Study of the electron → photon
misidentification rate in the ATLAS
detector
Diplomarbeit
vorgelegt von Johannes Haase
Januar 2011
Gutacher
Prof. Dr. Johannes Haller
Prof. Dr. Caren Hagner
Januar 2011
Institut für Experimentalphysik
MIN-Fakultät
Universität Hamburg
Abstract
In this thesis, the misidentification of electrons as photons (fake rate) is investigated
using the first 7 TeV data of the ATLAS detector at the CERN Large Hadron Collider.
A method for the measurement of the fake rate in data, using pure electrons from
the Z 0 → e+ e− decay, called tag-and-probe, is presented. The results are studied as
functions of kinematic variables in order to show effects on the detector performance.
A cross check with a so-called truth-matching method in Monte Carlo is applied. In
addition, the fake rate for Gauge Mediated Supersymmetry Breaking events is estimated
and compared with Z 0 → e+ e− studies.
Zusammenfassung
In dieser Diplomarbeit wird die Fehlidentifikationsrate von Elektronen als Photonen
mit den ersten 7 TeV Daten vom ATLAS Detektor am Large Hadron Collider bestimmt.
Für die Messung der Fehlidentifikationsrate, werden reine Elektronen vom Z 0 Zerfall
ausgewählt und mit der sogenannten tag-and-probe Methode in Daten untersucht. Die
Ergebnisse werden als Funktionen der kinematischen Variablen dargestellt, wobei der
Aufbau, sowie die Abhängigkeit der Fehlidentifikationsrate vom Detektors sichtbar wird.
Außerdem wird die tag-and-probe Methode durch die sogenannte truth-matching Methode im Monte Carlo verifiziert, indem die Information der generierten Teilen im Monte
Carlo verwendet wird. Zusätzlich wird die Fehlidentifikationsrate für Ereignisse aus dem
Gauge Mediated Supersymmetry Breaking Modell dargestellt und mit den Studien aus
dem Z 0 → e+ e− Zerfall verglichen.
Contents
1 Introduction
1
2 Theoretical Background
2.1 The Standard Model . . . . . . . . . . . . . . . .
2.2 The Shortcomings of the Standard Model . . . . .
2.3 Supersymmetry . . . . . . . . . . . . . . . . . . .
2.4 Analyis Methods . . . . . . . . . . . . . . . . . .
2.4.1 Tag-and-Probe Method . . . . . . . . . . .
2.4.2 Truth-matching Method . . . . . . . . . .
2.5 Z 0 → e+ e− production in proton-proton collisions
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3
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3 The LHC and the ATLAS Detector
3.1 The Large Hadron Collider . . . . . . . . . . . . . . .
3.2 The ATLAS detector . . . . . . . . . . . . . . . . . .
3.2.1 Geometry and coordinate system . . . . . . .
3.2.2 The Inner detector . . . . . . . . . . . . . . .
3.2.3 The Calorimeter System . . . . . . . . . . . .
3.2.4 Muon System . . . . . . . . . . . . . . . . . .
3.2.5 Trigger and data acquisition . . . . . . . . . .
3.3 Electron and photon reconstruction and identification
3.3.1 Cluster reconstruction . . . . . . . . . . . . .
3.3.2 Track reconstruction and association . . . . .
3.3.3 Full cluster reconstruction . . . . . . . . . . .
3.3.4 Electron identification . . . . . . . . . . . . .
3.3.5 Photon identification . . . . . . . . . . . . . .
3.3.6 Overlap Removal . . . . . . . . . . . . . . . .
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4 Tag and Probe Analysis
4.1 Data sets and Monte Carlo samples
4.1.1 Monte Carlo Samples . . . .
4.1.2 Data Sets . . . . . . . . . .
4.2 Event Selection . . . . . . . . . . .
4.2.1 Preselection . . . . . . . . .
4.2.2 Object selection . . . . . . .
4.2.3 Control Plots . . . . . . . .
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4.3
4.4
Tag-and-Probe Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Problematic (η, φ) regions for the Photons . . . . . . . . . . . . .
5 Truth-matching Method and application to GMSB
5.1 Event Selection for Truth-matching Method . . . . . . . . . . . .
5.2 Comparison between Tag-and-probe and Truth-matching Methods
5.2.1 Kinematic differences . . . . . . . . . . . . . . . . . . . . .
5.2.2 Fake rate cross check with the truth-matching method . .
5.3 Application to GMSB . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Conclusions
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A Photon Conversion
65
Bibliography
67
Acknowledgments
69
Selbständigkeitserklärung
71
List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Particles of the Standard Model . . . .
The Higgs potential . . . . . . . . . . .
Constraints on the Higgs mass . . . . .
The running of the coupling constants
Proton decay . . . . . . . . . . . . . .
Schematic SUSY breaking . . . . . . .
Tag and Probe event in ATLAS . . . .
Drell-Yan process . . . . . . . . . . . .
Proton parton density function . . . .
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
The LHC accelerator and its experiments . . . . . . . . . . . . . . . . .
Collected luminosity at the LHC . . . . . . . . . . . . . . . . . . . . . .
The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Barrel region of the Inner Detector . . . . . . . . . . . . . . . . . . . .
The Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . .
The electromagnetic calorimeter . . . . . . . . . . . . . . . . . . . . . .
The Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The ATLAS Tigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstruction window size for different particles . . . . . . . . . . . .
Several detector materials as a function of φ . . . . . . . . . . . . . . .
Probability of photon conversions as a function of the radius R . . . . .
Total reconstruction efficiency for conversions from 20 GeV pT photons
Electron, converted and non-converted photon reconstruction process .
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4.1
4.2
4.3
The pT distribution of the electrons at different stages of the selection . .
The η distribution of the electrons at different stages of the selection . .
The invariant mass distribution of two electrons at different stages of the
selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The invariant mass distribution of an electron and a photon at different
stages of the selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kinematic distributions as a function of η, φ, and pT for the electrons . .
Kinematic distributions as a function of η, φ, and pT for the photons . . .
Fake rate (η, φ, pT ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fake rate (pT , φ) in the barrel region . . . . . . . . . . . . . . . . . . . .
Comparison between all- and converted photons . . . . . . . . . . . . . .
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4.4
4.5
4.6
4.7
4.8
4.9
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4.10 Comparison between single and double-track conversion photons . . . . .
4.11 B-layer hits as a function of η and φ . . . . . . . . . . . . . . . . . . . .
5.1
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Kinematic distributions (η, φ and pT ) for the tag-and-probe and truthmatching methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cross check of the tag-and-probe method . . . . . . . . . . . . . . . . . .
Fake rate (η, φ, pT ) for the tag-and-probe and truth-matching method. .
Kinematic distributions (η,φ,pT ) for GMSB and Z → e+ e− . . . . . . . .
Fake rate (η, φ, pT ) for GMSB and Z → e+ e− . . . . . . . . . . . . . . .
Fake rate (φ, pT ) in the barrel region . . . . . . . . . . . . . . . . . . . .
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A.1 Probability of photon conversion . . . . . . . . . . . . . . . . . . . . . . .
A.2 Feynman diagrams for photon conversion . . . . . . . . . . . . . . . . . .
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5.2
5.3
5.4
5.5
5.6
List of Tables
2.1
2.2
Standard Model particles with their SUSY partners . . . . . . . . . . . .
Z properties and decay branching ratios . . . . . . . . . . . . . . . . . .
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3.1
Electron and Photon Definition . . . . . . . . . . . . . . . . . . . . . . .
27
4.1
4.2
4.3
4.4
Monte Carlo samples . . . .
Data samples . . . . . . . .
Object selection for electrons
Object selection for photons
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Chapter 1
Introduction
The aim of elementary particle physics is to describe the fundamental constituents of
matter and their interactions. The current theoretical knowledge is summarized in the
Standard Model. Even though it is a very successful theory, there are theoretical and
experimental difficulties, such as the existence of dark matter in our universe and the
unification of the coupling constants, which cannot be included in the Standard Model.
Nevertheless, any new theory has to include the Standard Model as low-energy limit.
The most promising extension of the Standard Model is Supersymmetry, a new symmetry connecting bosons (force carriers) with fermions (matter particles). Supersymmetry
has to be broken since it postulates a superpartner for every Standard Model particle
and none of these particles have been observed so far.
One of the main goals of the ATLAS detector at the CERN Large Hadron Collider
is to search for evidence of supersymmetric particles in accordance with predictions of
supersymmetric models. One of these models is the Gauge Mediated Supersymmetry
Breaking (GMSB) model, which contains of high energetic photons in the final state.
Therefore, a high photon reconstruction efficiency of the detector is of major importance. A possible background consists of electrons because they can be misidentified as
photons.
In this thesis, the misidentification of electrons as photons (fake rate) is investigated by
using pure electrons from the Z 0 decay. The so-called tag-and-probe method is applied
to measure the fake rate in data. Therefore, a sample of tag electrons is selected. For
each tag a probe candidate, either an electron or a photon, is selected. The invariant
mass of the tag and probe particles is required to be close to the Z 0 mass. As a cross
check the so-called truth-matching method, which relies on the truth particle information in Monte Carlo, is applied as well. The fake rate measured in data and Monte
Carlo samples as function of kinematic variables is presented, which reflects the performance of the detector. Finally, the fake rate for GMSB events is studied in Monte
Carlo and compared with fake rate in Z 0 → e+ e− . The data samples were collected in
7 TeV proton-proton collisions during 2010 and correspond to an integrated luminosity
of about 34 pb−1 .
This thesis is organized as follows. In chapter 2, a brief overview of the Standard Model,
its shortcomings and the idea of Supersymmetry with a focus on the GMSB model is
presented. Accordingly, the motivation of the fake rate analysis including the principles
2
Introduction
of the tag-and-probe and truth-matching methods are discussed. The chapter concludes
with a description of Z 0 → e+ e− production in proton proton collisions. Chapter 3
describes the LHC, the ATLAS detector and the standard methods used in ATLAS
for electron and photon reconstruction. Chapter 4 explains the applied tag-and-probe
method and shows the results of the data and Monte Carlo comparison. Then the cross
check with the truth-matching method and the comparison to GMSB events is presented
in Chapter 5. A conclusion is given in Chapter 6.
Chapter 2
Theoretical Background
This chapter gives an overview of the current knowledge of the Standard Model [1], the
fundamental constituents of matter and their interactions. After describing shortcomings of the Standard Model, Supersymmetry (SUSY) as an extension of the Standard
Model, is presented.
In addition, a brief summary about GMSB, the associated motivation for the fake rate
studies as well as the applied tag-and-probe and truth-matching analysis methods are
presented. Finally, as a theoretical aspects of the analysis, the Z 0 → e+ e− production
in proton proton collisions is described.
2.1
The Standard Model
The Standard Model (SM) describes all known particles and their interactions (mediated
by gauge bosons) except gravity. All matter consists of fermions which have spin 12
unlike gauge bosons which have a spin of 1. The strong and electroweak SM forces [2]
are described by local gauge symmetry with the symmetry group:
SU (3)C × SU (2)L × U (1)Y .
(2.1)
The following gauge bosons exist for this group:
• Eight massless gluons for SU (3)C and the colour charge gauge field associated to
them.
• W ± (M = 80.4 GeV), Z (M = 91.2 GeV), massless γ bosons for the electroweak
(EW) interaction.
The fermions are split up into six leptons and six quarks [3]. They are arranged in
three generations, which are ordered by increasing mass (Figure 2.1). Each generation
consists of a doublet of an up-type quark and a down-type quark with an electric charge
of + 32 and − 13 respectively. In addition, each generation includes a doublet including a
charged lepton and its corresponding neutral neutrino. To each fermion an anti-fermion
4
Theoretical Background
Figure 2.1: Particles of the Standard Model.
exists, featuring the same mass, but opposite internal quantum numbers like electric
charge. Quarks alone carry a quantum number called color, which can be either red,
green or blue. For that reason, quarks participate in strong and EW interactions while
leptons underlie only EW processes.
The interactions between the matter particles are mediated by the gauge bosons. In
order to retain the local gauge invariance of the Lagrangian, the masses of the bosons
need to be zero. However, unlike the γ and gluons, the Z and W ± are found to be
massive. The generation of these masses can be explained by the Higgs Mechanism [4].
Therefore a Higgs Field is introduced:
φ=
φ+
φ0
!
,
(2.2)
It consists of an isospin doublet of complex fields. The potential is given by
V (φ) =
λ + 2
µ +
φ φ+
φ φ ,
2
4
(2.3)
2.2 The Shortcomings of the Standard Model
5
Figure 2.2: The Higgs potential.
with λ > 0 and µ2 < 0. The potential is shown in Figure. 2.2.
Applying this potential to the SM, four new scalar fields are introduced. Three of
them are massless, the so-called Goldstone bosons, which give masses to the weak gauge
bosons. The fourth boson is the physical neutral Higgs boson. It couples to the fermions
proportional to their masses; however the photon and the gluon cannot couple to the
Higgs boson and remain massless. Until this day, the Higgs particle is the only particle
of the SM which has yet to be discovered in an experiment. The most likely mass is
at 95.7 GeV with an uncertainty of +30.6 GeV and −24.2 GeV (Figure 2.3) [5]. The
estimation of the Higgs mass could be achieved by a comparison of measurements of
EW observables at the Large Electron-Positron collider (LEP), Tevatron, SLAC Large
Detector (SLD) and theoretic predictions including loop corrections of the Higgs. Exclusions from direct Higgs searches at LEP and Tevatron (mainly from the decay channels
e+ e− → HZ 0 and p+ p− → H → W + W − ) are indicated by the gray shaded regions:
• LEP: The lower limit is set to MH = 114.4 GeV.
• Tevatron: 158 GeV < MH < 175 GeV is excluded.
2.2
The Shortcomings of the Standard Model
The Standard Model has substantial success describing and predicting the fundamental
particles and their interactions. However, evidence is mounting that there are problems
which can not be solved by the SM. These issues and their causes will be briefly explained
in the following:
• Measurements from astroparticle physics predict that only 4% of the matter is
described by the SM, while 20% is made of dark matter and around 76% consists
of dark energy [6]. The candidates for the dark matter are restricted since these
particles must only interact via the gravitational or weak interaction. The only
candidate in the SM is the weakly interacting neutrino, which can not amount for
all dark matter due to its small mass.
• The SM is not able to unify the gauge forces, as in the so-called Grand Unified
Theory (GUT). Extrapolating the coupling constants to the GUT scale should
6
Theoretical Background
Figure 2.3: The exclusion limits of the Higgs mass. The most likely mass is at 95.7 GeV,
with an uncertainty of +30.6 and -24.2 GeV.
lead to a unification of the coupling constants (Figure. 2.4 right). This is not
achieved within the SM (Figure. 2.4 left).
• The introduction of the Higgs mechanism in the SM solves, on one hand, the
problem of symmetry breaking, but, on the other hand, induces new issues, e.g.
the so-called hierarchy problem. The problem occures because the Higgs mass
underlies quantum corrections from all particles which couple to the Higgs. These
corrections largely contribute to the Higgs mass. Supersymmetric theories can
neutralize these loops by establishing new heavy charged scalar particles which
cancel the fermion loops due to their opposite sign.
• Since the gravitation is not embedded in the SM, there must be a more general
theory.
2.3
Supersymmetry
Supersymmetry (SUSY) [8] is able to solve a variety of shortcomings in the SM. The
latter one needs to be embedded in SUSY due to its excellent description at the low
energy limit. SUSY introduces a symmetry between fermions and bosons; therefore
new particles are predicted. To every fermion a bosonic partner is introduced and vice
versa, the so-called superpartner. A particle and its superpartner have exactly the
same quantum numbers, apart from the spin, which differs by half a unit. The fermion
2.3 Supersymmetry
7
Figure 2.4: Running of the inverse coupling constants in the SM and the minimal
supersymmetric model (MSSM) as a function of the energy scale [7].
Spin
SM particles
Superpartner
Spin
1
2
Leptons (`)
f
Sleptons (`)
0
1
Quarks (q)
Squarks qe
0
Gluons (g)
Gluinos ge
0
W
Wino
0
Z
Zino
0
Photon
Photino
1
2
1
2
1
2
1
2
1
2
Table 2.1: The extended particle spectrum. To each SM particle exists a superparnter
with different spin.
e while the partner particles of the gauge
e and sleptons (`),
partners are called squarks (q)
bosons are called gauginos. The symbols for SUSY particles are generally over-lined
with a tilde (cf. Table 2.1)
The introduction of a new particle spectrum can solve several problems related to the
SM. The different spin-statistical nature of bosons and fermions leads to opposite sign
in the radiative loop corrections of bosons and fermions to the Higgs boson mass. The
corresponding corrections to the Higgs mass cancel each other and solve the hierarchy
problem. In addition, the new particles make sure that the running coupling constants
αi converge at approximately 1016 GeV. This is a necessary requirement for any unified
theory (cf. Figure 2.4). The problem remains that none of the supersymmetric particles
have been observed so far. The masses of the new superpartner particles must be higher
with respect to the SM particles. Therefore, SUSY must be a broken symmetry. The
cancellation of the Higgs boson mass corrections has to be maintained, in order to keep
SUSY as a solution for the hierarchy problem. Hence, the SUSY breaking scale ΛSU SY
needs to be of the order of 1 TeV.
8
Theoretical Background
Figure 2.5: Proton decay to π 0 and e+
In some SUSY models the proton decay is allowed within ∼ 10−2 s by processes such
as the one shown in Figure. 2.5. Since the proton lifetime is larger than 1033 years
and the decay has never been observed, an additional multiplicative quantum number
is introduced, called R-parity, which is given by
R = (−1)3(B−L)+S ,
(2.4)
where B is the baryon number, L is the lepton number and S is the spin. All SUSY
particles obtain R = −1 and all SM particles R = 1. All SUSY models which are
described in this thesis are R-parity conserving. It is a mulitplicative quantum
number, which excludes the fast proton decay. Every interaction vertex contains an
even number of supersymmetric particles and there can be no mixing between SUSY
and SM particles. R-parity conservation has two profound consequences:
1. Supersymmetric particles must be produced in pairs in interactions of SM particles.
2. The lightest supersymmetric particle (LSP) is stable.
The LSP must be neutral, massive and weakly interacting in order to make it an excellent
candidate for the cold dark matter observed in the universe.
The minimal supersymmetric extension of the SM (MSSM) contains 124 free parameters. The number of parameters can be reduced by requiring underlying physics at high
energy, such as Grand Unification. Any spontaneous SUSY breaking requires the extension of the MSSM. The breaking mechanism is shown in Figure 2.6. The most common
approach is to assume that the SUSY breaking takes place in a hidden sector and is
mediated via a flavor-blind messenger interaction to the visible sector. Two important
well studied examples include minimal SUperGRAvity (mSUGRA), where the breaking
is mediated via gravity, and Gauge Mediated Supersymmetry Breaking (GMSB), where
the gauge interactions are responsible for symmetry breaking. The former one reduces
the number of parameters significantly from 124 to only five:
m0 , m 1 , A0 , tan(β), sign(µ).
2
2.3 Supersymmetry
9
Figure 2.6: The correlation between the hidden sector, where SUSY is broken, and the
visible sector via a flavour-blind interaction [8].
Three of these parameters are defined at the GUT scale, MGU T ≈ 2 × 1016 GeV: m0 is
the universal scalar mass, m 1 is the universal fermion mass and A0 is the universal
2
trilinear coupling between the Higgs and the left- and right-handed sfermions.
Gauge Mediated Supersymmetry Breaking
GMSB is a SUSY model in which the breaking in the hidden sector is mediated to the
visible sector via gauge interactions [9]. All particles have the same mass at the GUT
scale. The renormalization group equations (RGE) connect the weak scale with the
GUT scale. GMSB includes six free parameters:
1. Λ : The effective visible sector breaking parameter. This hinges on two main
values given by Λ = MFMSess . FS is the breaking order parameter and MM ess is a
free parameter, which is explained below. Λ scales linearly with the superpartner
masses.
2. N5 : The number of required messengers multiplets. The choice of an overly high
value does not lead to the unification of the running couplings. Further, the NLSP
mass depends on this number. For larger values the slepton is the NLSP, while
√
lower values lead to a neutalino as the NLSP. All sfermion masses scale with N5
whereas the gaugino mass scales linearly.
3. MM ess : This is the mass scale of the messenger sector. The lifetime of the NLSP
2
is proportional to MM
ess . The requirement MM ess > Λ must be maintained to
avoid charge and color breaking in the messenger sector.
4. tanβ: This is the ratio of the vacuum expectation value of the Higgs fields.
5. signµ: The sign of the mass parameter of the Higgs field.
6. Cgrav : A dimensionless scale factor of the gravitino coupling given by Cgrav . The
NLSP lifetime depends quadratically on Cgrav .
GMSB assumes R-parity conservation, which ensures the production of two superpartners in each decay chain. The next-to-lightest SUSY particle (NLSP) is either a
slepton or a neutralino. In the latter case, which is considered in this thesis, the NLSP
10
Theoretical Background
Figure 2.7: The top view of a tag and probe event in the ATLAS detector. The inner yellow area is the ID and the green cricle represents the electromagnetic calorimeter (ECal).
In this case the two particles are absorbed in the ECal, as for Z → e+ e− .
decays into a photon and a gravitino. The gravitino is the lightest superpartner in
GMSB SUSY models with a mass less then 1 keV; thus it is stable and escapes the
detection. Hence, the GMSB signatures at the LHC are large missing transverse energy
and two high energetic photons. In order to observe this particular final state signal, it
is highly important to ensure a good photon reconstrution efficiency. A possible background consists of electrons because they can be misidentified as photons in the detector.
The measurement of this photon fake rate using real data recorded by the detector is a
key task in the following analysis (Chapters 4 and 5). A sample containing pure electrons is an important condition in this study. Only with this condition, a reasonable
fake rate estimation is possible. Therefore, the Z boson is used as “standard candle”
and an abundant source of electron candidates.
2.4
Analyis Methods
In this thesis the fake rate is measured by analysing data samples with the so-called
tag-and-probe method (Section. 2.4.1). In addition, as a cross-check an analysis of
Monte Carlo (MC) samples is performed with the so-called truth-matching method (Section. 2.4.2).
2.4.1
Tag-and-Probe Method
The tag-and-probe method is an appropriate procedure which is based on the definiton
of a “probe-like” object. A suitable “tagged” sample is associated with it. The tag electron is a well identified electron. The probe candidate is most likely the second electron
coming from the Z if the momenta of the two electrons result in the invariant mass of
2.5 Z 0 → e+ e− production in proton-proton collisions
11
the Z boson. If the probe candidate is reconstructed as a photon and the invariant mass
coincides with the Z mass, the photon is counted as a misidentified electron, and the
electron-photon fake rate can be estimated in this way.
The tag-and-probe method can be used to measure various quantities related to the
detector performance. Such as trigger and reconstruction efficiencies, particle identification efficiency and fake rates. To make sure that all effects are modelled correctly by the
simulation, data-driven techniques are developed for comparison with MC. It has been
succesfully used in previous experiments, e.g. at the Tevatron. The advantage of this
method is that these quantities can be obtained using real data. More details about the
tag-and-probe method and the selection of electrons and photons is given in Section 5.1
and Section 4.2.2, respectively.
2.4.2
Truth-matching Method
The truth-matching method is a powerful tool to identify all reconstructed particles
using the corresponding generated particles. . For each reconstructed particle property,
the generated value, the so-called “truth” value of this property, is available in the
MC sample. In this method each reconstructed electron/positron cluster is required to
match the cluster of the generated (“truth”) electron/positron by measuring the distance
between the reconstructed and the truth particles. This distance 4R should be smaller
than a certain predefined value and is defined as
4R =
q
(4φ)2 + (4η)2 ,
(2.5)
where 4φ = |φ1 − φ2 | and 4η = |η1 − η2 | are angles in ATLAS (Section 3.2.1).
The same requirement is applied for the reconstructed photons. If the reconstructed
photon lies within a cone with a given radius around the truth electron, this photon is
considered as an electron misidentified as a photon. In this way, the electron-photon
fake rate can be measured. To allow for comparisons with data, a large amout of MC
samples with Z → e+ e− events have been produced for various analyses in ATLAS.
By comparing reconstructed with generated quantities, different detector effects can be
studied. More details about the truth-matching method and the selection of electrons
and photons is given in Section 5.1 and Section 4.2.2, respectively.
2.5
Z0 →
sions
e+e− production in proton-proton colli-
To discover physics beyond the SM, the detector needs to be well understood. Due to
the well measured and theoretically well understood Z 0 and W ± production processes,
the detector can be calibrated and reconstruction algorithms can be verified. Properties
like the total width ΓZ , the mass mZ and the partial decay width Γi of the Z boson
have been measured accurately at CERN by the LEP experiments and by the SLC at
SLAC. Some values of the Z boson properties are listed in Table. 2.5
12
Theoretical Background
Figure 2.8: Drell-Yan process at the LHC.
Decay modes
Fraction
Γi
Γ
e+ e−
3.363 ± 0.004 %
µ+ µ−
3.366 ± 0.007 %
+ −
3.370 ± 0.008 %
τ τ
invisible
20.00 ± 0.06 %
hadrons
69.91 ± 0.06 %
mZ
91.876 ± 0.0021 GeV
ΓZ
2.4952 ± 0.0041 GeV
Table 2.2: Z properties and decay branching ratios
In high energy proton-proton (pp) colliders, such as the LHC, Z bosons can be
produced in quark-antiquark collisions (Figure 2.8). The “Drell-Yan” process is the
main production channel:
q q̄ → Z/γ → f + f − .
(2.6)
The annihilation of a quark-antiquark pair leads to a production of the Z boson,
which decays into a fermion pair of opposite charges. The Drell-Yan process can just
proceed via the parton sea. The parton sea contains gluons, quarks and antiquarks,
which each carry a small fraction of the momentum of the proton [10]. The effective
center of mass energy is given by:
ŝ = xq xq s.
(2.7)
The reduced centre of mass energy is sb and the centre of mass energy of the proton
is given by s. Moreover, xq and xq stand for the momentum fraction of partons in the
proton.
The cross section at leading order, with no additional QCD interactions, for qq → Z
is:
2.5 Z 0 → e+ e− production in proton-proton collisions
GF
σb (qq → Z 0 ) = 8π √ · MZ2 gV2 + gA2 δ sb − MZ2 ,
2
13
(2.8)
where GF is the Fermi constant and gV and gA are the vector and axial vector
couplings, respectively. To describe the total Z production cross section in pp collisions,
the parton density functions (pdf), denoted by fq , need to be included [11]:
σtot (sb) qq → Z 0
=
Z
dx1dx2σbZ
X
{fq (x1) fq (x2) + fq (x1) fq (x2)}
(2.9)
The PDFs describe the probability of finding a quark, antiquark or gluon with momentum fraction x. As an example, Figure 2.9 shows the combined results from the
ZEUS and H1 experiments for the valence quarks (xdu and xdv ), the gluons (xg) and
sea quarks (xS).
The total cross section for the Z 0 production with√a decay into two electrons was measured at the LHC for a center of mass energy of s = 7 TeV to be (0.75 ± 0.09(stat)
± 0.08(syst) ± 0.08(lumi)) nb. The branching ratios of the Z 0 are listed in Table .
The relatively large cross section for producing a Z boson and its subsequent decay into
an electron-positron pair generates a clear signature in the detector, which is especially
suitable for measurements of the photon fake rate with good precision. Data and Monte
Carlo samples of such events will be used in the following analysis (Chapters 4 and 5),
after presenting the experimental setup in the next chapter.
14
Theoretical Background
Figure 2.9: Parton density functions of the valence quarks uv, dv, the gluons g and sea
quarks S as obtained from the combined results of the ZEUS and H1 collaborations.
Chapter 3
The LHC and the ATLAS Detector
In this chapter, the Large Hadron Collider (LHC) will be discussed, followed by the
ATLAS detector with its several subcomponents.
3.1
The Large Hadron Collider
The LHC is a proton-proton (pp) collider designed to operate at a center of mass energy
of 14 TeV. More details can be found in [12] [13]. It is situated in an underground
tunnel of 27 km circumference between 50 m and 175 m below the surface near Geneva.
The LHC is designed to accelerate 2808 bunches with up to 1.15 × 1011 protons and
collide them at a rate of 40 MHz. This corresponds to a nominal stored energy of
360 MJ per beam. These beam parameters are achieved through a complex system
of accelerators (Fig. 3.1) that increase the energies of the protons up to the maximal
energy, which are injected into the next accelerator or stored in the LHC. Not only the
beam energy is important in discovering new physics, it is also of great interest to have
a sufficiently large number of collisions N within a reasonable time t. The event rate
can be calculated by multiplying the the cross section σ with the luminosity L
dN
= σ · L.
dt
(3.1)
The luminosity can be expressed by
L=f
k n 1 n2
Rφ ,
4πσx σy
(3.2)
where n1 and n2 are the numbers of particles in each of the k bunches in each beam,
σx and σy are the horizontal and vertical beam widths, respectively. f is the revolution
frequency of 11 kHz and Rφ is a geometric reduction factor. The design instantaneous
luminosity of the collider is L = 1034 cm−2 s−1 .
The most interesting physics reactions occur with low cross sections. Therefore, to
obtain a sufficient number of events for such collisions, high luminosity is required while
ensuring safe machine operation. Improvement in luminosity is achieved by varying the
number of bunches (k), the bunch intensity (n1 , n2 ), and by "squeezing" the beam sizes
16
The LHC and the ATLAS Detector
Figure 3.1: The LHC accelerator and its experiments.
at the interaction point.
The LHC started operating in 2009 with a center of mass energy of 900 GeV. The
energy increases stepwise and is scheduled to reach the maximum of 14 TeV in 2015.
Throughout 2010, the energy was fixed to 7 TeV. Instantaneous luminosity above 2 ×
1032 cm−2 s−1 was reached by increasing the number of bunches up to 368 per beam using
nominal bunch intensities and 150 ns spacing between bunches. Operation with 25 MJ
stored beam energy was accomplished. The delivered integrated luminosity was above
48 pb−1 (Fig. 3.2).
Around the interaction points four detectors are situated to detect and study the pp
collision products. ATLAS (A Toroidal LHC ApparatuS) [14] and CMS (Compact Muon
Solenoid) [15] are large, general purpose detectors which focus on the search of the Higgs
boson, and physics beyond the SM. The two remaining experiments are ALICE (A Large
Ion Collider Experiment), focused in the study of heavy ion collisions, and LHCb (Large
Hadron Collider beauty), which was built to measure hadrons with b-quarks.
3.2
The ATLAS detector
The ATLAS detector is one of two general purpose detectors at the LHC (Figure 3.3).
It is a layered collider detector with an onion-like structure featuring almost full solid
angle coverage. The detector has radial and forward-backward symmetry, consisting of a
barrel and two end-cap parts. The task is to reconstruct all particles from the interaction.
Therefore different detector layers are built to collect all possible information.
A particle from the collision point first passes through the tracking system which is
divided into three parts. The innermost part of the tracking system is the pixel detector,
followed by the silicon microstrip tracker (SCT) and the Transition Radiation Tracker
Total Integrated Luminosity [pb-1]
3.2 The ATLAS detector
17
60
ATLAS Online Luminosity
50
s = 7 TeV
LHC Delivered
ATLAS Recorded
40
Total Delivered: 48.1 pb-1
Total Recorded: 45.0 pb-1
30
20
10
0
24/03
19/05
14/07
08/09
03/11
Day in 2010
Figure 3.2: The total collected integrated luminosity is shown in days in 2010.
(TRT). The entire tracking system is surrounded by a superconductive solenoid with
a magnetic field of 2 T in order to calculate the momentum and the charge of the
particles. The electromagnetic and hadronic calorimeter surround the Inner Detector.
The outermost part contains another tracking detector to measure muons. The magnet
system consists of a barrel and two endcap toroids providing a magnetic field of 0.5 T
and 1 T, respectively.
3.2.1
Geometry and coordinate system
The origin of the coordinate system is at the nominal interaction point in the center of
the detector. The x-axis points to the center of the LHC ring, while the y-axis points
upwards. Perpendicular to the x-y plane, the z-axis points anticlockwise to the beam
direction. The azimuthal angle φ is defined around the beam axis and the polar angle
θ is defined as the angle from the positive z-axis. The pseudo-rapidity is defined as
!
θ
.
η = −ln tan
2
(3.3)
The distance between two objects in the η − φ plane is given as
4R =
q
with 4φ = |φ1 − φ2 | and 4η = |η1 − η2 |.
(4η)2 + (4φ)2 ,
(3.4)
18
The LHC and the ATLAS Detector
Figure 3.3: The ATLAS detector in a schematic overview [16].
3.2.2
The Inner detector
The Inner detector [17] can reconstruct tracks of a charged particle with high precision (Figure 3.4). It has a length of 6.2 m and a diameter of 2.1 m and is placed around
the beam pipe. Primary and secondary vertices of charged particles can be measured
precisely down to a transverse momenta pT of 100 MeV with full φ coverage and within
|η| < 2.5. A solenoid magnet located between TRT and Calorimeter provides a 2 T magnetic field parallel to the z-axis. This configuration provides a deflection for charged
particles proportional to their transverse momentum. Thus only pT can be reconstructed
by this system.
The tracking system is of prime importance for the analysis, as electrons and photons
can be distinguished through a track which electrons leave in the Inner detector due to
their charge.
The Pixel Detector
The pixel detector is the closest subsystem to the interaction point. The reconstruction
of all charged tracks as well as the measurement of the primary (secondary) vertex takes
place in this part. The system consists of three cylindrical layers (0, 1, 2), and three
disks on each side as shown in Figure 3.5. The so-called B-layer (0) is the innermost
layer positioned at a distance of 50.5 mm to the z-axis. Layer 1 and 2 have a radial
distance of R = 88.5 mm and R = 122.5 mm, respectively. The length of all three layers
parallel to the beam pipe is 800.1 mm. The discs are perpendicular to the z-axis and
3.2 The ATLAS detector
19
Figure 3.4: Schematic view of the ATLAS Inner Detector[14].
located at z = ±495,±580 and ±650 mm with a radial range of 88.8 < R < 149.6 mm.
The tracking coverage extends up to |η| < 2.5 if each track crosses the three layers.
The barrel layers and the discs consist of a total of 1744 modules with 47232 pixels
each. Each sensor module is identical and operates at a bias voltage of ∼ 150 V up to
600 V. Over 90 % of the pixel modules have a size of 50 × 400µm2 and the remaining,
50 × 600µm2 . Due to space constraints, only 46080 readout channels exist which lead to
a total number of 80.4 million readout channels. This design allows a spatial resolution
of Rφ × z = 10µm × 115µm. The readout chips will be exposed to radiation loss of over
300kGy and 5 × 1014 neutrons/cm2 during a ten-year period of operation time. It was
foreseen to replace the B-layer after three years of data taking at nominal luminosity.
Semiconductor Tracker
The semiconductor tracker (SCT) covers the radial range between 299 mm and 560 mm
by providing an average of 8 hits per track in the radial direction (Figure 3.5). It provides
contribution to the measurement of momentum, impact parameter and vertex position.
The SCT is designed similar to the pixel detector with a barrel part and two endcaps.
The barrel region is built out of four double layers of silicon microstrip detectors and
the endcaps of nine axial wheels. The SCT contains 63 m2 of silicon detectors in 4088
modules; 2112 of the modules belong to the barrel part and the remaining 1976 are
attached to the endcap. Each module covers 6.36 × 6.40cm2 a area and has 780 readout
strips. 6.2 million readout channels due to a spatial resolution of Rφ×z = 17µm×580µm.
Transition radiation tracker
The outermost part of the tracking system is the transition radiation tracker (TRT),
which extends radially from 554 mm to 1082 mm with a tracking coverage of up to
20
The LHC and the ATLAS Detector
Figure 3.5: Barrel region of the ATLAS inner detector. Shown is a particle (η = 0.3)
traversing the three subsystems Pixel, SCT and TRT [14].
|η| < 2.0. The detection technology of the TRT is based on a drift chamber system with
about 370000 straw tubes containing a gas mixture of 70% Xe, 27% CO2 and 3% O2 .
The diameter of each straw tube is 4 mm. As the Pixel and the SCT system, the TRT
detector is divided into a barrel region, where 50000 straws with a length of 144 cm run
parallel to the z-axis (Figure 3.5), and two endcaps, where 370000 straws with a length
of 37 cm are aligned parallel to the radial distance.
The task of the TRT is to detect charged particles through ionization in the gas. It
provides only two-dimensional measurements in the Rφ-plane with a spatial resolution
of 130 µm which is lower then the Pixel and the SCT. The straw tubes enable, on the one
hand, the distance from a track to a wire, and on the other hand, the boundary between
tracking and transition radiation hits, respectively. Ultra relativistic charged particles
emit radiation when they cross the surface between two media. The TRT is able to
identify electrons due to transition radiation fibres which are interleaved between the
staws. Electrons and pions can be distinguished using this radiation. In addition to that
two thresholds, 200 eV and 5 keV, are provided to discriminate tracking and transition
radiation hits. The tracking hits pass the lower threshold and the transition radiation
hits pass the higher one.
3.2.3
The Calorimeter System
The purpose of a calorimeter system is to measure the engery of final state particles.
Particles interact with the material of the calorimeter whereby a shower of secondary
particles occurs. These are then absorbed by the material depending on whether they
interact electromagnetically or hadronically. In the former case, particles interact with
the electromagnetic field of the nuclei of the active material emitting Bremsstrahlung.
The only exception are photons which create electron-positron pairs. In the latter case,
3.2 The ATLAS detector
21
Figure 3.6: Cut-away view of the ATLAS calorimeter system [14].
hadrons interact strongly with the nuclei.
The ATLAS calorimeter [18] has a sampling design consisting of a active and a passive
absorber material, respectively. The active one is where particles deposit their energy
and the passive one allows for shower development. Additionally, the calorimeter contributes to a measurement of missing transverse energy. Therefore a high coverage of
the solid angle is necessary. Gaps in the detector due to electrical, optical and cryogenic
services lead to a minor distortion of the missing energy.
Due to different properties, the ATLAS calorimeter is divided into an electromagnetic
and hadronic section (Figure 3.6), whereby the latter one is sub-divided in a hadronic
barrel, a hadronic endcap and a forward part.
The Electromagnetic Calorimeter
The electromagnetic calorimeter (ECal) has an accordion structure and consists of layers
of lead as absorber and liquid argon as active material. This accordian shaped structure
provides a complete symmetry in φ (Figure 3.7). Its main purpose is the energy measurement of electrons and photons. Only in conjunction with the tracking information,
can electrons and photons be distinguished. The ECal is split up into a barrel part
(|η| < 1.475) and two endcaps (1.375 < |η| < 3.2), each housed in its own cryostat.
It has a thickness of more than 24 and 22 radiation lengths in the endcaps and in the
barrel, respectively. A presampler is added in front of the calorimeter in the region
|η| < 1.8 to correct the energy loses of incident particles as they pass through the Inner
Detector, cryostats and the solenoid before reaching the calorimeter. The region that
matches with the inner detector (|η| < 2.5) is segmented into three sections in depth for
22
The LHC and the ATLAS Detector
Cells in Layer 3
∆ϕ×∆η = 0.0245×0.05
Trigge
r Towe
∆η = 0 r
.1
2X0
47
0m
m
η=0
16X0
Trigge
Tow r
∆ϕ = 0er
.0982
m
m
4.3X0
15
00
1.7X0
∆ϕ=0.0
245x
36.8m 4
mx
=147.3 4
mm
ϕ
Square cells in
Layer 2
∆ϕ = 0
.0245
∆η = 0
.025
m/8 =
4
∆η = 0 .69 mm
.0031
Strip cells in Layer 1
37.5m
η
Figure 3.7: Sketch of a barrel module of the electromagnetic calorimeter. The granularities in φ- and η-direction for each of the three layers and of the trigger towers is also
shown [14].
precision measurements. The first layer is equipped with very fine strips to achieve a
high resolution in η. The majority of the energy is deposited in the second layer of cells
with surface of 4η × 4φ = 0.025 × 0.025. The resolution in φ direction is better then
in the first sampling and allows the determination of the φ position of a particle. The
η direction of a photon is determined from the η position of the cluster in the first and
second layer. The third sampling records the leakage of the shower into the hadronic
calorimeter.
The Hadronic Calorimeter
The Hadronic calorimeter (HCal) is designed to measure jet energies and their directions.
In conjunction with the ECal and the muon spectrometer, the reconstruction of missing
transverse energy can be made. It is divided into three subsystems: The tile calorimeter
(|η| < 1.7), the hadronic endcap (1.5 < |η| < 3.2) and the forward calorimeter (3.1 <
|η| < 4.9).
The tile calorimeter is placed directly outside the ECal. Its barrel extends to |η| < 1.7
and its two extended barrels cover the region 0.8 < |η| < 1.7. Steel of 4-5 mm thickness
for absorption and 3 mm thick scintillating plastic plates, so-called tiles, are used as
active material.
The hadronic endcap consists of two wheels. Liquid-argon was chosen as an active
material due to its recondition ability to radiation, which alternates with copper plates
for absorption.
3.2 The ATLAS detector
23
The forward calorimeter covers down to 1◦ to the beam pipe and consists of three
modules in each end cap. One module is made of copper for the optimization of electromagnetic measurements while the other two are made of tungsten, to distinguish
hadronic products.
Figure 3.8: Cut-away view of the muon system [14].
3.2.4
Muon System
The muon system is the outermost part of the ATLAS detector. Its main components
are displayed in Fig. 3.8 . It was designed to detect muons which are minimal ionizing
particles (MIPs). Although muons and electrons are similar, the mass differs between
the two. Specifically, the muons have greater mass, which leads to almost no energy
deposit in either of the calorimeters. The muon system consists of a toroid magnet in
the barrel (|η| < 1.4) and one in each endcap (1.6 < |η| < 2.7) to measure the momenta
by reconstructing the track.
3.2.5
Trigger and data acquisition
The ATLAS trigger system is needed due to the high interaction rate (40 MHz) in pp
collisions. The trigger system was designed to select rare and interesting events while still
providing a high rejection rate. The ATLAS trigger reduces this incoming interaction
rate to ∼ 200 Hz.
The trigger system has three levels which will be described below briefly [19]. An
overview is shown in Figure 3.9.
Level-1 Trigger: The Level-1 Trigger (L1) is hardware based and reduces the event
rate down to 25 kHz. It is designed to search for signatures from high-pT muons,
electrons, photons, jets, and τ leptons decaying into hadrons. Further events
with large transverse energy and large missing transverse energy are selected.
24
The LHC and the ATLAS Detector
Figure 3.9: Design of the ATLAS three level trigger system [19].
Electrons and photons are selected by the calorimeter information. The L1 makes
a decision within 2,5 µs while 1 µs of this time is spent in signal propagation in
cables. Because of these constraints, the L1 uses information from the calorimeters
(with reduced granularity) and the muon system. L1 defines so-called Region −
of − Interests (RoIs) which contain processes with interesting features.
Level-2 Trigger: The Level-2 (L2) Trigger is software based and reduces the event
rate to 3.5 kHz. At this stage, the RoIs identified in L1 are investigated more
precisely. L2 uses full granularity and Inner detector informations (approximately
2 % of the total event data) with an event processing time of 40 ms.
Event Filter: The Event Filter (EF) runs after the event builder and reconstructs the
whole event with the complete detector information. The event rate has to be
reduced down to 200 Hz with a time latency of 4 s. At this level, offline reconstruction algorithms are used.
3.3
Electron and photon reconstruction and identification
Due to the particular interest of electrons and photons in the analysis, both the reconstruction and identification of these objects, will be described in this section. Finally,
the overlap removale between electrons and photons is discussed. The reconstruction
and identification of electrons and photons consists of four steps:
1. Identification of suitable energy deposits (cluster seeds) in the calorimeter.
2. Track reconstruction and matching to the cluster seeds.
3.3 Electron and photon reconstruction and identification
25
3. Full calorimeter cluster reconstruction.
4. Application of identification criteria to the photon or electron candidates.
The procedure for the electrons and photons in the different phases is almost identical
due to the similar looking showers in the calorimeter. The main distinction between the
two particles is the electrons existing track in the ID.
3.3.1
Cluster reconstruction
At the very beginning of the cluster reconstruction, suitable cells in the ECal need to be
identified. The ECal is subdivided into a grid of Nη ×Nφ = 200×256 elements with a size
4η × 4φ = 0.025 × 0.025. A rectangular window, with a size 4η × 4φ = 0.125 × 0.125
moves across each element of the grid. Local maxima of the deposited energy within
the size of the window are detected by the algorithm. The so-called sliding-window
algorithm is used for this purpose up to |η| < 2.5. These cluster seeds are handed over
to the following reconstruction step.
3.3.2
Track reconstruction and association
The track reconstruction starts from the inside outwards. The hits in the pixel detector
and the first layer of the SCT are associated into the first track candidate. While adding
the other hits from the SCT, a track candidate is fit using the Kalman filter technique.
Accordingly, ambiguities are remedied and outlying points are removed. After that, the
final refitting is done and the tracks are extrapolated to the TRT. Photon conversion
can be reconstructed at this point when detecting tracks in the TRT, which do not fit
to inner tracks.
Here, a further complication occurs due to radiation of Bremsstrahlung photons by
the electrons as they pass through the ID. The radiated photons may end up very closely
to the electron. The energy determination in this case is a major challenge and cannot
always be made.
The association between the clusters and tracks are essential since this is the key
difference to separate electrons from photons. This matching consists of a very loose
spatial separation ( 4η < 0.05 and 4φ < 0.1) between the track and the cluster.
A cluster associated to a track, which matches to photon conversion, is no longer an
electron candidate.
3.3.3
Full cluster reconstruction
Until this point, the electron/photon classification was performed and the full reconstruction of the clusters can be made. The energy depositions in neighboring cells are
summed to form clusters within rectangular windows in η − φ space. The size of the
window is a compromise, on the one hand, between reduction of noise and pile-up and,
on the other hand, efficient collection of the deposited energy. In the barrel, the sizes
for electrons and photons are chosen differently (Figure 3.10), since electrons and conversions give wider showers in the φ direction due to interaction with the magnetic field
26
The LHC and the ATLAS Detector
Figure 3.10: Reconstruction window size for different particle types in the barrel and
endcap.
and Bremsstrahlung. This field is weaker in the endcaps, leading to a uniform φ size of
the window for the electron/photon classification.
Also important is the correction for energy losses in front of the calorimeter due to
the material in the ID. The value of this energy is estimated by measuring the energy
deposited in a presampler located in front of the calorimeter.
3.3.4
Electron identification
At this stage the signal to background ratio for electrons is small. To improve this ratio,
standard sets of electron identification cuts are applied. Several variables are defined for
the selection of the electrons, based on ID and calorimeter measurements (Table 3.1).
The cuts are usually applied in three different groups, the so-called “loose”, “medium”
and “tight” selection.
The main properties of each selection are:
• Loose: This basic selection includes the shower shape information from the second
layer of the EM calorimeter. This covers the lateral shower containment as well
as the width of the shower. Further, the energy lost into the hadronic calorimeter
is deduced. A high identification efficiency is provided by this setup although it
has a low background rejection.
• Medium: This selection provides a cluster-track matching. The distance 4η between the track and the cluster is extrapolated to the first layer of the calorimeter.
In addition the hadronic rejection is improved by calculating the energy deposition patterns in the first layer of the calorimeter. By requiring minimum number
of hits in the pixel and silicon tracker, the track quality is enhanced and poorly
reconstructed tracks are removed. Extra calorimeter variables are used for photon
conversion and the rejection of π 0 → γγ.
• Tight: This selection rejects charged hadrons as well as secondary electrons from
conversions by using the full identification potential of the ATLAS detector. Electrons from conversion are removed by requiring at least one B-layer hit in the pixel
detector and by applying a conversion-flagging algorithm. Further cuts such as on
3.3 Electron and photon reconstruction and identification
Type
Description
Loose Electron and photon cuts
Acceptance of the det.
|η| < 2.47 for electrons, |η| < 2.37 for photons (1.37 < |η| < 1.52 excluded)
Hadronic leakage
Ratio of ET in the 1st sampling of the hadronic calorimeter 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)
Middle layer of the
Ratio in η of the cell energies in 3 × 7 versus 7 × 7 cells.
EM calorimeter
Lateral width of the shower
EM calorimeter
Lateral width of the shower
Medium electron cuts ( in addition to the loose cuts)
Strip layer of the
Total lateral shower width (20 strips)
EM calorimeter
Ratio of the energy difference between the largest and second largest
energy deposits over the sum of these energies
Track quality
Number of hits in the pixel detector (at least one)
Number of hits in the pixels and SCT (at least seven)
Transverse impact parameter (<5mm)
Track matching
4η between the cluster and the track in the strip layer of the EM calorimeter
Tight electron cuts (in addition to the loose cuts)
B-layer
Number of hits in the B-layer (at least one)
Track matching
4φ between the cluster and the track in the middle layer of the EM calorimeter
Ratio of the cluster energy to the track momentum
TRT
Total number of hits in the TRT
(used over the acceptance of the TRT, 4η < 2.0 )
Ratio of the number of high-threshold hits to the total number of TRT hits
(used over the acceptance of the TRT, 4η < 2.0 )
Tight photon cuts (in addition to the loose cuts, applied with stricter threshold)
Middle layer of the
Ratio in φ of cells energies
in 3 × 3 and 3 × 7 cells
EM calorimeter
Strip layer of the
Shower width for three strips around maximum strip
Total lateral shower width
EM calorimeter
Fraction of energy outside core of three central strips but within seven strips
Difference between the energy of the strip with the second largest
energy deposit and the energy of the strip with the smallest energy deposit
between the two leading strips
Ratio of the energy differences associated with the largest and second largest
energy deposits over the sum of these energies
27
Name
Rhad1
Rhad
Rη
w2
w2
wstot
Eratio
d0
4φ2
E/P
-
Rφ
ws3
wstot
Fside
4E
Eratio
Table 3.1: Definition of variables which define the “loose”, “medium” and “tight” selection for electrons and photons.
the number of hits in the TRT and ratio of cluster energy to track momentum are
applied.
These three sets are inclusive, meaning that the previous requirements are always added.
3.3.5
Photon identification
The photon identification is similar to the electron identification. Unlike to the electrons,
the photon candidates lack a track associated to their cluster. Furthermore, only two
reference sets of cuts are defined for photons: “loose” and “tight”. Electrons and photons
share a common set of loose cuts and cut thresholds. An additional difference is the
smaller |η| range which ends at |η| < 2.37 due to the rejection of π 0 decays, for which
the fine granularity of the first layer of the calorimeter is used. The “tight” selection
presents the following features:
Tight: The tight photon requirements are optimized to provide good rejection of isolated leading π 0 s, which is the most sensitive background. Additional cuts on the
28
The LHC and the ATLAS Detector
middle layer and especially the strip layer are applied to separate γ from π 0 .
Photon Conversion
Photons can convert into an electron-positron pair in the ID due to the interaction with
the material in the tracker. The conversion is a result of the interaction between photons
and the material. The probability of photon conversion is proportional to the amount
and density of material on the trajectory of the photon. This is measured in terms of
radiation length and its η dependence is shown in Figure 3.11.
As a consequence the probability of a conversion depends on the η and the distance to
the interaction vertex, which is shown in Figure 3.12. The probability is lowest in the
most central region because of the reduction of the amount of material and non existing
services. It can be observed that the overall conversion probability in the inner detector
is around 50% before reaching the calorimeter. Therefore several recovery procedures
have been developed.
Figure 3.11: The radiation length of the different detector materials as a function of the
pseudorapidity φ.
The type of tracking algorithms depends on the distance to the vertex where the
conversion occurs. Within 300 mm the standard silicon-seeded tracking algorithm, the
so-called inside-out tracking is used. Since many photon conversion arise at larger
distance, as it can be seen in Figure 3.12, other strategies are needed. In this case two
other algorithms are appropriate for the reconstruction: the outside-in and standalone
TRT tracking. The latter one is seeded with TRT hits and the former one requires
additional hits from the silicon tracker.
• Inside-out tracking: For the track reconstruction three space-points in the Pixel
detector and SCT are used at the beginning. Afterwards, a geometrical tool provides the search for additional hits. Every new hit is verified by a fitting procedure.
Tracks are discarded if they do not pass the selection criteria. After this stage the
3.3 Electron and photon reconstruction and identification
29
Figure 3.12: Probability that a photon converts inside the Inner Detector as a function
of the radius R (distance from the beam axis) for several pseudorapidities φ.
tracks are extrapolated into the TRT. A refit of the whole track is done including
the TRT hits. If the TRT extension has a worse track quality than before or no
extension has been found, the track without the extension is stored. The Insideout track algorithm requires at least seven SCT hits. Thus, it is unsuitable for the
reconstruction of late photon conversions.
• Outside-in tracking: Unlike the Inside-out tracking, the TRT is the starting area
for this algorithm. A histogramming technique is used to extract track parameters.
A minimal number of straw tube hit has to be applied. The reconstructed TRT
segments are extended into the SCT. At least two hits in the SCT are required.
Including the extension in the inner detector, the track can be refit. To avoid
double counting as well as to reduce the reconstruction time, hits which are already
assigned to Inside-out tracks are excluded. The track reconstruction efficiency
increases in a region between 300 mm to 450 mm.
• Standalone TRT tracking: All remaining TRT segments that are not allocated to
one of the above explained tracking methods are formed to tracks by the Standalone TRT tracking. All tracks which share too many hits are rejected. A
refitting of the tracks is not done. In addtion to the Outside-in tracking, the track
reconstruction efficiency improves from the radial distance of 450 mm to the end
of the ID, as it is shown in Fig. 3.13.
The full reconstruction efficiency for photon conversion as a function of the radius R
is shown in Figure 3.13. Both, converted and non-converted photon candidates, which
were described in this section are used in the following analysis.
30
The LHC and the ATLAS Detector
Figure 3.13: Total track reconstruction efficiency for conversions from 20 GeV pT photons. The individual contributions from inside-out plus outside-in tracking and standalone TRT tracking are also shown [20].
3.3.6
Overlap Removal
The overlap removal is an important step in the following analysis. The overlap represents the fact that part of the reconstructed objects are identified as electrons and
photons. To distinguish this issue, the understanding of the electron and photon reconstruction as explained in Chapter 3.3, is essential (Fig. 3.14).
After the cluster reconstruction and track association electrons and photons can be distinguished. If a cluster is associated with a reconstructed track, an electron candidate
is formed, otherwise the search for a photon conversion match is made. Here again, two
cases of photon candidates are probed. If a conversion match occurs the candidate is
flagged as a converted photon, otherwise as a non-converted photon. In this way the
electron and photon containers are filled. Due to the reconstruction process, a conversion match can still be found for electrons. This original electron is put into the photon
container as “recovered photon” while it remains in the electron container.
Thus, the overlap removal essentially consists in removing the electrons recovered as
photons from the electron container. In this analysis a simple procedure is applied in
both the truth-matching and the tag-and-probe method and consist in the following. If
at least one photon is found within a cone with radius R = 0.2 around the electron, the
electron is rejected.
3.3 Electron and photon reconstruction and identification
31
Cluster Track Match No Conversion Match Electron Conversion Match Non-­‐converted Photon Yes Yes Electron container No Converted Photon Yes Object copied to the photon container Photon container Photon conversion recovery Figure 3.14: Illustration of electron, converted and non-converted photon reconstruction.
32
The LHC and the ATLAS Detector
Chapter 4
Tag and Probe Analysis
In the following analysis, the decay of a Z 0 boson into an electron-positron pair is used
to estimate the electron-photon fake rate, that is, the rate at which electrons or positrons
(e± ) are misidentified as photons (γ) in the ATLAS detector. First, the data sets and
Monte Carlo samples used in this analysis are presented in Section 4.1. Afterwards, the
event selection is described in Section 4.2 followed by the tag and probe method used
in this analysis (Section 4.2). Finally, the results are described in Section 4.4.
4.1
Data sets and Monte Carlo samples
In this section the Monte Carlo and data samples used in this analyis are presented.
Additionally, a brief overview of the Monte Carlo generation and detector simulation
is given. All data and MC samples were produced centrally by the official ATLAS
production team.
4.1.1
Monte Carlo Samples
For this analysis different MC samples are used, as listed in Table 4.1. These are all
fully simulated and produced using Athena version 15 for an LHC center of mass energy
of 7 TeV. The main sample is the Z 0 → e+ e− one, which represents the signal for the
studies in this thesis. The process of Z production and decay is analyzed in data and
MC, and is also used for a comparison with the GMSB sample (see Section 5.3). The
other MC samples are used for estimation of the background in the Z 0 → e+ e− sample.
All MC samples are simulated by release 15.3 and digitized and reconstructed by release
15.6.
The listed samples contain no extra partons in the generated hard interaction (“Np0”).
For the Z 0 , W ± and dijet samples, QCD higher-order events with up to 5 additional
partons are considered for this analysis (“Np1”,...,“Np5”), which are not specified in
Table 4.1, for brevity.
34
Tag and Probe Analysis
Sample
Z → e+ e−
0
GMSB
W ± → e± ν
W ± → µ± ν
W ± → τ ±ν
W ± → bb
dijet
γ + jet
Z → µµ
Z → ττ
Z → νν
Dataset
mc09_7TeV.107650.AlpgenJimmyZeeNp0_pt20.
merge.AOD.e529_s765_s767_r1302_1306.000504
mc09_7TeV.114007.SPS8_110_jimmy_susy.merge.
NTUP_SUSY.e530_s765_s767_r1302_r1306_p305
mc09_7TeV.107680.AlpgenJimmyWenuNp0_pt20.
merge.AOD.e511_s765_s767_r1302_r1306.000504
mc09_7TeV.107690.AlpgenJimmyWmunuNp0_pt20.
merge.AOD.e511_s765_s767_r1302_r1306.000504
mc09_7TeV.107700.AlpgenJimmyWtaunuNp0_pt20.
merge.AOD.e511_s765_s767_r1302_r1306.000504
mc09_7TeV.106280.AlpgenJimmyWbbNp0_pt20.
merge.AOD.e524_s765_s767_r1302_r1306.000504
mc09_7TeV.105009.J0_pythia_jetjet.merge.
merge.AOD.e468_s766_s767_r1303_r1306.000504
mc09_7TeV.108087.PythiaPhotonJet_Unbinned17.
merge.AOD.e505_s765_s767_r1302_r1306.000505
mc09_7TeV.107660.AlpgenJimmyZmumuNp0_pt20.
AOD.e529_s765_s767_r1302_r1306.000504
mc09_7TeV.107670.AlpgenJimmyZtautauNp0_pt20.
merge.AOD.e529_s765_s767_r1302_r1306.000504
mc09_7TeV.107710.AlpgenJimmyZnunuNp0_pt20.
merge.AOD.e529_s765_s767_r1302_r1306.000504
σ [pb]
664
0.1
6870
6871
6873
8.4
9×109
2×104
663
662
3538
Table 4.1: The generated physics processes with their cross section are given for each
set. Addtionally, QCD higher-order events with up to 5 partons are considered for each
set.
Monte Carlo generation
Before results of a massive experiment such as the ATLAS detector can be analyzed, each
subcomponent needs to be understood in detail. In order to design an optimal detector
setup, generation of several physics processes is needed. While the first data are being
taken, detailed simulation studies are crucial for comparison with and understanding of
the data.
During the first step, events are generated by a Monte Carlo event generator. This
implements various physics processes that describe the interaction between the quarks
(and gluons) inside the colliding protons. In the second step, the interaction of the
produced particles with the detector are simulated in detail. All these stages are combined in the ATLAS software framework called ATHENA. The generation of events is
briefly described here. The events of colliding particles are generated. The incoming
particles in the ATLAS detector are protons. Several physical aspects need to be taken
into account due to the interaction and outgoing particles. The components are briefly
mentioned in the following:
4.1 Data sets and Monte Carlo samples
35
• The primary hard scattering is determined from the matrix elements calculated
using perturbative QCD.
• Initial and final state QCD radiative corrections by adding gluon and photon
emission from initial and final state particles, W ± and Z 0 .
• Hadronization of partons in the final state.
• Decay of short-lived resonances.
• Multiple interactions due to the composition of the proton of multiple partons.
In this analysis the MC generator Alpgen for the generation of Z → e+ e− processes is
used.
Monte Carlo detector simulation
An important step in the design and understanding of the experimental setup is a
detailed detector simulation to estimate the detector response to the generated particles.
This can be done with the GEometry ANd Tracking (GEANT4) program. GEANT 4
is used for design studies, detector optimisation and to develop and test reconstruction
tools. Physics effects like interactions of the particles with the magnetic field and the
material are simulated. The exact knowledge of the geometry of all subsystems is
required. The energy deposition, along a particle trajectory, is collected as so-called
hits. The digitization of the hits allows for simulation of the output signals from the
detector. GEANT4 generates Bremsstrahlung or particles like electron-positron pairs.
In particluar, photon conversion which are important to this thesis, are simulated in
this step.
Period
Run Range
A
B
C
D
E
F
G
H
I
152166-153200
153565-155160
155228-156682
158045-159224
160387-161948
162347-162882
165591-166383
166466-166964
167575-167844
Luminosity
[nb−1 ]
1.5
6.5
8
288
937
1711
5655
7046
19000
Trigger
L1_EM14
L1_EM14
L1_EM14
L1_EM14
L1_EM14
EF_e15_medium
EF_e15_medium
EF_e15_medium
EF_e15_medium
Table 4.2: Data sets used in this analysis. For each period the run range, the integrated
luminosity and the trigger name are given.
36
4.1.2
Tag and Probe Analysis
Data Sets
The analyzed data samples were collected from 7 TeV pp-collisions taken between April
and October 2010 with a corresponding integrated luminosity of 34 pb−1 . The recorded
data were taken during periods of stable beam operation while all ATLAS subdetectors
were running at nominal bias voltages.
The data taking runs are grouped into periods according to the LHC instantaneous
luminosity. The instantaneous luminosity is approximately uniform within each period
and it rises in steps with each subsequent period. A period corresponds to a given
range of several runs, where a run is normally the period of data taking time from
the point at which stable beams are declared until the beams are dumped in the LHC
machine. Further runs can be subdivided in luminosity blocks (LBs) which correspond
to approximately two mintues of data taking. The total integrated luminosity for each
period and the corresponding trigger are listed in Table 4.2. The trigger nomenclature
is explained in the next section.
4.2
Event Selection
The event selection is performed in several steps as described in the following. At the
first stage, a preselection is applied. Next, the electrons and photons are selected by
applying particular requirements adopted for this analysis. The final selection consists
of choosing two candidates (e+ e− /eγ) within a mass window around the Z 0 mass.
To show agreement between data and MC, as well as to give an estimate of the
background, control plots are presented at different stages of the selection.
4.2.1
Preselection
For all events, a Good Runs List (GRL), Trigger and a vertex requirement are applied
in the preselection:
Good Run List: A GRL criterion is applied to select LBs that satisfy the quality
criteria, namely, the LB are required to be flagged as “GOOD” by the SUSY
analysis group. That implies that the inner detector and both calorimeters were
working correctly. Further, the magnet was on at the appropriate current.
Trigger: The trigger choice is constrained by the following requirements: The trigger
should be unprescaled and have as low as possible pT threshold. Accordingly, two
different triggers are used to select events for the following analysis. For periods
A-E the L1_EM14 trigger is used for which a minimum pT of 14 GeV is required.
The trigger EF_e15_medium is used for periods F-I. The change of the trigger is
on the one hand, due to improved settings in the “medium” selection and on the
other hand, because of the higher instantaneous luminosity in the later periods.
Vertex: At least one vertex is required with at least 3 tracks associated to it.
4.2 Event Selection
37
The electrons and photons which are used in the following analysis are part of the SUSY
object definition. In the next subsections, the electron and photon cuts are presented.
The overlap removal between these two objects was described in Section 3.3.6.
4.2.2
Object selection
Electrons
The cuts which are used to select electrons are listed in Table 4.3. More details about
each cut are listed below.
• Momentum: Electrons are required to pass a high pT threshold due to the poor
reconstruction efficiency for low pT -electrons. To compare electrons with photons
The commonly used cut is pT > 10 GeV, however as the electrons are compared
with the photons, the electron momentum cut is adjusted to the photon threshold.
• B-layer hit: Each electron is required to have at least one hit in the Pixel B-layer.
By means of this cut the signal electrons can be distinguished from electrons
originating from photon conversion.
• Author: Two different algorithms are used for the reconstruction of tracks in the
inner detector. This cut makes sure that the selected electrons are reconstructed
by one or the other of the two possible algorithms, which are indicated by 1 or 3.
ensures that the energy in a cone with
• Isolation: The cut on the ratio ET cone20
pT
radius R = 0.2 around the electron cluster does not exceed a certain threshold.
This cut removes anomalous events with badly reconstructed electron tracks. The
value of 0.15 is higher for the electrons in comparison to the photons (see Chapter 4.4) because of the contribution from Bremsstrahlung photons which remain
very close to the electron track and thus fall into the cone.
• Pseudorapidity: The |η| cut reflects two important detector features. First, tracks
can only be reconstructed in a region up to |η| < 2.37. Secondly, the range
1.37 < |η| < 1.52 is considered as the transition region (“crack” region) between
the barrel and the end-cap. This region is omitted for the analysis due to the
decreased performance.
• RobustMedium: This cut corresponds to the “medium” definition defined in Chapter 3.3.4. RobustMedium is a particular case of the “medium” selection set, which
incorporates changes resulting from the improved understanding of the data and
the detector. It should be emphasized that in the tag-and-probe method both electrons are required to be RobustMedium. This choice has been made as a result of
the comparison between the truth-matching and the tag-and-probe method, which
is described in Section 4.4.
• OTX: This cut is used to exclude objects (photons and electrons) which fall into
dead regions of the calorimeter. A cluster is rejected if any of the following cases
38
Tag and Probe Analysis
Table 4.3: The variables and the corresponding values for the cuts used to select electrons.
Cut
Value
PT
> 20 GeV
B-layer hit
≥1
Author
1||3
Isolation
< 0.15
|η|
(|η| < 1.37 || |η| > 1.52) && |η| < 2.37
RobustMedium
true
OTX
6=3
occur: its core (3×3 in the middle) contains an isolated “bad” cell, it involves a
dead Front End Board (FEB) or a High Voltage (HV) region in strips, middle or
pre-sampler.
Table 4.4: The variable and the corresponding value for the cuts used to select photons.
Cut
Value
pT
> 20 GeV
Isolation
< 0.1
|η|
(|η| < 1.37 || |η| > 1.52) && |η| < 2.37
RobustTight
true
OTX
6=3
Photons
Similar cuts are applied to the photons 4.4. The track cuts (B-layer hit and author) are
omitted because of the missing track.
• Momentum: Photons are required to pass a high pT threshold because of the
expected high energetic photons in GMSB events.
• Isolation: The expression is the same as the electrons, but the value is different
due to improvement in the SUSY analysis.
• Pseudorapidity: This cut is the same in accordance with the electrons.
• RobustTight: The photons are required to be “tight”, which is the strictest selection. The reason for this choice is to guarantee a good quality of the selected
photon sample, in particular for the GMSB events, in which the final state consists
of two high energetic photons. The same argumentation is valid for the RobustTight with respect to the “tight” selection as for the electrons.
• OTX: The same cut as for the electrons is applied.
4.2 Event Selection
4.2.3
39
Control Plots
Before studying the fake rate as a function of η, φ and pT in data and MC, control
plots and the final kinematic distributions of electrons and photons are presented. To
understand the effect of the selection cuts on both the data and the MC samples, a
comparison is performed at different stages of the selection process. A brief summary
of the general features of the kinematic distributions (η, φ, pT ) for the Z → e+ e− decay
is given:
• η: A symmetric distribution around η = 0 is expected due to the forward-backward
symmetry of the detector.
• φ: A flat distribution is expected because physics processes are independent of φ.
• pT : It is expected to have a peak at M2Z ≈ 45 GeV (Jacobian peak) because in
most cases the Z mass is split equally between the particle momenta of the e+ e−
pair.
The signal MC is described by the Z 0 → e+ e− sample and the remaining samples
correspond to the background. It is important to mention that all MC samples, i.e.
signal and background (see Section 4.1.1), are used. Thus the distribution of different
processes as a function of the cut variables can be studied. The goal at the end of the
selection is to optimize the signal to background ratio to ensure a pure electron sample
for the following fake rate studies. The control plots for electrons are shown in Figures 4.1 - 4.3. It can be observed that the pT distribution in Figure 4.1 is dominated
by the background after the requirement of the GRL, trigger, vertex and OTX cut.
Further the data to MC comparison shows disagreements for low pT (< 20 GeV) as well
as for high pT (> 40 GeV) values. After the requirement of a pT , B-layer hit, Author
and isolation cut the signal and the Jacobian-peak are clearly visible. After applying all
cuts, except the invariant mass cut, the Jacobian-peak is dominated by the signal. In
Figure 4.2 the η distribution is shown at the same stages of the selection. At the first
stage of the selection the background is dominating the signal and regional disagreements are visible. After the first step the signal clearly overbalances the background.
According to the last step the background is negligible and the detector specific shape
of the distribution with its barrel and two endcaps is distinguishable.
In Figure 4.3 and Figure 4.4 the invariant mass of two electrons and an electron with a
photon are shown, respectively. These plots are from great interest in this analysis since
both electron and photon candidates are selected within a mass window of the Z 0 mass.
Again, it is noticeable that the signal is significantly lower than the background for the
first selection stage. After applying further cuts, as described above, the invariant mass
peak in data and MC is clearly visible. After the last step the high signal to background
ratio is obtained.
All MC samples except QCD are weighted to the measured value of integrated luminosity. The QCD distribution is scaled separately to the remaining number of data events,
since the description of QCD processes is less accurate in MC. One remark should be
made: The measurement of the luminosity has an uncertainty of 10 % which causes
distinctions between data and MC.
40
Tag and Probe Analysis
The final kinematic distributions, i.e. after all cuts are applied, for η, φ and pT for electrons and photons are shown in Figure 4.5 and Figure 4.6, respectively. The different
distributions directly affect the fake rate distributions, as it is described in Section 4.4.
In these plots, the MC is weighted to the number of data events. It can be observed
that a better agreement between data and MC is given for the electrons than for the
photons. The η distribution for the electrons shows a reasonable agreement over the
whole range. The φ distribution presents a flat shape with particular discrepancies for
the data. However, a good agreement for the Jacobian peak in the pT distribution is
visible. The kinematic distributions for the photons in Figure 4.6 shows differences in
η. More photons are reconstructed within the barrel region. A similar performance
can be seen for the φ distribution, where regional disagreement can be observed. The
pT distribution shows less events in data for smaller pT values (< 40 GeV) and more
events for higher values (> 45 GeV). Finally, as a result of the selection the remaining
background is found to be negligible, therefore it will be not taken into account in the
following analysis.
10
41
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Events
4.2 Event Selection
5
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Events
Events
p T [GeV]
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p T [GeV]
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30
40
50
60
70
80
90
p T [GeV]
data
MC Z->e+eMC QCD
MC W->lν
MC Z->τ+τ-,µ+µ-,ν ν
Figure 4.1: The pT distribution of the electrons is shown at different stages of the
selection. The plot on the left top contains the requirement of the GRL, trigger, vertex
and OTX cut. Additionally, these cuts are applied to the plot on the top right: pT ,
B-layer hit, Author and isolation. The distributions on the bottom plots are the same
and include an η and RobustMedium cut. The only difference between the two is the
logarithmic and linear view.
42
Tag and Probe Analysis
10
Events
Events
10 6
5
10 4
10 3
10 2
10 3
10
10 2
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Events
Events
η
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-1
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-3
-2
-1
0
1
2
3
η
data
MC Z->e+eMC QCD
MC W->lν
MC Z->τ +τ -,µ+µ-,ν ν
Figure 4.2: The η distribution of the electrons is shown at different stages of the selection.
The plot on the left top contains the requirement of the GRL, trigger, vertex and OTX
cut. Additionally, these cuts are applied to the plot on the top right: pT , B-layer hit,
Author and isolation. The distributions on the bottom plots are the same and include
an η and RobustMedium cut. The only difference between the two is the logarithmic
and linear view.
43
10 6
Events
Events
4.2 Event Selection
10 5
10 3
10 4
10 2
10 3
10 2
10
10
1
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Events
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70
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90
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110
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data
MC Z->e+eMC QCD
MC W->lν
MC Z->τ +τ -,µ+µ-,ν ν
Figure 4.3: The invariant mass of two electrons is shown at different stages of the
selection. The plot on the left top contains the requirement of the GRL, trigger, vertex
and OTX cut. Additionally, these cuts are applied to the plot on the top right: pT ,
B-layer hit, Author and isolation. The distributions on the bottom plots are the same
and include an η and RobustMedium cut. The only difference between the two is the
logarithmic and linear view.
Tag and Probe Analysis
Events
Events
44
105
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102
10
1
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Events
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70
80
90
100
110
Inv. mass [GeV]
data
MC Z->e+eMC QCD
MC W->lν
MC Z->τ +τ -,µ+µ-,ν ν
Figure 4.4: The invariant mass of an electron and a photon is shown at different stages
of the selection. The plot on the left top contains the requirement of the GRL, trigger,
vertex and OTX cut. Additionally, these cuts are applied to the plot on the top right:
pT , B-layer hit, Author and isolation. The distributions on the bottom plots are the
same and include an η and RobustMedium cut. The only difference between the two is
the logarithmic and linear view.
45
Events
Events
4.2 Event Selection
1200
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20
40
60
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140
pT
data
MC Z→ e+eMC QCD
Figure 4.5: The kinematic distributions as a function of η, φ, and pT are shown when
all cuts are applied to the electrons (Section 4.2). The MC is weighted to the number
of data events.
Tag and Probe Analysis
140
Events
Events
46
120
100
220
200
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120
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60
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200
150
100
50
10
20
30
40
50
60
70
80
90
pT
data
MC Z→ e±γ
MC QCD
Figure 4.6: The kinematic distributions as a function of η, φ, and pT are shown when
all cuts are applied to the photons (Section 4.2). The MC is weighted to the number of
data events.
4.3 Tag-and-Probe Selection
4.3
47
Tag-and-Probe Selection
In this analysis, two samples are defined to select electron and photon candidates (Section 2.4.1). At first, the electrons that pass the object definition cuts (Section 4.2.2) are
selected in a sample labeled the tag sample. The probe electron is required to pass the
same object definition cuts as the tag electron. For each tag electron, either a probe
electron or a probe photon is selected. These two cases define the two samples. For
the former case, the invariant mass (Mee ) of these two electrons is required to be in the
range:
80 GeV < Mee < 100 GeV
(4.1)
After an event was selected with 4.1, both the tag electron and the probe electron
are counted (Ne± ). The number of events containing three or more electrons, where
different electron combinations pass the invariant mass cut, is negligible. However, if
the latter case is considered, the invariant mass (Meγ ) of the tag electron and a probe
photon is computed. If a match is found to be in the range
80 GeV < Meγ < 100 GeV,
(4.2)
the tag electron (Ne± ) and the probe photon (Nγ ) are counted.
It should be noted that if a probe electron and a probe photon are matched to the tag
electron, this method is not able to select the true probe candidate from the Z 0 . This
case is rejected in the following analysis.
4.4
Results
The fake rate f used in this following analysis is defined as:
f =
Nγ
,
Ne± + Nγ
(4.3)
where Ne± and Nγ are the selected electrons and photons, respectively, which were
explained in the previous section. The overlap between e± and γ is taken into account,
as explained in Section 3.3.6. The results for the total fake rate in data and MC are
10.5 ± 0.3 % and 11.5 ± 0.06 %, respectively. 11468 electrons and 1349 photons were
selected in data. It should be noted that these numbers only valid for Z 0 → e+ e− events.
The statistical error 4f of the fake rate is calculated by the binominal formula:
4f =
v
u
uf
t
× (1 − f )
Ne± + Nγ
(4.4)
48
Tag and Probe Analysis
If the underlying kinematic distributions (η, φ, pT ) for photons and electrons had
the same shape, the fake rate would be uniform. Since this is not the case ( Figure 4.5 and 4.6) the fake rate depends apparently on η, φ and pT .
The fake rate as function of η, φ and pT are shown in Figure 4.7. It is observed
that the data points are in general lower than the MC. The disagreement in the fake
rate (η, φ, pT ) can be attributed to the different shapes of the underlying kinematic
distributions in data an MC. It should be noted that indeed the shapes, not the bin
entries, are of main importance. Therefore, in the following discussion a reference to
these distributions is made.
The η fake rate for data is described well by MC in the barrel region, whereas in the
endcaps significant distinctions are seen. This is caused by the different shapes of the
data and MC η distribution for photons (Figure 4.6).
For the fake rate dependence on φ, two peaks at 2.0 < φ < 2.4 and -2.2 < φ < -2.6
stand out, which is unexpected. These regions arise due to dead modules in the B-layer.
The detailed explanation is given in the next Section 4.4.1. In addition, it has to be
noted that the data shows regional differences.
The pT fake rate distribution is of particular interest due to the possibility of using it
for extrapolation with GMSB data samples. A significant discrepancy is distinguishable
at smaller pT values. The fake rate for data is lower in this region, and rises at higher pT
values. In the range between 40 GeV < pT < 70 GeV the MC shows a good agreement
with the data. A comparison for higher values is difficult to perform due to the low
statistics in data.
Since the fake rate depends on the three parameters η, φ and pT , and since the
particular agreement between data and MC, a more detailed look is necessary to find
a phase space(η, φ, pT ) with reasonable agreement. An example is given in Figure 4.8.
The fake rates for pT and φ are shown within the barrel region (−1.3 < η < 1.3). A
better agreement between data (9.8 ± 0.3 %)and MC (9.9 ± 0.07 %) is visible. 10410
electrons and 857 photons were selected in data. The disagreement in the problematic
φ region still appears, which is explained with more detail in the next section. The
barrel region is chosen due to the appropriate agreement between data and MC in this
area (Figure 4.6). Hence, the disagreement in the primary pT distribution causes the
disagreement in the endcaps (1.3 < |η|).
4.4.1
Problematic (η, φ) regions for the Photons
Physics processes are generally independent on φ and have symmetric behavior in η. For
the former case, a uniform distribution is expected, and for the latter case, a symmetric distribution. However, the photon distribution in this analysis does not show these
properties in φ and η. To understand these problematic regions, the photons need to be
investigated in more detail.
Photons can be separated into conversion and non-conversion as shown in Figure 4.9.
Further, the conversion can be subdivided into single-track conversions, which are defined as those electromagnetic objects associated with one track having no B-layer hit,
and otherwise double-track conversions. The conversion vertex for the single-track conversion is made at the first hit of the track in the ID. Double-track conversion requires
fakerate
4.4 Results
49
0.3
0.25
data
0.2
MC
0.15
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0
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90
p [GeV]
T
Figure 4.7: Fake rate(η, φ, pT ) comparison with data and MC.
Tag and Probe Analysis
0.35
fakerate
fakerate
50
0.3
-1.3 < η < 1.3
0.25
0.35
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0
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-3
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1
2
3
φ
Figure 4.8: The fake rate in the barrel region (−1.3 < η < 1.3) is shown for pT (left)
and φ (right).
that each track has a B-layer hit, or neither of them. Thus, the ambiguity between electrons and single-track conversion photons increases due to the requirement of a single
hit in the B-layer. If a track of an electron is reconstructed in the region of dead B-layer
modules, it is reconstructed as a single-track conversion photon.
The photon distributions in φ and η are shown in Figure 4.9. In this and the following
two Figure, the empty areas are due to dead cells in the calorimeter. The problematic
regions are visible. For comparison on the right side the (η, φ) distribution for nonconverted photons is shown, where it can be observed that these regions disappear.
When looking at the photons from a conversion, the scenario discussed above is visible
(Figure 4.10).
Finally, the unexpected distributions in φ and η occur due to dead modules in the
B-layer. This conclusion is supported by the distribution of B-layer hits which is shown
in Figure 4.11. A decrease of the number of B-layer hits leads to a significant increase
of single-track conversions. When looking at the figure it is obvious that the B-layer
efficiency is lower in the endcaps but higher in special regions in the barrel. The two
elongated regions result in two peaks in the φ distribution. Once more, the asymmetry
in the η distribution is recognizable because the dead B-layer modules have asymmetric
positions in η.
A disagreement between data and MC in regions with lower B-layer efficiency can be
noted (Figure 4.11). This issue occurs due to additional transient problems in certain
B-layer modules, which are not dead but having problems along the read out chain
during single runs. This fact is not taken into account in MC.
4.4 Results
51
4
φ
φ
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3
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-2
-1
0
1
2
η
3
0
η
φ
5
φ
Figure 4.9: The (η, φ) distribution for all photons is shown on the left hand side, where
non-uniform asymmetric regions are visible in addition to the holes which correspond to
dead cells in the calorimeter. On the right side the same distribution for non-converted
photons is shown which has no such regions.
3
4.5
3
12
2
4
2
10
1
8
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1
3
0
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-3
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0
1
2
3
η
0
2
-3
-2
-1
0
1
2
3
0
η
Figure 4.10: The (η, φ) distribution for double-track conversion photons (left hand side)
is uniform, apart from holes corresponding to dead calorimeter cells. The distribution
for single-track conversion photons (right hand side) is non-uniform and asymmetric due
to lower B-layer efficiencies.
52
Tag and Probe Analysis
φ
50
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30
0
25
20
-1
15
-2
10
-3
5
-3
-2
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1
2
3
0
η
Figure 4.11: Distribution of B-layer hits as a function of η and φ. Regions of lower
efficiencies are visible which results in an increase of single-track conversion in these
regions(Figure 4.10).
Chapter 5
Truth-matching Method and
application to GMSB
In this chapter the tag-and-probe analysis (Chapter 4) is cross checked with the truthmatching method in MC. Furthermore, its application to GMSB studies is described.
In Section 5.1 the event selection is discussed. Its purpose is to ensure that true
electrons are selected with the tag-and-probe method. Results are presented for the
Z → e+ e− MC sample. Also a comparison using a GMSB MC sample is made to prove
that the tag-and-probe results can be applied to GMSB events.
5.1
Event Selection for Truth-matching Method
For all generated (truth) particles only electrons/positrons with a Z boson as direct
mother particle are selected. The reconstructed electron/photon is matched to the
truth electron by requiring that the reconstructed object are located into a cone with
radius R = 0.1 around the truth object. Different cases may occur during the matching
process:
• If more than one reconstructed electron lies within the cone the electron with
highest pT is selected.
• If more than one reconstructed photon lies within the cone the photon with highest
pT is selected.
• The case that both, an electron and a photon lie within the cone can not occur due
to the overlap removal: The electron is rejected if a photon is found in a cone with
radius R = 0.2 around the electron during the object selection (see Section 3.3.6).
Like the tag-and-probe method, events, in which a probe electron and a probe photon
...., are rejected in order to to ensure an identical event selection of the two methods.
It should be noted that the following case is rejected like in the tag and probe
method (Section 4.3): A probe electron and a probe photon are matched to the same
tag electron. This is done to make sure that both methods select the same events.
54
Truth-matching Method and application to GMSB
5.2
5.2.1
Comparison between Tag-and-probe and Truthmatching Methods
Kinematic differences
The kinematic distributions of the tag-and-probe method and the truth-matching method
are essential for the comparison of the fake rates. The distributions for η, φ and pT are
shown in Figure 5.1.
On the left top the electron momentum is displayed. It is visible that both distributions have the Jacobean peak around 45 GeV and that they rapidly fall down.
Concerning the photons, as shown on the right top, it can be seen that the pT shapes
are similar as for the electron.
In the middle left, the η distribution for electrons is shown. It can be observed
that more electrons are reconstructed in the barrel region than in the endcaps for both
methods. This is due to the lower acceptance in the endcaps and the kinematic of the
Z 0 decay . Furthermore, the truth-matching method reconstructs more electrons in the
barrel and less electrons in the endcaps in comparison with the tag-and-probe method.
On the right hand side the η distribution for photons is plotted. The distribution has
a similar shape for both methods and it is asymmetric. This can be explained by
inefficiencies in the B-layer (Section 4.4.1). The performance in the barrel and endcap
regions for the two methods is opposite for the electrons. Photons occur more often in
the endcaps due to more material in that region.
On the left bottom the φ distribution for the electrons is shown. The shape is not
as uniform as expected which can be explained by the photon distribution. The known
B-layer problems (Figure 4.11) cause an increase of the photons which is directly related
to the decrease of the electrons. Additionally, the OTX cuts are distinguishable in the
non uniform shape. However, a reasonable agreement in φ is given for electrons and
photons. Finally, the different event selection of both methods is understood reasonable
well. With an additional invariant mass cut for the truth-matching method almost
perfect agreement can be achieved, as shown in Figure 5.2.
It should be noted that the two methods have different phase spaces and therefore
different kinematic distributions. Two main properties distinguish the phase spaces:
1. The truth-matching method requires one candidate while the tag-and-probe method
requires two candidates to be reconstruted.
2. Unlike for the truth-matching method, an invariant mass cut of 80 GeV < M < 100 GeV
is applied for the tag-and-probe method.
As a result of this, the final step of the comparison, the invariant mass cut is applied to
the truthmatching method. This is to demonstrate that both methods select the same
events (Figure 5.2).
Entries
Entries
5.2 Comparison between Tag-and-probe and Truth-matching Methods
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3
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0
1
2
3
φ
Figure 5.1: Comparison of the kinematic distributions (η, φ and pT ) for the tag-andprobe and the truth-matching methods. The left column shows the electron and the
right column the photon distributions.
Truth-matching Method and application to GMSB
Entries
Entries
56
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Tag and Probe
250
25
20
Tag and Probe
Truthmatching
Truthmatching
15
200
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50
00
20
40
60
80
100 120 140
pT [GeV]
0
-3
-2
-1
0
1
2
3
φ
Figure 5.2: Cross check of the tag-and-probe method when applying the invariant mass
cut for the truth-matching method. The pT and φ distribution for the electrons (left)
and photons (right) are shown, respectively.
5.2.2
Fake rate cross check with the truth-matching method
The results for the fake rate f(η, φ, pT ) from Chapter 4 can be consolidated with a cross
check with the truth-matching method. Since the truth-matching method can only be
applied to MC the cross check is done between the tag-and-probe method and the truthmatching method using MC. Any differences in the kinematic distributions affect the
fake rate directly. It is visible in Figure 5.3 as a general feature that both methods show
a very good agreement. Thus, the tag-and-probe method is a relieable tool to estimate
the true fake rate.
5.3
Application to GMSB
The final step in this analysis is a feasibility study of estimating the fake rate for GMSB
samples. Until now, a comparison of the fake rate between data and a Z → e+ e−
MC sample (Section 4.7) and the cross check with the truth-matching method was
performed (Section 5.2.2). It was shown that the results from the Z → e+ e− MC
sample agree reasonably well with the data in the barrel region. The next task consists
of a comparison of the fake rates from the Z → e+ e− MC sample and a GMSB MC
sample. The comparison is done using the truth-matching method for both MC samples.
For the GMSB MC sample the requirement on the mother truth particles is relaxed.
Electrons from W bosons and from any SUSY particles are considered.
Additionally, the direct mother particles from the truth electrons are required to be
any SUSY particles in order to accept electrons from SUSY decays as well.
The distributions of the kinematic variables (η, φ, pT ) for electrons and photons are
shown in Figure 5.4. Two features are observed, namely, the shapes dissagree due to
the different phase spaces and unlike for the Z → e+ e− sample the statistics is rather
fakerate
5.3 Application to GMSB
57
0.3
0.25
Tag and Probe
0.2
Truthmatching
0.15
0.1
0.05
fakerate
0
-3
-2
-1
0
1
2
3
η
0.3
0.25
Tag and Probe
0.2
Truthmatching
0.15
0.1
0.05
fakerate
0
-3
-2
-1
0
1
2
3
φ
0.3
0.25
Tag and Probe
Truthmatching
0.2
0.15
0.1
0.05
0
10
20
30
40
50
60
70
80
90
p [GeV]
T
Figure 5.3: The fake rate as a function of η, φ and pT for the tag-and-probe and truthmatching methods.
58
Truth-matching Method and application to GMSB
low for the GMSB sample. Both of these differences make it difficult to compare the
two samples directly.
The shape of the pT distributions is different for the two MC samples. While the
rate decreases with pT for both, it falls smoothly and reaches higher pT values up to
150 GeV for the GMSB compared to the Z → e+ e− sample. The η distributions also
differ. For the GMSB sample events peak in the barrel region at η ≈ 0 and decrease in
the endcaps, whereas the Z → e+ e− η distribution is flatter. Finally, the φ distributions
agree reasonably well.
5.3.1
Results
The fake rate results as a function of η, φ, and pT for the GMSB and the Z → e+ e−
MC samples are shown in Figure 5.5. Two general statements can be made: Firstly, the
GMSB fake rate is on average higher than that for Z → e+ e− . Secondly, the statistical
uncertainty is larger for the GMSB sample because of the limited size of this MC sample
as seen from the underlying kinematic distributions (Figure 5.4). A look at the plots in
more detail shows that in a certain region around φ = 0 a better agreement is found. For
the η distribution discrepancies are seen in the barrel region as well as in the endcaps.
Fair agreement is observed over the entire pT range.
Again, as for the data to MC comparison 4.8, only the barrel region can be selected
in order to compare the fake rate distribution as a function of pT and η. This result is
shown in Figure 5.6. It can be concluded that the fake rate dependence on pT and η
agrees well within the statistical uncertainty the barrel region for GMSB and Z → e+ e− .
The Monte Carlo analysis presented in this chapter shows that the fake rate can be estimated with high accuracy using a Z → e+ e− sample and as a reasonable approximation
the result can be applied to a GMSB sample. This conclusion is also valid for data
samples due to the good agreement between data and Monte Carlo that was found for
the fake rate estimation in Chapter 4. However, several caveats need to be taken into account. The good agreement between data and Monte Carlo was restricted to the barrel
region only, while for the endcaps where the results differ, further investigation would
be required. In addition, a larger GMSB MC sample would allow for consolidation of
the present conclusions.
59
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5.3 Application to GMSB
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Entries
Entries
0
-3
350
250
50
200
40
150
30
100
20
50
10
-2
-1
0
1
2
3
0
φ
0
1
2
3
η
70
60
-3
-1
80
300
0
-2
-3
-2
-1
0
1
2
3
φ
Z->ee
GMSB
Figure 5.4: Comparison of the kinematic distributions (η,φ,pT ) for the GMSB and
Z → e+ e− sample. The truth-matching method is applied for both cases. The left
column shows the electron and the right column the photon distributions.
Truth-matching Method and application to GMSB
0.5
fake rate
fake rate
60
0.45
0.5
0.45
0.4
0.35
0.4
0.35
0.3
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
-3
-2
-1
0
1
2
3
0
-3
-2
-1
0
fake rate
η
1
2
3
φ
0.5
0.45
0.4
0.35
GMSB
0.3
0.25
Z → ee
0.2
0.15
0.1
0.05
0
10 20 30 40 50 60 70 80 90 100
pT [GeV]
Figure 5.5: The fake rate as a function of η, φ and pT for the GMSB and Z → e+ e−
sample.
0.3
0.25
-1.3 < η < 1.3
61
fakerate
fakerate
5.3 Application to GMSB
0.3
-1.3 < η < 1.3
0.25
0.2
GMSB
0.2
GMSB
0.15
Z → ee
0.15
Z → ee
0.1
0.1
0.05
0.05
0
0 10 20 30 40 50 60 70 80 90 100
pT [GeV]
0
-3
-2
-1
0
1
2
3
φ
Figure 5.6: The fake rate (pT , φ) is shown within a special η region (-1.3 < η < 1.3). A
better agreement with respect to the integrated pT distribution is visible.
62
Truth-matching Method and application to GMSB
Chapter 6
Conclusions
The Large Hadron Collider at CERN is a crucial instrument for searches of physics
beyond the Standard Model which reaches a new energy frontier in high- energy particle physics. The most promising extension of the Standard Model is Supersymmetry.
The Gauge Mediated Supersymmetry Breaking model describes a particular mechanism
needed to provide the link from the high energetic to the observed particle spectra.
Some parameter regions of this model consist of two photons in the final state.
In this thesis, the misidentificationrate of electrons as photons (fake rate) has been investigated using data from 7 TeV proton-proton collisions corresponding to an integrated
luminosity of about 34 pb−1 .
A pure sample of electrons was selected using the Z 0 → e+ e− decay process. The fake
rate was found to depend particularly on the ATLAS detector performance. It was studied as functions of the relevant kinematic variables. The present analysis comprises part
of the efforts towards obtaining a profound detector understanding, which is important
for supersymmetric searches with photons.
As a result, it was shown that the fake rate measured with data is described well by
Monte Carlo in the barrel region of the detector. Additionally, as a cross check, a pure
electron sample using generator information in Monte Carlo events was applied in order
to confirm with high probability that true events were selected with the tag-and-probe
method. Finally, the fake rate was estimated using a GMSB MC sample. These results
were compared to those from the Z 0 → e+ e− MC sample and a good agreement was
found in the barrel region. In conclusion, the fake rate estimated from Z 0 → e∗ e− events
represents a reasonable approximation of that for GMSB events in both data and MC
samples.
64
Conclusions
Appendix A
Photon Conversion
Photon Conversions are e+ e− pairs which can produced when a photon interacts with
matter [21]. This is an important issue as it is related to the reconstruction of photons
and electrons which is a key ingredient of the analysis in this thesis.
The photons interact with the material of the inner detector (Sec. 3.2.2). The Feynman diagrams of this process are shown in Fig. 2.5.
High energetic photons (> 1 GeV) predominantly loose their energy by e+ e− pair
production. Processes like the photoelectric effect, Compton or Rayleigh scattering are
negligibly small above this energy (Fig. 2.8).
The radiation length X0 is defined as 79 of the mean free path for pair production.
The radiation length for a known material is given by the following expression:
X0 =
716, 4A
Z (Z + 1) ln
287
√
Z
gcm−2 ,
(A.1)
where A is the atom mass and Z the atomic number of the nucleus. The total cross
section can be approximated by:
σ =
7 A
,
9 X0 NA
(A.2)
with the Avogadro number NA = 6.02 × 1023 .
A photon conversion is an interaction between a photon and an atom. The initial momentum is not equally shared between the e+ and e− . On the contrary, high asymmetric
momenta are possible. Especially low energic photons may be difficult to reconstruct.
An electron (positron) energy could lie under the reconstructable energy threshold and
the partner could be above. This can be avoided by applying a high photon momentum
cut, which is done in this analysis (pT > 20 GeV).
66
Photon Conversion
Figure A.1: Probability of a photon conversion. At 1 GeV the photon produces to 100%
an e+ e− pair independent of the material.
Figure A.2: The leading-order Feynman diagrams for photon conversion.
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Acknowledgments
Ich würde mein Diplom heute nicht in den Händen halten, wenn es nicht viele Menschen
um mich herum gäbe, die mich immer unterstützt haben. Daher möchte ich mein Diplom
zum Anlass nehmen um mich bei diesen Leuten zu bedanken.
Anfangen möchte ich bei Herr Prof. Dr. Johannes Haller, der mich während der
Anfertigung meiner Diplomarbeit begleitet und mich mit zahlreichen Tipps und Anregungen und noch mehr Geduld unterstützt hat und bei Frau Prof. Dr. Hagner für ihre
Bereitschaft, meine Diplomarbeit als Zweitgutachterin zu beurteilen.
Mein Dank geht auch an meine Betreuer Martin Wildt und Dr. Wolfgang Ehrenfeld,
welche stets mit Denkanstößen und Verbesserungsvorschlägen zur Stelle waren. Weiterhin möchte ich Martin Goebel, Dörthe Ludwig und Jörgen Samson danken, die sich
immer Zeit für mich genommen haben, wenn ich Fragen und Probleme hatte. Mein
Dank geht weiterhin Kristin Heine, Mareike Meyer und Dr. Michele Viti die das tägliche
Büroleben immer sehr angenehm gemacht haben und immer sehr hilfsbereit waren.
Bei Dr. Ivana Hristova möchte ich mich besonders für die Hilfsbereitschaft, diverse
Verbesserungsvorschläge und Ihre nette Art bedanken.
Sehr bedanken möchte ich mich an dieser Stelle bei Maximilian Schmidt, ohne den ich
die letzten 5 Jahre niemals diese Arbeit hätte schreiben können. Sein Dasein, vor allem
außerhalb der Physik, hat mich sehr geprägt. In diesem Zuge möchte ich zudem Niklas
Hegemann und Michel Meyer erwähnen, mit denen ich Seite and Seite durch das Studium gegangen bin.
Zum Schluß möchte ich mich ganz herzlich bei meiner Familie bedanken. Meine Eltern
haben mich die letzten 24 Jahre zu dem gemacht was ich heute bin. In jedem Lebensabschnitt haben sie jegliche Grundsteine für meinen Weg gelegt und waren immer für
mich da. Ein großer Dank geht an meine große Schwester Lucia, die sich immer für mich
eingesetzt hat und immer das Beste für mich wollte. Vergessen möchte ich nicht meine
beiden kleinen Geschwister Laurens und Helena für die ich sehr dankbar bin.
70
Selbständigkeitserklärung
Hiermit erkäre ich, dass ich die vorgelegte Diplomarbeit eigenständig, ohne unerlaubte
fremde Hilfe und unter der Zuhilfenahme der angegebenen Quelle verfasst habe.