .
Electron isolation . . . . . . . . . . . . . . .
Performance of electrons with high ET . . .
4.6.1 Energy reconstruction . . . . . . . .
4.6.2 Bunch-crossing identification . . . . .
4.6.3 Trigger and identification efficiencies

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55
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5 Simulation of signal and background processes
5.1 Standard Model backgrounds . . . . . . . . . .
5.2 Samples . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Event generators . . . . . . . . . . . . .
5.2.2 Samples and cross-sections . . . . . . . .
5.3 Corrections to the simulated samples . . . . . .
5.3.1 Efficiencies . . . . . . . . . . . . . . . . .
5.3.2 Energy resolution . . . . . . . . . . . . .
5.3.3 Calorimeter electronics . . . . . . . . . .
5.3.4 Pile-up . . . . . . . . . . . . . . . . . . .

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65
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6 Event selection and comparison with Standard Model expectations
6.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Cutflows and acceptance . . . . . . . . . . . . . . . . . . . . . .
6.2 QCD background estimation from data . . . . . . . . . . . . . . . . . .
6.2.1 Multijet shape estimate . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Multijet background normalization . . . . . . . . . . . . . . . .
6.2.3 Cross-checks with alternative methods . . . . . . . . . . . . . .
6.3 Comparison of data with Standard Model expectations . . . . . . . . .
6.3.1 Event yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Kinematic distributions . . . . . . . . . . . . . . . . . . . . . . .
6.4 Muon channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Comparison of data with Standard Model expectations . . . . .
7 Statistical treatment and results
7.1 Systematic uncertainties . . . . . . . . .
7.2 Statistical analysis . . . . . . . . . . . .
7.3 Signal search . . . . . . . . . . . . . . .
7.4 Limits . . . . . . . . . . . . . . . . . . .
7.4.1 Electron results . . . . . . . . . .
7.4.2 Combination with muon channel
7.5 Discussion of results . . . . . . . . . . .
7.5.1 Interpretation . . . . . . . . . . .
7.5.2 Comparison to other analyses . .
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7.5.3

Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8 Conclusion

120

Appendix

123

A Determination of identification efficiency
Probe
A.1 Definitions . . . . . . . . . . . . . . . . .
A.2 Method . . . . . . . . . . . . . . . . . .
A.3 Background estimation . . . . . . . . . .
A.4 Systematic uncertainty . . . . . . . . . .
A.5 Results . . . . . . . . . . . . . . . . . . .
A.6 Limitations and improvements . . . . . .

correction factors with Tag-and123
. . . . . . . . . . . . . . . . . . . . 123
. . . . . . . . . . . . . . . . . . . . 124
. . . . . . . . . . . . . . . . . . . . 127
. . . . . . . . . . . . . . . . . . . . 129
. . . . . . . . . . . . . . . . . . . . 129
. . . . . . . . . . . . . . . . . . . . 131

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

vii

134

LIST OF TABLES

2.1

Fermion fields in the SM and their charges. . . . . . . . . . . . . . . . . . . .

9

2.2

Several motivated choices of θE and the corresponding models. . . . . . . .
6

26

2.3

Charges of SM fermions in the E6 model. . . . . . . . . . . . . . . . . . . . .

26

2.4

Combined mass limits at the 95% C.L. on the E6 -motivated Z ′ models using
40 pb−1 of ATLAS dimuon and dielectron data. . . . . . . . . . . . . . . . .

31

4.1

Description of the electron identification cuts. . . . . . . . . . . . . . . . . .

58

5.1

List of background samples. . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.2

′
LO cross-sections for the ZSSM and some of the E6 models. . . . . . . . . .

71

5.3

¯
LO cross-sections for the RS graviton with different values of k/MP l . . . . .

71

5.4

Higher order QCD and electroweak correction factors for DY samples produced with the MRST2007lomod PDF. . . . . . . . . . . . . . . . . . . . . .

72

′
Event numbers after selection cuts for the data sample and a simulated ZSSM
sample (m ′ = 1500 GeV). . . . . . . . . . . . . . . . . . . . . . . . . . . .
Z

81

6.2

Comparison of the different QCD multijet, W + jets estimates. . . . . . . . .

89

6.3

Expected and observed number of events after selection cuts. . . . . . . . . .

91

6.4

Expected and observed number of events in the dimuon channel. . . . . . . .

94

7.1

Systematic uncertainties on the expected signal and background yields at
mee = 1.5 TeV for the Z ′ and RS graviton analysis. . . . . . . . . . . . . . . 103

7.2

′
Dielectron 95% C.L. mass limits on the ZSSM boson and the E6 Z ′ bosons.

6.1

viii

113

7.3

Dielectron 95% C.L. mass limits on the RS graviton with different values of
¯
k/MP l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.4

′
Combined dielectron and dimuon 95% C.L. mass limits on the ZSSM boson
and the E6 Z ′ bosons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.5

Combined dielectron and dimuon 95% C.L. mass limits on the RS graviton
¯
for different values of k/MP l . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.6

′
Observed limits on the lower mass of the ZSSM boson as obtained by different
experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.7

¯
Observed limits on the lower mass of the RS graviton with k/MP l =0.1 as
obtained by different experiments. . . . . . . . . . . . . . . . . . . . . . . . . 117

ix

LIST OF FIGURES

2.1

Feynman diagram of the DY process. . . . . . . . . . . . . . . . . . . . . . .

13

2.2

Strong and electroweak higher order contributions to the DY process. . . . .

14

2.3

Reconstructed dielectron invariant mass distribution of electron candidate
pairs passing the Tight identification cuts for events selected by low ET
threshold dielectron triggers. . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

2.4

Feynman diagrams for Z ′ boson and graviton exchange. . . . . . . . . . . . .

21

2.5

′
Mass peaks of the ZSSM and several E6 bosons, assuming a pole mass of
1500 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2.6

Suppression of the graviton wave function at the standard brane. . . . . . . .

27

2.7

Line shapes of Kaluza-Klein resonance peaks of a 1500 GeV RS graviton. . .

29

2.8

¯
Excluded regions in the space spanned by k/MP l and the graviton mass
measured at the 95% C.L. by the D/ collaboration. . . . . . . . . . . . . . .
0

30

3.1

CERN accelerator complex. . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.2

Coordinate system of the ATLAS detector. . . . . . . . . . . . . . . . . . . .

39

3.3

Schematic view of the ATLAS detector. . . . . . . . . . . . . . . . . . . . . .

40

3.4

Schematic view of the ATLAS Inner Detector. . . . . . . . . . . . . . . . . .

44

3.5

Schematical illustration of an electron shower in the EM calorimeter. . . . .

46

3.6

Schematic view of the ATLAS calorimeters. . . . . . . . . . . . . . . . . . .

47

3.7

Accordion structure of the EM calorimeter. . . . . . . . . . . . . . . . . . . .

48

3.8

Barrel module, showing the different layers of the EM calorimeter. . . . . . .

49

x

4.1

Event display of a Z → ee event. . . . . . . . . . . . . . . . . . . . . . . . .

4.2

′
Simulated dielectron invariant mass distributions of the ZSSM boson and the
′
Zχ boson before and after electron reconstruction and application of event
selection cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Identification efficiency with respect to reconstructed electrons as a function
of ET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

Trigger efficiency with respect to the electrons used in this analysis as a function of ET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

4.3

4.4

52

5.1

′
Reweighted invariant mass distributions for different masses of the ZSSM boson. 69

6.1

Event display of the dielectron event with the highest invariant mass (mee =
993 GeV) after full event selection. . . . . . . . . . . . . . . . . . . . . . . .

82

(η, φ)-map of all electrons passing the full selection in data and in the simulated DY background sample. . . . . . . . . . . . . . . . . . . . . . . . . . .

84

6.2

6.3

Efficiency of the selection cuts for different mZ ′ . . . . . . . . . . . . . . . . .

6.4

The invariant mass spectrum obtained by reversing the shower shape cuts in
the first layer of the EM calorimeter is fitted with a dijet function. . . . . . .

86

6.5

Template fit used to normalize the QCD multijet shape to data. . . . . . . .

88

6.6

Dielectron invariant mass distribution after full event selection, comparing the
SM backgrounds to data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

η distribution of the leading and subleading electrons after full event selection,
comparing the SM backgrounds to data. . . . . . . . . . . . . . . . . . . . .

93

ET distributions of the leading and subleading electron after full event selection, comparing the SM backgrounds to data. . . . . . . . . . . . . . . . . .

95

Dielectron rapidity and dielectron pT after full event selection, comparing the
SM backgrounds to data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

6.10 Calorimeter isolation distributions of the leading and subleading electron after
full event selection, comparing the SM backgrounds to data. . . . . . . . . .

97

6.7

6.8

6.9

xi

85

6.11 Calorimeter isolation distributions of the leading and subleading electron after
full event selection, comparing the SM backgrounds to data. Only events with
mee > 130 GeV are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

6.12 Dimuon invariant mass distribution after full event selection, comparing the
SM backgrounds to data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

7.1

Reduced likelihoods to have an excess caused by new physics for different Z ′
test masses and cross-sections. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2

95% C.L. limits on the cross-section times branching ratio for different Z ′
¯
models and the RS graviton with different values of k/MP l as obtained from
the dielectron invariant mass distribution. . . . . . . . . . . . . . . . . . . . 111

7.3

95% C.L. limits from 1000 pseudo-data distributions for a test mass mZ ′ =
810 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

7.4

95% C.L. limits on the cross-section times branching ratio for different Z ′
¯
models and the RS graviton with different values of k/MP l as obtained from
the dielectron and dimuon invariant mass distributions. . . . . . . . . . . . . 118

7.5

2D limits on the masses of technimesons in the context of the Low Scale
Technicolor model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

A.1 Illustration of the QCD jet background estimation under the Z peak. . . . . 125
A.2 Invariant mass distribution of tag and probe pairs for QCD jet background
from a simulated sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.3 Identification efficiencies obtained from data and a simulated Z → ee sample,
as well as calculated SF for electrons fulfilling the Medium requirements. . . 130
A.4 Efficiencies and SF for the B-layer cut as well as calorimeter isolation, calculated with respect to Medium electrons. . . . . . . . . . . . . . . . . . . . . . 131

xii

Chapter 1
Introduction
For a long time it has been a human endeavor to understand what the universe is made of
and why it looks the way it does. Today we know that the matter we find on earth consists
of atoms: nuclei of protons and neutrons surrounded by electrons. Protons and neutrons
are not fundamental particles but contain quarks and gluons. The quarks and electrons that
make up ordinary matter have heavier relatives which, soon after they are produced, decay
into lighter particles. Elementary particles can interact with each other through exchange
particles like the photon. For all particle types there exist antiparticles, with the same masses
but opposite charges (some particles like the photon are their own antiparticles).
The goal of particle physics is to understand what the elementary particles are and how
they interact with each other. During the 20th century, the Standard Model of Particle
Physics (SM) was developed, a very successful theory describing fundamental particles and
their interactions. The SM has not only been confirmed in many precision measurements,
but has also been able to predict observations like the discovery of the Z boson in 1983
[1, 2]. However, the SM cannot describe the subatomic world completely and has several
1

shortcomings: Among other things it does not include gravitation and it cannot explain why
there is more matter than antimatter in the universe.
One of the biggest quests in particle physics today is therefore to understand what lies
beyond the SM. This is done experimentally by searching for particle interactions that are not
predicted by the SM. As the SM has been under scrutiny for decades, the new interactions
are expected to be quite rare or only possible when the particles interacting with each other
have very high energies. The LHC (Large Hadron Collider) at the CERN (Conseil Europ´en
e
pour la Recherche Nucl´aire) laboratory in Geneva, Switzerland, collides particles with the
e
highest energies ever achieved in a particle accelerator and offers the unique opportunity to
directly search for physics inaccessible anywhere else. Large particle detectors like ATLAS
(A Toroidal LHC ApparatuS) are required to detect, filter and record the outcome of these
interactions. Their size is determined by the need to reconstruct the properties of the
produced particles.
This thesis describes a search for a heavy (> 130 GeV), electrically neutral particle
which is produced in proton-proton collisions at the LHC and decays into an electron and a
positron1 . We select collision events resulting in two electrons because such a heavy particle
decays too fast to be observed and the ATLAS detector can only record its decay products.
The invariant mass of the two electrons corresponds to the mass of the new particle and its
unique signature is a narrow resonance peak in the dielectron mass spectrum. The position of
this peak depends on the mass of the new particle, and its size on the production cross-section
as well as the branching ratio with which it decays into electrons. A high-mass dielectron
resonance is not predicted by the SM, but by some of its extensions like the E6 model [3, 4],
1 From here on, “electron” will be used representatively for both electrons and positrons.
2

which is one of the Grand Unified Theory models, suggesting that all fundamental forces
(except for gravity) are the same at very high energies. Another example is the RandallSundrum model [5], which proposes the graviton as the exchange particle for gravitation,
and which suggests the existence of at least one extra dimension. Finding the graviton or
another new exchange particle would significantly contribute to our understanding of the
fundamental forces. If we do not see a resonance, we can exclude at least parts of the
proposed extensions to the SM.
Besides this thesis, this analysis is published in [6]. The thesis is organized in 8 chapters:
1. Introduction.
2. This chapter describes the SM, focusing on the electroweak interaction. Successes
and shortcomings of the SM are discussed, as well as potential extensions that could
produce a high-mass dielectron resonance.
3. The LHC as well as the ATLAS detector are explained, with emphasis on the parts
necessary to find electron pairs: Tracks of electron candidates are recorded in the Inner
Detector and their energy is measured in the electromagnetic calorimeter.
4. Dedicated triggers filter events containing electron candidates whose energy and direction need to be reconstructed. Identification cuts increase the probability of an electron
candidate to be a real electron. Furthermore, the specific properties of electrons that
have high energies are described.
5. This chapter lists the simulated samples for signal and background processes used to
compare the data to the SM background plus potential signal, and the corrections that
need to be applied to the simulation to improve the modeling.
3

6. The event selection and the comparison between data and SM expectations for the
dielectron invariant mass distribution and other kinematic distributions are shown. The
estimate of QCD multijet production, which is obtained from data, is also described.
7. This chapter outlines the search for significant excesses in the dielectron invariant mass
distribution in data as compared to the SM background. Since no significant excess
is found, the Bayesian procedure for setting 95% confidence level limits on the crosssection times branching ratio and the signal mass is described and the resulting limits
are shown.
8. Conclusion.

4

Chapter 2
Standard Model of Particle Physics
and beyond
In this chapter, the SM is discussed, as well as possible extensions that could result in
high-mass dielectron resonances. In spite of spectacular successes describing and predicting
interactions between fundamental particles, the SM in its current form is considered to
be incomplete. In order to understand observations not explained by the SM, many models
have been suggested, some of which predict a new heavy particle decaying into two electrons.
Examples are models that allow the unification of fundamental forces at high energies as well
as models predicting extra dimensions.

2.1

Standard Model of Particle Physics

The SM describes almost every phenomenon observed in the subatomic world. It contains
the elementary particles of matter - quarks and leptons, which are fermions - and describes
the interactions between them as exchanges of force-carrying bosons. The W + /W − and Z
5

bosons as well as the photon (γ) mediate the electroweak force, while gluons (g) carry the
strong force. The SM also contains a Higgs field generating the masses of the fundamental
particles. The corresponding Higgs boson has not been found yet.
While the SM is incomplete (compare Sec. 2.2), it fits most of the available data to very
high precision and can be used to make reliable predictions. Examples of past successes of the
SM are the prediction of the existence and the properties of the weak bosons W + /W − and
Z. These were discovered [7, 8, 1, 2] at the Super Proton Synchroton, CERN, more than 10
years after the formulation of the electroweak theory [9, 10, 11].
In the following, the fundamental principles and building blocks of the SM are described,
followed by a discussion of electroweak interactions with a focus on the Drell-Yan process
(DY, q q → Z/γ∗ → e+ e− ). Not only is the DY process the largest background in this
¯
analysis, but many proposed new interactions leading to high-mass dielectron resonances
have very similar structures and could actually modify it, as shown in Sec. 2.2.3.

2.1.1

Symmetries and fields

The SM is a gauge theory in which the fundamental particles are represented by quantized
fields. In gauge theories, the Lagrangian is invariant with respect to certain local transformations, i.e. changes of the participating fields that can be different at any point in space-time.
In contrast to this, global transformations like translations change a field the same way at every point. Gauge theories are very powerful tools because they are renormalizable [12]. This
means they provide a way to cancel divergences, infinities that may arise in the calculation of
physical quantities. Furthermore, every gauge invariance leads to a conserved quantity [13]
as well as a number of force carriers, called gauge bosons, which only act on fields carrying
6

some of the conserved charge. This can easily be seen by looking at the electromagnetic
interaction, where the need to make the Lagrangian invariant with respect to phase changes
of the electron field leads to the introduction of an additional vector field, the photon. This
has to be massless since a photon mass term would not be gauge invariant. The conserved
quantity in this example is the electromagnetic charge.
Transformation invariances can be described by symmetry groups, whose members are
the generators of the transformation, e.g. unitary matrices in case of rotations. The SM is
described by the following combination of gauge symmetry groups:

SU(3)C × SU(2)L × U(1)Y

(2.1)

Here, U(1) corresponds to a unitary group of degree 1. It has one generator and describes
the invariance of the Lagrangian when the fields are multiplied by any given phase factor.
SU(2) is a special unitary group of degree 2. It has three generators, which can be represented by 2 × 2 matrices whose determinant is 1. SU(2)L × U(1)Y corresponds to the
electroweak interaction. According to the number of generators, U(1)Y contributes one
gauge boson, called B, while SU(2)L has three, W 0 , W 1 , W 2 . The conserved quantity in
U(1)Y is the weak hypercharge Y , in SU(2)L it is the weak isospin I. These quantities are
not independent; their relation to the electromagnetic charge Q is Y = Q − I 3 , where I 3 is
the third component of the weak isospin [12]. The electroweak interaction is chiral, which
means particles are treated differently depending on whether they are left- or right-handed:
Right-handed particles and left-handed antiparticles do not interact with the SU(2)L gauge
bosons. Spontaneous Symmetry Breaking (SSB, see Sec 2.1.2) results in an unbroken group
U(1)Q , whose gauge boson is a massless photon and consists of a linear combination of B
7

and W 0 . The photon interacts with particles that have electromagnetic charge. The orthogonal linear combination of B and W 0 produces a neutral Z boson, whose mass has been
measured to be 91.19 GeV [14]. The remaining force carriers of the weak interaction are
the charged W + and W − bosons, which correspond to linear combinations of W 1 and W 2 .
Their mass has been experimentally determined to be 80.40 GeV [14].
SU(3)C describes the strong interaction. Its generators can be represented by 3 × 3
matrices and correspond to eight massless gluons. The conserved quantity is the color charge.
The strong force only acts on particles carrying color; these are the gluons themselves as
well as the six flavors of quarks.
Table 2.1 shows the fermion fields of the SM, including their charges. The table for
the antiparticles looks identical, except for a sign-flip in the charges. Each quark can have
one of three color indices. There are three generations of quarks and leptons. The righthanded fermions are SU(2)L singlets, which means they do not interact with the W bosons.
The leptons do not have color charge, thus they do not participate in the strong interaction.
Likewise, the neutrinos are electromagnetically neutral, so they cannot interact with photons
directly. Right-handed neutrinos have never been observed; however, oscillations have been
detected between the three generations of neutrinos, which enforce the inclusion of righthanded neutrinos as an extension to the SM (compare Sec. 2.2.1).

2.1.2

Lagrangian

This section describes the Lagrangian density of the SM with focus on the neutral electroweak
interaction, as this part could be modified by the new physics we search for in this analysis.
A short description of SSB is given, and the electroweak Lagrangian is shown before and
8

I

Generation
II
III

Color?

Charges
I3
Y

Q

Quarks

u
d L
uR
dR

c
s L
cR
sR

t
b L
tR
bR

Yes
Yes
Yes
Yes

1/2
-1/2
0
0

1/6
1/6
2/3
-1/3

2/3
-1/3
2/3
-1/3

Leptons

νe
e L
eR

νµ
µ L
µR

ντ
τ L
τR

No
No
No

1/2
-1/2
0

-1/2
-1/2
-1

0
-1
-1

Table 2.1: Fermion fields in the SM and their charges [14]. Each quark can have one of three
color indices.

after including SSB.
The Lagrangian describes the dynamics of fields and their interactions. It is defined as

L = T − V,

(2.2)

where T is the kinetic energy and V is the potential energy. In field theory, the Lagrangian
density L is used instead of the Lagrangian, with L = L d3 x. A Lagrangian in field theory
can contain terms for the free propagation of particles, their masses, and their interaction
with other particles as well as with themselves.
The Lagrangian density of the SM can be split into four parts [12]:

L = LF ermion + LGauge + LHiggs + LY ukawa

(2.3)

LF ermion describes the kinetic energy of the fermions as well as interactions of the fermions
with the gauge bosons. If the weak eigenstates of the fermions are described in 4-component
vectors F , the part of the Lagrangian density that describes the free motion of the fermions
9

can be written as:

¯
/
L0 = F (x)(i∂ − m)F (x),

/
∂ = γµ

∂
= γ µ ∂µ ,
∂xµ

(2.4)

¯
where γ µ is the set of Dirac matrices and the Dirac adjoint is defined as F = F † γ 0 . If the
fermion field F is written as F = FL + FR , where FL(R) corresponds to left-(right-)handed
fermions, FL = F (1 − γ 5 )/2 and FR = F (1 + γ 5 )/2, it becomes clear that only mass
¯
¯
terms survive that contain a left- and a right-handed field, since FL FL = FR FR = 0.
The Lagrangian density for the electroweak sector, LEW , can be written as:
LEW =

¯
¯
/
/
FLf iDFLf + FRf iDFRf .

(2.5)

f

D is the derivative in the free Lagrangian density, which is made gauge invariant with respect
i
to SU(2)L and U(1)Y by adding the fields Wµ and Bµ :
Dµ FLf = (∂µ + ig I · Wµ + ig ′ YLf Bµ )FLf
Dµ FRf = (∂µ + ig ′ YRf Bµ )FRf .

(2.6)

Here, g and g ′ are the gauge coupling constants for SU(2)L and U(1)Y respectively. I
corresponds to the weak isospin, while Y is the weak hypercharge. There is no mass term
since a term mixing left- and right-handed fields would break the gauge symmetry.
LGauge contains the kinetic terms of the gauge bosons B, W i and g as well as the selfinteraction terms for all gauge bosons but B, which does not self-interact. The Lagrangian
density for the Higgs field LHiggs (Eq. 2.7) consists of the kinetic energy and the self10

interaction of the Higgs boson as well as terms for interactions between the Higgs and the
gauge bosons. The Yukawa term LY ukawa describes the couplings between the Higgs boson
and the fermions, giving the latter their masses.

Like for fermions, explicit mass terms for gauge bosons violate the gauge invariance.
However, we know that the weak gauge bosons have mass, thus the gauge symmetry of the
electroweak interaction must be broken. In the SM, this happens through SSB. Charges
are still conserved, since SSB does not introduce any explicit symmetry breaking. The
Lagrangian density of the Higgs field φ preserves the gauge symmetry:

LHiggs = (Dµ φ)† (Dµ φ) − V (φ),

(2.7)

where φ is the complex scalar Higgs field, and
ig ′
Bµ)φ.
Dµ φ = (∂µ + ig I · Wµ +
2

(2.8)

V (φ) needs to be gauge invariant with respect to SU(2)L × U(1)Y as well, and has the form
V (φ) = µ2 φ† φ + λ(φ† φ)2 .

(2.9)

The ground state of φ can be found by looking for the minimum of V (φ), and can be written
0
as φ0 = v , where v =

−µ2 /λ. If µ2 < 0, φ has a non-zero vacuum expectation value

and φ can be written as φ = φ0 + φ′ , where φ′ is a field with a zero vacuum expectation
value. In terms of φ′ , the SU(2)L × U(1)Y symmetry in Eq. 2.7 is broken and mass terms
for the weak bosons emerge. These are now a mixture of the original gauge bosons. The
11

electroweak mixing angle θW is defined as

tan θW =

g′
.
g

(2.10)

The Z boson can be expressed in terms of this angle and the gauge bosons B and W 3 :

3
Zµ = −Bµ cos θW + Wµ sin θW .

(2.11)

The photon is the orthogonal linear combination:

3
Aµ = Bµ cos θW + Wµ sin θW .

(2.12)

The couplings g and g ′ are not independent, instead they are related to the electromagnetic
coupling e and the neutral weak coupling gZ by

e = g sin θW ,

gZ =

g
g′
e
=
=
.
cos θW
sin θW
sin θW cos θW

(2.13)

Now the Lagrangian density for the neutral electroweak interaction of fermions can be
3
written down. It can be obtained by replacing Bµ and Wµ with Aµ and Zµ according to
Eq. 2.11 and 2.12 in Eq. 2.5:

LEW,n = −e
− gZ

¯
ψf γ µ Qf ψf Aµ

(2.14)

f

f

3
¯
¯
[ψLf γ µ (If − Qf sin2 θW )ψLf Zµ + ψRf γ µ (−Qf sin2 θW )ψRf Zµ ].
12

q
¯

e−
Z/γ∗

q

e+

Figure 2.1: Feynman diagram of the DY process.
The first line describes the electromagnetic interaction. Its strength is independent of the
chirality of the leptons and depends on the coupling constant e and the fermion charge Qf .
This part of the electroweak Lagrangian can also be derived directly from the requirement
of gauge invariance of the Lagrangian with respect to phase changes in the electron fields.
The second line describes the neutral weak interaction, which is chiral, having a different
strength for left- and right-handed fermions. The Lagrangian density is now written in terms
of mass eigenstates ψ, instead of weak eigenstates F .
Sec. 2.2 shows how the electroweak Lagrangian is modified by additional neutral Z ′ gauge
bosons.

2.1.3

Feynman diagrams and cross-section calculations

Feynman diagrams simplify the calculation of the probability that particles interact with
each other in a certain way. The diagrams help visualize the initial, intermediate, and final
states, and they help determine the importance of different sub-processes.
The Feynman diagram in Fig. 2.1 shows two of the possible ways in which two quarks
can annihilate: The production of a Z boson or a photon and the subsequent decays of the
intermediate particle into two electrons. In this process, countless additional interactions are
possible, for example radiation of gluons and photons as well as particle loops. These sub13

q
¯

e−

q
¯

e−

Z/γ∗

Z/γ∗

g

γ

g
q

e+

q

e+

(a)

(b)
q
¯

e−
Z/γ∗
γ

q

e+

(c)
Figure 2.2: Strong and electroweak higher order contributions to the DY process: Radiation
of a gluon in the initial state (a), a gluon loop in the initial state and the emittance of a
photon in the final state (b), and a photon loop in the final state (c).
processes can be illustrated in different Feynman diagrams (see Fig. 2.2 for a few examples).
Since the probability amplitude of every particle interaction is proportional to the coupling constant, the less particle-particle vertices a Feynman diagram for a given sub-process
has, the more likely it is. Furthermore, higher order contributions involving gluons are larger
than those involving photons because the strong interaction has larger couplings than the
EW interaction. The Feynman diagram in Fig. 2.1 illustrates the dominant, leading order
(LO) contribution to the q q → e+ e− X process (X denotes additional radiation). In this
¯
sense, Feynman diagrams are tools of perturbation theory; they allow to split up the infinite
number of possible interactions in a process into different orders of probability.
Using the corresponding diagrams, one can in principle calculate cross-sections up to a
required precision, however, for higher order processes it is necessary to introduce normaliza14

tion and factorization scales. These are artificial cut-offs removing infinities which can occur
if not all orders of the perturbation series are taken into account. Furthermore, perturbation
theory can only be applied as long as the coupling constants are small. This is the case for
electroweak interactions, but not necessarily for interactions involving the strong force. Since
we are looking at dielectron final states, strong interactions can only happen in the initial
state. The factorization theorem [15] states that perturbation theory still applies for the
hard scattering process itself, because the quarks are asymptotically free at high energies.

The Feynman rules give a prescription on how to turn Feynman diagrams into matrix
elements, which correspond to probability amplitudes of the interactions. These rules are
obtained from the Lagrangian [16]. In order to calculate the matrix element, the 4-momenta
of the incoming and outcoming particles must be known. If they are defined for the incoming
particles, the inclusive cross-section is proportional to the absolute square of the matrix
element, integrated over all possible momenta of the final state particles. However, at hadron
colliders like the LHC which collides protons, the reacting quarks carry an unknown fraction
of the proton momenta. In order to calculate cross-sections, one usually integrates over all
possible incoming quark momenta, using probability functions for the momentum fraction
of the quarks (parton distribution functions, PDFs) which are obtained from fits to data
[17, 18, 19]. Since the quarks in the protons are bound by the strong interaction, the PDFs
include non-perturbative effects, and can account for higher order QCD corrections in the
initial state.
15

2.1.4

Drell-Yan process

In the DY process, a quark and an antiquark produce a photon or a Z boson, which then
decays into quarks or leptons. The final state considered in this analysis is the dielectron
decay (q q → Z/γ∗ → e+ e− ). Figure 2.1 shows the Feynman diagram of the LO DY process.
¯
The DY process is the most important SM background to the search for new physics
with dielectron final states. Its electroweak structure serves as a model for interactions with
new heavy neutral gauge bosons. The inclusion of new gauge bosons in the electroweak Lagrangian does not necessarily lead to a simple cross-section addition of the different processes,
but can cause shifts in the peak mass of the Z boson and its couplings to the fermions (mass
mixing, [20]) as well as cross-section enhancement/suppression due to positive/negative interference. Neglecting mass mixing, we write down the electroweak Lagrangian and the
matrix element of the DY and the new Z ′ boson in Sec. 2.2 (Eq. 2.22, 2.23). In this section,
the components of the pure DY matrix element are explained.
In order to write down the LO equation for the DY matrix element [21], the following
4-momenta (p, k) and helicities (σ, τ ) are assigned to the incoming and outgoing particles:

q(p1 , σ1 ) + q (p2 , σ2 ) → e− (k1 , τ1 ) + e+ (k2 , τ2 ).
¯

(2.15)

The Mandelstam variables are defined as

ˆ
s = (p1 + p2 )2 , t = (p1 − k1 )2 , u = (p1 − k2 )2 .
ˆ
ˆ

(2.16)

Here, s corresponds to the center-of-mass (CM) energy of the collision and is, at LO, equal
ˆ
to the invariant mass of the two outgoing electrons (k1 + k2 )2 .
16

Applying the Feynman rules [16], one can write down the chirality dependent matrix
element for the full DY process at LO as [21]:

e
Mσ,τ (ˆ, t, u) =
s ˆˆ
s
ˆ

V =γ,Z

τ
στ
cσ
s
qqV ceeV PV (ˆ) M .

(2.17)

For the weak interaction, the couplings between fermions f and exchange bosons depend on
the chiralities σ = σ1 = −σ2 and τ = τ1 = −τ2 . The couplings c are taken directly from
the electroweak Lagrangian (Eq. 2.14) and can be written as:

L/R
= −eQf ,
c
ffγ

3
If − sin2 θW Qf
L
cf f Z = e
,
sin θW cos θW

cRf Z = −eQf
f

sin θW
.
cos θW

(2.18)

The propagators for the two exchange particles are:

Pγ = 1,

PZ =

s
ˆ
.
2 + iˆΓ /M )
(ˆ − MZ
s
s Z Z

(2.19)

Since the Z boson is not a stable particle, its width ΓZ is inserted into the Z boson propagator. This is done in the “running width” scheme, which illustrates the change of the width
with different CM energies.

The “standard” matrix element M στ depends on the polarization of the incoming and
outgoing fermions. Two different chirality combinations are allowed,

M LL = M RR = 2ˆ,
u

ˆ
M LR = M RL = 2t.
17

(2.20)

2.2

Beyond the Standard Model

The SM is quite successful in describing the interactions of fundamental particles throughout
the experimentally available energy range. However, there are many missing pieces, observations not explained by the SM or even contradicting its predictions. Furthermore, there are
theoretical concerns and arguments which suggest that the SM can only be part of a larger
theoretical framework.

2.2.1

Limitations of the Standard Model

Some observations not covered by the SM are the matter-antimatter asymmetry in the
universe without which there would be no stable matter, as well as the existence of dark
matter. The SM predicts neutrinos to be massless, but the observation of neutrino oscillations
requires neutrinos to have mass [22, 23, 24, 25]. The latter is fortunately quite easy to
incorporate in the SM by adding right-handed neutrinos. The largest discrepancy between
theory and observation can be found in the value of the cosmological constant, usually
considered to describe the energy density of the vacuum [26]. Astronomers have measured
the rate with which the universe expands and have found this expansion to be accelerating,
leading, in the framework of general relativity, to a very small, positive cosmological constant
[27, 28]. However, the SM as a quantum field theory predicts a value orders of magnitudes
above the one suggested by astronomical measurements.
Theoretical concerns include the ∼20 parameters of the SM, like the number of generations and masses of the fermions, which cannot be derived, but have to be experimentally
determined. Furthermore, no explanation is given why the electric charges of electrons and
protons cancel each other. Another important issue is gravity, which is the only one of the
18

four fundamental forces which the SM does not describe. But even assuming some underlying gravitational theory, the SM cannot explain why gravitation is so weak compared to
the other forces. This is known as the “hierarchy problem”, and is closely related to the
“fine tuning problem”: The Higgs field is constrained by the known masses of the W and Z
bosons, and cancellations of the order of 1016 times the Higgs boson mass are required in
order to reconcile its value with the huge quantum corrections from fermion and gauge boson loops predicted by the SM. Another point is the observation that the coupling constants
depend on the energy of the particles involved in the interaction, and that in the SM these
coupling constants almost but not fully coincide when extrapolated to high energies.

2.2.2

Models predicting a dilepton resonance

Historically, dilepton resonances have been a window to a better understanding of fundamental particles and forces. Figure 2.3 shows the reconstructed invariant mass distribution
of ATLAS electron candidate pairs passing a Tight set of identification cuts (see Sec. 4.4).
The resonance peak of the J/ψ meson, which is a c¯ bound state, was found at a mass of
c
∼3.1 GeV. The discovery of the J/ψ resonance in 1974 [29, 30] is called November Revolution, since it confirmed, together with subsequent discoveries of charmed baryons and
mesons [31, 32, 33], the existence of a fourth quark and showed that the electroweak theory
can be applied to hadrons. The resonance peak of the Z boson was discovered at a mass
of 91.2 GeV in 1983 [1, 2]. Together with the charged gauge bosons W + and W − , it was
predicted by the electroweak theory (see Sec. 2.1) and helped to firmly establish the latter
as part of the SM. The discovery of a dilepton resonance beyond the peak of the Z boson
could have a similar effect on currently postulated extensions to the SM.
19

Entries / GeV

105

ATLAS Data 2010, s=7 TeV

J/ψ

104

∫Ldt ≈40 pb-1

Υ

Z

3

10

102

J/ ψ

105

10
ψ (2S)

104

1
10-1
1

2.5

3

3.5

4

2 3 45

10

20 30

100 200

1000
mee [GeV]

Figure 2.3: Reconstructed dielectron invariant mass distribution of electron candidate pairs
passing the Tight identification cuts for events selected by low ET threshold dielectron
triggers [34]. The number of events is normalised by the bin width. Errors are statistical
only.

There are several models that predict a resonance beyond the Z boson peak. Many of
them try to solve specific problems of the SM, others use theoretical arguments like the
unification of forces to motivate extensions to the SM.
Supersymmetric (SUSY) models [35, 36, 37] solve the hierarchy problem by assigning
every SM particle a supersymmetric partner, canceling its loop contribution to the Higgs
field. Since SUSY must be broken, one of the heavier superpartners of the SM particles
could be discovered as a high-mass dilepton resonance.
Technicolor theories [38, 39, 40], inspired by how the strong interaction is modeled, avoid
the hierarchy problem completely by proposing an alternative way of SSB which does not
require a Higgs boson. Like QCD, technicolor models predict a zoo of composite particles,
20

q
¯

q /g
¯

e−

e−
G∗

Z′

q

q/g

e+

(a)

e+

(b)

Figure 2.4: Feynman diagrams for Z ′ boson (a) and graviton (G*) (b) exchange.
which could be visible as dilepton resonances.
Additional U(1) symmetries lead to the emergence of new neutral gauge bosons, called Z ′
bosons, which might be heavy and observable as resonances in the dielectron spectrum (see
Sec. 2.2.3 and Fig. 2.4(a)). Examples are the Sequential Standard Model, which is described
in Sec. 2.2.4, the little Higgs models [41] and the higgsless Stueckelberg model [42]. The new
U(1) symmetries could be due to Grand Unified Theories (GUTs). GUTs try to unify all
three SM forces at high energies within large symmetry groups, which break at lower energies
into the SM group and other symmetry factors. Suggested GUT models (among others) are
the E6 model, which is discussed in detail in Sec. 2.2.5, and the left-right symmetric models
[43, 44, 45].
Extra dimensions might be the explanation for the extreme differences between the
strengths of the fundamental forces. By allowing the graviton, the postulated exchange boson of gravitation, to propagate into extra dimensions, only a fraction of its strength might
be visible in the standard 4-dimensional space-time. The Randall-Sundrum (RS) model of
extra dimensions is discussed in Sec. 2.2.6. Its force carrier, the RS graviton, obtains mass
through Kaluza-Klein excitations and decays into two electrons (compare Fig. 2.4(b)), hence
it could be discovered in a dilepton search.
21

2.2.3

Additional U(1) symmetries

A large number of models predict the SM symmetry (Eq. 2.1) to be extended by at least
one additional U(1)′ group:
SU(3)C × SU(2)L × U(1)Y × U′ (1).

(2.21)

If this symmetry is broken, e.g. by the Higgs mechanism, a massive, neutral gauge Z ′ boson
with spin-1 emerges. The addition to the electroweak Lagrangian density (Eq. 2.14) can be
written as

LEW,n+U (1)′ = LEW,n − gZ ′

f

′
′
¯
¯
[ψLf γ µ Q′ ψLf Zµ + ψRf γ µ Q′ ψRf Zµ ].
Rf
Lf

(2.22)

The structure of the additional term in the Lagrangian density is the same as the term
describing the exchange of a SM Z boson (compare the second line in Eq. 2.14). The coupling
gZ ′ , the charges Q′ and Q′ , and the mass of the additional boson depend on the model
Rf
Lf
which predicts the additional symmetry. In addition, couplings to exotic new fermions could
be possible, and are even required in some models, in order to cancel anomalies (triangle
Feynman diagrams in which the gauge symmetry would not be conserved).
Here, mass mixing between the Z and the Z ′ boson is neglected. Mass mixing can happen
if there are mixed Z/Z ′ terms in the kinetic part of the Higgs Lagrangian, where the masses
of the bosons are generated. Diagonalizing the resulting mass matrix shows the Z and Z ′
bosons as linear combinations of mass eigenstates Z1 and Z2 . Precision measurements at
the Z boson mass peak have put stringent limits on such a mixing, and it can be safely
ignored here [20].
22

The matrix element of the DY process in Eq. 2.17 can now be extended to also include
a term for the Z ′ boson:
e2
Mσ,τ (ˆ, t, u) =
s ˆˆ
s
ˆ

V =γ,Z,Z ′

τ
στ
cσ
s
qqV ceeV PV (ˆ) M .

(2.23)

The couplings cσ ′ are model dependent, the propagator however is assumed to be the
ffZ
same as for the Z boson (Eq. 2.19), with the exception of the width, which might differ
because of new couplings, possible decays into exotic fermions, as well as the inclusion of the
¯
tt decay channel for Z ′ bosons with masses larger than twice the top quark mass.
The addition of the Z ′ boson as an exchange particle in the DY process happens in the
matrix element. Therefore the total cross-section, which is proportional to |M|2 , will not
just be the sum of the cross-sections of DY and the new process. Instead there will be
model-dependent interference effects.

2.2.4

Sequential Standard Model

In this analysis, the Sequential Standard Model (SSM) Z ′ boson [4] is used as a refer′
ence model. The ZSSM boson has the same couplings to the SM fermions as the Z boson
(Eq. 2.18), but differs in mass and width (ΓZ ′ ∝ MZ ′ ). It can only exist if it couples to
additional exotic fermions or as an excited state of the Z boson in the context of extra dimensions [47], but it is a very useful baseline model to make comparisons between the reach
of different experiments.
′
The mass peak of the ZSSM is shown in Fig. 2.5, assuming a pole mass of 1500 GeV. The
distributions in this figure are produced using the Pythia [46] generator (compare Sec. 5.2.1,
23

Events/10 GeV

1

10-1

SSM
χ
η
ψ
DY

10-2

10-3
600

800 1000 1200 1400 1600 1800 2000
mee [GeV]

′
Figure 2.5: Mass peaks of the ZSSM and several E6 bosons, assuming a pole mass of
1500 GeV. The distributions are produced with the Pythia [46] generator; their normalization corresponds to 1 fb−1 of pp collison data at a CM energy of 7 TeV. For interpretation
of the references to color in this and all other figures, the reader is referred to the electronic
version of this dissertation.
detector effects like resolution are not included) and correspond to 1 fb−1 of data. It can
be seen that below the mass peak, the differential cross-section for the DY process alone is
′
larger than the combined cross-section for DY and ZSSM due to destructive interference.
However, the additional cross-section at the peak dominates the shape, therefore interference
effects are neglected in this analysis.

2.2.5

E6 model

GUTs are interesting because they unify electroweak and strong forces by postulating one
single gauge symmetry at a very high energy (referred to as the GUT scale). This can help
24

to explain relations between quarks and leptons, since both can be part of the same group
representation. The GUT considered in this analysis is a model based on the symmetry
group E6 [3, 4], which can be derived from superstring theories. At the GUT scale, the E6
symmetry successively breaks into weaker symmetries,

E6 → SO(10) × U(1)ψ → SU(5) × U(1)χ × U(1)ψ ,

(2.24)

where SU(5) breaks into the SM symmetry (Eq. 2.1). The model suggests that a linear
combination of the two additional U(1) gauge groups is broken at the electroweak scale
(about 1 TeV), producing one additional gauge boson whose charges depend on the fermions
f , their chiralities σ and the mixing angle θE :
6
Q′σ (θE ) = Qσ χ cos θE + Qσ ψ sin θE ,
f
f
f
6
6
6

0 ≤ θE < π.
6

(2.25)

The coupling in the matrix element (Eq. 2.23) can be written as:

cσ ′ =
ffZ
where the factor

5 e
Q′σ (θ ),
3 cos θW f E6

(2.26)

5 e
′
3 cos θW corresponds to the U (1)Y coupling g (see Eq. 2.13), with an

additional normalization factor to unify the SM gauge groups into an SU(5) group at GUT
energies.

Table 2.2 lists the names of models for several choices of θE [3, 4], which can be derived
6
from different GUT scenarios and could be detectable at the LHC.

As mentioned above,

the charges Qσ χ and Qσ ψ depend on the type of fermion and the helicity. They are listed
f
f
25

θE

′
Zχ

′
Zψ

′
Zη

0

Model

π/2

− arctan

6

′
ZI
5/3

π + arctan

3/5

′
ZN
√
arctan 15

′
ZS
√
arctan 15/9

Table 2.2: Several motivated choices of θE and the corresponding models [3, 4].
6

√
2 10 Qχ
√
2 6 Qψ

uL , d L

uR , e R

dR

eL

-1

1

-3

3

1

-1

-1

1

Table 2.3: Charges of SM fermions in the E6 model [3, 4].
in Table 2.3 for the first fermion generation, but are the same for the other generations.
According to the underlying larger symmetries, some of the quarks and leptons share the
same charges.
All of the E6 models predict right-handed neutrinos, and most need the addition of exotic
fermions in order to cancel anomalies [20]. Right-handed neutrinos and exotic fermions are
assumed to be too heavy to participate in the Z ′ decay.
′
′
′
Figure 2.5 shows the dielectron invariant mass peaks of the Zχ , Zη and Zψ bosons,
produced by the Pythia [46] event generator assuming a pole mass of 1500 GeV.

2.2.6

Randall-Sundrum graviton

As a gauge theory (see Sec. 2.1.1), the SM predicts exchange bosons for the electromagnetic,
strong and weak forces. Since gravitation is also a force, the graviton has been postulated
as its exchange boson. Its spin would be 2, because of the mathematical structure of the
interaction. However, no viable quantum field theory of gravitation has been developed yet,
due to infinities arising in the calculations. The “classical limit” of such a theory would be
26

Planck brane

standard brane

graviton
probability
function

φ = 0

φ = π

Figure 2.6: Suppression of the graviton wave function at the standard brane.

the theory of general relativity [48]. In this limit, it is possible to look at different space-time
scenarios and their effects on SM interactions, the gravitational force and its hypothetical
exchange particle, the graviton.
In the last few decades, models with extra dimensions have been proposed to explain
why gravity is so much weaker than the other fundamental forces, or, formulated differently,
why the Planck scale (MP l ≈ 1016 TeV) is so much higher than the electroweak scale
(MEW ≈ 1 TeV). While the model of Large Extra Dimensions [49] leads to a new hierarchy,
the Randall-Sundrum (RS) model [5] manages to remove the hierarchy problem completely.
In its minimal form, the RS model introduces one extra dimension φ which is considered
to be finite, forming a circle with radius rc at every point in the standard 4-dimensional
space-time. Two 4-dimensional subspaces, called branes, are suggested to be located at
angles φ = 0 and φ = π of this circle: the standard space-time brane at φ = π and a Planck
brane at φ = 0 (see Fig. 2.6). All SM particles are confined to the standard brane; only
the graviton field extends into the extra dimension. In the framework of general relativity,
27

this extra dimension results in a 5-dimensional space-time metric with a “warping” factor in
front of the standard 4-dimensional metric:

2
ds2 = e−2krc φ gµν dxµ dxν + rc dφ2 ,

(2.27)

where xµ , xν are the standard 4-dimensional coordinates, φ is the extra dimension, and k is
√
¯
a scale of the order of the reduced Planck scale MP l = MP l / 8π ≈ 2 10−18 . As a result of
the warping factor e−2krc φ , the graviton probability functions are exponentially suppressed
away from the Planck brane, as illustrated in Fig. 2.6. This reduces the real masses m0 of
particles in the standard brane to an apparent mass m:

m = e−krc π m0 .

(2.28)

If krc ≈ 12, the electroweak scale is MEW ≈ e−12π MP l , solving the hierarchy problem.
As the graviton field propagates through finite extra dimensions, it can undergo KaluzaKlein excitations, which can be compared to excited states of a quantum harmonic oscillator.
Just like the excited oscillator states have higher energies than the ground state, the graviton
can obtain a mass, which depends on the order of the excitation n [50]:

mn = kxn e−krc π .

(2.29)

Here, xn is the nth root of the Bessel function j1 . If the mass of a certain order as well as
the scale k are known, the couplings and width of the excited graviton states can be derived.
In this analysis, we set limits on the first excitation of the graviton, whose mass is
28

Figure 2.7: Line shapes of Kaluza-Klein resonance peaks of a 1500 GeV RS graviton, as they
¯
might be produced at the LHC. From top to bottom, the curves are for k/MP l = 1, 0.5,
0.1, 0.05, and 0.01, respectively [52].
¯
expected to be at the TeV scale. Instead of k, the normalized scale k/MP l is used as the
¯
input parameter. If the RS model solves the hierarchy problem, a small k/MP l implies a
¯
large radius rc . This restricts the allowed values of k/MP l , since large extra dimensions are
easier to observe. On the other hand, if rc is too small, the theory becomes non-perturbative
¯
[51]. Values considered in this analysis are 0.01 ≤ k/MP l ≤ 0.1.
Among other channels, the graviton is predicted to decay into two electrons and, depending on its cross-section and width, its first excitation could be visible as a resonance in the
dielectron invariant mass spectrum. The shape (height and width) of the resonance peak
¯
depends on k/MP l as mentioned above and is illustrated in Fig. 2.7. Different from the Z ′
bosons, the graviton is a spin-2 particle, and its production does not interfere with the DY
29

k/MPl

0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0

excluded at 95% CL
expected limit
D0 PRL 100, 091802 (2008)

DØ, 5.4 fb-1

300 400 500 600 700 800 900 1000 1100
Graviton Mass M1 (GeV)

¯
Figure 2.8: Excluded regions in the space spanned by k/MP l and the graviton mass measured
at the 95% C.L. by the D/ collaboration [53].
0
process. Furthermore, it can be produced in gluon-gluon annihilation and decay into two
photons, which is not possible for the resonance in the other models.

2.2.7

Previous limits

′
Before summer 2011, the strongest constraints for a ZSSM boson came from precision measurements of the Z boson peak at the Large Electron Positron collider (LEP), CERN. A
potential Z ′ boson would change the shape of the Z boson mass peak by mixing (compare
′
Sec. 2.2.3). The combination of the indirect measurements [54, 55, 56, 57] excludes a ZSSM
boson with a mass below 1.787 TeV at the 95% confidence level (C.L.) [58].
Direct experimental limits are determined at hadron colliders by searching for resonances
in the dielectron, dimuon and, in the case of the RS graviton, diphoton invariant mass
30

spectra. The Tevatron collider at Fermilab, Batavia, USA, was shut down in fall 2011. Until
then it collided protons and antiprotons with

√

s = 1.96 TeV, while the LHC data used in

this analysis are produced by proton-proton (pp) collisons at

√

s = 7 TeV. Higher collision

energies increase the accessible search region in the invariant mass spectrum, allowing the
ATLAS and CMS collaborations at the LHC to obtain mass limits higher than the Tevatron
collaborations (CDF and D/), with only a fraction of the number of recorded collisions.
0
′
Limits obtained by the ATLAS, CMS and Tevatron collaborations for the ZSSM before
summer 2011 were all of the order of 1 TeV [59, 60, 61, 62], the highest being the limit by
′
CMS with 40 pb−1 of data, which excluded the ZSSM boson at the 95% C.L. for masses
below 1.140 TeV [60]. It was a combination of the measurements in the dielectron and
dimuon channel. Limits for the E6 Z ′ bosons were also determined by several collaborations
[59, 60, 61, 63]. Table 2.4 shows the 95% C.L. mass limits for different E6 models obtained
with 40 pb−1 of ATLAS dimuon and dielectron data [59].
Model
Mass limit [TeV]

′
Zψ

′
ZN

′
Zη

′
ZI

′
ZS

′
Zχ

0.738

0.763

0.771

0.842

0.871

0.900

Table 2.4: Combined mass limits at the 95% C.L. on the E6 -motivated Z ′ models using
40 pb−1 of ATLAS dimuon and dielectron data [59].

¯
Direct mass limits for the RS graviton with a coupling parameter k/MP l = 0.1 were
obtained by the CMS and Tevatron collaborations, and were of order 1 TeV, the highest
being 1.079 TeV by the CMS collaboration with 40 pb−1 of combined dimuon and dielectron
¯
data [60]. Figure 2.8 shows the excluded regions in the space spanned by k/MP l and the
graviton mass, measured at the 95% C.L. by the D/ collaboration using 5.4 fb−1 of Tevatron
0
data and combining the dielectron and diphoton decay channels.
31

Chapter 3
Experimental setup
The LHC is a circular collider at CERN in Geneva, Switzerland. This chapter gives an
overview over the technologies and strategies that allow the LHC to achieve record collision
energies at very high rates. As the data analyzed in this thesis were recorded with the
ATLAS detector, one of the four large detectors along the LHC ring, the second part of this
chapter describes its design, focusing on the components that are relevant for the detection
and reconstruction of electrons.

3.1

Large Hadron Collider

The most powerful accelerator ever built, the LHC [64, 65] was designed to collide two proton
beams 40 million times per second at a CM energy of 14 TeV (7 TeV per proton) with
an instantaneous luminosity of up to L = 1034 cm−2 s−1 . The instantaneous luminosity
measures the actual pp collision rate, which does not only depend on the frequency of the
beam crossings, but also on the density of the protons in the beam and the area in which
the two beams overlap. The LHC also has the functionality to collide heavy ions (e.g. lead)
32

and has done so successfully already. On a ring with a circumference of 27 km, the beams
are crossed at four interaction points, where the four large LHC experiments are located:
ATLAS, ALICE, CMS and LHCb. ATLAS and CMS are both general purpose detectors,
while LHCb was built for analyzing flavor physics and ALICE primarily for detecting heavy
ion collisions.

3.1.1

Accelerator chain

The LHC ring is the last link of the CERN accelerator chain [66] (see Fig. 3.1). A number
of accelerators are used to bring the protons successively to higher energies and to split the
beam into bunches. With the exception of the newly built LHC, the accelerators in the chain
are older machines. Updated to serve as preaccelerators for the LHC, they were originally
built for previous experiments, like the Super Proton Synchrotron (SPS), where the W and
Z bosons were discovered. Every component of the accelerator chain is optimized for a
certain energy range. It was decided to fill the LHC with protons only instead of protons
and antiprotons, because the production of the latter limits the collision rates that can be
achieved.
The chain starts with a bottle of pure hydrogen gas, which lasts for about a year of LHC
running [67]. The hydrogen is ionized in a duoplasmatron, which uses a cathode to emit
electrons. The electrons are focused and hit the hydrogen molecules, splitting and ionizing
them to produce bare protons, which are then extracted and accelerated by an electric field.
The next station for the protons is a 1 m long radiofrequency quadrupole, which consists
of sinusoidal electrodes. The proton beam is accelerated to 750 keV, as well as focused and
divided longitudinally into bunches.
33

The protons receive an energy of 50 MeV (which already gives them 30% of the speed of
light) in a linear accelerator called LINAC 2. This accelerator is 30 m long and consists of
three tanks; each of the tanks contains a line of drift tubes in an alternating electric field.
The frequency of the electric field is such that the protons are shielded within the tubes
when the field points in the wrong (decelerating) direction, so that they always gain energy
as they pass from tube to tube.
The protons are next accelerated in a series of synchrotrons where magnets are used
to bend the protons’ path to form a closed loop. The strength of the magnetic fields is
regulated and depends on the speed of the particles in order to keep the radius of the beam
trajectory constant. The energy that protons can reach in a synchrotron is usually limited by
the maximum strength of its bending magnets. To achieve further acceleration, the protons
must be transferred into another ring with larger radius and/or more powerful magnets. All
the synchrotrons in the LHC chain use resonating cavities, in which the electric field forms
a standing wave whose frequency and phase are timed to accelerate the protons.
The first circular accelerator in the chain is the Proton Synchrotron Booster (PSB). It
actually consists of four circular beam lines, stacked on top of each other, with a circumference of 157 m. The protons leave the PSB with an energy of 1.4 GeV (corresponding to 91%
of the speed of light) and are fed into the next machine as six bunches.
The Proton Synchrotron (PS) is the oldest machine in the chain, built in 1959. On a circle
of 682 m, it accelerates the protons to 25 GeV. Furthermore, it splits the six bunches into
up to 72, which circulate closely together in a so-called bunch train. The concept of bunch
trains is important, because each injection takes time. Bunch trains allow the injection of
several bunches into an accelerator at once, making it possible to fit more bunches into the
34

CMS

LHC

SPS
ALICE

LHCb

ATLAS

PS
PSB
LINAC2
Duoplasmatron
Figure 3.1: CERN accelerator complex.
ring.
The last accelerator before the LHC is the SPS, which has a circumference of 7 km.
There are two transfer lines to the LHC so that proton beams can be injected into the LHC
ring in both directions. The protons leave the SPS with an energy of 450 GeV as bunch
trains consisting of up to 4 · 72 bunches. A nominal LHC fill contains 2808 bunches in each
direction, produced in 12 SPS cycles, each cycle consisting of 3-4 PS fills.

3.1.2

LHC design

The LHC is a synchrotron located 50-175 m underground, in a tunnel with a circumference
of 27 km. It consists of two beam lines, in which two proton beams complete around 11,000
35

turns per second in opposite directions to be collided at four interaction points. An ultrahigh vacuum (10−10 Torr, corresponding to three million molecules per cm3 ) is necessary
in the beam lines to avoid deflecting protons on gas molecules.
To accelerate the protons, the LHC uses eight superconducting cavities per beam. The
superconducting material makes it possible to store large amounts of energy. This allows for
fast acceleration, while only tiny fractions of the field energy are given to the beam when
it passes, making the cavity fields quite insensitive to small variations in the beam current.
As protons lose little energy due to synchrotron radiation after the acceleration phase, the
cavities’ main task is to keep the bunches of protons longitudinally focused. This happens
because the cavities form so-called radiofrequency buckets, in which the synchronous protons
(the ones right in the middle of the bucket) are optimally accelerated, while the other protons
oscillate around these central protons, getting too much or too little acceleration. Since the
cavities need to be cooled down to 4.5 K to maintain their superconducting properties, they
are grouped as four within a cryostat.
In order to keep protons at energies of 7 TeV in a circular orbit, magnets with very large
fields (up to 8 T) are needed. For the wires of the magnet coils, a superconducting material,
niobium-titanium, is used. This allows for the creation of large fields and is important to save
energy, since the currents needed to produce such magnetic fields are huge (∼12 kAmp). For
bending the proton orbits, the LHC uses 1232 dipole magnets of 15 m length. Quadrupole
and sextupole magnets are used for transverse beam focusing. Additional magnets correct
errors and improve the beam quality. For the metal to be superconducting and able to
transport large currents in the presence of a strong magnetic field, the magnets have to be
cooled down to 1.9 K.
36

Because the LHC uses so much superconducting technology, a very powerful cooling
system is required. 10,000 tons of liquid nitrogen are used to bring the temperature of
around 100 tons of helium down to 80 K. Refrigeration units achieve further cooling. Below
2 K, liquid helium is superfluid, which means it has excellent heat transfer properties and
can propagate into tiny cracks in the magnet coils to absorb heat.
This design enables the LHC to achieve unprecedented collision rates at record CM
energies. The strength of the dipole magnets and the design of the cavities allow for protons
with very high energies. In addition, the accelerators further up the chain were upgraded
to accelerate large numbers of protons and divide them into many bunches. The higherorder magnets (quadrupoles, sextupoles etc.) increase the density of the proton bunches, by
squeezing them transversally. The cavities keep the bunches compressed longitudinally. The
colliding frequency is further enhanced by using bunch trains, with very few and short gaps
between the bunches, so that more bunches per turn can be brought to collide at a given
interaction point. Finally, the beams are aligned to cross with a large overlap.

3.1.3

LHC status 2011

The LHC started colliding protons with protons in November 2009 and reached a CM energy
of 7 TeV (3.5 TeV per beam) in March 2010. Collisions at 8 TeV are foreseen in 2012. The
design CM energy of 14 TeV is expected to be achieved in 2014 after an extended technical
stop. The lower energy also limits the luminosity. While the LHC is planned to eventually
run with 2808 bunches per beam and an instantaneous luminosity of L = 1034 cm−2 s−1 , in
2011, the maximum number of bunches per beam were 1380 and the maximum instantaneous
luminosity L = 3.65 · 1033 cm−2 s−1 .
37

3.2

ATLAS detector

ATLAS [68] is a general purpose detector, built to detect, filter and record high energy pp
and heavy ion collisions produced by the LHC. It was designed for precision measurements
of SM parameters as well as the search for a wide variety of possible new physics phenomena.
The detector is located 92.5 m underground at one of the LHC collision points. It is constructed cylindrically around the beamline, weighs 7000 tons and is 44 m long. The ATLAS
collaboration was formed in 1992. Today it consists of ∼3000 physicists from 38 countries.
The detector was constructed between 2003 and 2008.

3.2.1

Coordinate system

The coordinate system of the ATLAS detector is illustrated in Fig. 3.2. The origin is set at
the nominal interaction point in the center of the detector. The positive x-axis points to the
center of the ring, the positive y-axis upwards. The z-axis follows the beam line. The angle
φ is defined with respect to the positive x-axis and wraps around the beam axis, while the
angle θ is defined with respect to the positive y-axis.
|p|+pz
. For relativistic
|p|−pz
E+p
objects (|p| ≈ E), the pseudo-rapidity corresponds to the rapidity y = 1/2 ln E−pz . The
z
miss are
transverse momentum pT , transverse energy ET , and missing transverse energy ET
The pseudo-rapidity is defined as η = − ln tan(θ/2) = 1/2 ln

defined in the x-y plane. Furthermore, the distance ∆R in the pseudorapidity-azimuthal
space is defined as ∆R =

∆η 2 + ∆φ2 .
38

y
x (to ring center)

φ
θ
z (beam line)

Figure 3.2: Coordinate system of the ATLAS detector.

3.2.2

Design

As a general purpose detector, ATLAS needs to be able to discover a wide range of new
physics phenomena. Thanks to the record high CM energy of the LHC, we can search for
heavier particles than ever before. In order to be able to detect and reconstruct possible
decay products up to very high energies, ATLAS has to be as hermetical as possible and
cover a large η range. In order to identify electrons in the presence of the large QCD multijet
background produced in pp collisions, calorimetric resolution as well as tracking capabilities
must be excellent. Subdetectors with high resolution close to the beam line are needed to
find jets produced by b-quarks, which, due to their lifetime, can be tagged by looking for
a small distance (a couple of mm) between the primary and secondary interaction vertices.
Furthermore, new physics is rare. In order to find it, the design number of pp collisions
at the LHC is 40 million times per second, which requires very fast detection and efficient
filtering at a very early stage in the data flow.

39

Figure 3.3: Schematic view of the ATLAS detector [69].

40

The ATLAS detector is built like an onion around the beam line (see Fig. 3.3). From
the inside out, it consists of an inner detector for tracking, a calorimeter system for particle
identification and measuring the energy of electrons, photons and quark/gluon jets, as well as
a muon spectrometer. There are two magnet systems, a solenoid around the inner detector
and a large toroid for the muon system. The magnets bend the tracks of charged particles
and allow for charge/momentum determination.
The ATLAS Inner Detector consists of three subdetectors submerged in a solenoidal
magnetic field (2 T). It records the tracks of charged particles. Pattern recognition allows
the determination of the interaction vertex as well as of additional vertices from particles
with a long life-time, like B-mesons.
Located outside the Inner Detector’s solenoid are the electromagnetic (EM) and hadronic
calorimeters. They use a sampling technique, which means they consist of alternating layers
of absorbing and ionizable material. The EM calorimeter uses lead as the absorber and
liquid argon (LArg) as the active layer. The hadronic calorimeter is constructed using steel
and scintillating tiles in the barrel and copper (as well as tungsten in some parts) with LArg
in the forward regions.
Muon momenta are measured in the muon spectrometer, consisting of three layers of
high precision tracking chambers. Most of these chambers are drift tubes, filled with gas
that can be ionized by a traversing muon. The alignment of the chambers has to be done
very carefully to achieve good momentum resolution, especially for particles with high pT
(the design resolution is 10% for muons with pT = 1 TeV). The chambers are surrounded
by an air core toroid system. Of course, charged particles other than muons, which traverse
the calorimeters, could be detected by the system as well.
41

At nominal luminosity, the ATLAS trigger system needs to filter 200 interesting events per
second out of 40 million others. It consists of three stages, Level 1 (L1), Level 2 (L2) and the
Event Filter (EF). L1 is hardware based, and uses a reduced granularity in the calorimeters
as well as specialized, fast muon chambers to trigger on high transverse energy/momentum
miss and large total transverse energies. L1 chooses regions of interest (ROI),
objects, ET
which are picked up by L2 and analyzed with dedicated software algorithms on the full
detector granularity. The EF employs offline analysis algorithms to pick interesting events.
A menu of different cut combinations exists at all stages and it is possible to set prescales
to record only a fraction of the events triggered by a certain menu item.

A fast, efficient data acquisition system (DAQ) is needed to cope with the large amounts
of data. The data have to be channeled from the electronic read-outs of the different detector
systems to the storage disks. Event fragments from the different subdetectors are buffered
while the L1 trigger makes its decision. The requested ROI information is transferred to the
L2 trigger. Once L2 accepts an event, the full event information is assembled by the Event
Builder, so that the event can be analyzed by the EF. Accepted events are then moved to
the storage disk. The amount of data written to disk is still enormous; around 1000 million
events are recorded per year with a typical event in 2011 having a size of 1.1 MB [70].

Both the Inner Detector and the EM calorimeter need to be understood very well to allow
for the reconstruction of electrons and are therefore discussed in more detail in Sec. 3.2.3
and Sec. 3.2.4. Electron triggers are discussed in Sec. 4.2.
42

3.2.3

Inner Detector

In order to provide high momentum and vertex resolution as well as good tracking abilities,
the ATLAS Inner Detector [68] consists of three subdetectors, which are submerged into a
solenoidal magnetic field (see Fig. 3.4). The inner layers, the Pixel detector and the Semiconductor Tracker (SCT), have very high granularities and typically provide three (Pixel
detector) and eight (SCT) hits per track, while the outermost detector, the Transition Radiation Tracker (TRT), offers around 36 hits per track with less precision but over a larger
volume, thus contributing significantly to the momentum reconstruction.
The Pixel detector and the SCT cover a pseudo-rapidity range up to |η| < 2.5. They
consist of semiconducting silicon elements with an applied electric field (∼150 V). Charged
particles passing through the semiconducting material set charge carriers free that accumulate at the electrodes. This results in a charge difference which is turned into a signal current.
Both detectors are exposed to immense amounts of radiation from the proton beams. The
innermost Pixel layer is as close as 5 cm to the beam line and will have to be replaced after
three years of running at design luminosity. Both detectors are cooled to reduce the leakage
current, which increases with irradiation.
The Pixel detector consists of 80 million silicon pixels (each with a size of 50 by 400 µm).
It has three barrels around the beam line and three disks at each side, covering radii between
5 and 15 cm. The SCT, covering radii up to 52 cm, contains silicon microstrips, measuring
80 µm by 12.6 cm. The microstrips are arranged in double layers, each layer with two sets
of strips at a small angle to each other, in order to obtain a 3D measurement.

43

Figure 3.4: Schematic view of the ATLAS Inner Detector [69].

44

The TRT is a drift tube system, extending to |η| < 2. It consists of straw tubes that are
4 mm wide and up to 1.44 m long and are filled with a Xe/CO2/O2 gas mixture. Within the
tubes are gold-plated tungsten wires, serving as anodes, kept at ground potential, while the
tubes themselves are used as cathodes, with a potential of -1530 V. Charged objects ionize
the gas and the resulting ions travel to the electrodes. The drift time (max. 45 ns) allows
for a determination of the objects’ crossing R, φ coordinates with a resolution of 170 µm.
The TRT does not provide information about the z-coordinate. In addition to its tracking
capabilities, the TRT can contribute to particle identification. The straws are surrounded by
polypropylene, which produces transition radiation (photon emission if a relativistic particle
crosses the boundary of two materials). The xenon gas reacts with the photons, causing a
larger signal than the passing charged particles. A two-threshold system makes it possible
to distinguish between tracking and transition radiation signals. Since electrons are lighter
than hadrons, the necessary ET for an electron to cause transition radiation is O(1 GeV),
while for pions, which are almost 300 times heavier, the necessary ET is O(100 GeV). Of
course, this discrimination breaks down for particles with very high ET .

3.2.4

Electromagnetic calorimeter

The EM calorimeter [68] has alternating layers of absorbing lead and LArg, which serves as
the active medium. Submerged into the LArg are electrodes creating electric fields. Charged
particles traversing the lead interact with it through bremsstrahlung and produce secondary
particles, which can interact with the material themselves, thus creating tertiary particles
(see Fig. 3.5). This showering can also be initiated by a photon converting into an electron
pair and continues until all the energy is absorbed [71]. When the shower particles travel
45

γ

e−
γ

e−

e−
e+

e+

γ

e−

e+
e−

e−

e+

γ
e−

γ
e−

Figure 3.5: Schematical illustration of an electron shower in the EM calorimeter.
through the LArg, they ionize the liquid. The ions travel to the electrodes, where they
produce a current proportional to the applied voltage and the energy deposited in the LArg.
The coverage of the EM calorimeter is up to |η| < 3.2 overall, and up to |η| < 2.5 with
fine granularity, matching the Inner Detector. It consists of a barrel and two endcap wheels
(see Fig. 3.6). The barrel (|η| < 1.475) is constructed of two halves, separated by a small
gap (4 mm) at z = 0. The endcap wheels are each divided into an inner and an outer wheel.
In order to achieve uniformity in φ, to avoid azimuthal cracks, and to allow for very fast
read-out, the EM calorimeter is constructed like an accordion. Lead absorbers, LArg, and
electrodes are folded following a zig-zag pattern (see Fig. 3.7). In the barrel, the folds are
parallel to the beam line, and the angle is varied with the radius to keep the width of the
LArg gap constant. For the endcaps, the geometry is more complicated. Here, the accordion
folds are perpendicular to the beam line and the angle and amplitude of the folding vary with
the radius. The width of the LArg gap therefore varies, which is accounted for by changing
the applied voltages with η.

46

Figure 3.6: Schematic view of the ATLAS calorimeters [69]. The outer radius is about 4 m, while the extension along the
beamline is 12 m.

47

Figure 3.7: Accordion structure of the EM calorimeter [69].
The precision region is made up of three layers with different granularities in η and φ [72]
(see Fig. 3.8). In η and depth the partition is achieved by etching the electrodes, in φ by
bundling electrodes. The first layer consists of narrow strips, used for position measurements,
that are very important e.g. for the determination of photon directions. Most of the energy
is collected in the second layer, which is the deepest. The third layer has a very coarse
granularity and is installed to absorb objects with very high energies. Underneath the three
layers, for |η| < 1.8, a presampler, consisting of a thin layer of LArg, is used to estimate the
energy lost in the Inner Detector. In order to keep the argon liquid, the barrel and the two
endcaps are surrounded by cryostats, which cool the material down to 88 K.

48

Figure 3.8: Barrel module, showing the different layers of the EM calorimeter [68]. X0
describes the radiation length, which is the travel distance for a relativistic electron during
which it loses all but ∼1/e of its original energy.

49

Chapter 4
Electrons in the ATLAS detector
In order to search for high-mass dielectron resonances, we look for central, highly energetic
electrons, produced in pp collisions at the center of the ATLAS detector. Since electrons
are charged, they leave a track in the Inner Detector (see Sec. 3.2.3 and 4.1). Furthermore,
they deposit their energy across several cells in the EM calorimeter (compare Sec.

3.2.4

and 4.1). Since no interesting events should be missed, the electron trigger, reconstruction
and identification efficiencies in ATLAS need to be high. On the other hand, many pp
collisions contain hadronic jets, which can fake electron signatures in the detector and during
reconstruction. These need to be rejected to reduce backgrounds and, in the case of the
trigger, to decrease the amount of data to be processed and stored. This chapter describes
how electrons in the ATLAS detector are triggered, reconstructed and identified.

4.1

Z → ee event display

Figure 4.1 illustrates the signature of a Z → ee event in the ATLAS detector [69]. Two
different perspectives of the detector are shown, as well as a lego plot, which illustrates the
50

energy deposited in the EM calorimeter. The numbers denote various detector components:
1. Pixel detector
2. SCT
3. TRT
4. EM calorimeter
5. Hadronic calorimeter
The two electrons are depicted by the yellow pattern. The letters correspond to parts of the
electron signature in the detector:
a) Tracking hits in the Inner Detector
b) TRT high threshold hits
c) Energy cluster in the EM calorimeter

51

Run Number: 154817

ET

Event Number: 968871
mee = 89 GeV

η
φ

Figure 4.1: Event display of a Z → ee event [69]. Two different perspectives of the detector are shown (left, bottom right), as
well as a lego plot (top right), which illustrates the energy deposited in the EM calorimeter.

52

4.2

Electron trigger

The purpose of the ATLAS trigger system is to filter 200 interesting events out of the 40
million pp collisions happening per second in the ATLAS detector (see Sec. 3.2.2). The
trigger also does a first categorization, separating events with electrons and photons from
events with muons or jets only.
The ATLAS trigger is an event selection system, consisting of three stages, L1, which
reduces event rates of 40 MHz to 75 kHz, L2 (reduction to 3.5 kHz) and EF (reduction to
200 Hz). The triggers used in physics analyses are actually trigger chains, with one link
for each trigger level. A menu of different cuts, called trigger items, exists at every stage.
Here, only functionalities of the triggers that are used to select electron events are described.
These triggers cover a range of |η| < 2.5.

4.2.1

Level 1 Calorimeter trigger

The first step in triggering electrons is the hardware-based Level 1 Calorimeter (L1Calo)
trigger [73]. Since the time between two pp collisions is too short for a complete trigger
decision, the data are pipelined, which makes it possible to have a trigger decision for every
collision, albeit with a small latency (< 2.5 µs). To save processing time, the L1Calo trigger
does not use the full granularity of the EM calorimeter. Instead, it performs analog sums
over the three vertical layers and the cells, resulting in 3500 trigger towers with a dimension
of ∆η × ∆φ = 0.1 × 0.1 in the barrel middle layer (illustrated in Fig. 3.8). For every trigger
tower, the recorded analog pulse is associated with a bunch-crossing of the LHC, corrections
are applied and it is digitized, i.e. translated into an energy measurement. An L1 EM
trigger item with a simple energy threshold is passed if there are two neighboring trigger
53

towers whose energies sum up to a value larger than the threshold. If the central 2 × 2
window passes at least one of the L1 trigger items, the 4 × 4 window around it is called
the Region of Interest (ROI) and its coordinates are sent to the next level, the L2 trigger.
Events without a region that passes any item of the L1 trigger menu are discarded.

4.2.2

High Level Trigger

The High Level Trigger (HLT) [74] is software-based and consists of L2 and EF. Since the
time constraints are less stringent than at L1, the full granularity of the EM and hadronic
calorimeters, as well as information from the Inner Detector can be used. Both levels employ
a number of selection algorithms on the reconstructed energy clusters and tracks, similar to
the offline identification cuts (see Sec. 4.4). For electrons, three baseline selections with
increasing jet rejection capabilities (and decreasing efficiencies) are chosen: Loose, Medium,
and Tight.
The L2 trigger receives the coordinates of the ROIs defined by L1. Using the full calorimeter granularity and starting from the cell with the highest energy in the ROI, it reconstructs
the energy clusters. This reconstruction includes potential energy deposits in the hadronic
calorimeter. The values of several variables describing the shape of the energy showers are
determined, since these shower shapes differ for electrons and jets and can therefore serve
as discriminants. Depending on the L2 trigger item, a number of cuts are applied on the
shower shape variables. For reconstructing tracks as fast as possible, the IDScan algorithm
first determines the z coordinate of the interaction vertex. Only tracks are reconstructed
that point to the interaction vertex. Finally clusters and tracks are matched to each other
to build L2 electron objects, and cuts can be applied on variables describing the quality of
54

the matching.
If at least one ROI passes the L2 trigger, the corresponding event is fully assembled
using all available information from the different subdetectors. Thus the EF has access
to the complete event, but usually only uses the ROIs provided by L2. Cluster and track
reconstruction are the same as in the offline case (see Sec. 4.3). The situation is similar for
the identification cuts (Sec. 4.4), however, unlike the offline cuts, the EF cuts are not ET
dependent.

4.3

Electron reconstruction

Central electrons (|η| < 2.5) are reconstructed by the standard e/gamma algorithm [75],
which matches energy clusters in the EM calorimeter to tracks in the Inner Detector.
Electrons usually leave their energy in more than one calorimeter cell. The appropriate
cell energies have to be combined into energy clusters [76]. The first part of the algorithm
looks for seed clusters. The energies in the layers of the EM calorimeter are summed into
towers of size 0.025 × 0.025 in η, φ (in the second layer) and a 3 × 5 window slides over
these towers to find local energy maxima above a certain energy threshold. Using a smaller
window, the position of the seed cluster is determined by finding the energy weighted center.
If two clusters are too close to each other, only the one with the larger energy is kept.
Track reconstruction in ATLAS [77] is challenging due to the large amount of QCD
multijet production in pp collisions. Two complementary tracking algorithms are used: The
main algorithm starts with finding track seeds in the Pixel and SCT parts of the Inner
Detector (see Sec. 3.2.3). A combination of global and local pattern recognition is applied
and the tracks are extended to the TRT. For tracks without or with only a few hits in the
55

Pixel detector/SCT, a track finding algorithm starting from the TRT is used.
Tracks and energy clusters are matched to each other by extrapolating from the last track
measurement point to the second layer of the EM calorimeter and then comparing the η,
φ coordinates of this extrapolation with the coordinates of the seed clusters. If ∆η < 0.05
(this cut is only applied to tracks with hits in the Pixel detector/SCT) and ∆φ < 0.05, a
track is matched to a cluster. Possible bremsstrahlung (electrons radiating photons while
accelerating, losing energy and therefore being bent more by the magnetic field), which might
affect the quality of the extrapolation, is accounted for by allowing ∆φ < 0.1 in the direction
where the track is bent. If more than one track is matched to a given cluster, all matched
tracks are kept, and the one with the smallest ∆R is considered the best match. Tracks with
silicon hits are preferred over tracks without, since the latter are more likely to come from
photon conversions (photons converting into an electron-positron pair).
Energy clusters with matched tracks are considered electron candidates. For each candidate, the cluster is recomputed with an optimized cluster size, separately for each layer,
starting with the coordinates of the seed cluster [77]. All cells in a 3 × 7 window (in middle
layer cell units) are considered part of the cluster. Energy corrections are applied. The
electron candidate’s 4-momentum is calculated by taking the energy from the cluster and its
direction from the best matched track, if this track contains hits in the Pixel detector/SCT.
If not, the η, φ coordinates of the cluster are used.

4.4

Electron identification

Among the reconstructed electron candidates are not only electrons from the processes we
are interested in, but also jets, electrons from conversions, and electrons from pion decays,
56

which can all leave tracks in the Inner Detector and energy clusters in the calorimeters.
Additional algorithms are needed to reduce this background.
Electron identification [75, 34] in ATLAS is done by applying a number of cuts on the
shapes of the showers in the EM calorimeter, on the tracks in the Inner Detector and on
the matching between clusters and tracks. This is effective, since jets tend to have wider
showers than electrons, as well as more tracks. Conversions and electrons from pion decays
are usually produced a bit off the center of the detector, and therefore can miss the first
layers of the Inner Detector. The TRT can help with particle identification by measuring
the transition radiation of relativistic particles (see Sec. 3.2.3).
The identification cuts have been optimized to allow for the best possible electron efficiencies while maintaining high rejection rates for QCD jets. As part of the optimization, the
cuts are binned in η and ET of the electron candidates. The cuts are binned in ET because
the showers for both jets and electrons are narrower at higher energies. Both shower shapes
and tracks in the Inner Detector depend on the amount of material the electrons have to
traverse, which makes binning in η necessary. Harmonized with the triggers, three reference
cut sets are defined, Loose, Medium, Tight, with increasing jet rejection from Loose to Tight.
The Loose cut set relies on cuts on shower shape variables in the middle layer of the
EM calorimeter and on a cut on the energy leakage into the hadronic calorimeter. On top
of that, the Medium set includes cuts on the shower shapes in the first layer of the EM
calorimeter, as well as track quality cuts and cuts on the track matching. The Tight set
applies more stringent cuts on the track matching and on the track quality; furthermore
cuts on the TRT hits are added, including cuts on the high threshold hits, which come from
transition radiation.
57

An overview of the different cuts used for electron identification in ATLAS is given in
Table 4.1 [75, 34].
Type of cut

Description
Loose
Ratio of the energy in 3 × 7 cells to the energy in 7 × 7
Middle layer of EM calorimeter
cells centered at the electron cluster position
Width of the shower in η
Ratio of ET in the first layer of the hadronic calorimeter
Hadronic leakage
to ET of the EM cluster (used over the range |η| < 0.8
and |η| > 1.37)
Ratio of ET in the hadronic calorimeter to ET of the
EM cluster (used over the range |η| > 0.8 and |η| <
1.37)
Medium (in addition to Loose cuts)
Total shower width
First layer of EM calorimeter
Ratio of the energy difference between the largest and
second largest energy deposits in the cluster over the
sum of these energies
Number of hits in the Pixel detector (≥ 1)
Track quality
Number of total hits in the Pixel detector/SCT (≥ 7)
Transverse impact parameter (|d0 | < 5 mm)
Track-cluster matching
∆η between the cluster position in the first layer of the
EM calorimeter and the matching extrapolated track
(|η| < 0.01)
Tight (in addition to Medium cuts)
∆φ between the cluster position in the middle layer and
the matching extrapolated track (∆φ < 0.02)
Track-cluster matching
Ratio of the cluster energy to the track momentum
Tighter ∆η requirement (∆η < 0.005)
Track quality
TRT

Against conversions

Tighter transverse impact parameter cut (|d0 | < 1 mm)
Total number of hits in the TRT
Ratio of the number of high-threshold hits to the total
number of hits in the TRT
Number of hits in the first layer of the Pixel detector
(≥ 1)
Veto electron candidates matched to reconstructed photon conversions

Table 4.1: Description of the electron identification cuts [75, 34].

58

4.5

Electron isolation

In addition to the electron identification cuts, it is possible to require the tracks and/or the
calorimeter cluster of the electron candidate to be isolated [75]. This allows for an enhanced
rejection of QCD jets, which usually consist of a bundle of tracks and wide clusters. In the
case of track isolation, a cut is applied on the sum of the scalar pT of the tracks that fall
into a cone with an opening angle R around the electron. For calorimeter isolation, the ET
deposited in the EM and hadronic calorimeters in a cone around the electron is summed
up. Of course, the ET of the electron cluster itself is subtracted. Corrections are applied to
account for pile-up effects (see Sec. 5.3.4) and energy in the cone that actually belongs to
the electron. As this leaked energy is ET dependent, so are the corrections.

4.6

Performance of electrons with high ET

The performance of electrons in ATLAS, i.e. the efficiency and quality of electron triggers,
reconstruction and identification, has been studied very well. The focus of these studies has
been on electrons with ET up to around 100 GeV, due to feasibility and physics analyses’
needs: Most electrons from low mass Higgs, W and Z bosons as well as top quark decays
have energies below 100 GeV. However, in this analysis, we look for signatures with mass
peaks up to 2 TeV. The electrons from these resonances can have transverse energies above
500 GeV and we need to understand their properties in order to detect them efficiently and
correctly reconstruct their energies. Furthermore we have to make sure that we can control
the background from QCD jets faking electron signatures.
Studies of the properties of high ET electrons in ATLAS data are very challenging because
59

of low statistics and the difficulty of obtaining a clean electron sample in data without jet
contamination. At lower energies, this is achieved using the characteristic decays of Z and
W bosons (see App. A), but at high energies no such handle is available and most studies
rely on calibration runs and simulations.

4.6.1

Energy reconstruction

The energy resolution at sampling calorimeters [78] can be parameterized as
√
σ(E)/E = a/ E ⊕ b/E ⊕ c,

(4.1)

where ⊕ represents addition in quadrature, and E is the energy in GeV. The first term is
stochastic, the second one is due to pile-up and electronic noise and the third is the constant
term. The constant term is the result of imperfect reconstruction of the cluster energies,
which can happen because of unaccounted energy deposits in the Inner Detector or other
calibration issues. At high energies, the constant term dominates the resolution, and a lot
of work has been done to decrease it. For |η| < 1.37, the constant term (and therefore the
resolution for highly energetic electrons) has been measured in data at transverse electron
energies of ∼50 GeV to be 1.1%, while for 1.52 < |η| < 2.47, it is 1.8%, a bit larger due
to additional material in front of the calorimeter. Calibration runs, using electronic pulses,
showed that high energy signals up to 2 TeV do not cause unexpected deterioration of
the resolution [79]. Figure 4.2 shows the effect of the electron resolution on the dielectron
′
′
invariant mass peaks of the ZSSM boson and the Zχ boson assuming a peak mass of 1.5
TeV. Thanks to the excellent electron resolution, after reconstruction, the two models can
still be distinguished due to their shape.
60

Events

1

10-1

SSM, reco
SSM, gen
χ, reco
χ, gen

10-2

10-3
1
mee [TeV]
′
Figure 4.2: Simulated dielectron invariant mass distribution of the ZSSM boson and the
′
Zχ boson for an assumed peak mass of 1.5 TeV. The distributions are normalized to unit
area and shown before (“gen”) and after electron reconstruction and application of event
selection cuts (“reco”, see Sec. 6.1 for a description of the selection cuts).
The uncertainty on the absolute energy scale in ATLAS ranges from 0.5-1.5%, depending
on ET and η [80]. Again, calibration runs using pulses with a wide variation of energies
have been employed to determine the linearity of the electronic response and its effect on the
energy reconstruction. Nothing problematic has been seen throughout the range of tested
energies (up to 2 TeV) [79].

4.6.2

Bunch-crossing identification

The L1Calo trigger (Sec. 4.2) saturates if the transverse energy per trigger tower is larger
than 255 GeV [73]. In principle, this is not a problem since every event with a saturated
61

L1Calo signal automatically passes the trigger. However, the identification of the correct
LHC bunch-crossing depends on the shape of the analog pulse, so it could be impacted
by the saturation [81]. If the saturated signal from a high ET electron is associated with
a bunch-crossing too early or too late, the wrong event will be triggered, and therefore
the trigger efficiency will be decreased for events with highly energetic objects. Dedicated
algorithms for saturated signals have been employed to deal with this issue [81]. Preliminary
studies in 2011 show no inefficiency for energies up to 3 TeV in the barrel (η < 1.37), and
up to 2.1 TeV in the calorimeter endcaps.

4.6.3

Trigger and identification efficiencies

Trigger and identification efficiencies for electrons with ET below ∼100 GeV can be determined from data by applying the Tag-and-Probe method on Z boson decays (this is
documented in detail for identification efficiencies in App. A). In this energy range, Tag-andProbe studies show rising efficiencies in ET . However, at higher energies, the Tag-and-Probe
method suffers from low statistics and cannot be used reliably any more. One important
alternative is to study efficiencies in simulated samples.
The identification criteria chosen for this analysis are the Medium set (see Table 4.1) and
two additional cuts: the requirement of a hit in the innermost layer of the Pixel detector
(B-layer) to reject electrons from photon conversions and a cut on the calorimeter isolation
(see Sec. 4.5) to decrease the background due to QCD jets.
Fig. 4.3(a) shows the efficiency of these cuts with respect to reconstructed electron candidates in bins of ET . A simulated sample of Z ′ events is used for this study. No efficiency
decrease with ET is expected for the selection according to the simulation. This can be
62

understood by looking at the details of the cuts: Since highly energetic electrons tend to
have more focused showers (the momentum in the direction of flight dominates), the shower
shape cuts are actually less stringent than at low ET (for this reason the cuts are binned
in ET , though the highest ET bin starts at 80 GeV). The energy leakage into the hadronic
calorimeter is expected to be larger for high ET electrons, but the applied cut (compare
Table 4.1) is a ratio cut, thus no efficiency should be lost. The track cuts are not expected to
cause problems with increased energy either. As can be seen in Fig. 4.3(b), the B-layer cut
actually becomes more efficient with higher ET . However, this efficiency gain is cancelled
by the isolation requirement, whose efficiency drops slightly with rising ET . This is due to
imperfect leakage corrections (compare Sec. 4.5).
The trigger chain used in this analysis is L1 EM14 - L2 e20 medium - EF e20 medium.
Figure 4.4 shows that the efficiency for this trigger with respect to the electrons used in this
analysis is very high (∼99%), and flat in ET .

63

0

Efficiency

Efficiency

1
0.98
0.96
0.94
0.92
0.9
0.88
0.86
0.84
0.82

1.04
1.02
1
0.98
0.96

M
M+BL
M+BL+Iso

(M+BL)/M

0.94

200 400 600 800 1000
ET [GeV]

0

(M+BL+Iso)/(M+BL)
200 400 600 800 1000
ET [GeV]

(a)

(b)

Trigger Efficiency

Figure 4.3: Identification efficiency with respect to reconstructed electrons as a function of
ET . M = Medium, BL = B-layer and Iso = isolation requirements. (b) shows the effects of
the B-layer and isolation cuts individually. Both plots are made with a simulated “flat” Z ′
sample (see Sec. 5.2.2) and integrated over η between -2.47 and 2.47, excluding the transition
region between barrel and endcap calorimeters.

1
0.98
0.96
0.94
0.92
0

L1_EM14
L2_e20_medium
EF_e20_medium
200 400 600 800 1000
ET [GeV]

Figure 4.4: Trigger efficiency with respect to the electrons used in this analysis as a function
of ET . The plot is made with a simulated “flat” Z ′ sample (see Sec. 5.2.2) and integrated
over η between -2.47 and 2.47, excluding the transition region between barrel and endcap
calorimeters.

64

Chapter 5
Simulation of signal and background
processes
In this analysis, we are looking for a resonance in high-mass electron pairs. In order to
estimate the SM background, it is important to understand which SM processes can produce
the same signature (two reconstructed electrons) in the detector. This chapter describes the
simulated signal and background samples, as well as data-driven corrections, which need to
be applied to them to increase the quality of the modeling.

5.1

Standard Model backgrounds

The largest, irreducible background in this analysis is the DY process, the production of a
Z boson or an excited photon which then decays into an electron and a positron (compare
Sec. 2.1.4, Fig. 2.1 and 2.4).
All other backgrounds are smaller than the DY process by at least a factor of ten:
65

• Diboson production, the production of two Z bosons, two W bosons or one Z and one
W boson, can lead to a dielectron final state, if one (in case of a Z boson) or two (in
case of W W production) bosons decay into electrons.
¯
• The same is true for tt production, the simultaneous production of a top and an antitop
quark. Both top quarks decay into a bottom quark and a W boson. If both W bosons
decay into electrons (and neutrinos), the event has a dielectron final state.
A second class of backgrounds involves the misidentification of QCD jets as electrons:
• A W boson can be produced in association with one or more jets. The electron from
the W boson and one of the jets could be misinterpreted as an electron pair.
• Because the LHC collides protons at very high energies, a large fraction of events
contains multiple QCD jets. Two jets which are wrongly reconstructed and identified
as electrons contribute to the SM background as well.
Dedicated electron identification and isolation requirements are applied (compare Sec. 4.4
and 6.1), which reduce the background from misidentified QCD jets very efficiently. However,
a non-negligible fraction survives these cuts, since the cross-sections for W + jets and QCD
multijet production are very large.

5.2

Samples

In this analysis, all SM backgrounds, except for the QCD multijet production, are taken
from simulated samples. The background contribution from QCD multijets is estimated
from data (see Chapter 6.2), as a huge number of QCD multijet events would have to be
66

simulated, given the small rate of jets misidentified as electrons. Furthermore, there is a
large uncertainty on the simulation of the misidentification rate itself.

5.2.1

Event generators

Simulated samples are made with event generators, computer programs that produce final
states of a chosen number of particle collisions for a variety of physics processes. These event
generators receive probabilities as input: The PDFs, as well as the Feynman diagrams for
given physics processes (see Sec. 2.1.3). They simulate the final state particles and their
properties by integrating over the allowed phase space using a random number sampling
(Monte Carlo).
A number of event generators have been developed with different strong and weak points.
Pythia [46] and Herwig [82] are general purpose generators, starting from LO matrix elements. They include the decays of particles and apply corrections due to beam remnants,
electroweak and QCD radiation. The latter is often described as showering, since one emitted parton can result in a large number of hadrons. Alpgen [83] does not solely rely on
dressing up the LO process with showers, but calculates the matrix elements individually for
different jet multiplicities. This is important for realistic modeling of hard parton radiation.
MC@NLO [84] combines the additional processes in a more consistent way than Alpgen
and includes matrix elements for all next-to-leading order (NLO) processes that contain real
gluon or quark emissions and virtual particle loops.
In order to compare the simulated final states with real data, the detector response must
be replicated as well. For this, ATLAS feeds the output of the event generators into a
detector simulation program called Geant4 [85], which propagates the final state particles
67

through the detector. For example, electrons are translated into hits in the Inner Detector
and energy deposits in the calorimeters.

5.2.2

Samples and cross-sections

Table 5.1 shows simulated samples of the SM processes used for the background estimates
in this analysis. The table also contains the production cross-section σ times the branching
ratio B which corresponds to the fraction of events decaying into two electrons.
In order to calculate the expected event yield N of a given process,

N = σBALint ,

(5.1)

the following ingredients are needed:
• The production cross-section σ.
• The branching fraction of events B decaying into the final state we are interested in,
for example two electrons.
• The acceptance, which is the fraction of produced events recorded by the ATLAS
detector. This is usually not one, due to kinematic cuts and inefficiencies in particle
detection (see Sec. 4.6.3).
• The integrated luminosity Lint - the number of pp collisions, corresponding to the
integral of the instantenous luminosity: Lint =

Ldt (compare Sec. 3.1).

¯
With the exception of the tt process, all samples are simulated at LO, using a PDF set
¯
called MRST2007lomod [19] (CTEQ6.1 [86] for W +jets). The tt sample is produced at NLO
68

Events
10-1

10-2

10-3

10-4

0.5

1

1.5

2

2.5

3

3.5
4
mee [TeV]

′
Figure 5.1: Reweighted invariant mass distributions for different masses of the ZSSM boson.
The histograms are all normalized to unit area.
with the CTEQ6.6 PDF [87]. However, the overall cross-sections are scaled to the highest
¯
known order: NLO for dibosons, NNLO for W + jets and approximate NNLO for tt [88, 89].
The DY as the dominant background is corrected using mass-dependent correction factors
(see below).
Table 5.2 and 5.3 show a representative selection of possible signal processes and their
cross-sections. All signal samples are produced at LO with Pythia and interference between
Z ′ production and the DY process is neglected. For the Z ′ process, instead of separate signal
samples, we use a sample which is flat in bins of dielectron mass. To produce this sample, the
Breit-Wigner resonance curve and exponential cross-section drop due to parton luminosities
were removed. It can be reweighted to obtain the dielectron mass distribution for any given
Z ′ mass (see Fig. 5.1).
In order to improve the LO estimate for the DY process as the dominant SM background,
69

Process

Generator

Order

Filter

Binning

DY

Pythia

LO

2 electrons

mee [GeV]

Dibosons

Herwig

LO

1 electron/
muon

process

W + jets

Alpgen

LO

1 electron

jets

¯
tt

MC@NLO NLO

2 electrons

mee [GeV]

Bins
> 60
75-120
120-250
250-400
400-600
600-800
800-1000
1000-1250
1250-1500
1500-1750
1750-2000
> 2000
WW
WZ
ZZ
1
2
3
4
5
30-150
150-300
300-450
> 450

σB [pb]
856
819.9145
8.711065
0.415835
0.067136
0.011168
2.7277 · 10−3
9.1646 · 10−4
2.4942 · 10−4
7.6876 · 10−5
2.6003 · 10−5
1.5327 · 10−5
17.46
5.543
1.261
1551.6
452.5
121.1
30.4
8.3
3.0240
0.34669
0.028965
4.81 · 10−3

Table 5.1: List of background samples. The DY cross-sections are shown at LO, while the
cross-sections of the other background samples are scaled to the highest available order.

correction factors are calculated as a function of the dielectron invariant mass [90]. These
k-factors are determined for NNLO QCD corrections (gluon loops and radiation) as well as
for electroweak corrections. Pythia already includes photon emissions, thus the additional
corrections that are accounted for are gauge boson loops. Gauge boson emissions are not
included, which results in an underestimate of the DY cross-section of 2%. Since the electroweak k-factor depends on the coupling of W and Z bosons to the exchange particle, only
the QCD k-factor can be applied to Z ′ production, assuming that slightly different couplings
70

′
σB(ZSSM ) [pb]

′
σB(Zχ ) [pb]

′
σB(Zψ ) [pb]

250

27.35

15.89

8.132

500

2.038

1.163

0.5968

750

0.3668

0.2101

0.1069

1000

0.09477

0.05183

0.02690

1250

0.02960

0.01556

1500

0.01033

1750

3.876 · 10−3

5.064 · 10−3

8.171 · 10−3

Mass [GeV]

2000
2250
2500

1.747 · 10−3

1.579 · 10−3

6.410 · 10−4

6.935 · 10−4

2.493 · 10−4

3.296 · 10−4

1.044 · 10−4

2.732 · 10−3

9.833 · 10−4
3.706 · 10−4
1.422 · 10−4
5.668 · 10−5

′
Table 5.2: LO cross-sections for the ZSSM and some of the E6 models [90]. The generator is
Pythia, a dielectron filter is applied and interference between the Z ′ and DY is neglected.

Mass [GeV]
300
500
800
1000
1250
1500

¯
σB(k/MP l = 0.01) [pb]
0.5216
0.04046
2.996 · 10−3
0.7839 · 10−3
-

¯
σB(k/MP l = 0.1) [pb]
0.2982
0.07734
0.01838
5.288 · 10−3

¯
Table 5.3: LO cross-sections for the RS graviton with different values of k/MP l [90]. The
generator is Pythia and a dielectron filter is applied.

to the initial state quarks do not change the correction. No higher order correction factors
are currently available for RS graviton production [91, 92]. Table 5.4 shows values of the correction factors for different invariant masses for samples produced with the MRST2007lomod
PDF [19].
71

mee [GeV]

500

750

1000

1250

1500

1750

2000

k∗
QCD

1.131

1.109

1.080

1.041

0.990

0.929

0.860

k∗
EW

1.032

1.016

1.000

0.986

0.971

0.956

0.941

Table 5.4: Higher order QCD and electroweak (EW) correction factors [90] for DY samples
produced with the MRST2007lomod PDF [19].

5.3

Corrections to the simulated samples

The simulation of electrons and their signatures in the ATLAS detector is in good agreement
with results obtained from real data. The main reason for imperfect modeling of electron
signatures is missing knowledge of the exact distribution of material in the ATLAS detector
[93]. An example is the modeling of electron shower shapes. Discrepancies were found
between data and simulation of electron shower widths. These differences are largely due to
a simplified description of the absorber layers in the EM calorimeter: Instead of the actual
sandwich structure iron-glue-lead-glue-iron, the simulation assumes a homogenous mixture
of materials.

The difference in shower widths affects the efficiency of the identification cuts, as some of
these cuts are applied on shower shape variables (compare Table 4.1). In order to do a fair
comparison between data and simulation, this efficiency discrepancy needs to be corrected for
using scale factors applied to simulated samples. A description of these and other necessary
corrections to the simulated samples is described in the following sections.
72

5.3.1

Efficiencies

The imperfect description of the detector in the simulation causes small differences between
data and simulated samples concerning electron trigger, reconstruction and identification
efficiencies. In order to correct this and allow for an unbiased comparison between data and
simulated signal and SM backgrounds, scale factors (SF) are calculated as the ratio between
the efficiencies (ǫ) for true electrons in data and in the simulated samples:

SF =

ǫ in data
.
ǫ in simulation

(5.2)

To account for changes of the efficiency in different regions of the detector and for electrons
with various energies, the SF are binned in η and ET .
The biggest challenge in the efficiency measurement consists of getting a sample of electrons from data on which to perform the efficiency determination. This sample should consist
of real electrons, not QCD jets, and no cuts should be applied to these electrons that could
bias the efficiency measurement. The method of choice is the Tag-and-Probe method, which
makes use of the characteristic signatures of the Z → ee and W → eν decays. In the case
of Z → ee Tag-and-Probe, very strict cuts are applied on one of the two decay electrons
(called “Tag”), and the second electron candidate (“Probe”) is used for the measurements.
Additional cuts, which ensure that the invariant mass of the two objects is close to the Z
boson mass, and that the two electrons have opposite charge, greatly enhance the chance
that the second, unbiased electron candidate is a real electron. The Tag-and-Probe method
is described in detail in App. A.
73

5.3.2

Energy resolution

For electrons with high ET the constant term dominates the energy resolution parametrization (see Eq. 4.1 in Sec. 4.6.1). The constant term used in the simulated samples is smaller
than what can currently be achieved by detector calibration in data, which means the energy
of each simulated electron needs to be varied according to a Gaussian distribution in order
to artificially worsen its energy resolution. The parameters for this Gaussian smearing are
obtained by comparing the mass peak of the Z boson as measured in data with the one
obtained from a simulated Z → ee sample [34].

5.3.3

Calorimeter electronics

For a fraction of the data taking period, a small region (0.8%) of the EM calorimeter
(Sec. 3.2.4) was not functioning. Since it is not possible to correctly reconstruct the energy of
electrons falling into or close to the problematic region, these electrons are not considered in
this analysis. The whole EM calorimeter is assumed to be working in the simulation, which
means the detector acceptance is overestimated. In order to be able to compare kinematic
distributions and achieve the same electron acceptance in the simulation as observed in data,
electrons passing the problematic region must not be considered. This should happen only
for a fraction of each simulated sample, which corresponds to the fraction of corrupted data.

5.3.4

Pile-up

The LHC collides protons at higher rates than any other accelerator before. Collision rates
of 40 MHz can only be achieved if the protons are concentrated in dense bunches, and if these
bunches cross each other at very high frequencies (compare Sec. 3.1.2). A side effect of high
74

proton densities in the beam is that multiple protons might collide in one bunch-crossing and
that collisions from subsequent bunch-crossings can overlap in the detector. These effects
are called in-time and out-of-time pile-up respectively. Over the whole data-taking period,
in order to provide as much data to the experiments as possible, the LHC was continuously
increasing the collision rates, and therefore also the pile-up.
The simulations include pile-up; however, the conditions are not exactly the same as in
data since the increase of collision rates was not completely known at the time the simulated
samples were made. Since the amount of pile-up can affect the electron reconstruction and
identification efficiency, the simulated samples have to be reweighted to contain the same
fraction of events with a given amount of pile-up as the data.

75

Chapter 6
Event selection and comparison with
Standard Model expectations
This chapter describes how the data used in this analysis are selected. Selection cuts, filtering
events with two reconstructed electrons that pass identification cuts, are applied to data as
well as to simulated signal and SM background samples. The QCD multijet background is
estimated from data by reversing electron identification cuts. The invariant mass distribution
is calculated and the observed data counts are compared to the expected SM backgrounds.
Other kinematic distributions are compared as well to ensure good modeling of the SM
backgrounds.

6.1

Event selection

This analysis uses LHC collision data obtained by the ATLAS detector between March and
June 2011. Only collisions are considered during which the LHC beam quality is good and
the necessary parts of the ATLAS detector are functioning. This amount of data corre76

sponds to an integrated luminosity of 1.08 fb−1 , which can be translated into one event
of a hypothetical process with a cross-section of 1.08 fb or ∼1 million Z bosons decaying
into electrons. In order to find a dielectron resonance, events are selected that contain two
electron candidates. This section describes the selection cuts that enhance the probability
for the electron candidates to be real electrons. Unless noted otherwise, the same selection
cuts are applied to data and the simulated signal and SM background samples.

6.1.1

Event selection

• Data quality
Only collision data are used that have been recorded when the protons in the LHC
beams are circulating in a stable orbit and are well focused, in order to avoid stray
protons or other beam radiation faking collision events in the detector. For data used
in an electron analysis, it is required that the calorimeters and the Inner Detector are
functioning at the time of collisions, and that the solenoidal magnetic field is switched
on, since it is needed for the momentum determination of the particles in the Inner
Detector. Furthermore, no irregularities in the e/gamma trigger performance (like
sudden rate drops) are allowed.
• Vertex
Only events in which there is at least one reconstructed collision point with more than
two tracks in the Inner Detector are used.
• Trigger
Events are selected if they pass the trigger EF e20 medium (compare Sec. 4.2). This
means they were recorded because they have at least one electron candidate with
77

ET > 20 GeV.
• Two reconstructed electrons
Since we are looking for dielectron resonances, we only want events with at least two
electron candidates reconstructed by the standard e/gamma reconstruction algorithm,
which is seeded by an energy cluster in the EM calorimeter (see Sec. 4.3).

The following selection cuts are applied to all electron candidates in the event; only
electron candidates that pass the previous cuts are considered at each stage. Events which
have less than two electron candidates fulfilling all requirements are discarded.

• η
The Inner Detector can only detect tracks up to |η| < 2.5 (compare Sec. 3.2.3), therefore
a selection cut of |η| < 2.47 is applied to the electron candidates. Furthermore, electrons
are rejected which fall into the transition regions (1.37 < |η| < 1.52) between the barrel
and the endcap of the EM calorimeter (Sec. 3.2.4), since the energy reconstruction in
these areas is not very accurate.
• ET
A selection cut of ET > 25 GeV is applied to the electron candidates to be consistent
with the trigger. Since we are looking for high-mass resonances, in principle the ET
cut could be far higher but the mass peak of the Z boson is used for normalization and
as a sanity check, thus electrons coming from the Z boson decay (most of which fulfill
30

ET [GeV]

60) should be kept. Before the ET cut is applied, the energy of the

electron candidates in data is calibrated by corrections which are obtained comparing
78

the Z boson mass peak to the prediction [34]. Energy smearing in the simulated
samples is described in Sec. 5.3.2.
• Electron quality
Electron candidates are not considered if they fall into problematic regions of the
EM calorimeter. Which regions are problematic changes with time, due to hardware
problems like broken electronics as well as irregularities in the applied voltage [94]. The
treatment of these time-dependent selection cuts in the simulated samples is described
in Sec. 5.3.3.
In addition, we reject events that contain corrupt event data or obvious electronic
malfunctions, like noise bursts which illuminate a large fraction of the cells in the EM
calorimeter.
• Identification
In order to enhance the probability that electron candidates are real electrons, they
are required to pass the Medium identification cuts (compare Sec. 4.4).
• B-layer
To avoid electrons from photon conversions, we require that electrons have a tracking
hit in the innermost layer of the Pixel detector (B-layer).
In events with more than two electrons at this stage of the selection cut flow, the two
electrons with the highest ET are chosen.
• Isolation
In order to reduce the fraction of electron fakes from QCD multijet production, the
energy cluster of the leading electron (the electron with the highest ET ) must be
79

isolated (compare Sec. 4.5). We require that the ET in a cone of ∆R < 0.2 around
the electron is less than 7 GeV. Corrections are applied accounting for pile-up effects
and energy in the cone that actually belongs to the electron. Since the subleading
electron often has less energy because it lost a fraction due to radiation, it usually is
less isolated and we do not require it to pass the isolation cut.
• Invariant mass
The invariant mass of the two electrons is calculated by taking the square root of the
square of the sum of the two electron 4-momenta and is required to be above 70 GeV.
The threshold is chosen to be below the Z boson mass peak (∼91 GeV) as mentioned
above.

6.1.2

Cutflows and acceptance

Table 6.1 shows the number of events passing the different selection cuts for data and for a
′
simulated ZSSM sample (m ′ = 1500 GeV). The absolute efficiencies of the cuts as applied
Z
to the signal sample are shown as well. The event numbers for the simulated sample contain
all corrections as described in Sec. 5.3, and they are weighted to an integrated luminosity of
1.08 fb−1 .
After applying the event selection cuts to the data, 266543 events are left, as shown in
Table 6.1. Figure 6.1 illustrates the event with the highest dielectron invariant mass (mee =
993 GeV). In this event, the ET of the two electrons is 257 and 207 GeV respectively. The
(η, φ) values for the leading electron are (-0.76, 1.14), for the subleading electron (2.05, -2.05).

80

Selection cuts

′
ZSSM + DY

Data

′
eff(ZSSM + DY)

(mee > 750 GeV)
Before cuts

152750511

16.53

1.00

Data quality

132525884

16.53

1.00

Vertex

132399372

16.53

1.00

Trigger

61869726

16.29

0.99

Two reconstructed electrons

40238063

15.97

0.97

η

36465364

15.29

0.93

ET

1747586

14.28

0.86

Electron quality

1710056

13.59

0.82

Identification

299073

11.60

0.70

B-layer

274997

11.25

0.68

Isolation

273929

10.98

0.66

Invariant mass

266543

10.98

0.66

′
Table 6.1: Event numbers after selection cuts for the data sample and a simulated ZSSM
sample (mZ ′ = 1500 GeV, mee > 750 GeV). The numbers for the simulated sample include
all corrections as described in Sec. 5.3, as well as the weighting to the data luminosity.
Furthermore, DY events with invariant masses above 750 GeV are included in the count
(they contribute ∼20%).

81

ET

η
φ

Run Number: 183462
Event Number: 48979599

Figure 6.1: Event display of the dielectron event with the highest invariant mass (mee = 993 GeV) after full event selection
[95].
82

Figure 6.2(a) shows the (η, φ)-map of all electrons in the data sample that pass the full
selection. The region centered at (η, φ) = (0.7, -0.7) has less electrons than the surrounding
areas. This is a part of the EM calorimeter that was not fully functioning during a fraction
of the data taking. The cut on the electron quality ensures that electrons falling into this
region are not considered, since their energy cannot be reconstructed reliably. To allow
for a consistent comparison between data and the simulated backgrounds, as described in
Sec. 5.3.3, this region is also excluded for a fraction of the simulated samples, which can be
seen in Fig. 6.2(b).
The acceptance of the selection cuts can be seen in Fig. 6.3 for different mZ ′ . The
problematic region in the EM calorimeter reduces the acceptance by about 4% (absolute).
The turn-on as well as the drop at high mZ ′ is mainly due to the invariant mass cut as well
as the cuts on electron η: The increase in mZ ′ up to ∼2 TeV produces more Z ′ bosons at
rest, which causes the decay electrons to be more central, leading to more events passing the
η cuts. However, above mZ ′ of ∼2 TeV, it becomes less and less likely that the colliding
quarks have enough energy to produce a Z ′ event at the peak mass, and a low mass tail
develops (compare Fig. 5.1), whose decay electrons are again less central.

6.2

QCD background estimation from data

Applying the event selection cuts reduces the probability that events are chosen which contain
one or two QCD jets instead of a real electron pair. However, due to the high production
rates for QCD jets in pp colliders, the event sample still contains a non-negligible number of
jets faking electrons.
The shape of the kinematic distribution of the QCD multijet background is estimated
83

φ

3

300

2

250

1

200

0

150

-1

100

-2

50

-3
-3

-2

-1

0

1

2

3

0

η

φ

(a)
3

300

2

250

1

200

0

150

-1

100

-2

50

-3
-3

-2

-1

0

1

2

3

0

η

(b)
Figure 6.2: (η, φ)-map of all electrons passing the full selection in data (a) and in the
simulated DY background sample (b). Regions colored in violet/blue have less events than
regions colored in yellow/red.

84

Acceptance

1
0.9
0.8
0.7
0.6
0.5
0.4
without problematic EM calo region

0.3
0.2

with problematic EM calo region

0.1
0

0.5

1

1.5

2

2.5
mZ ’ [TeV]

Figure 6.3: Efficiency of the selection cuts for different m ′ .
Z
from data by inverting some of the cuts on the electron identification. The normalization is
determined in a two-component template fit of the QCD shape and the other backgrounds
to the invariant mass distribution in data. Two additional estimation methods are used as
a cross-check and to assign systematic uncertainties.

6.2.1

Multijet shape estimate

We request data events to pass all selection cuts of the standard cutflow (compare Sec. 6.1.1)
except for the Medium identification cut (see Sec. 4.4). In order to select QCD jets that
might be able to fake real electrons, we require the objects to pass the Loose identification.
85

Events

103
102
10
1
10-1
10-2
103
mee [GeV]

102

Figure 6.4: The invariant mass spectrum obtained by reversing the shower shape cuts in the
first layer of the EM calorimeter is fitted with a dijet function [90]. The probability of this
fit function to describe the reverse identification distribution correctly is 77%.

This ensures that the energy showers of the jets in the second layer of the EM calorimeter
are similar to real electron showers. In order to avoid selecting real electrons, two cuts of the
Medium identification (compare Table 4.1) are reversed which describe the shower shapes in
the finely binned first layer of the EM calorimeter.
In order to smoothen the distribution and extrapolate it to high invariant masses, the
resulting invariant mass distribution is fitted with an analytical function (see Fig. 6.4):

f (x) = p0 xp1 xp2 · Logx .

(6.1)

This function describes the dijet invariant mass spectrum very well [96, 97] and Fig. 6.4
shows that it is also an appropriate model in this analysis.
86

6.2.2

Multijet background normalization

The dielectron invariant mass spectrum between 70 and 200 GeV is used as a discriminator
to find the fraction of the QCD multijet background in data. Three samples are used: Data,
the QCD shape obtained as described above, and the sum of the remaining backgrounds after
event selection taken from simulated samples and weighted according to their corresponding
theory cross-sections (compare Sec 5.2.2).
As shown in Fig. 6.5, a two component template fit of the two background histograms
to the data distribution determines the normalization of the QCD multijet background. To
avoid biases, the complete Z boson mass peak is covered by a single bin, since the simulated
DY sample does not model the shape of the peak perfectly. The remaining shape differences
between the QCD dijet distribution and the other backgrounds, dominated by DY, are large
enough to constrain the fit.
To assign systematic uncertainties to this multijet estimation method, different electron
cuts are inverted, and the QCD normalization uncertainty from the two-component template
fit is propagated to the full mass range.

6.2.3

Cross-checks with alternative methods

In order to obtain systematic uncertainties on the estimated QCD multijet distribution and
to cross-check the baseline method, the QCD multijet background is determined using two
independent methods [90].
The “Isolation Fits method” uses the distribution of the isolation variable as a discriminating variable. This works because real electrons deposit far less energy in a cone around
themselves than QCD jets which contain several particles. Templates for QCD multijets are
87

Events

105

χ2/dof=13/17

104
103
102
10
1

80

100

120

140

160

180

200

mee [GeV]
Figure 6.5: Template fit used to normalize the QCD multijet shape to data (black dots).
The green, dotted line shows the QCD estimation as it results from the log likelihood fit,
while the blue curve describes the full background estimation (QCD estimate plus all other
backgrounds from simulated samples).

derived from data by requiring a maximum fraction of high-threshold hits in the TRT. This
enriches the sample in QCD fakes, as pions are less relativistic than the lighter electrons
and therefore produce less transition radiation (compare Sec. 4.4, 3.2.3). Templates for real
electrons are obtained by applying cuts that select electrons from W boson decays. These
isolation templates are fitted to data passing the full event selection (Sec. 6.1.1). The fits are
performed separately for the leading and subleading electron in bins of ET and mee , and
the resulting QCD jet yields are combined to determine the amount of QCD multijet and
W + jets background for each dielectron invariant mass bin. The systematic uncertainty is
dominated by the uncertainty on the normalization from the fit.
An alternative QCD multijet estimation method, the “Fake Rates method”, uses events
88

recorded with jet triggers. Jets faking electrons are obtained by requesting them to be
reconstructed as electrons and to pass a subset of the Loose identification cuts (Sec. 4.4).
Real electrons from Z boson and W boson decays are removed by applying cuts on the
miss
dielectron invariant mass and ET . The fake rate is calculated by determining the fraction
of events in this sample passing the Z ′ electron selection criteria. This rate is obtained
for different η and ET bins and has a systematic uncertainty of ∼40%, obtained from the
comparison of samples selected by different jet triggers. The fake rate is applied to a selection
of electron-jet events, in which the jets are required to fail the Medium identification cuts,
but otherwise pass the same cuts as the sample used to calculate the fake rates. This results
in a combined estimate of QCD multijet and W + jets backgrounds.
Table 6.2 shows the resulting amount of QCD multijet and W + jets background in this
analysis after full selection as obtained by the three methods. The W + jets yield from the
simulated sample is normalized to the theory cross-section and luminosity and is added to
the results of the baseline method to allow for a comparison between the methods. The
predicted yields of the three methods agree within their large uncertainties, and the largest
differences to the baseline estimate are used as an additional systematic uncertainty.

Mass range [GeV]
70 < mee < 110
110 < mee < 130
130 < mee < 150
150 < mee < 200
200 < mee < 800
800 < mee < 3000

Baseline method
482.3 ± 85.2
136.7 ± 24.2
90.4 ± 16.1
113.7 ± 20.2
85.2 ± 15.2
0.2 ± 0.2

Isolation Fits
107.0 ± 46.0
116.3 ± 45.1
147.6 ± 58.3
149.8 ± 52.4
-

Fake Rates
72.8 ± 29.2
104.9 ± 42.0
106.4 ± 42.6
-

Table 6.2: Comparison of the different QCD jet estimates [90]. As the Isolation Fits and the
Fake Rate methods include W+jets, the W+jets number from simulation has been added to
the results of the baseline method.

89

6.3

Comparison of data with Standard Model expectations

¯
The full event selection (Sec. 6.1) is applied to the DY, Diboson, W + jets, and tt simulated samples. The resulting invariant mass distributions are weighted by the corresponding
cross-sections (see Sec. 5.2.2) and added together. The estimated QCD background (see
Sec. 6.2) is subtracted from the data distribution, and the sum of the other SM backgrounds
is normalized to the remaining invariant mass distribution between 70 and 110 GeV. This
normalization of the simulated samples to data simplifies the treatment of systematic uncertainties, since all systematic uncertainties on the SM background that are mass independent,
like the luminosity uncertainty, cancel out.

6.3.1

Event yields

Table 6.3 shows the predicted SM background as well as the observed event counts in data
after the selection cuts. The errors include both statistical and systematic uncertainties,
except for the uncertainty on the total background in the normalization region (70-110 GeV)
which corresponds to the square root of the number of observed events. For each bin in
dielectron invariant mass, the observed number of data events agrees with the SM background
within ±1σ.

6.3.2

Kinematic distributions

This section shows a comparison of kinematic distributions from data after full event selection
with the estimated SM backgrounds.
90

mee [GeV]
DY
¯
tt
Dibosons
W+jets
QCD
Total
Data

70-110
258481.5±413.9
218.1±23.0
368.2±18.8
150.1±42.8
332.2±59.1
259550.0±421.3
259550

110-130
3185.4±106.9
86.9±10.5
30.9±2.3
56.7±17.0
79.9±41.9
3439.9±116.6
3419

130-150
1182.9±46.4
64.1±7.6
23.8±2.0
40.0±12.5
50.4±19.7
1361.2±52.5
1362

150-170
607.9±28.0
50.9±5.2
14.9±1.4
26.8±8.7
32.2±7.3
732.8±30.7
758

170-200
473.0±23.6
51.2±5.2
15.7±1.5
26.1±8.4
28.6±6.5
594.6±26.4
578

mee [GeV]
DY
¯
tt
Dibosons
W+jets
QCD
Total
Data

200-240
311.8±17.6
37.0±3.8
13.5±1.4
19.5±6.4
19.0±15.2
400.8±24.5
405

240-300
196.1±8.6
30.4±3.1
7.8±0.9
14.2±5.0
11.6±9.3
260.0±14.0
256

300-400
105.0±5.2
14.9±1.4
7.5±1.1
9.0±3.5
5.5±4.4
141.9±7.9
147

400-800
53.8±3.1
5.4±0.5
3.1±0.5
4.6±2.0
1.8±1.4
68.8±4.0
65

800-3000
2.8±0.4
0.1±0.0
0.3±0.1
0.2±0.4
0.0±0.0
3.4±0.6
3

Table 6.3: Expected and observed number of events after selection cuts. The errors quoted
include both statistical and systematic uncertainties, except for the uncertainty on the total
background in the normalization region (70-110 GeV) which corresponds to the square root
of the number of observed events. Entries of 0.0 indicate a value < 0.05.

In the dielectron invariant mass spectrum (Fig. 6.6), the mass peak of the Z boson
can clearly be seen. This is the distribution in which we look for an additional resonance
′
peak. Three ZSSM distributions with different masses are overlayed for illustration. The
η distribution of the leading and subleading electron is shown in Fig. 6.7. The gaps in
the distribution are due to the selection cuts rejecting electrons that fall into the transition
region between the barrel and endcap of the EM calorimeter (1.37 < |η| < 1.52). The
asymmetry in η is due to the region of the calorimeter that was not fully functional during
a fraction of the data taking. Other variations in the measured η rates, like the dip around
0, are in part due to detector properties. Only the DY background is shown, since the other
background contributions are too small to be visible in linear scale. Figure 6.8 shows the
′
ET distributions of the leading and the subleading electron separately. Again, three ZSSM
91

Events

106

ATLAS

105

∫

4

10

L dt = 1.08 fb

-1

s = 7 TeV

103
102

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD
Z’(1000 GeV)
Z’(1250 GeV)
Z’(1500 GeV)

10
1
10-1
10-2
80 100

200

500

1000

2000

mee [GeV]
Figure 6.6: Dielectron invariant mass distribution after full event selection, comparing the
′
SM backgrounds to data. Three ZSSM distributions are added for illustration.
distributions with different masses are overlayed for illustration. The dielectron rapidity and
dielectron pT can be seen in Fig. 6.9. The isolation distributions are shown in Fig. 6.10
for the full dataset and in Fig. 6.11 for events that have a dielectron invariant mass above
130 GeV. These distributions are important checks of the QCD multijet estimate, since this
background dominates at the high end of the isolation spectrum. In all distributions the
estimated SM background describes the data very well.

6.4

Muon channel

We also performed this analysis in the dimuon channel. This section gives a brief overview
over the event selection and comparison between data and expected SM background. More
92

Electrons / 0.1

×103
22
20
18
16
14
12
10
8
6
4
2
-3

Data 2011
Z/γ *

ATLAS

∫ L dt = 1.08 fb

-1

s = 7 TeV

-2

-1

0

1

2

3
η

Figure 6.7: η distribution of the leading and subleading electrons after full event selection,
comparing the SM backgrounds to data.
details can be found in [6] and [90].

6.4.1

Event selection

In order to obtain the dimuon mass spectrum, events with two muon candidates with opposite
charge are selected. Both muons have to fulfill pT > 25 GeV and they have to pass quality
cuts in the Inner Detector. Furthermore at least three hits are required in each of the inner,
middle, and outer layers of the muon system. Muons are only considered if they have tracks
close to the nominal interaction points in order to suppress cosmic rays. In order to reduce
background from QCD multijet events, the muon tracks have to be isolated. The total signal
acceptance in the muon channel is 40%, much lower than in the electron channel, which is
mainly due to the need to improve the pT resolution by only accepting muons that pass very
93

strict cuts.

6.4.2

Comparison of data with Standard Model expectations

mµ+ µ− [GeV]
DY
¯
tt
Diboson
W +jets
QCD
Total
Data

70-110
236318.6±319.7
193.1±21.0
306.7±15.9
1.3±0.7
1.3±1.2
236821.0±486.6
236821

110-130
3132.1±87.5
70.0±9.1
24.9±2.2
0.4±0.4
0.3±0.2
3227.8±88.0
3210

130-150
1073.4±35.9
50.7±7.0
19.4±2.0
0.0±0.0
0.1±0.1
1143.7±36.6
1132

150-170
548.7±21.8
34.2±3.6
13.3±1.6
0.2±0.2
0.1±0.1
596.5±22.2
621

170-200
416.3±18.3
37.7±3.9
11.7±1.5
0.0±0.0
0.0±0.0
465.8±18.7
443

mµ+ µ− [GeV]
DY
¯
tt
Diboson
W +jets
QCD
Total
Data

200-240
249.4±13.0
30.5±3.2
10.1±1.4
0.0±0.0
0.0±0.0
290.0±13.5
279

240-300
152.9±7.1
20.6±2.2
8.0±1.1
0.0±0.1
0.0±0.0
181.5±7.6
195

300-400
80.8±3.9
11.7±1.2
6.7±1.1
0.0±0.0
0.0±0.0
99.3±4.2
83

400-800
40.3±2.5
4.2±0.4
1.7±0.5
0.0±0.0
0.0±0.0
46.1±2.6
51

800-3000
2.0±0.3
0.1±0.0
0.0±0.0
0.0±0.0
0.0±0.0
2.1±0.3
5

Table 6.4: Expected and observed number of events in the dimuon channel [6]. The errors
quoted include both statistical and systematic uncertainties, except the total background in
the normalization region which corresponds to the square root of the number of observed
events. Entries of 0.0 indicate a value < 0.05.

Table 6.4 shows the comparison between the predicted SM background and the observed
event counts in data after the selection cuts. The errors include both statistical and systematic uncertainties, except for the uncertainty on the total background in the normalization
region (70-110 GeV) which corresponds to the square root of the number of observed events.
The invariant mass distribution in data and for the SM backgrounds is shown in Fig. 6.12.
′
Three ZSSM distributions with different masses are overlayed for illustration.

94

Electrons

106

ATLAS

∫ L dt = 1.08 fb

105
104

-1

s = 7 TeV

3

10

102

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD
Z’(1000 GeV)
Z’(1250 GeV)
Z’(1500 GeV)

10
1
10-1
100

200

300

400

500

600

Leading Electron ET [GeV]

Electrons

(a)

106

ATLAS

105

∫ L dt = 1.08 fb

104

-1

s = 7 TeV

3

10

102

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD
Z’(1000 GeV)
Z’(1250 GeV)
Z’(1500 GeV)

10
1
10-1
100

200

300

400

500

600

Subleading Electron ET [GeV]
(b)
Figure 6.8: ET distribution of the leading (a) and subleading electron (b) after full event
′
selection, comparing the SM backgrounds to data. Three ZSSM distributions are added for
illustration.
95

Events / 0.2

25

×103
Data 2011
Z/γ *

ATLAS
20

∫ L dt = 1.08 fb

-1

s = 7 TeV
15
10
5

-3

-2

-1

0

1

2

3

Dielectron Rapidity

Events

(a)

105

ATLAS

104

∫ L dt = 1.08 fb

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD

-1

s = 7 TeV

103
102
10
1
10-1

100

200

300

400

500

600

Dielectron pT [GeV]
(b)
Figure 6.9: Dielectron rapidity (a) and dielectron pT (b) after full event selection, comparing
the SM backgrounds to data.

96

Electrons / 2 GeV

106

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD

ATLAS

∫ L dt = 1.08 fb

105
104

-1

s = 7 TeV

3

10

102
10
1
10-1
0

5

10

15

20

25

30

35

40

Leading Electron Isolation [GeV]

Electrons / 2 GeV

(a)

106

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD

ATLAS

∫ L dt = 1.08 fb

105
104

-1

s = 7 TeV

3

10

102
10
1
10-1
0

5

10

15

20

25

30

35

40

Subleading Electron Isolation [GeV]
(b)
Figure 6.10: Calorimeter isolation distribution of the leading (a) and subleading electron (b)
after full event selection, comparing the SM backgrounds to data.

97

Electrons / 1 GeV

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD

104

∫ L dt = 1.08 fb

103

-1

s = 7 TeV
102
10
1
10-1
0

5

10

15

20

25

30

35

40

Leading Electron Isolation [GeV]

Electrons / 1 GeV

(a)

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD

104

∫ L dt = 1.08 fb

103

-1

s = 7 TeV
102
10
1
10-1
0

5

10

15

20

25

30

35

40

Subleading Electron Isolation [GeV]
(b)
Figure 6.11: Calorimeter isolation distribution of the leading (a) and subleading electron (b)
after full event selection, comparing the SM backgrounds to data. Only events with mee >
130 GeV are shown.
98

Events

106

ATLAS

105

∫

4

10

L dt = 1.21 fb

-1

s = 7 TeV

103
102

Data 2011
Z/γ *
Diboson
tt
W+Jets
QCD
Z’(1000 GeV)
Z’(1250 GeV)
Z’(1500 GeV)

10
1
10-1
10-2
80 100

200

500

1000

2000

mµµ [GeV]
Figure 6.12: Dimuon invariant mass distribution after full event selection, comparing the
′
SM backgrounds to data [90]. Three ZSSM distributions are added for illustration.

99

Chapter 7
Statistical treatment and results
This chapter starts with a description of the theoretical and experimental systematic uncertainties. The dielectron invariant mass spectrum in data is searched for peak-like deviations
from the SM background. Since no statistically significant excess is found, 95% C.L. upper
limits are set on the cross-section times branching ratio of Z ′ bosons and RS gravitons using
a Bayesian approach [98, 99].

7.1

Systematic uncertainties

The treatment of systematic uncertainties is facilitated by normalizing all SM backgrounds to
data between dielectron invariant masses of 70 and 110 GeV. As a result, mass-independent
uncertainties, like the luminosity uncertainty, need not to be considered because they would
result in an overall shift of the distribution which is however fixed by the normalization at
the Z boson mass peak.
The largest systematic uncertainty on the cross-sections of simulated signal and background processes is due to incomplete knowledge of the PDFs (see Chapter 5 and Sec. 2.1.3)
100

and the strong coupling constant αS . This uncertainty grows with invariant mass because
the input values for the PDFs are measured at low energies. In order to determine the size of
′
the uncertainty, DY, ZSSM , and G∗ cross-sections produced with systematic PDF variations
are compared to the nominal ones. For further comparison, cross-sections are produced with
PDF sets which correspond to variations of αS [90]. The resulting Z ′ /G∗ /DY cross-section
uncertainty is 10% at an invariant mass of 1.5 TeV.
In order to improve the cross-section estimate of the simulated DY and Z ′ samples, which
are produced at LO, k-factors are calculated (compare Sec. 5.2.2). The uncertainties on the
mass-dependent QCD k-factors are determined by varying the normalization and factorization scales by a factor of two around the nominal values (compare Sec. 2.1.3). Furthermore,
the k-factors are reevaluated for Z boson production only instead of Z/γ ∗ production and
the difference, less than 1%, is included in the uncertainty. The total uncertainty of the
QCD k-factor is 3% at an invariant mass of 1.5 TeV. The corresponding uncertainty on the
electroweak k-factor is 4.5% to account for real boson emission and higher order corrections
as well as differences between the generator used for calculating the electroweak corrections
and Pythia, with which the DY samples are simulated.
The experimental uncertainties in this analysis are quite small:
• The uncertainty on the energy calibration of the EM calorimeter ranges from energy
shifts of 0.5% to 1.5%, depending on transverse energy and η [80].
• For high energies, the energy resolution is dominated by the constant term (see Sec. 4.6.1),
which has a negligible uncertainty.
• Uncertainties on trigger and identification efficiencies are independent of the invariant
mass above ∼90 GeV.
101

• The isolation cut has been shown in the simulation to cause an efficiency drop of 1.5%
for an invariant mass of 1.5 TeV. As illustrated in Fig. 4.3 in Sec. 4.6.1, this drop
is cancelled by the rising efficiency of the B-layer cut, but in order to account for
possible differences between the modeling and data, a conservative uncertainty of 1.5%
is assigned.
• The largest contribution to the uncertainty on the estimation of the QCD multijet
background is the comparison to alternative estimates (compare Sec. 6.2). This uncertainty is very large, however the QCD multijet background is only a small fraction
of the total SM background (compare Table 6.3), so the overall uncertainty on the
background yield is only 1.5% at an invariant mass of 1.5 TeV.

Table 7.1 lists the systematic uncertainties that are applied when searching for a signal and setting limits. The uncertainties are presented as the relative changes in the signal/background yields for variations of 1σ. Other systematic uncertainties below 3% are
neglected in the analysis, since they do not change the results visibly. The uncertainty on
the QCD estimate is considered nonetheless since it is the only uncertainty that can be larger
at lower invariant masses. No theoretical uncertainties are applied on the signal. However,
the luminosity normalization of the SM background to the data under the Z boson mass
peak has a 5% uncertainty due to the Z boson cross-section uncertainty.

7.2

Statistical analysis

This section describes the likelihoods used for the signal search and for limit setting, as well
as the treatment of systematic uncertainties.
102

Source

Dielectrons
Signal Background
5%
NA
NA
10%
NA
3%
NA
4.5%
NA
1.5%
5%
11%

Normalization
PDFs/αS
QCD k-factor
Weak k-factor
QCD estimate
Total

Table 7.1: Systematic uncertainties on the expected signal and background yields at
mee = 1.5 TeV for the Z ′ and RS graviton analysis. NA means not applicable [90].
According to Poisson statistics, the likelihood to observe n events for a predicted yield
of µ can be calculated as

L(n|µ) =

µn e−µ
.
n!

(7.1)

The predicted yield is the sum of background and potential signal, while the observed events
are the event counts in data:

µ=

Nj = Nsig + Nbkg ,

n = Ndata .

(7.2)

j
Nbkg is predicted and Ndata is measured; the parameter of interest is Nsig .
Systematic uncertainties, like a change in the QCD k-factor, could change the predicted
yield:

µ=

Nj
j

(1 + G(θij , δij )).

(7.3)

i

According to the Bayesian treatment of systematic uncertainties, G is the probability density
function of the nuisance parameter θij which is usually chosen to be Gaussian with a mean
103

of zero and a σ that corresponds to the relative uncertainty δij .
In this analysis, the likelihood is calculated for every bin k in the search range of the
invariant mass spectrum (mee > 130 GeV), and the results of all bins are multiplied to form
an overall likelihood:
n
µ k e−µk
k
L(n|Nj , θij ) =
,
nk !
k

(7.4)

where µ is defined in Eq. 7.3 and n, Nj , and θij are now vectors whose dimensions correspond
to the number of mass bins.
Using a binned likelihood takes advantage of the peak-like shape of the signal, which
makes the analysis more robust toward broad underestimates of the SM background and more
sensitive to finding a peak than a single bin counting experiment. Eq. 7.4 takes into account
possible correlations of systematic uncertainties not only between signal and background but
also between different bins.
In order to obtain a reduced likelihood L′ that is only a function of Nsig , a multidimensional integral over the probability functions of the nuisance parameters is performed. This
is done by integrating numerically using the Bayesian Analysis Toolkit [98]:

L′ (n|Nsig ) =

L(n|Nsig , Nbkg , θ0 , θ1 , θ2 ...)dθ0 dθ1 dθ2 ...

(7.5)

Instead of the number of signal events Nsig , the cross-section times branching fraction
σsig B is used when calculating the likelihood. The translation is done according to Eq. 5.1
by replacing the integrated luminosity Lint with the number of Z boson events NZ , the Z
104

boson cross-section σZ and acceptance AZ :

σsig B =

Nsig A
Z σ B.
Asig NZ Z

(7.6)

This approach has the advantage that all mass-independent uncertainties cancel out; however, the uncertainty on σZ has to be included (compare Sec. 7.1). Mass-dependent uncerA
tainties on NZ and A Z are small enough to be neglected. This thesis correctly includes
sig
higher order corrections to NZ and σZ (compare Sec. 5.2.2). The resulting limits are slightly
more stringent than in Ref. [6], where higher order effects were accounted for twice.

7.3

Signal search

The first part of the statistical analysis is to quantify possible excesses in the data invariant
mass spectrum as compared to the SM background (see Fig. 6.6). The reduced likelihood over
the mass spectrum, starting well above the normalization region at 130 GeV, is calculated
′
using the ZSSM model as a reference (see Eq. 7.5).
Figure 7.1 shows the reduced likelihoods for different test masses and cross-sections. The
red regions have higher likelihoods than the blue regions and correspond to local excesses in
the dielectron spectrum in the data compared to the SM prediction (compare Fig. 6.6). The
most likely values for MZ ′ and σZ ′ are MZ ′ = 600 GeV and σZ ′ = 0.012 pb.
The next step is to determine the statistical significance of the excess. For this, we
compute the probability for the SM background to fluctuate to the observed data. The
Neyman-Pearson lemma [100] states that the best discriminant between two hypotheses, in
our case (signal+background) vs. (background only), is the log-likelihood ratio (LLR). The
105

mZ’ [Tev]

5
2

4.5

ATLAS

1.8

∫ L dt = 1.08 fb

1.6

4

-1

3.5

s = 7 TeV

1.4
1.2

3

Z’ → ee

1

2.5

Signal Scan, Best Fit

0.8

68% Contour

1.5

0.6

1

0.4
0.2
0

2

0.5
0.02

0.04

0.06

0.08

0.1

0.12

0.14 0.16
σZ’ [pb]

0

Figure 7.1: Reduced likelihoods to have an excess caused by new physics for different Z ′ test
masses and cross-sections.

ˆ
likelihood for the MZ ′ = 600 GeV and σZ ′ = 0.012 pb as well as the background-only
ˆ
hypotheses are calculated. Then the LLR value is determined as:
ˆ
ˆ
L(n|ˆZ ′ , MZ ′ , θi )
σ
ˆ ˆ
ˆ
LLR(ˆ ′ , M ′ , θi , θi ) = ln
σ
.
Z
Z
ˆ
L(n|ˆZ ′ = 0, θi )
σ

(7.7)

ˆ
ˆ
Here, θi and θi are the values of the nuisance parameters, determined by integrating over all
other parameters and finding the maximum of the respective reduced likelihoods.
A large number of background-only pseudo-data distributions are produced: First, values
of the nuisance parameters are chosen by sampling from their Gaussian distributions, then the
106

SM background distribution, shifted by the systematic uncertainties, is sampled according
ˆ
ˆ
to a Poisson distribution. For each of the pseudo-data distributions, MZ ′ and σZ ′ are
ˆ
determined, and the LLR is calculated. Since MZ ′ and σZ ′ are free parameters and can be
ˆ
different for every pseudo-data distribution, the look-elsewhere effect is naturally taken into
account. This effect describes the reduction of the significance of an excess when considering
the probability that a statistical fluctuation might appear anywhere in the mass range. The
fraction of pseudo-experiments in which an LLR value as large or larger than the one in
data is found is called p-value,

p = p(LLR ≥ LLRdata |SM only).

(7.8)

The common convention is that a p-value less than 1.35 × 10−3 constitutes evidence for a
signal and a p-value less than 2.87 × 10−7 constitutes a discovery. (These are one-sided
integrals of the tails of a unit Gaussian distribution beyond +3σ and +5σ, respectively.)
In this analysis, the p-value from the LLR test is 0.54, which means more than half the
background-only pseudo-data distributions show an excess at least as significant as the one
found in data, thus the observed excess is not statistically significant.
The search for a significant excess is also performed in an alternative fashion, independent
of the Z ′ mass shape. The BumpHunter algorithm [101] divides the invariant mass spectrum
into ranges with varying widths, and determines the local p-value for each range. Only
ranges are considered in which the data have a higher yield than the background, and for
which there is an agreement between data and SM background in sidebands half as wide
as the ranges themselves. The window with the smallest local p-value, and therefore the
most significant excess is determined. This smallest local p-value is used as a test statistic
107

in a large number of background-only pseudo-data distributions. For each of the pseudoexperiments, the smallest local p-value could be in a different mass range, which accounts
for the look-elsewhere effect. An overall p-value is calculated by determining the fraction of
the pseudo-data distributions which have a smallest local p-value smaller or equal to the one
determined from data. The overall p-value thus obtained is 0.79, thus both methods state
that there is no significant excess in the dielectron invariant mass spectrum as obtained from
data by our event selection.

7.4

Limits

Since no significant excess is found in the dielectron invariant mass spectrum, limits are set
′
at the 95% C.L. on the cross-section times branching fraction of the ZSSM boson and the RS
¯
graviton model with k/MP l = 0.1 (compare Sec. 2.2.6). These σsig B limits are obtained
′
for a range of signal pole masses and are translated into lower mass limits on the ZSSM
boson, different E6 Z ′ bosons (compare Sec. 2.2.3), and the RS graviton with various values
¯
of k/MP l .
L′ (n|σsig B) (see Eq. 7.5, 7.6) gives the likelihood to find n data events given a signal
cross-section and branching ratio. In order to translate this into an equation which describes
the likelihood that there is a signal with σsig B given that we see n data events, Bayes’
theorem [102] is employed:

L′ (σsig B|n) = L′ (n|σsig B)

π(σsig B)
π(n)

∝ L′ (n|σsig B),

(7.9)

where π(n) is the prior for the number of observed events and π(σsig B) is the prior for
108

σsig B. π(n) is the same for all possible values of σsig B:

π(n) = const.

(7.10)

Since we do not have any information about σsig B, we set its prior to be flat as well,
following the common convention:

π(σsig B) = const.

(7.11)

The value for σsig B, which includes 95% of the integral over the likelihood starting at zero,
is called 95% C.L. limit:
(σsig B)95 ′
L (σsig B|n)d(σsig B)
0.95 = 0 ∞ ′
.
0 L (σsig B|n)d(σsig B)

(7.12)

The limits which are listed in Sec. 7.4.1 and 7.4.2 are all 95% C.L. limits, which means, we
state with 95% C.L. that σsig B is smaller than the quoted limit (σsig B)95 .

7.4.1

Electron results

′
Figure 7.2 shows the limits on σsig B for different test masses of the ZSSM boson (spin¯
1, 7.2(a)) and the RS graviton with k/MP l = 0.1 (spin-2, 7.2(b)) as well as theoretical
cross-section curves for several models. The mass at which the theoretical cross-section line
intersects the limit curve is the lower mass limits.
The red line shows the σsig B limits as they are observed in data. It is not smooth due
to local excesses and deficits in the dielectron invariant mass spectrum in data compared
109

to the SM background expectation (see Fig. 6.6). The cross-sections times branching ratios
above the limit line are excluded at the 95% C.L..
The plots also show expected limits and their 1σ and 2σ envelopes. These are the
limits expected in the absence of signal. They are obtained by using 1000 background-only
pseudo-data distributions as input for the limit setting. As for the signal search, the SM
background histogram is modified by sampling values of the nuisance parameters from their
Gaussian distributions. Then pseudo-data distributions are sampled from these background
histograms according to a Poisson distribution. Figure 7.3 shows the σB limits for mZ ′ =
810 GeV from 1000 pseudo-data distributions. The dashed line indicates the median of the
distribution, while the green and yellow areas show the 68% (1σ) and 95% (2σ) envelopes.
′
′
The theoretical cross-sections (times branching fractions) for the ZSSM , the Zχ and
′
the Zψ boson are shown in Fig. 7.2. The same peak shape and acceptance is assumed for
all Z ′ models, which is a valid approximation as interference is neglected and the widths
′
of the Z ′ bosons in the E6 models under consideration are smaller than the ZSSM boson
width (compare Fig. 2.5), making the limits slightly more conservative. For the RS graviton,
¯
the cross-section curves for k/MP l = 0.1, 0.05, 0.03, 0.01 are presented. Again, the signal
¯
template and acceptance curve is the one for k/MP l = 0.1, which has the largest width.
Uncertainties on the cross-sections due to the QCD k-factor (in the Z ′ case) and the PDF
(compare Sec. 7.1) are illustrated representatively by the thickness of the curve with the
highest cross-section values.

110

σ B [pb]

s = 7 TeV
Z’ → ee

1

10-1

Expected limit
Expected ± 1σ
Expected ± 2σ
Observed limit
Z’SSM
Z’χ
Z’ψ

10-2
ee: 1.08 fb-1
10-3 0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8 2
m [TeV]

σ B [pb]

(a)

s = 7 TeV
G* → ee

1

10-1

Expected limit
Expected ± 1σ
Expected ± 2σ
Observed limit
k/MPl = 0.1
k/MPl = 0.05
k/MPl = 0.03
k/MPl = 0.01

10-2
ee: 1.08 fb-1
10-3 0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8 2
m [TeV]

(b)
Figure 7.2: 95% C.L. limits on the cross-section times branching ratio for different Z ′ models
¯
(top) and the RS graviton with different values of k/MP l (bottom) as obtained from the
dielectron invariant mass distribution.
111

Number(PE)

80

mZ’ = 810 GeV

70

Expected limit

60

Expected ± 1σ
Expected ± 2σ

50
40
30
20
10
0.005

0.01

0.015

0.02

95% C.L. limits on σ B
Figure 7.3: 95% C.L. limits from 1000 pseudo-data distributions for a test mass mZ ′ = 810
GeV. The dashed line indicates the median of the distribution, which is quoted as expected
limit, while the green and yellow areas show the 68% (1σ) and 95% (2σ) envelopes.

112

The lower mass limits for Z ′ bosons are listed in Table 7.2 and the limits on RS gravitons
in Table 7.3. The expected and observed limits agree very well; small deviations are due to
fluctuations in the data distribution.

′
ZSSM
′
Zχ
′
ZS
′
ZI
′
Zη
′
ZN
′
Zψ

Observed mass
limit [TeV]
1.74
1.56
1.52
1.49
1.46
1.44
1.42

Expected mass
limit [TeV]
1.74
1.56
1.52
1.49
1.45
1.43
1.41

′
Table 7.2: Dielectron 95% C.L. mass limits on the ZSSM boson and the E6 Z ′ bosons.

¯
k/MP l
0.1
0.05
0.03
0.01

Observed mass
limit [TeV]
1.55
1.26
0.99
0.72

Expected mass
limit [TeV]
1.54
1.25
1.05
0.67

Table 7.3: Dielectron 95% C.L. mass limits on the RS graviton with different values of
¯
k/MP l .

7.4.2

Combination with muon channel

We also performed a search for resonances in the dimuon channel [6, 90]. No significant
excess is found in the dimuon invariant mass spectrum (see Fig. 6.6): The p-value obtained
by the LLR test is 24%. Electron-muon combined limits are obtained by extending the
likelihood (Eq. 7.4) to also include the dimuon reconstructed invariant mass bins. By using
σsig B instead of Nsig (compare Eq. 7.6), different acceptances and integrated luminosities
113

are automatically taken into account. As before, statistical uncertainties are independent
for each mass bin, but systematic uncertainties can be correlated between the bins, and
therefore also between the different channels.
The expected and observed combined limits are shown in Fig. 7.4(a) for different Z ′
¯
bosons and in Fig. 7.4(b) for RS gravitons with different values of k/MP l . The theoretical
curves are the same as for the dielectron limit (Fig. 7.2); the addition of the dimuon channel
′
increases the dataset. The expected and observed limits on the pole masses of the ZSSM and
¯
different E6 Z ′ bosons as well as RS gravitons with different values of k/MP l are shown in
Tables 7.4 and 7.5. They differ slightly from the results in Ref. [6], as explained in Sec. 7.2.

′
ZSSM
′
Zχ
′
ZS
′
ZI
′
Zη
′
ZN
′
Zψ

Observed mass
limit [TeV]
1.88
1.68
1.64
1.60
1.58
1.56
1.54

Expected mass
limit [TeV]
1.87
1.67
1.63
1.59
1.57
1.55
1.53

′
Table 7.4: Combined dielectron and dimuon 95% C.L. mass limits on the ZSSM boson and
the E6 Z ′ bosons.

¯
k/MP l
0.1
0.05
0.03
0.01

Observed mass
limit [TeV]
1.67
1.37
1.09
0.72

Expected mass
limit [TeV]
1.66
1.35
1.12
0.72

Table 7.5: Combined dielectron and dimuon 95% C.L. mass limits on the RS graviton for
¯
different values of k/MP l .

114

7.5

Discussion of results

The LHC collides protons with record CM energies, which allows us to probe the SM by
searching for new physics in regions of phase-space that have never been tested before. The
main result of this analysis is that using ∼1 fb−1 of ATLAS data we have not found any
statistically significant peak-like excess over the SM background in the dielectron and dimuon
invariant mass distributions.

7.5.1

Interpretation

The non-existence of any significant excess is quantified by limits on the cross-section times
branching ratio for two representative models: The SSM, which predicts a spin-1 Z ′ boson,
as well as the RS model, which predicts excitations with spin-2. Lower mass limits can
be obtained from the respective σB limit curves for any spin-1/spin-2 model, as long as
peak-shape and acceptance are similar.
′
In this analysis we use the ZSSM boson cross-section limit curve to set lower mass limits
on the E6 model for different choices of the mixing angle θE . We also set limits on the RS
6
graviton mass for different couplings. These mass limits do not exclude either of the tested
models, but significantly limit their allowed parameter space.
A reinterpretation of the spin-1 limits was done by ATLAS in the context of the Low
Scale Technicolor model [39, 103] by setting mass limits on technimesons [104]. As can be
seen in Fig. 7.5, the analysis excluded masses of 130-480 GeV for the techni-rho and techniomega, dependent on the mass of the techni-pi. The limits just barely excluded the mass
values (πT = 160 GeV, ρT = 290 GeV) suggested in [105] as explanation of the W jj excess
seen by the CDF collaboration [106].
115

Other models predicting high-mass dielectron/dimuon resonances can also be restricted,
for example little Higgs models [41, 107, 108].

7.5.2

Comparison to other analyses

The CMS collaboration also searched for dielectron/dimuon resonances in ∼1 fb−1 of LHC
collision data [109]. The combined lower mass limits are shown in Tables 7.6 and 7.7. They
are higher than the results of this analysis, mainly because of a larger acceptance in the
muon channel due to a different muon detector design. Tables 7.6 and 7.7 also contain the
limits set by the CDF and D/ collaborations at the Tevatron. Due to the higher CM energy
0
at the LHC, ATLAS and CMS have a larger search range and obtain higher mass limits,
even when less collision events are evaluated.
Looking at other ATLAS analyses, limits on the RS graviton were obtained in a diphoton
resonance search using ∼2 fb−1 of LHC data [110]. The combination of dielectron, dimuon
¯
and diphoton channels yields a mass limit of 1.95 TeV for k/MP l = 0.1.
Furthermore, both the ATLAS and CMS collaborations released preliminary updates to
the dielectron/dimuon search using the full 2011 dataset (∼5 fb−1 ) [111, 112]. No significant
excess was found and the results are shown in Tables 7.6 and 7.7.
Experiment

Channel

Luminosity [fb−1 ]

Mass [TeV]

Reference

D/
0
CDF
ATLAS (2011)
CMS (2011)
ATLAS (2012)
CMS (2012)

ee
µµ
ee + µµ
ee + µµ
ee + µµ
ee + µµ

5
5
1
1
5
5

1.023
1.071
1.88
1.940
2.21
2.320

[62]
[61]
this analysis
[109]
[111]
[112]

′
Table 7.6: Observed limits on the lower mass of the ZSSM boson as obtained by different
experiments.

116

Experiment
D/
0
CDF
ATLAS (2011)
CMS (2011)
ATLAS (2011)
CMS (2011)
ATLAS (2012)
CMS (2012)

Channel

Luminosity [fb−1 ]

Mass [TeV]

Reference

ee + γγ
ee + γγ
ee + µµ
ee + µµ
(ee + µµ) + γγ
γγ
ee + µµ
ee + µµ

5
6+5
1
1
1+2
2
5
5

1.050
1.058
1.67
1.780
1.95
1.84
2.16
2.135

[53]
[113]
this analysis
[109]
[6], [110]
[114]
[111]
[112]

¯
Table 7.7: Observed limits on the lower mass of the RS graviton with k/MP l =0.1, as
obtained by different experiments.

Z ′ bosons and RS gravitons are also searched for by the ATLAS collaboration in the
ditau and top-antitop channels [115].

7.5.3

Outlook

The sensitivity of the search for high-mass dilepton resonances towards lower cross-sections
and higher pole masses increases with the number of recorded events and the CM energy.
In 2012, the LHC will collide protons at

√

s = 8 TeV, extending the accessible combined

′
dielectron and dimuon signal range in 10 fb−1 of data to ∼2.7 TeV for a ZSSM boson [116].
This could vary depending on the achieved acceptance, of course.
Possible improvements to this analysis would be the consideration of interference between
the Z ′ bosons and the DY background as well as variations of the width of the resonance
for different models and different coupling values. Furthermore, angular distributions could
be used to increase the sensitivity of the signal search, as done by the CDF collaboration in
2006 [117].

117

σ B [pb]

s = 7 TeV
Z’ → ll

1

10-1

Expected limit
Expected ± 1σ
Expected ± 2σ
Observed limit
Z’SSM
Z’χ
Z’ψ

10-2
ee: 1.08 fb-1
µµ: 1.21 fb-1
10-3 0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8 2
m [TeV]

σ B [pb]

(a)

s = 7 TeV
G* → ll

1

10-1

Expected limit
Expected ± 1σ
Expected ± 2σ
Observed limit
k/MPl = 0.1
k/MPl = 0.05
k/MPl = 0.03
k/MPl = 0.01

10-2
ee: 1.08 fb-1
µµ: 1.21 fb-1
10-3 0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8 2
m [TeV]

(b)
Figure 7.4: 95% C.L. limits on the cross-section times branching ratio for different Z ′ models
¯
(a) and the RS graviton with different values of k/MP l (b) as obtained from the dielectron
and dimuon invariant mass distributions.
118

m(πT) [GeV]

600

Dilepton 95% Exclusion
Expected Limit

500

Expected ± 1 σ
m(ρ /ω T) - m(πT) = 100 GeV
T

Excluded: m(πT) > m(ρ /ω T)
T

400
300

∫
µµ: ∫ L dt = 1.21 fb
ee:

200

-1

L dt = 1.08 fb

-1

100

150 200 250 300 350 400 450 500 550 600
m(ρT/ωT) [GeV]
Figure 7.5: 2D limits on the masses of technimesons in the context of the Low Scale Technicolor model [39, 103]. The red area is the 95% CL excluded region depending on the assumed
πT and ρT /ωT masses. The dashed line shows the expected limit with the green dashed
lines showing the ±1σ bands. The hashed region where m(πT ) > m(ρT /ωT ) is excluded by
theory. This plot is taken from Ref. [104].

119

Chapter 8
Conclusion
We have performed a search for high-mass dielectron resonances in ∼1 fb−1 of proton-proton
collision data. The collisions were produced at a center-of-mass energy of

√

s = 7 TeV by

the Large Hadron Collider, CERN, Switzerland, between March and June 2011 and recorded
with the ATLAS detector. The dielectron invariant mass spectrum from data is compared
to Standard Model expectations which are predicted using simulated samples and estimates
from data in control regions. No statistically significant excess is found: The dielectron
invariant mass spectrum contains no evidence for a high-mass resonance due to new physics.
We know that the Standard Model cannot describe all aspects of the fundamental particles and interactions that make up our universe. The LHC with its record collision energies
gives us the unique opportunity to look for additional particles and forces, allowing us to
probe the Standard Model’s validity in so-far untested regions of phase-space. There are
possible reasons why we have not seen any indication of physics beyond the Standard Model
in this analysis:

• The so-far unknown additional particles are too heavy to produce a dielectron resonance
120

peak at the current CM energy. This year, the LHC will run with energies of
8 TeV, and in a couple of years with

√

√

s=

s = 14 TeV, increasing our search region

considerably.
• The rate of interactions not included in the Standard Model is even lower than we
assume. More collisions, as planned to be produced in the following years by the LHC,
will allow us to test for even rarer processes.
• There are many proposed extensions to the Standard Model and not all of them contain
dielectron or dimuon resonances within our reach, instead predicting different event
signatures. A large number of analyses at the LHC and other research facilities look
for different ways new physics could manifest itself.
Since no significant excess is found, in combination with the dimuon analysis, 95% confidence level lower limits are set on the masses of the Sequential Standard Model Z ′ boson
(1.88 TeV), E6 Z ′ bosons (1.54 - 1.68 TeV) as well as the Randall-Sundrum graviton (0.72 ¯
1.67 TeV) for couplings ranging from k/MP l = 0.01 to 0.1.
These limits restrict the allowed parameter space for the models under consideration and
other proposed extensions to the Standard Model, constituting an important step in our
quest for understanding elementary particles and forces.

121

APPENDIX

122

Appendix A
Determination of identification
efficiency correction factors with
Tag-and-Probe
The differences between electron signatures in data and simulated samples (compare Sec. 5.3)
make it necessary to correct the simulation for an unbiased comparison between data and
SM backgrounds. This section shows how the factors for correcting identification efficiencies
of electrons are obtained using the Tag-and-Probe method.

A.1

Definitions

The efficiency for true electrons passing a cut Y to also pass a cut X is defined as

ǫX =

#electrons passing Y and X
.
#electrons passing Y
123

(A.1)

Efficiency scale factors (SF) are the ratio between the efficiencies (ǫ) for true electrons in
data and in simulated samples (see Eq. 5.2).
Identification efficiencies are calculated with respect to reconstructed electron candidates
and are binned in η and ET (compare Sec. 4.4).

A.2

Method

The biggest challenge in the efficiency measurement consists of getting a sample of electrons
from data on which to perform the efficiency determination. This sample should consist of
real electrons, not QCD jets, and no cuts should be applied to these electrons that could
bias the efficiency measurement. The method of choice is the Tag-and-Probe method, which
makes use of the characteristic signatures of the Z → ee and W → eν decays. In the
case of Z Tag-and-Probe, very strict cuts are applied on one of the two decay electrons
(called “tag”), and the second electron candidate (“probe”) is used for the measurements.
See Fig. 2.1 for an illustration of Z boson production and decay. Additional cuts which
ensure that the invariant mass of the two objects is close to the Z boson mass, and that
the two electrons have opposite charge, greatly enhance the chance that the second electron
candidate is a real electron while remaining unbiased. A simulated Z → ee sample, on which
the same tag and probe selection is applied as in data, is used for the denominator of the
miss from the
SF. The W Tag-and-Probe method, which is not discussed here, uses the ET
neutrino as the tag, and the single electron in the event as the probe.

124

Events

S1

M

S2

104

opposite sign
same sign
103

60

70

80

90

100

110

120

mee [GeV]

Events

(a)

Data
Fit (Sig + Bkg)
Fit (Sig component)
Fit (Bkg component)

103

102

10

40

60

80

100

120

140

160

180

mee [GeV]

(b)
Figure A.1: Illustration of the QCD jet background estimation under the Z peak. Both plots
show tag and probe pairs in which the tag is a Tight electron and the probe is a reconstructed
electron candidate. (a) shows the sideband method applied for the efficiency determination
in η bins, (b) shows as an example a 2-component fit applied to pairs in which the probe
fulfills 35 GeV ≤ ET ≤ 40 GeV.
125

Events

0.08

0<|η|<0.8
0.8<|η|<1.37
1.37<|η|<1.52
1.52<|η|<2.01
2.01<|η|<2.47

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

20 40 60 80 100 120 140 160 180 200
mee [GeV]

(a)
E 20-30 GeV
T
E 30-40 GeV
T
E 40-50 GeV
T
E > 50 GeV

0.04
0.035
0.03

T

0.025
0.02
0.015
0.01
0.005
0
0

20

40

60

80

100 120 140 160 180 200
mee [GeV]

(b)
Figure A.2: Invariant mass distribution of tag and probe pairs for QCD jet background
from a simulated sample, (a) for bins in η, (b) for bins in ET [118]. The distributions are
normalized to unit area.

126

A.3

Background estimation

Identification efficiencies are determined with respect to reconstructed electron candidates.
In spite of the strict cuts on the tag electron and additional event cuts, there is a nonnegligible background of QCD jets in the probe sample, coming from QCD multijet production as well as the W + jets process. Since we are interested in the identification efficiency
of real electrons and not jets, this background needs to be accounted for.

In order to subtract the jet background for the identification efficiency measurements,
two data-driven methods are employed, depending on whether the efficiencies are binned in
η or ET . These methods are chosen because they perform best in closure studies where the
background is known [118]. In both cases, the discriminating variable is the tag and probe
invariant mass coming from the characteristic shape of the Z peak (compare Fig. A.1).

Figure A.2(a) shows the jet background taken from simulation for bins in η. Although
the statistics are low, this figure demonstrates that the background shape between 60 and
120 GeV does not change very much for bins in η. We assume a linear shape in this window
and subtract it using a sideband method as illustrated in Fig. A.1(a): For each η bin, the
number of oppositely charged pairs (M ) is counted in the signal window around the Z pole,
and the number of same-sign pairs is determined in the two sidebands (S1, S2). The number
of real electron pairs Nsig in the signal region is then calculated as

Nsig = M −
127

S1 + S2
,
2

(A.2)

if the windows have the same width, and otherwise as

Nsig = M −

S1
S2
−
w2 w1

2
wM + w1 w2
S1 wM
+
,
w1 + wM + w2
w1

(A.3)

where w1(2) is the width of sideband 1(2) and wM is the width of the middle band. It is
assumed that for QCD jets the number of events in which tag and probe pairs have the same
charge is equal to the number of events in which tag and probe pairs have opposite charges.
This is in contrast to electron pairs from the decay of the Z boson which should always have
opposite charges. It is not possible to simply subtract the same-signed pairs under the Z
peak because of the small same-sign peak (compare Fig. A.1(a)), which is due to a very low
(< 2%) rate of charge misidentification affecting electrons from the Z boson decay.
The background subtraction for efficiencies in ET bins is more complicated due to the
more complex shape of the QCD jet background (see Fig. A.2(b)). Figure A.1(b) shows the
invariant mass distribution for tag and probe pairs where the probe is a reconstructed electron
candidate with 35 GeV ≤ ET ≤ 40 GeV and the tag is a Tight electron. The number of real
electrons in the signal region is estimated by a 2-component fit, with the QCD jet background
modeled by a function (a convolution of a Gaussian and an exponential). The Z peak shape
is estimated in two ways: by a function (Breit-Wigner convoluted with Crystal-Ball) as well
as by a simulated Z → ee template, as shown in Fig. A.1(b).
The QCD jet background is subtracted independently for every η/ET bin as well as for
the numerator and denominator of the efficiency calculation. For the numerator, where the
probe is requested to be an identified electron, the background contamination is much lower
than in the denominator, where the probe is only a reconstructed electron candidate.
Since a Z → ee sample is used, no QCD multijet background is subtracted in the simu128

lation. However, in order to reject jets produced in association with the Z boson, the probe
is required to be a true electron from the Z boson decay (this includes electrons that are
converted from photons radiated by the decay electrons).

A.4

Systematic uncertainty

The dominant source of systematic uncertainty in the efficiency determination is the QCD jet
background estimate. The uncertainty has two components. The first part is determined by
a closure test, performed on a simulated signal and background sample, showing the overall
bias of the two background estimation methods. For the sideband method this bias is ∼2%
in each η bin, while for ET bins it varies between ∼3% in the low mass bins to < 1% for
the highest ET bins where the QCD jet background is much lower. The second part of the
systematic uncertainty is obtained by varying the background estimation method itself. For
both the sideband and the fit method, the requirement on the tag is varied, changing the
QCD jet background yield. Furthermore, the signal window around the Z peak is changed.
In addition, the ranges of the sidebands are modified for the sideband method. In the fit
method, the fit range is varied, and the signal shape is estimated by different fit functions
and templates. The systematic uncertainty from these variations is 1-2% in η and 4-1% in
ET .

A.5

Results

The identification efficiencies obtained from data and a simulated Z → ee sample, as well
as the SF for electrons fulfilling the Medium requirement (compare Sec. 4.4) are shown in
129

Scale factors

Efficiency

1
0.95
0.9
0.85
0.8
0.75

medium
medium [MC]

0.7

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

Scale factors

Efficiency

η

(b)

1
0.95
0.9
0.85
0.8
medium
medium [MC]

0.7

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

η

(a)

0.75

1.02
1
0.98
0.96
0.94
0.92
0.9
0.88
0.86

20 30 40 50 60 70 80 90 100
ET [GeV]

(c)

1.02
1
0.98
0.96
0.94
0.92
0.9
0.88
medium
0.86
20 30 40 50 60 70 80 90 100
ET [GeV]

(d)

Figure A.3: Identification efficiencies obtained from data and a simulated Z → ee sample,
as well as calculated SF for electrons fulfilling the Medium requirements (compare Sec. 4.4).
The uncertainties are statistical and systematic, but the closure test bias is not included.

Fig. A.3. The uncertainties include statistical and systematic components with the exception
of the closure test bias. The identification efficiency measured in data is lower than in the
simulated Z → ee sample, which results in correction factors lower than 1. For physics
analyses, these numbers are combined with SF obtained from W Tag-and-Probe and are
factorized into SF in η with ET corrections.
Figure A.4 shows efficiencies and SF for the additional requirements in this analysis (Blayer cut as well as calorimeter isolation), calculated with respect to Medium electrons. The
130

Scale factors

Efficiency

1.02
1
0.98
0.96
0.94
0.92
0.9
0.88
0.86

1.08
1.06
1.04
1.02
1

B-layer
B-layer+Iso
B-layer [MC]
B-layer+Iso [MC]
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.98

B-layer

0.96

B-layer+Iso

0.94

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

η

(b)

1.02
1
0.98
0.96
0.94
0.92
B-layer
0.9
B-layer+Iso
B-layer [MC]
0.88
B-layer+Iso [MC]
0.86
20 30 40 50 60 70 80 90 100
ET [GeV]

Scale factors

Efficiency

(a)

η

1.08
1.06
1.04
1.02
1
0.98

B-layer

0.96

B-layer+Iso
0.94
20 30 40 50 60 70 80 90 100
ET [GeV]

(c)

(d)

Figure A.4: Efficiencies and SF for the B-layer cut as well as calorimeter isolation, calculated
with respect to Medium electrons. The uncertainties are statistical only.
uncertainties are statistical only. The B-layer efficiency drop for high |η| is larger in the
simulation than in data, which is reflected in the SF. The additional SF are almost flat in
ET .

A.6

Limitations and improvements

The efficiencies and SF were obtained with a fraction of the dataset available in 2011. More
statistics will allow an extension of the ET range, reducing the uncertainty on efficiencies at
131

high invariant masses. The ET range can also be extended by using high invariant mass DY
events, however, for this an alternative way of subtracting the background is needed since
the characteristic Z peak cannot be used. In W Tag-and-Probe, the calorimeter isolation
has already been shown to have enough discriminating power [34].
More data will also enable us to produce 2D SF binned in (η, ET ), which yield values
with smaller uncertainties, as the current factorization into η and ET bins is only an approximation. With higher statistics, and 2D bins, the current approximation of a linear QCD
background shape is no longer valid.
Another method to improve the efficiency determination is to reduce the QCD jet background by applying stricter tag requirements and additional cuts to the events, for example
miss cut to reduce the W + jets contribution. These additional cuts must not
a maximum ET
bias the probe sample, though.

132

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