Masters Thesis

University of Sussex

Search for Direct Production of Charginos and Neutralinos
in 3-Lepton events with Initial State Radiation using the
ATLAS experiment at the Large Hadron Collider
MPhys Final Year Project 2014–2015
Candidate - 75846
7th May, 2015

Supervisor
Antonella De Santo

Abstract
This project searches for the direct production of charginos and neutralinos in final states in which
three leptons, initial state radiation, and missing transverse momentum are present. The analysis
√
uses Monte Carlo generated data simulating s = 8 TeV proton-proton collisions at 20.3fb−1 integrated luminosity from the ATLAS detector at the Large Hadron Collider. Analysis is performed on
compressed Supersymmetric scenarios where the lightest chargino (χ
˜±
1 ) is mass degenerate with the
next-to-lightest neutralino (χ
˜02 ). The masses of the lightest chargino and lightest neutralino (χ
˜01 ) are
within 50 GeV. For the R-parity conserving simplified Supersymmetric model, mediated by gauge
bosons and no intermediate sleptons, four specific signal regions are shown to be excludable given the
above statistics. These are the regions where (mχ
˜±
˜02 , mχ
˜01 )=(100, 75), (125, 75) (100, 87.5) (125,
1 /mχ
100), in GeV.

Contents
1 Introduction

5

2 The Standard Model and Supersymmetry
2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Standard Model Limitations . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 R-Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Minimal Supersymmetric Extension to the Standard Model . . . . . . .
2.3 Solutions with the Minimal Supersymmetric Extension to the Standard Model
2.3.1 Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Grand Unified Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Simplified Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 SUSY Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Initial State Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 CERN, the LHC, and ATLAS
3.1 CERN . . . . . . . . . . . . . . . . . . . . .
3.2 The LHC . . . . . . . . . . . . . . . . . . .
3.2.1 Accelerator Complex . . . . . . . . .
3.3 ATLAS . . . . . . . . . . . . . . . . . . . .
3.3.1 Pseudorapidity . . . . . . . . . . . .
3.3.2 Inner Detector . . . . . . . . . . . .
3.3.3 Electromagnetic Calorimeter . . . .
3.3.4 Hadron Calorimeter . . . . . . . . .
3.3.5 Muon System . . . . . . . . . . . . .
3.3.6 Trigger . . . . . . . . . . . . . . . .
3.3.7 Trigger Level-1 . . . . . . . . . . . .
3.3.8 Trigger Level-2 . . . . . . . . . . . .
3.3.9 Event Filter . . . . . . . . . . . . . .
3.3.10 Missing Transverse Energy Detection
3.3.11 b-Tagging . . . . . . . . . . . . . . .
4 Analysis
4.1 Technical Framework . . . . . . . . .
4.2 Pre-selection . . . . . . . . . . . . .
4.3 Significance . . . . . . . . . . . . . .
4.4 Cuts . . . . . . . . . . . . . . . . . .
4.5 Irreducible vs Reducible Background
4.6 Important SM Backgrounds . . . . .
4.6.1 WZ . . . . . . . . . . . . . .
4.6.2 Z+Jets . . . . . . . . . . . .
4.6.3 t¯t . . . . . . . . . . . . . . .

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5 Selected Signal Regions and Preliminary Event Selection
5.1 Initial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Increasing Significance . . . . . . . . . . . . . . . . . . . . .
5.4 Other Explored Variables . . . . . . . . . . . . . . . . . . .
5.5 Preliminary Event Selection Results . . . . . . . . . . . . .

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6 Event Selection
6.1 3 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Same Flavour, Opposite Sign Request . . . . . . . . . . . . . . . . . .
6.3 Jet Multiplicity - ISR Request . . . . . . . . . . . . . . . . . . . . . . .
6.4 Leading Lepton Momentum . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Missing Transverse Momentum . . . . . . . . . . . . . . . . . . . . . .
6.6 b-Jet Veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Excluding Different Signal Regions with Multiple Cutflows . . . . . . .
6.8 Signal Region SRa . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.1 Invariant Mass of SFOS Pair . . . . . . . . . . . . . . . . . . .
6.8.2 Missing Transverse Momentum . . . . . . . . . . . . . . . . . .
6.8.3 Angle Between Leading Jet and Missing Transverse Momentum
6.9 Signal Region SRb . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9.1 Invariant Mass of SFOS Pair . . . . . . . . . . . . . . . . . . .

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7 Results
7.1 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 SRa Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 SRb Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
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8 Discussion

42

9 Conclusion and Outlook

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10 Acknowledgements

43

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List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
3.4
4.1
4.2
4.3
4.4
5.1
5.2
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10

Quantum Loop Corrections to Higgs Mass . . . . . . . . . . . . . . . . . .
Rotation Curve of a Galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . .
Grand Unified Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
˜02 Decay via W and Z Bosons . . . . . . . . . . . . . . . . . . . . . . . .
χ
˜±
1χ
Exclusion Contours for WZ Mediated Chargino and Neutralino Production
p-p → SUSY Cross Sections (8 TeV and 14 TeV) . . . . . . . . . . . . . . .
ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
η vs θ, Pseudorapidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ATLAS detector rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Significance vs Cut in Jet momentum - Logarithmic . . . . . . . . . . . . .
Significance vs Cut in Jet momentum - Linear . . . . . . . . . . . . . . . . .
‘Free Cut’ vs Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
tt¯ Production and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distribution of Transverse Mass . . . . . . . . . . . . . . . . . . . . . . . . .
2D Significance of SUSY Signal Regions After Preliminary Event Selection .
Initial Lepton Multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MET Distribution for 3 Lepton Cut . . . . . . . . . . . . . . . . . . . . . .
Leading Lepton Momentum Cut . . . . . . . . . . . . . . . . . . . . . . . .
Cut on Missing Transverse Momentum (Baseline) . . . . . . . . . . . . . . .
MET Distribution Before and After b-Veto . . . . . . . . . . . . . . . . . .
Cut on Invariant Mass of SFOS Pair (SRa) . . . . . . . . . . . . . . . . . .
Cut on Missing Transverse Momentum (SRa) . . . . . . . . . . . . . . . . .
Cut on ∆Φ Jet and MET (SRa) . . . . . . . . . . . . . . . . . . . . . . . .
Invariant Mass of SFOS pair (SRb) . . . . . . . . . . . . . . . . . . . . . . .
Significance of a Cut on Invariant Mass of SFOS Pair for (SRb) . . . . . . .
2

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7.1
7.2

2D Significance Plot for SRa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2D Significance Plot for SRb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40
42

List of Tables
2.1
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
7.1
7.2
7.3
7.4
7.5
7.6
7.7

Particle List of the MSSM . . . . . . . . . . . . . . . . . . . .
Initial Signal Regions For Preliminary Event Selection . . . .
Initial Cuts for Preliminary Event Selection . . . . . . . . . .
Baseline Cuts for Preliminary Event Selection . . . . . . . . .
Significance Optimising Cuts for Preliminary Event Selection
Selected Signals for Analysis . . . . . . . . . . . . . . . . . . .
Preliminary Event Selection Cutflow (a) . . . . . . . . . . . .
Preliminary Event Selection Cutflow (b) . . . . . . . . . . . .
Cutflow Differences for SRa and SRb . . . . . . . . . . . . . .
Baseline Cutflow (a) . . . . . . . . . . . . . . . . . . . . . . .
Baseline Cutflow (b) . . . . . . . . . . . . . . . . . . . . . . .
Excluded Points . . . . . . . . . . . . . . . . . . . . . . . . .
Final Significance of SRa . . . . . . . . . . . . . . . . . . . . .
SRa Final Cutflow . . . . . . . . . . . . . . . . . . . . . . . .
SRb Final Cutflow . . . . . . . . . . . . . . . . . . . . . . . .
Final Significance of SRb . . . . . . . . . . . . . . . . . . . .

3

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6
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41

Preface
The body of this analysis was performed using codes and data already set down by the framework,
by ATLAS and by the EPP team here at Sussex. The work involved codes that were not written by
myself, however they were extensively edited to be unique to this project and to my personal needs.
Any diagrams or tables taken from another piece of work will be attributed as such in the caption;
anything without can be assumed to be my own work. The theory and background in sections 2
through 4 was developed using a collection of papers and a thesis which are cited in the bibliography.
The decisions in the analysis regarding the event selections in sections 5 and 6 are my own work and
choices, though with advice from my supervisor Antonella De Santo and the PhD student Yusufu
Shehu. The reasoning and discussion in sections 8 and 9 are my own.

4

1

Introduction

This project performs a theoretical search for the direct production of Supersymmetric particles in
three lepton final states with initial state radiation (ISR) present at the ATLAS detector. The analysis
is performed using proton-proton collision data from Monte Carlo (MC) simulations at a centre-of√
mass energy of s = 8 TeV and 20.3fb−1 integrated luminosity, by implementing a series of cuts and
selections on the datasets. The aim is to produce an event selection that removes enough background
events that Supersymmetric signal regions can be excluded. A signal region is defined by the masses
of the relevant Supersymmetric particles. If this analysis shows that a MC generated signal region
can be ‘discovered’ to a 90% confidence interval, this region is said to be excluded. If, at this energy,
a discovery should be possible for a certain signal region, and there hasn’t yet been one at ATLAS,
Supersymmetry can confidently not be found there. Therefore this analysis works to show in which
regions Supersymmetry will not be found, given the above statistics, and to show which regions can
be excluded with real data. This event selection should be tailored depending on which signatures
are to be explored, as they are in section 5. The first section of the report outlines the background
theory, including the Standard Model, its limitations, and Supersymmetry. Part 3 discusses CERN
and the Large Hadron Collider (LHC), and goes into detail surrounding the ATLAS detector, while
part 4 explains both how the analyses are performed, and some important topics to consider. Parts
5 and 6 justify the preliminary and final event selections respectively, and part 7 states the results.
The final sections, parts 8 and 9, are the discussion and the conclusion. These sections wrap up the
analysis while discussing the project, some of its limitations, and its future.

2

The Standard Model and Supersymmetry

2.1

The Standard Model

The current Standard Model (SM)[1-2] is the collection of all known elementary particles, and the
descriptions of how they interact with one another. It contains the information of how light interacts
with matter, and how stars evolve through their life cycles. Important to the SM is the ability to
predict the outcomes of experiments. A good theory will have substantial predicting power, but few
free parameters. These are the parameters of the model that are not held constant, and can be
changed to provide meaningful insight. The Standard Model has 26 free parameters[3] and is not
considered complete. A perfect Theory of Everything (TOE)[4], for example, would have no free
parameters, and would be able to describe and predict the outcome of any experiment.
2.1.1

Standard Model Limitations

The Standard Model is not a complete description of the universe, and it has some short comings. For
example, with the SM alone the Higgs mass cannot be predicted, there is no explanation for neutrino
masses or their oscillations, and there is no candidate for dark matter. These limitations give a great
deal of motivation to search for new physics outside of the Standard Model, and one of these avenues
is a Supersymmetric (SUSY) extension. The addition of SUSY gives good predicting power and is
able to offer solutions to a number of the failures of the current Standard Model.

2.2

Supersymmetry

SUSY represents a new symmetry for the Standard Model. It exists as an operator, Q, changing a
particle’s spin by 1/2, thereby changing a fermion to a boson and vice versa.
Q|f ermioni = |bosoni
Q|bosoni = |f ermioni
The corresponding particle from this transformation is called a superpartner, or spartner, and is
usually denoted with an s- prefix, or -ino suffix, depending on whether the particle is a fermion or
boson respectively.
5

e.g
electron → selectron,
gluon → gluino.
˜ , the wino, is the superpartner to the W boThey are given a tilde in notation, for example W
son. The Standard Model has three main symmetries, the unitary group U (1)Y , and the special
unitary groups SU (2)L and SU (3)c . Each of these correspond to a fundamental force of nature, and
have corresponding gauge bosons. The electroweak gauge symmetry SU (2)L × U (1)Y has the gauge
bosons W + , W 0 , W − , and B 0 associated with it. The corresponding sparticles are the W˜+ , W˜ 0 , W˜− ,
and B˜0 . These are the winos and binos respectively. After electroweak symmetry breaking, W 0 and
B 0 gauge eigenstates mix to form the photon, γ, and the Z 0 bosons. The Supersymmetric versions
of these, mixing the W˜ 0 and B˜0 , give the Zino, Z˜0 , and photino, γ˜ . A list of the particles within the
minimal Supersymmetric extension to the Standard Model (MSSM) is in table 2.1.
Names

Spin 0

Spin 1/2

(˜
uL , d˜L )
u
˜R , d˜R
l˜L
l˜R
ν˜L

(uL , dL )
uR , dR
lL
lR
νL

(Hu+ , Hu0 )
(Hd0 , Hd− )
Spin 1

(H˜u+ , H˜u0 )
(H˜d0 , H˜d− )
Spin 1/2

g

g˜
˜
±
W , W˜ 0
B˜0

Mass Sector
squarks, quarks
×3 families
sleptons, leptons
×3 families
sneutrinos, neutrinos
Higgs Sector
Higgs, Higgsinos
Gauge sector
gluons, gluinos
W bosons, Winos
B bosons, Binos

W ±,

W0

B0

Table 2.1: List of particles in the MSSM before electroweak symmetry breaking. [5]

2.2.1

R-Parity

R-parity is a symmetry associated with SUSY, it is defined as
R = (−1)3(B−L)+2S ,

(1)

where B is the baryon number, L the lepton number, and S is the particle’s spin. R-parity is
+1 for the SM, -1 for SUSY particles, and is multiplicative. The implications of this parity are that
the lightest Supersymmetric particle (LSP) is going to be stable, and that when SUSY particles are
the result of a decay they must be produced in pairs. R-parity conservation is suggested by proton
stability. If baryon and lepton numbers are not conserved, as can happen in many grand unifying
theories (GUT), then, considering the first order couplings of R-parity violating couplings, the proton
could decay in approximately 10−2 s. Since this is not the case and the proton lifetime, if it does
decay, is around 1033 years, this gives a strong indication that R-parity should be conserved.
2.2.2

Minimal Supersymmetric Extension to the Standard Model

The MSSM is the theory that contains the current Standard Model and includes Supersymmetry. It
is ‘minimal’ as it only includes the minimal number of particles and interactions that are is consistent
with current phenomenology. Included are corresponding sparticles for each particle in the SM, and
6

two Higgs doublets. Table 2.1 gives the Standard Model and the corresponding sparticles, however
there are more that are relevant to this analysis. Each of the sleptons and gauginos, apart from
the gluino, can mix, resulting in mass eigenstates different to table 2.1. The neutral higgsino and
gauginos (H˜0 , W˜ 0 , B˜0 ) mix to form the neutralinos χ
˜01,2,3,4 , and the charged higgsinos and winos
(H˜± , W˜± ) from the charginos χ
˜±
˜01 is the
1,2 . The subscript number denotes the mass hierarchy, so χ
lightest neutralino, and χ
˜02 the second-to-lightest. The lightest neutralino is expected to have a mass
of order 100 GeV[6], and current theoretical limits have placed a minimal mass of 37 GeV[8] already.
It is considered to be the LSP, and is expected to be produced at the LHC at the current energy
range.

2.3
2.3.1

Solutions with the Minimal Supersymmetric Extension to the Standard Model
Hierarchy Problem

One of the most notable problems regarding the Standard Model, and signalling that it is not complete,
is that it is unable to accurately predict the Higgs mass, due to quantum loop corrections. When
particles interact they can have a number of quantum loop corrections to the interaction, see figure
2.1a. These can occur because for a short amount of time, virtual particles can spontaneously be
produced before annihilating. The time frames and energies of these particles exist within the limits
of the Heisenberg Uncertainty Principle, and can happen under quantum fluctuations. These loops
are higher order interactions, and usually have a asymptotic affect on interactions, and after one or
two extra orders, are negligible. However, with the Higgs interactions, this is not the case. Particles
couple to the Higgs field via the Yukawa term, λf , with the Lagrangian interaction term
˜
LY ukawa = −λf ψHψ,

(2)

where ψ is the Dirac field, and H the Higgs field. The Yukawa term, and therefore the coupling
strength, is proportional to the particle’s mass, so the Higgs will couple strongest to the most massive
particle, which is the t quark.
Quantum mass corrections to the Higgs mass squared are given by
∆m2H = −

|λf |2 2
[Λ + . . . ].
8π 2 U V

(3)

The term Λ2U V is the ultraviolet cut-off, which is the energy scale to which the SM is still valid.
An ultraviolet cut-off is simply the high energy limit used in calculations in order to avoid infinities.
If it is taken to be on the order of the Planck scale, the equation becomes a quadratically diverging
Lagrangian, which results in an infinite correction to the Higgs mass. A solution to this is offered by
SUSY. According to spin statistics theorem[9], the loop corrections due to fermions is negative, and
bosons positive. Therefore if there is a bosonic superpartner for each fermion and vice versa, every
term will cancel, and there will be no correction to the Higgs mass. The calculation using SUSY
corresponds with the experimentally confirmed Higgs mass of mH = 125 GeV, and is further evidence
in support of Supersymmetry.

7

(a)

(b)
Figure 2.1: Quantum loop corrections to the mass of the Higgs. (a) is the correction due to the top quark and (b) due
to the corresponding stop. From [10]

2.3.2

Dark Matter

In cosmology today there are still questions regarding the existence and make-up of dark matter.
Observations have shown that galaxies have much more mass than can directly detected. When
astronomers plotted the rotational velocities of galaxies, they found that the rotations were much
faster than expected, and did not tail off as would be suggested by the visible matter within the disk.
Figure 2.2 is a rotational velocity curve of the galaxy NGC 3198. The line marked disk represents
the rotational velocities expected due to the visible matter, but the data shows that this is not the
case. There is more mass present causing the rotational velocities to remain relatively constant as a
function of radius. This is theorised to be caused by a halo of dark matter.

Figure 2.2: The curve marked ’disk’ is what is expected from the visible matter. The data shows that there is more
mass than what can be seen. This is called the dark matter halo. From [11]

Since dark matter can not be easily detected, it must not be very interactive, and it does not
interact with photons or by electromagnetism, otherwise it would be seen. There are a few candidates for dark matter, but one of the strongest theories includes weakly interacting massive particles
(WIMPs). The required properties for a WIMP correspond with a stable LSP predicted by SUSY,
providing further motivation towards it. However, due to recent results failing to find direct detection
of dark matter from LUX and similar poor results from the LHC to find SUSY, some doubt has been
cast on its existence.
2.3.3

Grand Unified Theory

A Grand Unified Theory (GUT) is a theory postulating that, above a certain energy, ΛGU T , believed
to be the Planck scale, the three fundamental forces, electromagnetic, weak, and strong, become equal
in strength and merge into a single, unified force. By merging gravity also, this would become a theory
8

of everything (TOE); a GUT is considered a good first step to this. If the Standard Model alone is
used, at ΛGU T , the three forces almost meet, though they miss by a small amount. With the addition
of the MSSM, they do, and unify conveniently at the Planck scale. Figure 2.3 shows how the forces
nearly meet if the SM alone is used. This near miss seems as if it may be due to a lapse in theory,
as a unification is convenient, and very close. With the addition of the MSSM the three forces do so,
and at the Planck scale.

Figure 2.3: Reciprocal of coupling strength vs log of the energy scale. SU(3) represents the strong interaction of the
three colours of quarks and gluons, SU(2) the weak interaction and the up and down doublet of leptons and quarks, and
U(1) the single photon and electromagnetism. The green shows how the forces nearly meet with the SM, and the orange
shows the unification with the MSSM. The yellow line at 1TeV represents a kink in the lines, where the lines will now
meet at 1016 GeV, or the Planck scale, as expected. This is further evidence for SUSY as this is the energy scale it is
expected to be discovered at. From [12]

2.4

Monte Carlo Simulations

Monte Carlo generators are ways of using random samples to create numerical data. In the scope of
this project, MC generators have been used to generate SM processes and SUSY signals instead of
using real data from ATLAS. This is favourable over real data at this point because each signal can
be attributed to a certain process, which makes cuts and selections on the data much more comprehensive, because it explicitly shows how each process is affected. The signals have been generated to
behave exactly as they would in the detector, including all the specifications and errors that come
with it. It is generated to be as similar to ATLAS collision data as possible. The following processes
are used in the analysis:
[ZZ, W W, W Z], diboson (V V ),
[W W W, ZW W, ZZZ], triboson (V V V ),
tt¯V
single t
tV
Z+Jets
W +Jets
Higgs
SUSY Signals
Each of these signals represent data from specific products in p-p collisions. If a ZZ pair is produced, all the possible decays and their final states can be described with the signals generated by
that MC generator. A number of different MC generators are used, as some generators are better at producing different signals, for example the SUSY signals are produced with the Herwig++
9

generator, and tt¯ with the Powheg+Pythia generator.

2.5

Simplified Models

Multiple simplified Supersymmetric model (simplified models) are used, which impose physical constraints, such as a conservation of R-parity or a mass hierarchy on certain sparticles. The MSSM
has 105+19 free parameters, and in order to perform any analyses, some of these parameters must
be constrained. Simplified models will set the masses of experimentally relevant particles to certain
values, and set the masses of irrelevant particles to either infinity, high enough that they could not
be produced in collisions at a given energy. In this model, R-parity is conserved, and the lightest
chargino, χ
˜±
˜02 . Their actual
1 , is set to be mass degenerate with the second-to-lightest neutralino, χ
masses are dependent on the signal region. Sleptons and sneutrinos are ‘heavy’, and the lightest
neutralino, χ
˜01 , will have a mass similar to the mass degenerate chargino/neutralino pair’s. This mass
difference will also depend on the specific signal region.

2.6

SUSY Scenarios

The chargino/neutralino pair can decay to a number of final states, and in order to make the analysis
possible, these cross sections and branching ratios are set. The scenarios used involve SUSY decays
via mediating W and Z bosons to three leptons, with no intermediate sleptons or sneutrinos, as they
are sufficiently heavy. The feynman diagram for this process is described in figure 2.4. In this scenario
the branching ratio to this process is 100%. The only possible decays are
χ
˜02 → Z + χ
˜01 ,
and
±
˜01 .
χ
˜±
1 →W +χ

The scenarios explored are those when χ
˜01 ≈ χ
˜±
1 . When these masses are similar, the scenarios are said
to be compressed. Now only the masses and decay modes of (χ
˜01 , χ
˜02 ) are the remaining free parameters.
±
˜01 is entirely of the bino
The χ
˜02 and χ
˜1 are assumed to be entirely of the wino component, while the χ
component, which affects the branching ratios of possible decays. This is motivated by unsuccessful
lab searches for sparticles at LEP[6].

Figure 2.4: Decay of χ
˜±
˜02 via W and Z bosons. From [7]
1 χ

2.7

Initial State Radiation

If an initial (pre-collision) state is energetic enough, it can produce a virtual gluon which will then
scatter inside the detector. After scattering it will form more gluons quark-antiquark pairs, which will
in turn form more. This chain reaction of coloured particle production is called hadronisation, and
10

will appear in the detector as a burst of energy in an effective cone from the initial gluon. This shower
of particles is called a jet. The ISR will carry away some of of the momentum from the collision,
reducing the amount of energy available to the final state, which in turn reduces the kinetic energy of
the pair produced chargino/neutralino pair. With little kinetic energy, their decay products will have
a similar mass to their progenitors. The selection of events with ISR chooses events where the mass
of the LSP is similar to that of the chargino/neutralino pair.

2.8

Motivation

The search for direct production of charginos and neutralinos is motivated by their large cross section
at 8 TeV at the LHC. Three leptons are chosen because they represent a large portion of the possible
final states of the sparticles, and tri-lepton events have little SM background. This project explores
the scenarios where the mass of the LSP, χ
˜01 , is similar to that of the lightest chargino, χ
˜±
1 , because
signals where these masses are notably different have already been well explored by other analyses,
figure 2.5. The regions close to the diagonal line marking χ
˜01 = χ
˜±
˜02 have not yet been excluded,
1 /χ
making this work original in that respect. Out of the possible Supersymmetric pair productions,

Figure 2.5: Observed and expected 95% exclusion contours for chargino and neutralino production, W Z-mediated[7].
The yellow band is the ±1σ variation of the expected limit, and the red dotted line is the ±1σ variations of theoretical
limits. These uncertainties include all uncertainties except theoretical uncertainties on the signal cross-section. The blue
lines are from the 7TeV limit from ATLAS three-lepton analysis. From [13].

χ
˜±
˜02 has the largest cross section that results in three leptons, figure 2.6a, so this project focusses
1 ,χ
is on these scenarios. 2.6b shows that, once the LHC increases its energy to 14 TeV, the cross section
will go up considerably, whilst still remaining the largest relative cross section at these masses. This
supports this line of analysis to continue, and increases the likelihood of obtaining better results once
the LHC energy upgrade has commenced.

3
3.1

CERN, the LHC, and ATLAS
CERN

CERN is a mostly European scientific research facility on the Franco-Swiss border, near Geneva.
There are 21 member states, and it has over 2,000 active staff members. CERN is centered around
nuclear research and specifically on the use of large particle accelerators for high energy physics (HEP)
11

(a) 8 TeV

(b) 14 TeV

Figure 2.6: Cross section of p-p→ SUSY vs mass of particles for 8 TeV and 14 TeV. From [14]

research. It is famous for its collaborative atmosphere in which scientists from all over the world meet
towards common goals. Because of the accelerators on site a large number of HEP experiments have
been performed at CERN. It is home to a collection of accelerators, notably the linear accelerators
Linac2 and Linac3, and formerly LEP[15], the Large Electron-Positron collider. CERN is also home
to the Large Hadron Collider[16].

3.2

The LHC

The Large Hadron Collider is currently the world’s largest scientific experimental facility, and the
world’s largest particle collider. It went live briefly in 2008 then again in 2009 and has subsequently
run tests at 3.5 TeV (2010,11) and 4 TeV (2012). It is currently upgrading its energy to 6.5TeV and
has already begun circulating the beams in the former beam tunnel for LEP. The collider sits in a
27km circumference tunnel up to 175 meters below the ground. The LHC is designed for protonproton collisions, but can also accelerate lead (Pb) nuclei, and it contains two beam pipes that meet
at four different locations.
3.2.1

Accelerator Complex

The beam reaches its target energy by a series of accelerators in the accelerator complex[17]. The
proton source is a canister of hydrogen gas which uses a strong electric field to strip it of its electrons,
leaving only protons, or hydrogen nuclei. Linac2 accelerates the protons to 50MeV, and injects
them into the Proton Synchrotron Booster (PSB), which accelerates them to 1.4 GeV. The Proton
Synchrotron (PS) reaches 25 GeV, then the protons are fed into the Super Proton Synchrotron (SPS),
which accelerates them to 450 GeV. They are then injected into the two beam pipes in the LHC,
moving in opposite directions to each other. Here the protons are accelerated to their final energies.
The four locations the beams can collide correspond to the detectors ALICE, ATLAS, CMS, and
LHCb. In order to accelerate Pb nuclei the lead is vapourised and fed from Linac3, to the Low
Energy Ion Ring (LEIR) before following the same route as the protons. The LHC has a design
luminosity of 32cm−2 s−1 .

3.3

ATLAS

ATLAS [19] is a multi-purpose detector built at CERN coaxially along the main beam pipe. It is
one of a number of experiments and detectors there, including CMS, ALICE, and LHCb. It is built
with similar scientific goals and search capabilities as CMS but with a different magnet system design.
Beams of particles collide at the centre of the detector and the resultant final states pass through a
six substage detection system.
12

Figure 3.1: Accelerator complex at CERN showing the stages of acceleration before reaching the beam pipe at the LHC.
From [18]

Figure 3.2: An cut-away view of the ATLAS Detector at CERN. From [20]

3.3.1

Pseudorapidity

Pseudorapidity is a spatial coordinate which describes the angle of a particle relative to the beam
axis. It is defined as

 
θ
η ≡ −ln tan
,
(4)
2
where θ is the angle between the particle’s three momentum compared to the positive direction of the
beam axis. In order to visually understand how η relates to the angle, see figure 3.3. Pseudorapidity
is preferred over the angle for particle physics because particle production is constant as a function
of η, and not of θ. Differences is pseudorapidity are also Lorentz invariant, and so a measurement of
η is not dependent on a reference frame.
3.3.2

Inner Detector

The Inner Detector (ID) is the first stage of detection, and consists of a silicon pixel detector, a
semiconductor tracker, and a semiconductor radiation detector. It is surrounded by a 2T axial solenoid
and has a detective pseudorapidity of |η| <2.5. The pixel detector has a total of 140 million pixels on
2228 silicon semiconductor modules, and this resolution is able to give the ID a spatial resolution of
10µm in r–φ and 50µm in z. The semiconductor tracker (SCT) provides eight precision measurements
13

Figure 3.3: A graph representing the connection between η and θ. From [21]

per track. The SCT contributes to the measurements of the particle’s momentum, impact parameter
and vertex position. The impact parameter is the distance from the primary vertex (collision point)
that the particle was produced. The radiation detector is based on the use of straw drift detectors.
These are small (4mm) straws filled with Xenon gas, that are able to detect transition radiation
photons created by particles between them.
3.3.3

Electromagnetic Calorimeter

The second stage consists of a high-granularity lead/liquid-Argon (LAr) calorimeter for measuring
the energy and position of electromagnetic showers, caused by electrons or photons, within |η| < 3.2.
Similar LAr calorimeters detect hadronic showers in the front and end caps in the (3.1 < |η| <4.9)
and (1.5 < |η| < 3.2) regions respectively. Over the η region which is the same as the ID, there is
high granularity, and this is perfect for precise measurements of photons and electrons. The other
regions however, are suitable for jet reconstruction and missing transverse momentum (MET, ETmiss )
measurements. The way ATLAS reconstructs events is susceptible to mistakes. A real lepton is a
genuinely isolated lepton that has been correctly attributed as such by the detector. A fake lepton
is a non-isolated lepton that can arise from mis-identification of light flavour jets, or from the misattribution of a track in the inner detector to an energy deposit in the calorimeter. These fake leptons
can cause events to have too many leptons attributed to them, and will cause extra SM background
to be classed as having a three lepton final state.
3.3.4

Hadron Calorimeter

The next stage, the hadron calorimeter, consists of three parts. There are concentric barrels of
iron/scintillator tiles that measures hadronic showers, i.e from jets, in the region 0.8 < |η| < 1.7, and
two end caps of copper/LAr in the region of 1.5 < |η| < 3.2. There is also a forward calorimeter with
alternating layers of copper and tungsten, with scintillating tiles, extending over 3.1 < |η| < 4.9[22].
The iron is designed to stop incoming hadrons, forcing them to deposit all their energy inside the
detectors, and the scintillators will detect these deposits. The scintillation is proportional to the
hadron’s energy, so the detector is able to resolve the momenta of incoming jets.
3.3.5

Muon System

The Muon detector lies outside the previous sections, and must do so in order to detect the muons
which, because of their energy, are more penetrating than most particles. Because their dE
dx is so
small, they do not leave much of an energy deposit in the EM calorimeter. They will also leave a
small deposit in the hadron calorimeter as they pass through. There is a system of tracking chambers,
|η| < 2.7, and large superconducting toroidal magnets which bend the muons, forming another set
of tracks. These can be attributed to the first set, in the ID, to identify it as a muon. The muon

14

detector contains a barrel region coaxial to the beam pipe, and two end caps. Within the barrel region
the tracks are measured in three cylindrical layers. In the cap regions, the chambers are planal and
perpendicular to the beam pipe, and are also in three layers.

Figure 3.4: The subsectioned detectors at ATLAS. The concentric rings are: The ID, the EM calorimeter, the hadronic
calorimeter, and the muon system. The green lines represent the tracks made in the ID by charged particles. The
blue line is a detected muon. There are energy deposits in the EM and hadronic calorimeters and the red dotted line
represents the missing ET. This could be caused by neutrinos or, in the case of this project, by SUSY as well. From [23]

3.3.6

Trigger

The information rate due to the design luminosity of 32cm−2 s−1 is around 1GHz[19] (events/s).
The data recording is limited to around 200Hz (events/s) due to current technologies and storage
capabilities. This means there is a rejection factor of 5 × 106 . The LHC uses a three levelled trigger
and filter in order to make sure as much relevant data is being kept as possible while reaching the
required 200Hz rate. The level-1 (L1) trigger cuts down the data to around 75kHz, whilst the final
two, the level-2 (L2) trigger and the event filter (EF), reach the required 200Hz.
3.3.7

Trigger Level-1

The first (L1) trigger only has access to information from the calorimeters and the muon detector.
It uses signals in coarse granularity to search for muons, electrons, photons, jets
τ -leptons with
P and
high transverse-momentum decaying into hadrons, alongside large ETmiss and
ETtotal . The triggers
makes these decisions based on information from the muon spectrometer and calorimeters. The L1
trigger is able to define Regions-of-Interest (RoI’s), where ‘interesting features’ have been identified.
This information is passed on to the high-level triggers.
3.3.8

Trigger Level-2

This is seeded by RoI information and uses the ID to select events with tracks. The L2 trigger is
designed to reduce the data rate to around 3.5kHz. A hypothesis algorithm determines whether the
features defined meet the criteria of triggering, like an ET threshold or shower shape. If an event
passes the L2 trigger, the event fragments from all RoIs combined are sent to the event builder, and
then passed on to the EF.
3.3.9

Event Filter

The event filter has access to the full detector information, as well as algorithms used in ATLAS’s
offline event reconstruction[24]. It is designed to reject events after 1s in order to restrict its event
output. The EF reduces the data rate to the required 200Hz.
15

3.3.10

Missing Transverse Energy Detection at ATLAS

Missing transverse momentum is very important in understanding a collision, as not all particles will
be detected by ATLAS. There is no way of directly measuring MET, as the total transverse momentum
isn’t known, but it can be calculated by understanding the momentum imbalance. Because momentum
is conserved, and the transverse momentum can be considered zero at the time of the collision, if the
total vector sum of the detected momentum is not zero, some must be missing. MET is therefore
calculated as the negative of the vector sum of the detected transverse momentum.
ETmiss = −

N
X

p~T i

(5)

i

The detected transverse momentum is only counted if ATLAS reconstructs it to originate from the
primary vertex, or if the the impact parameter d0 , is within a small enough range. MET will be
detected when particles like neutrinos or the LSP are present in a process. These particles will not
react with any part of the ATLAS detector, so their presence must be inferred by the missing energy.
Since muons are so penetrating, and they will only leave small energy deposits in the EM and hadronic
calorimeters, some MET may arise because of them. The detector may also have some ‘hot’ or ‘dead’
zones within the calorimeters which over or understate the amount of momentum in an area. This
can lead to a miscalculation of MET.
3.3.11

b-Tagging

When a b-quark is produced in a collision, either directly or from a t-quark, it will decay a small
distance from the primary vertex, because of its non-negligible lifetime. This decay will result in
hadronisation and a jet, detected in the hadronic calorimeter. The small distance, the impact parameter, that the b decays from the primary vertex can be detected by ATLAS, which will then mark
the resultant jet as having derived from a b-quark. This is called b-tagging. The process behind
b-tagging is not perfect however, and many b-jets can be overlooked, as well as many normal jets
being mis-tagged as having derived from b-quarks.

4
4.1

Analysis
Technical Framework

The ATLAS framework contains a large repository of libraries and codes in order to perform the tasks
required for the analysis, from plotting, tabulating, or selecting datasets. The framework resides in
the file repositories of the Feynman HPC cluster at the university, and this cluster performs all
the computational tasks. The Monte Carlo simulation data is stored as ROOT[25] NTuples, each
containing information regarding each event’s final states, for example the momenta, energies and
directions of particles. These pieces of information can be tabulated or plotted in order to get a
representation of how the distributions of these variables look for the data. There is one NTuple for
each process, e.g ZZ → 4e and a script can take each of these background processes and combine
them into a single NTuple, for example ZZ, or Z+Jets. The framework was copied from another
user’s file repositories and was relevant to their analyses. Although this was sufficient for some of
the initial analysis, many extensive edits had to be made, and in order to do them, a capability in
C++, ROOT, and Python was required, as these are what the framework is based upon. In order to
make the analysis unique to this project, I had to understand NTuples, how they stored information,
and how to accurately manipulate them. These skills were used in creating variables which could be
explored to gain further insight into the project. The plots seen in this report are created using a
script already used within the ATLAS framework. It stacks the histograms of each of the backgrounds
and superimposes the SUSY signals. The significance plots are created with an algorithm sent to me
by Yusufu Shehu.

16

4.2

Pre-selection

Each event must first pass the pre-selection defined by the ATLAS framework, which selects events
based on their quality and on trigger requirements. This occurs on each of the datasets before any
analysis is done on them, so the initial data is all pre-selected.

4.3

Significance

In order to tell whether a discovery has been made, it must first be shown that a statistical fluctuation
could not cause the seen effects. Significance is the confidence that an effect is not due to one of these
random fluctuations. A higher significance across as many signal regions as possible is what each
cut or selection tries to achieve, up to the point of exclusion, which is after a significance of σ =
1.64. After exclusion it is within reason to believe that the signal points are not due to any statistical
fluctuations, and the data can be described by new physics. A discovery in particle physics requires
5σ, which is a 1 in 3.5 million chance of a statistical anomaly, a standard set purposefully very high
by organisations such as CERN. A significance of 1.64σ corresponds to a 90% confidence interval, a
1 in 10 chance of the results being randomly caused. Significance can be simply formulated as the
strength of the signal over the square root of the background.
σ=√

Signal
.
Background

(6)

This form works generally, but it has some limitations. Firstly, it does not take into account any
statistical fluctuations that the background or signal may have, and, when the background approaches
zero, it becomes unnaturally large, which is problematic. Instead, ZN is used. This takes into account
more of the statistical nature of the signals and background and is able to return a far more accurate
value. The algorithm plotting significance within the framework uses
ZN = Φ−1 (1 − p0 (S, B, ∆B)),

(7)

where Φ−1 is the cumulative distribution of the standard Gaussian and S and B are the number
of events for signal and background. ∆B is the systematic uncertainty of the background signal, and
for this analysis it is 30%. This uncertainty comes from the fact that a Monte Carlo simulation will
not be able to replicate real data perfectly, and this formula accounts for this. p0 is the p-value, which
is the probability that the data is more signal-like than signal and background together. In order to
deal with infinities and negatives, the algorithm will set all negative values to zero, and will truncate
ZN at 8. The ZN algorithm returns plots for each explored variable, and how the significance would
change given a certain cut location. Figure 4.1 shows how significance depends where a left-handed
cut is made for five different signals.
Figure 4.1 is how the framework originally displayed significance plots. I found that, because the
significance only ranges between around 0 and 3, a logarithmic y-axis is unnecessary, and much better
resolution could be found with a linear axis, figure 4.2·

4.4

Cuts

Cuts, selections, and their implications make up the bulk of this project. A cut is a selection on the
datasets, which chooses to keep or remove all events above or below a certain threshold. A cut can
be made on any measurable variable from the NTuples, for example missing transverse momentum
or jet multiplicity. The cuts are chosen in order to isolate data specific to our analysis and to remove
as much of the background as possible. The Monte Carlo simulations will show how each cut affects
each background signal type individually, which is impossible using real data. Because of the different
nature of the SUSY signals and their decays compared to the SM background, the cuts will have
different effects on each distribution. For example, processes with SUSY in their final states will
have high missing transverse momentum so a cut, removing all events with low MET, will remove
background whilst keeping the bulk of the SUSY signal. There are two types of cut, left-handed or

17

Figure 4.1: How significance depends on a cut on the x-axis. The x-axis shows the location of a left-handed cut on the
invariant mass of three leptons, and each of the different coloured lines represents a different signal region. This plot
is from data that has already been cut a number of times previously. The best cut would be one which maximises the
significance for as many signals as possible.

undercuts, and right-handed or uppercuts. The left-handed cuts remove all events under a threshold,
and right-handed cuts over. At the beginning of the analysis there are many cuts that can be made
without affecting the SUSY signal at all. These are dubbed ‘free cuts’ and are very useful because of
how greatly they increase the signal to background ratio, figure 4.3.
If a cut is made on a variable, say MET, it can change the distribution of events in every other binned
variable. Events with low MET may, for example, have high jet momenta. A cut removing the low
MET events will therefore mean the remainder all have lower jet momenta. Each cut will have a
different effect depending on which point in the analysis it is made. For this reason it is important to
check each variables’ distributions at each point. The aim of these cuts is to increase the significance
of the signal. This gives a set of criteria. They should make a cut relevant to the analysis, significantly
reduce the background, or increase the significance to the point where a signal can be excluded.

4.5

Irreducible vs Reducible Background

The SM background can be categorised in two ways, whether it is reducible, or irreducible compared
to the signal. Reducible backgrounds end in final states with at least one fake lepton, and can be easily
excluded from the data with a few cuts. For example, almost all (183,476,746→6) of the W +Jets
events are removed by asking for exactly three Leptons. The remaining six events will be due to
misidentified fake leptons. Irreducible backgrounds are more troublesome, and are when a process
has three genuine leptons in the final state. Dealing with this background is the real challenge of this
project.
W Z/γ∗, triboson (V V V ) and tt¯ + V /V V are the main irreducible backgrounds for this analysis, as
they can all end in three leptons, while tt¯, tV , Z+jets and W W are the main reducible backgrounds.

4.6
4.6.1

Important SM Backgrounds
WZ

Because the SUSY signal has a 100% branching ratio to be mediated with W Z bosons, the biggest
irreducible background will be the W Z processes. A differentiator between the W Z and SUSY final
states is the larger ETmiss due to the undetected neutralinos. The W Z signals are produced by the
Powheg+Pythia8 MC generators.

18

Figure 4.2: A similar plot to figure 4.1 but with a linear y-axis instead of a logarithmic. The resolution is much better,
leading to easier, and more accurate cut placement.

Figure 4.3: On the left is an example of a ‘free cut’. The events with min. mSFOS > 35 can be removed without
affecting the SUSY signal. On the right, there is no obvious place to cut, and a compromise will have to be made, or
this variable overlooked.

4.6.2

Z+Jets

Z+jets offers a problem because it creates two real leptons, and has a high chance of creating a third
fake lepton in the jets. These jets will have a low MET compared to the SUSY signals, and a fairly
low MET cut will deal with this background. Z+jet signals are produced by the Alpgen+Pythia
Generators.
4.6.3

t¯t

tt¯ will decay via W ± and a b quark, figure 4.4. The SUSY signals are not mediated by any b quarks,
and so, due to the b tagging capabilities of ATLAS, a request to veto any events with b quarks should
remove this background. These signals are produced by the Powheg+Pythia MC generators.

5

Selected Signal Regions and Preliminary Event Selection

The aim of this project is to exclude as many signal regions as possible via a series of cuts and an
event selection. It is important to tailor this event selection to exclude specific regions, as one selection
cannot exclude every point. Not all regions can be excluded at all with the current level of statistics,
19

Figure 4.4: Leading order feynman diagram for tt¯ production and decay from parton-parton collisions. From [26]

or be excluded at the same time as others. In order to find which signals can be properly explored, six
were chosen, representing the regions where mχ
˜±
˜01 . These were chosen to have a wide range of
1 ≈ mχ
masses along the diagonal so as to represent as many signal regions as possible. These initial points
are stated in table 5.1. A preliminary event selection is designed that endeavours to obtain the highest
significance for the six regions. The following section will lightly explain the reasoning behind each
of the preliminary cuts, the sequence of which is called a cutflow. However, most of the detail will be
covered in section 6, as that represents a more full analysis.
mχ
˜±
1

mχ
˜01

100
100

75
87.5

150
150

125
137.5

200
200

175
187.5

Table 5.1: The initial signal regions chosen for the preliminary event selection. These points best represent a wide mass
range along the diagonal mχ
˜±
˜01 .
1 ≈ mχ

5.1

Initial Cuts

The following cuts represent the basis of the analysis. This project focusses on events with three
leptons and with ISR, so the first cuts ask for three leptons, and at least one jet. A request is also
made for a SFOS pair. SFOS means Same Flavour, Opposite Sign, and refers to pair produced light
leptons like e+ , e− or µ+ , µ− . Light in this contexts means non τ -leptons. This request is required for
a cut later on, and since a SFOS pair will be produced by the Z boson in the W Z mediated SUSY
decays, this will not affect the signals strongly.
Initial Cuts
≡ 3 Leptons
has a SFOS pair
≥1 Jet
Table 5.2: The initial cuts for the preliminary event selection. These reflect the basis of the analysis.

20

5.2

Baseline

The baseline is a series of cuts selected to reduce a large quantity of background, and remove some of
the specific signals. Cuts are made on the leading lepton momentum, the MET, and whether or not a
b-quark is present. An uppercut, removing events with more than 40 GeV leading lepton momentum,
is first. Events with an MET below 20 GeV are cut, and since there are no b-quarks present in the
SUSY final states, events with b-jets were also removed with a b veto. The b veto is specifically to
remove tt¯ events. These cuts are able to remove most of the background signals, but the majority
of the remaining background is from the W Z processes, as their final states are very similar to the
SUSY signals.
Baseline Cuts
1st Lepton Momentum < 40 GeV
MET > 20 GeV
b-veto
Table 5.3: The baseline cuts for the preliminary event selection. These are chosen in order to reduce background.

5.3

Increasing Significance

Once the baseline has been established, cuts are made with the specific target of increasing the
significance for as many of the signal regions as possible. The aim of this preliminary cutflow is to
see which signal regions are viable to exclude, but not necessarily to exclude any. Cuts are made
on the invariant mass of the SFOS pair (mSFOS) and the invariant mass of the three lepton system
(mlll ). Further cuts are made on the leading jet momentum, the angle between this jet and the
missing energy, and another cut on the MET. Each of these aims to increase the significance of each
of the selected signal regions. These cuts were chosen by finding the variables in which the largest
difference in distribution between signal and background could be found, then specifically optimising
for significance each time.
Optimisation Cuts
Invariant Mass of SFOS pair < 20 GeV
1st Jet Momentum > 110 GeV
∆φ between 1st Jet and MET > 2.9
MET > 110GeV
Invariant Mass of Three Lepton System > 20 GeV
Table 5.4: Final set of cuts in the preliminary event selection. These are selected to raise the significance for each of the
selected SUSY signal regions in order to evaluate which signals will be possible to exclude.

5.4

Other Explored Variables

Designing this preliminary event selection involved looking at dozens of different variables and how
they affected the signal distributions. Before this selection was established, the angles between the
two SFOS leptons, the momenta of the 2nd and 3rd leptons and jets, and the transverse mass were all
considered. The angles (∆Φ) between many of the variables were usually very uniform for both signal
and background and did not favour any direction, so did not offer any places to cut, as shown in figure
4.3 earlier. 5 GeV slices were taken of mSFOS between 0 GeV and 30 GeV and investigated. I wanted
to know how the distributions of other variables depended on mSFOS. Some of the regions, especially
low energy, had high proportions of diboson events and offered insight into how small differences
in cuts would affect different signals but, unfortunately, no particular method of reducing the W Z
background. The aim of using the transverse mass, mT , was to try and veto events with an on-shell
W boson, in an attempt to reduce the prominent W Z background. The transverse mass is calculated
21

using the ETmiss and the lepton that is not part of the SFOS pair, as this lepton would have originated
from the W decay. It has the form
q
(8)
pTl · p~lmiss , [7]
mT = 2plT ETmiss − 2~
where plT is the lepton momentum, and p~Tmiss is the missing transverse momentum. A peak at the W
mass of 80.4 GeV was expected, however this did not turn out to be the case, figure 5.1, and therefore
did not offer any solutions.

Figure 5.1: Distribution of transverse mass. A peak at the W mass of 80.4 GeV was expected in the diboson signal, but
is not there. Transverse mass was therefore not useful to the analysis.

22

5.5

Preliminary Event Selection Results

The preliminary event selection was able to exclude one of the analysed points, and nearly exclude
another. A 2D significance plot shows how the preliminary event selection affected a wider range of
signal regions. From this plot it is clear which regions would be possible to exclude, or nearly exclude,
with a similar event selection.

Figure 5.2: 2D plot of significance for SUSY signal regions after a preliminary event selection. this plot is able to
represent which of the SUSY signals are likely to be excludable.

Mass of χ
˜01 [GeV]

˜02 [GeV]
Mass of χ
˜±
1 /χ

75
75
87.5
100
125

100
125
100
125
150

Table 5.5: List of signal regions that should be explored following the preliminary event selection.

23

Figure 5.2 suggests a number of regions to explore further, and those selected for the rest of the
analysis are in table 5.5. It is important to note that these are not the only signal regions that can
be excluded, but are ones that potentially can be with a similar event selection to the preliminary.
If other signal regions are to be explored, a very different event selection would be required. It is
also worth noting that some of the signal regions may however, not be possible to exclude at all with
the current statistics and centre of mass energy, which unfortunately can not be avoided. The final
cutflows for the preliminary event selection can be found in tables 5.6 and 5.7. The cutflow shows
the affect that each cut has on each signal, and the significance as a result. Parts of the cutflow
denoted by 0.0 do not necessarily mean zero events or significance. Those points are considered zero
in accordance with the precision, which was one decimal place for the preliminary work, and increased
to two for the final analysis.

24

25
47.2±2.9
0.0
10.8±0.7
0.0
3.5±0.2
0.0
321.3±13.4
0.0
76.0±2.5
0.0
28.7±0.9
0.0

581.8±12.7
899.6±1.5
11.2±0.6
3335.9±13.9
5646.5±362.7
26.9±0.3
77.7±1.5
32.4±0.4
6.2±4.1
48.1±0.6
10713.1±363.2

≡3L

47.2±2.9
0.0
10.8±0.7
0.0
3.5±0.2
0.0
320.7±13.4
0.0
76.0±2.5
0.0
28.7±0.9
0.0

430.5±10.9
895.0±1.5
8.5±0.5
3313.8±13.8
5616.7±362.5
21.1±0.3
69.8±1.4
31.9±0.4
4.6±3.8
42.8±0.6
10468.8±363.0

has SFOS

24.8±2.1
0.0
5.3±0.5
0.0
2.0±0.2
0.0
128.2±8.5
0.0
33.2±1.6
0.0
13.7±0.6
0.0

408.8±10.7
342.6±0.9
5.2±.04
1534.0±9.4
1835.1±182.8
8.8±0.2
69.5±1.4
31.1±0.4
0.9±0.9
26.8±0.4
4287.0±183.4

≥1 Jet

22.3±2.0
0.0
5.2±0.5
0.0
2.0±0.2
0.0
104.8±7.7
0.1
28.2±1.5
0.0
11.8±0.6
0.0

77.4±4.6
101.5±0.5
1.1±0.2
205.0±3.4
671.7±167.5
0.7±0.0
3.5±0.3
1.9±0.1
0.0±0.0
5.5±0.1
1069.7±167.6

Lepton Pt <40 GeV

20.2±1.9
0.0
4.6±0.4
0.2
1.8±0.2
0.2
89.3±7.2
0.3
24.9±1.4
0.0
10.7±0.5
0.0

73.6±4.5
55.9±0.4
1.1±0.2
174.4±3.1
317.7±107.9
0.7±0.0
3.4±0.3
1.8±0.1
0.0±0.0
4.1±0.1
633.9±108.0

MET> 20 GeV

Table 5.6: Preliminary event selection, resulting in the exclusion of two points. This event selection is used to choose which signals to use in the full analysis. a

2454.9±21.2
0.0
569.8±4.9
0.0
186.2±1.6
0.0
7881.5±67.1
0.0
1160.8±9.8
0.0
394.2±3.3
0.0

1733485.5±699.1
7975.9±4.5
70567.5±44.7
54054.6±56.5
44225712.4±40973.4
210.4±0.9
3972.7±16.2
571.4±1.8
136936687.0±89357.7
5313.4±7.7
183476745.9±98308.3

ttbar
WW
ZZ
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 137.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 200; MN1 = 187.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 200; MN1 = 175[GeV]
Zn (30% ∆SM )

initial

Sample

26
15.6±1.6
0.0
3.7±0.4
0.0
1.6±0.2
0.0
68.2±6.2
0.5
20.9±1.3
0.0
9.0±0.5
0.0

5.0±1.1
25.2±0.2
0.3±0.1
107.9±2.4
160.3±104.1
0.2±0.0
0.1±0.1
0.2±0.0
0.2±0.0
1.4±0.1
301.1±1042

mSFOS<30 GeV

2.5±0.6
0.7
0.9±0.2
0.1
0.5±0.1
0.0
5.4±1.7
1.5
.4±0.5
0.9
1.9±0.2
0.5

0.5±0.3
0.2±0.0
0.0±0.0
3.8±0.4
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.1±0.0
4.7±0.5

JPt > 110 GeV

2.2±0.6
0.9
0.8±0.2
0.2
0.4±0.1
0.0
3.7±14
1.5
1.9±0.4
0.8
1.3±.2
0.5

0.1±0.1
0.0±0.0
0.0±0.0
2.2±0.3
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
2.4±0.4

∆Φ J/MET>2.9η

2.0±0.6
1.2
0.8±0.2
0.3
0.4±10.1
0.0
3.1±1.3
1.8
1.6±0.4
0.9
1.1±.2
0.6

0.0±0.0
0.0±0.0
0.0±0.0
1.1±0.2
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
1.2±0.2

MET>110 GeV

2.0±0.6
1.2
0.7±0.2
0.2
0.4±0.1
0.0
3.1±1.3
1.9
1.6±0.4
1.0
1.1±0.2
0.6

0.0±0.0
0.0±0.0
0.0±0.0
1.0±0.2
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
1.1±.2

mlll > 20 GeV

Table 5.7: Preliminary event selection, resulting in the exclusion of two points. This event selection is used to choose which signals to use in the full analysis.(b)

17.8±1.8
0.0
3.9±0.4
0.0
1.7±0.2
0.0
78.2±6.6
0.3
22.8±1.4
0.0
9.7±0.5
0.0

18.1±2.2
50.5±0.3
0.9±0.2
157.1±2.9
297.5±107.4
0.6±0.0
0.2±0.1
0.3±0.0
0.0±0.0
2.8±0.1
528.2±107.4

ttbar
WW
ZZ
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 137.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 200; MN1 = 187.5[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 200; MN1 = 175[GeV]
Zn (30% ∆SM )

b-veto

Sample

6

Event Selection

The final event selection is designed with the five specifically chosen signal regions in mind, instead
of the previous wider signal range. It aims to exclude all of the points above the threshold, ZN =1.64,
significance. The selection is heavily based upon the preliminary, with most of the cuts being very
similar. During the analysis it became clear that some of the points can not be excluded at the
same time as each other. Although high significances can be reached for many of the points at the
same time, only a few can reach exclusion simultaneously; two are mutually exclusive in that respect.
Two event selections, then, are used in order to exclude these two points, and they are denoted SRa
and SRb. The two event selections share a common baseline before they take different paths. The
following section outlines the sequence of cuts; each one is made in succession and the plots represent
data that has been cut upon by the sections before.

6.1

3 Leptons

The first cut asks for exactly three leptons, which is the basis of the project. This removes a large
amount of the background immediately, and some signal. Even though the SUSY signals have a 100%
branching ratio to result in three leptons in the final state, due to the ATLAS detector having difficulty
resolving high multiplicities of leptons from a single event, and because of the harsh triggering it has
on leptons, many of the SUSY events are incorrectly recorded as having less than three. Because of
this, many of the events are wrongly cut.

Figure 6.1: Lepton multiplicities after the preselection.

27

(a)

(b)

Figure 6.2: (a) is the initial MET distribution of Standard Model background and the five chosen signal regions. (b) is
the distribution once a cut for 3 leptons has been made.

6.2

Same Flavour, Opposite Sign Request

SFOS pairs are important because they are pair produced, allowing a calculation of their invariant
mass, and therefore an indication of which process they originate from. Although it does not greatly
reduce the background, this cut is necessary, as some of the cuts later ask for a limit on the invariant
mass of the SFOS pair. This requires that all the data have a pair of which can be cut. Plots have
not been included because this cut has little effect on the background.

6.3

Jet Multiplicity - ISR Request

A cut on the jet multiplicity is required so that there is at least one ISR jet present. Since the SUSY
process (see the feynman diagram in figure 2.4) does not result in any jets in the final state, any
remaining events after this will have at least one jet, due to ISR. This cut acts mainly as a selection
on the SUSY signals for the analysis, and not specifically to reduce background. Just like the SUSY
signals, any process can exhibit ISR, and many have final state jets.

6.4

Leading Lepton Momentum

Due to the presence of ISR the chargino and neutralino pair will not have much kinetic energy. The
same follows for their decay products, and the three leptons. These SUSY events have soft leptons
meaning they do not have much energy, whereas background events will have a wider distribution in
the lepton momentum. An upper-cut can be made, removing all events in which the leading lepton’s
momentum is greater than 30 GeV. This is different to the preliminary selection, which cut at 40 GeV.
This number is chosen with the aid of the ZN significance plot, which dictates which cut position
would yield the greatest return in significance, figure 6.3.

28

(a)

(b)
Figure 6.3: (a) is the distribution of the leading lepton momentum. (b) is the significance of the signal vs right-handed
cut location (meaning cutting all events above a certain limit). A cut at 30 GeV increases the significance to a non zero
values for three of the signals.

6.5

Missing Transverse Momentum

Since the final state LSPs do not interact with the detector, evidence of their existence must be
inferred by the MET. If the LSP is present, the events will show significant MET, more than for most
SM processes. A preliminary cut is made, removing all events with < 50 GeV, figure 6.4. This cut
is not with the intent to directly increase significance, although it does, it is done to remove events
with little or no MET, specifically Z+Jets, which, up until this point is the largest background.

29

(a)

(b)
Figure 6.4: (a) is the MET distribution before the cut has been made. (b) is the significance vs left-handed cut location.
A cut at 50 GeV will return a decent significance at this stage, and remove almost all of the Z+jets background

6.6

b-Jet Veto

In the W Z mediated SUSY process, there is no b-quark production, and because of ATLAS’ capabilities regarding b-tagging, a request can be made to remove any events which contain b-jets. This is a
b-veto, and is useful in removing the tt¯ background, as those events will almost always result in one
or more b-jets. This successfully removes ∼75% of the tt¯ background, while leaving the SUSY signals
relatively untouched. There is a small reduction in signal strength, but that is due to the ISR being
falsely tagged as b-jets, because they do not originate from the primary vertex. This also applies to
the background signals other than tt¯. The remaining tt¯ signal is due to the opposite, where b-jets
have failed to be tagged correctly.

30

(a)

(b)

Figure 6.5: (a) is the MET distribution before a b-veto has been made, and (b) is after. Note the decrease in the tt¯
signal.

6.7

Excluding Different Signal Regions with Multiple Cutflows

The previous cuts form the baseline of the two event selections, and at this point some of the signals
˜01 = (100 GeV, 87.5 GeV)
can be excluded with just a few more cuts, however the points mχ
˜±
1 , mχ
and mχ
˜±
˜01 = (125 GeV, 75 GeV) can not be excluded at the same time. Realising that they
1 , mχ
are mutually exclusive is important because previously, each cut tried to optimise for as many of the
signals as possible. Now, depending on which region is being focussed on, the other’s significance can
be disregarded so as to not make any unnecessary compromises on the first. The two event selections,
˜01 =
˜01 = (100 GeV, 87.5 GeV) and mχ
˜±
SRa and SRb, aim to exclude the points mχ
˜±
1 , mχ
1 , mχ
(125 GeV, 75 GeV) respectively. These are the target regions of these selections. Table 6.1 displays
the two cutflows, and how they differ past the baseline.
Baseline
3 Leptons
has SFOS pair
≥1 Jet
Lepton Pt <30 GeV
MET >50 GeV
b-jet veto
SRa
5 GeV< mSFOS <25 GeV
MET>130 GeV
∆Φ 1st Jet/MET > 2.9η

SRb
15 GeV<mSFOS<45 GeV

Table 6.1: Cutflow differences for SRa and SRb. The two cutflows target different SUSY signal regions, so cut on
different variables.

6.8
6.8.1

Signal Region SRa
Invariant Mass of SFOS Pair

Figure 6.6a shows that the mSFOS associated with the SUSY signals is much lower than most of the
background’s. There is a peak around 90 GeV. This is due to the Z bosons, in the W Z background
signal, producing the SFOS pair. The distribution for mSFOS is very similar to the cross section of Z
decay. Although the SFOS pairs present in the SUSY signals are from a mediating Z boson, for this
process it is off-shell, and therefore the invariant mass will not peak around mZ = 91.2 GeV. This is
useful, as it allows us to make a harsh cut, and leave the signal relatively untouched. Since SRa is

31

trying to exclude mχ
˜±
˜01 = (100 GeV, 87.5 GeV) (Red line in figure 6.6b) and not mχ
˜±
˜01 =
1 , mχ
1 , mχ
(125 GeV, 75 GeV) (dashed brown), a slice between 5 GeV and 25 GeV is cut.

(a)

(b)
Figure 6.6: (a) distribution of SFOS invariant mass before the cut in SRa. (b) is the significance vs right-handed cut
location. Cutting a slice between 5 GeV and 25 GeV returns the best significance for the signal regions SRa targets.

6.8.2

Missing Transverse Momentum

A cut has already been made on MET in section 6.5, and the reasoning for another is much the same,
though now there is room to make a harsher cut and remove even more background. At this point
most of the background signal events have relatively low MET compared to the SUSY signals and
come from W Z processes. These will have some MET due to the neutrinos in W ± → e± + ν¯/ν, but
there will not be as much as with the SUSY signals, as they are less massive. A left-handed cut is
made at 130 GeV even though this compromises the points (125, 100) and (100, 75), because the
target region takes priority, figure 6.7.
6.8.3

Angle Between Leading Jet and Missing Transverse Momentum

At this point there are very few events left. Only one of the variables offers a cut that will markedly
increase the significance for the target region. This is the angle between the leading jet and the

32

(a)

(b)
Figure 6.7: Distribution and significance of Missing Transverse momentum for SRa. A left-handed cut at 130 GeV is
made to maximise significance with (100, 87.5) as priority. Figure (b) shows that, for optimising SRa, a cut at 130 GeV
will raise its significance the most, however it compromises (125,100) and (100,75).

MET, and it is one of the variables in the preliminary selection. A left-handed cut is made at a
pseudorapidity of 2.8. This removes some of the SUSY events as well, but the priority is to exclude
the target region, so this is a considered compromise. This is the last selection in the SRa cutflow, as
it successfully excludes the region (100, 87.5).

33

(a)

(b)
Figure 6.8: Distribution of events for the angle between the leading jet and MET. A left-handed cut at η=2.8 increases
the significance of (100, 87.5) desirably. Although this removes some SUSY signals, because the priority is to exclude
the target region this compromise is made.

6.9
6.9.1

Signal Region SRb
Invariant Mass of SFOS Pair

Similar to SRa, the first variable cut is mSFOS, as there is a great difference between the distributions
of the signal to the background. Because the point (100 GeV, 87.5 GeV) now does not have to be taken
into account, this cut can be different. The best significance can be found by cutting a slice between
15 GeV and 45 GeV. With this cut alone, the significance for the three target signals increases above
exclusion, so no further action is required. Further cuts on MET and on the leading jet momentum
will increase the significance for many of the regions, but will both reduce it for the target point
(125 GeV, 100 GeV). A small (0.01) increase can be gained from a left-handed cut on mlll , however,
retaining as much statistics and number of events as possible is beneficial, as they are then less prone
to statistical fluctuations. Because of this the choice has been made to make no further cuts on these
signal regions.

34

Figure 6.9: Invariant Mass distribution for mSFOS after the baseline. A slice between 15 GeV and 45 GeV will be taken
in order to optimise for (125, 100). This shaves off background events at the start and end of the distribution, namely
the W Z events.

(a)

(b)

Figure 6.10: (a) Significance of a left-handed cut on mSFOS after the baseline. (b) Significance of a right-handed cut on
mSFOS after the baseline. The cuts at 15 GeV and 45 GeV are chosen to optimise for the point (125, 100), the dashed
black, while keeping the brown and cyan above ZN =1.64.

35

7
7.1

Results
Baseline

The baseline for the two event selections is a development on the preliminary, as that was found to
best increase the significance for a broad range of signals. It is chosen to have all five of the selected
signal regions reach as close to exclusion as possible, without compromising on any of the points
in particular. The preliminary event selection was only able to exclude one point (100, 75) with
ZN =1.86, though a second, (125, 100) with ZN =1.54 comes close. The event selection returned poor
significances on many of the regions because of their poor statistics. There are not enough events
to survive a cutflow this harsh. For example, the excluded point (100, 75) has 7881.5 initial points.
Three of the other preliminary points have under 600. Compared that to the 1.3×108 background
events and it is clear that resolving these signals will be difficult. Because of this, many of the signal
points likely can not be excluded with any event selection. The full cutflow for the baseline is almost
identical to the preliminary event selection except for two differences: The lepton momentum cut is
30 GeV instead of 40 GeV and the first MET cut is raised to 50 GeV instead of 20 GeV, because these
have a much greater effect on the significance. The two cuts now raise every point’s significance to a
non zero value and increase the point (100, 75) to ZN =1.24, whereas before, the highest significance
at this point in the cutflow was 0.3 for the same region. At the end of the baseline, that same point
has been excluded, and two others are around ZN = 1. The full cutflow for the baseline follows in
tables 7.1 and 7.2.

36

37

1733485.5±699.1
7975.9±4.5
70567.5±44.7
54054.6±56.5
44225712.4±40973.4
210.4±0.9
3972.7±16.2
571.4±1.8
136936687.0±89357.7
5313.4±7.7
183476745.9±98308.3
3385.6±28.8
0.00
1160.8±9.8
0.00
7881.5±67.1
0.00
3656.1±30.4
0.00
2454.9±21.2
0.00

ttbar
WW
ZZ
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

MC1,MN2 = 125; MN1 = 100[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 125; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )

155.9±6.2
0.00
76.0±2.5
0.00
321.3±13.4
0.00
426.6±10.2
0.00
47.2±2.9
0.00

581.8±12.7
899.6±1.5
11.2±0.6
3335.9±13.9
5646.5±362.7
26.9±0.3
77.7±1.5
32.4±0.4
6.2±4.1
48.1±0.6
10713.1±363.2

≡3L

155.9±6.2
0.00
76.0±2.5
0.00
320.7±13.4
0.00
425.7±10.2
0.00
47.2±2.9
0.00

430.5±10.9
895.0±1.5
8.5±0.5
3313.8±13.8
5616.7±362.5
21.1±0.3
69.8±1.4
31.9±0.4
4.6±3.8
42.8±0.6
10468.8±363.0

has SFOS

≥1 Jet

62.8±3.9
0.00
33.2±1.6
0.00
128.2±8.5
0.00
165.6±6.545.0
0.00
24.8±2.1
0.00

408.8±10.7
342.6±0.9
5.2±.04
1534.0±9.4
1835.1±182.8
8.8±0.2
69.5±1.4
31.1±0.4
0.9±0.9
26.8±0.4
4287.0±183.4

Table 7.1: Baseline cutflow before the analysis splits into SRa and SRb (a)

initial

Sample

41.1±3.1
0.03
21.9±1.3
0.00
84.9±7.0
0.27
3.3±
0.05
19.1±1.9
0.00

108.7±2.4
391.4±163.2
0.3±0.0
1.4±0.2
0.0±0.0
2.2±0.1
583.9±163.3

33.2±3.0
45.4±0.3
0.5±0.1

Lepton Pt < 30 GeV

38
18.9±2.1
0.64
11.3±1.0
0.32
34.2±4.4
1.24
20.8±2.2
0.72
8.1±1.2
0.18

MC1,MN2 = 125; MN1 = 100[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 125; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )

16.6±2.0
0.95
9.9±0.9
0.51
29.8±4.0
1.72
19.6±2.1
1.13
7.3±1.1
0.34

6.5±1.3
2.5±0.1
0.2±0.1
28.4±1.2
0.1±0.1
0.1±0.0
0.1±0.1
0.1±0.0
0.0±0.0
0.4±0.0
38.5±1.8

b-veto

Table 7.2: Baseline cutflow before the analysis splits into SRa and SRb (b)

26.7±2.7
2.8±0.1
0.3±0.1
32.3±1.3
0.1±0.1
0.1±0.0
1.0±0.2
0.5±0.1
0.0±0.0
0.7±0.1
64.6±3.0

Etmiss > 50GeV

ttbar
WW
ZZ
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

Sample

The final event selections are able to exclude four signal regions in total. For the two selections,
SRa and SRb, the following signal regions were excluded:
Mass of χ
˜01 [GeV]

Mass of χ
˜±
˜02 [GeV]
1 /χ

Event Selection

Significance

75
75
87.5
100

100
125
100
125

SRa, SRb
SRb
SRa
SRb

1.79, 2.66
2.12
1.67
1.69

Table 7.3: List of excluded signal regions, the event selection that excludes them, and their significance.

The Cutflows for SRa and SRb can be found in tables 7.5 and 7.6 respectively.

7.2

SRa Result

At the end of the cutflow there are only 0.5±0.1 background events remaining. The final significances
of the signal regions are in table 7.4. This cutflow is able to exclude two of the five points, and almost
a third. SRa successfully excludes two regions where mχ
˜±
1 =100 GeV raises the significance of some
adjacent points to reasonable levels.
Figure 7.1 shows how all the surrounding signal regions are affected by SRa.
Mass of χ
˜01 [GeV]

˜02 [GeV]
Mass of χ
˜±
1 /χ

ZN

75
75
87.5
100
125

100
125
100
125
150

1.79
0.91
1.67
1.53
0.91

Table 7.4: List of signal regions and their significances after the SRa cutflow. T of the target regions have been excluded.

39

Figure 7.1: 2D significance plot showing ZN for all available W Z mediated SUSY signal regions, at the end of SRa.

Sample

Baseline

5 <mSFOS<25

MET>130

∆ΦJet/MET> 2.8η

ttbar
WW
ZZ
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

6.5±1.3
2.5±0.1
0.2±0.1
28.4±1.2
0.1±0.1
0.1±0.0
0.1±0.1
0.1±0.0
0.0±0.0
0.4±0.0
38.5±1.8

1.6±0.6
1.5±0.1
0.1±0.0
16.8±0.9
0.0±0.0
0.0±0.0
0.1±0.1
0.0±0.0
0.0±0.0
0.1±0.0
20.2±1.1

0.4±0.3
0.0±0.0
0.0±0.0
0.6±0.2
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
1.1±0.4

0.0±0.0
0.0±0.0
0.0±0.0
0.5±0.1
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.5±0.1

MC1,MN2 = 125; MN1 = 100[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 125; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )

16.6±2.0
0.95
9.9±0.9
0.51
29.8±4.0
1.72
19.6±2.1
1.13
7.3±1.1
0.47

14.0±1.8
1.40
9.1±0.9
0.89
25.6±3.7
2.47
5.5±1.1
0.48
6.2±1.0
0.57

1.8±0.6
1.12
1.6±0.4
0.94
3.3±1.2
1.99
.1±0.5
0.62
2.2±0.6
1.35

1.8±0.6
1.53
1.4±0.3
1.11
2.2±1.1
1.79
1.1±0.5
0.91
2.0±0.6
1.67

Table 7.5: Final Cutflow for SRa. The baseline marks all the cuts up to the b-veto from section 6.6 The target point is
successfully excluded alongside another.

40

Sample

Baseline

15 GeV<mSFOS<45 GeV

ttbar
WW
ZZ 0.2
WZ
Z+Jets
triboson
ttbar+Boson
t+Boson
W+Jets
Higgs
Total Background

6.5±1.3
2.5±0.1
0.1±0.1
28.4±1.2
0.1±0.1
0.1±0.0
0.1±0.1
0.1±0.0
0.0±0.0
0.4±0.0
38.5±1.8

3.0±0.8
1.1±0.0
0.1±
8.8±0.7
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.0±0.0
0.2±0.0
13.4±1.0

MC1,MN2 = 125; MN1 = 100[GeV]
Zn (30% ∆SM )
MC1,MN2 = 150; MN1 = 125[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 125; MN1 = 75[GeV]
Zn (30% ∆SM )
MC1,MN2 = 100; MN1 = 87.5[GeV]
Zn (30% ∆SM )

16.6±2.0
0.95
9.9±0.9
0.51
29.8±4.0
1.72
19.6±2.1
1.13
7.3±1.1
0.47

12.3±1.7
1.69
7.1±0.8
0.97
20.2±3.3
2.66
15.6±1.9
2.12
1.1±0.5
0.00

Table 7.6: Final Cutflow for SRb. The baseline marks all the cuts up to the b-veto from section 6.6. The targeted point
is successfully excluded with two others.

7.3

SRb Results

SRb removes less background than SRa, with 13.4±1.0 events remaining. The final significances of
the selected signals are in table 7.7. The cutflow described above is able to successfully exclude the
target point with two more.
Mass of χ
˜01 [GeV]

Mass of χ
˜±
˜02 [GeV]
1 /χ

ZN

75
75
87.5
100
125

100
125
100
125
150

2.66
2.12
0.00
1.69
0.97

Table 7.7: List of signal regions and their significances after the SRb cutflow. The targeted point is successfully excluded
with two others.

Figure 7.2 shows how all the surrounding signal regions are affected by SRb. Many of the regions
around the point (100, 75) return reasonable significances, however it fails to reach non zero values
for all the signal regions with ∆m=12.5 GeV, nearest the diagonal.

41

Figure 7.2: 2D significance plot, showing ZN for all available W Z mediated SUSY signal regions for SRb.

8

Discussion

The signal region SRa (SRb) is able to exclude its target regions plus one (two) other(s). Ideally the
event selections would exclude a wide area surrounding the target point and the outcome would state
that points up to a certain mass range were successfully excluded. However, due to the widely varying
statistics between each signal region this is not the case. This would occur if nearby points exhibited
a similar signal shape or a similar number of events. To an extent they do, but an adjacent point may
differ wildly on both these counts. This is the case with the points (100, 75) and (100, 87.5), which
are adjacent, yet have 7881.53 and 2454.9 events respectively. When reducing the background to such
low levels and making cuts for small increases in significance, the statistical nature of the events mean
that the event selection may have a completely different effect when transferred to real data than on
MC simulations. The cuts are chosen on data with random statistical fluctuations, and will not act
identically on another similar sample. Many of the signals also have high proportional errors, some
almost 50%, and although the significance algorithm takes these uncertainties into account, it is the
results on events like these that will likely not replicate with real data. With more time, the signals
could be normalised to 300fb−1 integrated luminosity in order to boost the weaker signals. Although
the SM background would also increase, since the ZN algorithm is not linear this should still give
better results, and potentially exclude more regions. This is especially relevant to the regions where
∆m=12.5 GeV, near the diagonal, as these regions have very few events and cannot be excluded
because of it; a re-normalisation could solve this problem.
The selection SRa manages to exclude two points, both with mχ
˜±
1 =100 GeV. These points are at
the edge of the range of data that the analysis has access to, and none of the signal regions have
mχ
˜±
1 <100 GeV data. There is therefore no way of determining what effect the signal region has
on lower mass regions. The mass of the LSP is estimated to be on the order of 100 GeV, but signal
regions with even lower masses would be useful to the analysis to build a better picture of the cuts’
effects.

42

The selection SRb only adds a single cut to the baseline and still retains a relatively large number of events, it can therefore likely be developed on, as another baseline for different points. Figure
7.2 suggests the points (112.5, 50) and (150, 100) are close to exclusion, and with one or two more
cuts perhaps could be so. Although excluding more points is beneficial, it detracts from the aim of
this project, which is looking to specifically exclude points near the diagonal, and these points are at
the upper end of that region.
Attempts were made at producing a third event selection, SRc, in order to exclude the point (150,
125) but, due to its comparatively small size (∼50% of the next largest point (100, 87.5)) it was not
possible. The highest significance it reaches is in SRa with ZN =1.11. This is a confidence interval of
73%, which is reasonable, however it is not excluded. Given more time I would develop a drastically
different event selection with a different baseline, which could also focus on an different set of points,
in order to exclude more regions. The chance of success, given the current statistics, is unknown,
and it may be that no event selection can exclude these points, however once having increased the
integrated luminosity this line of analysis becomes more viable.

9

Conclusion and Outlook

This project’s analysis uses Monte Carlo simulated data based on 20.3fb−1 integrated luminosity
√
at s =8 TeV at the ATLAS detector. It aims to show that, given these statistics, compressed
signal regions where the masses of the lightest chargino and neutralino are similar, are possible to
exclude with a 90% confidence interval. The signals are mediated by gauge bosons, have initial state
radiation, no intermediate sleptons, and result in three lepton final states. Four signal regions close to
˜01 ,
the diagonal, where mχ
˜01 ≈ mχ
˜±
1 , are successfully excluded, with two event different selections, (mχ
±
0
˜2 )=(100, 75), (125, 75) (100, 87.5) (125, 100) where the masses are in GeV. Further signal
mχ
˜1 /mχ
regions, especially those at higher masses, near the diagonal, are not excludable at the given statistics,
due primarily to their low number of events. This analysis builds a foundation towards using data
√
from the LHC energy upgrade to s =14 TeV, where the cross sections of the aforementioned process
has an increased cross section. Given more more time I would like to perform the same analyses but
on MC data generated at the upgraded energies, and at an increase (300fb−1 ) integrated luminosity.
This would develop a greater understanding of what to expect with new data, and possibly exclude the
low event signals near the diagonal. I believe, due to the increased cross section at 14 TeV, the signals
would be better resolved against the background and more signal regions, specifically compressed
regions, would be excluded.

10

Acknowledgements

I would like to first thank my supervisor, Antonella De Santo, for her support throughout the project,
in giving me targets and a greater understanding of the wider subject area. I would also like to thank
the PhD students Zara Grout and Yusufu Shehu for guiding me through the (at first) complicated
framework, and for their advice.

43

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