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University of Sussex
Search for Direct Production of Charginos and Neutralinos
in 3-Lepton events with Initial State Radiation using theATLAS
experiment at the Large Hadron Collider
MPhys Final Year Project 20142015Candidate - 75846
7th May, 2015
Supervisor
Antonella De Santo
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Abstract
This project searches for the direct production of charginos and
neutralinos in final states in whichthree leptons, initial state
radiation, and missing transverse momentum are present. The
analysisuses Monte Carlo generated data simulating
s = 8 TeV proton-proton collisions at 20.3fb1 inte-
grated luminosity from the ATLAS detector at the Large Hadron
Collider. Analysis is performed oncompressed Supersymmetric
scenarios where the lightest chargino (1 ) is mass degenerate with
thenext-to-lightest neutralino (02). The masses of the lightest
chargino and lightest neutralino (
01) are
within 50 GeV. For the R-parity conserving simplified
Supersymmetric model, mediated by gaugebosons and no intermediate
sleptons, four specific signal regions are shown to be excludable
given theabove statistics. These are the regions where (m1 /m
02, m
01)=(100, 75), (125, 75) (100, 87.5) (125,
100), in GeV.
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Contents
1 Introduction 5
2 The Standard Model and Supersymmetry 52.1 The Standard Model .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 5
2.1.1 Standard Model Limitations . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 52.2 Supersymmetry . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 R-Parity . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 62.2.2 Minimal Supersymmetric
Extension to the Standard Model . . . . . . . . . . . 6
2.3 Solutions with the Minimal Supersymmetric Extension to the
Standard Model . . . . 72.3.1 Hierarchy Problem . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Dark Matter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 82.3.3 Grand Unified Theory . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 8
2.4 Monte Carlo Simulations . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 92.5 Simplified Models . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102.6 SUSY Scenarios . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 102.7 Initial State Radiation . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102.8 Motivation . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 11
3 CERN, the LHC, and ATLAS 113.1 CERN . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113.2 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 12
3.2.1 Accelerator Complex . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 123.3 ATLAS . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3.1 Pseudorapidity . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 133.3.2 Inner Detector . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3.3
Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 143.3.4 Hadron Calorimeter . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 143.3.5 Muon System . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
143.3.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 153.3.7 Trigger Level-1 . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.8
Trigger Level-2 . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 153.3.9 Event Filter . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 153.3.10 Missing
Transverse Energy Detection at ATLAS . . . . . . . . . . . . . . .
. . 163.3.11 b-Tagging . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 16
4 Analysis 164.1 Technical Framework . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 164.2 Pre-selection .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 174.3 Significance . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 174.4 Cuts . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 174.5 Irreducible vs Reducible Background . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 184.6 Important SM
Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 18
4.6.1 WZ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 184.6.2 Z+Jets . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.6.3 tt
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 19
5 Selected Signal Regions and Preliminary Event Selection 195.1
Initial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 205.2 Baseline . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
215.3 Increasing Significance . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 215.4 Other Explored Variables .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
215.5 Preliminary Event Selection Results . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 23
1
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6 Event Selection 276.1 3 Leptons . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.2 Same
Flavour, Opposite Sign Request . . . . . . . . . . . . . . . . . .
. . . . . . . . . 286.3 Jet Multiplicity - ISR Request . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 286.4 Leading
Lepton Momentum . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 286.5 Missing Transverse Momentum . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 296.6 b-Jet Veto . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 306.7 Excluding Different Signal Regions with Multiple
Cutflows . . . . . . . . . . . . . . . . 316.8 Signal Region SRa .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 31
6.8.1 Invariant Mass of SFOS Pair . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 316.8.2 Missing Transverse Momentum . . .
. . . . . . . . . . . . . . . . . . . . . . . . 326.8.3 Angle
Between Leading Jet and Missing Transverse Momentum . . . . . . . .
. 32
6.9 Signal Region SRb . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 346.9.1 Invariant Mass of SFOS
Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7 Results 367.1 Baseline . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 367.2 SRa Result .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 397.3 SRb Results . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 41
8 Discussion 42
9 Conclusion and Outlook 43
10 Acknowledgements 43
List of Figures
2.1 Quantum Loop Corrections to Higgs Mass . . . . . . . . . . .
. . . . . . . . . . . . . 82.2 Rotation Curve of a Galaxy . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Grand
Unified Scale . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 92.4 1
02 Decay via W and Z Bosons . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 10
2.5 Exclusion Contours for WZ Mediated Chargino and Neutralino
Production . . . . . . 112.6 p-p SUSY Cross Sections (8 TeV and 14
TeV) . . . . . . . . . . . . . . . . . . . . . 123.1 ATLAS Detector
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 133.2 ATLAS Detector . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 133.3 vs , Pseudorapidity
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 143.4 ATLAS detector rings . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 154.1 Significance vs Cut in
Jet momentum - Logarithmic . . . . . . . . . . . . . . . . . . .
184.2 Significance vs Cut in Jet momentum - Linear . . . . . . . .
. . . . . . . . . . . . . . . 194.3 Free Cut vs Standard . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4
tt Production and Decay . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 205.1 Distribution of Transverse Mass . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2 2D
Significance of SUSY Signal Regions After Preliminary Event
Selection . . . . . . . 236.1 Initial Lepton Multiplicity . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.2 MET
Distribution for 3 Lepton Cut . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 286.3 Leading Lepton Momentum Cut . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 296.4 Cut on Missing
Transverse Momentum (Baseline) . . . . . . . . . . . . . . . . . .
. . . 306.5 MET Distribution Before and After b-Veto . . . . . . .
. . . . . . . . . . . . . . . . . 316.6 Cut on Invariant Mass of
SFOS Pair (SRa) . . . . . . . . . . . . . . . . . . . . . . . .
326.7 Cut on Missing Transverse Momentum (SRa) . . . . . . . . . .
. . . . . . . . . . . . . 336.8 Cut on Jet and MET (SRa) . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 346.9 Invariant
Mass of SFOS pair (SRb) . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 356.10 Significance of a Cut on Invariant Mass of
SFOS Pair for (SRb) . . . . . . . . . . . . . 35
2
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7.1 2D Significance Plot for SRa . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 407.2 2D Significance Plot for SRb
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
List of Tables
2.1 Particle List of the MSSM . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 65.1 Initial Signal Regions For
Preliminary Event Selection . . . . . . . . . . . . . . . . . .
205.2 Initial Cuts for Preliminary Event Selection . . . . . . . .
. . . . . . . . . . . . . . . . 205.3 Baseline Cuts for Preliminary
Event Selection . . . . . . . . . . . . . . . . . . . . . . . 215.4
Significance Optimising Cuts for Preliminary Event Selection . . .
. . . . . . . . . . . 215.5 Selected Signals for Analysis . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.6
Preliminary Event Selection Cutflow (a) . . . . . . . . . . . . . .
. . . . . . . . . . . . 255.7 Preliminary Event Selection Cutflow
(b) . . . . . . . . . . . . . . . . . . . . . . . . . . 266.1
Cutflow Differences for SRa and SRb . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 317.1 Baseline Cutflow (a) . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.2
Baseline Cutflow (b) . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 387.3 Excluded Points . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397.4
Final Significance of SRa . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 397.5 SRa Final Cutflow . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407.6
SRb Final Cutflow . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 417.7 Final Significance of SRb . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3
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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 bymyself,
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 2through 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 andchoices, though with advice from my supervisor
Antonella De Santo and the PhD student YusufuShehu. The reasoning
and discussion in sections 8 and 9 are my own.
4
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1 Introduction
This project performs a theoretical search for the direct
production of Supersymmetric particles inthree lepton final states
with initial state radiation (ISR) present at the ATLAS detector.
The analysisis performed using proton-proton collision data from
Monte Carlo (MC) simulations at a centre-of-mass energy of
s = 8 TeV and 20.3fb1 integrated luminosity, by implementing a
series of cuts and
selections on the datasets. The aim is to produce an event
selection that removes enough backgroundevents that Supersymmetric
signal regions can be excluded. A signal region is defined by the
massesof the relevant Supersymmetric particles. If this analysis
shows that a MC generated signal regioncan 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 hasnt yet been one at ATLAS,Supersymmetry can
confidently not be found there. Therefore this analysis works to
show in whichregions Supersymmetry will not be found, given the
above statistics, and to show which regions canbe excluded with
real data. This event selection should be tailored depending on
which signaturesare to be explored, as they are in section 5. The
first section of the report outlines the backgroundtheory,
including the Standard Model, its limitations, and Supersymmetry.
Part 3 discusses CERNand the Large Hadron Collider (LHC), and goes
into detail surrounding the ATLAS detector, whilepart 4 explains
both how the analyses are performed, and some important topics to
consider. Parts5 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 theanalysis 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 thedescriptions of how they
interact with one another. It contains the information of how light
interactswith matter, and how stars evolve through their life
cycles. Important to the SM is the ability topredict the outcomes
of experiments. A good theory will have substantial predicting
power, but fewfree parameters. These are the parameters of the
model that are not held constant, and can bechanged to provide
meaningful insight. The Standard Model has 26 free parameters[3]
and is notconsidered complete. A perfect Theory of Everything
(TOE)[4], for example, would have no freeparameters, 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. Forexample, with the SM
alone the Higgs mass cannot be predicted, there is no explanation
for neutrinomasses or their oscillations, and there is no candidate
for dark matter. These limitations give a greatdeal of motivation
to search for new physics outside of the Standard Model, and one of
these avenuesis a Supersymmetric (SUSY) extension. The addition of
SUSY gives good predicting power and isable 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 aparticles spin by 1/2, thereby
changing a fermion to a boson and vice versa.
Q|fermion = |bosonQ|boson = |fermion
The corresponding particle from this transformation is called a
superpartner, or spartner, and isusually denoted with an s- prefix,
or -ino suffix, depending on whether the particle is a fermion
orboson respectively.
5
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e.gelectron selectron,gluon gluino.
They are given a tilde in notation, for example W , the wino, is
the superpartner to the W bo-son. The Standard Model has three main
symmetries, the unitary group U(1)Y , and the specialunitary groups
SU(2)L and SU(3)c. Each of these correspond to a fundamental force
of nature, andhave corresponding gauge bosons. The electroweak
gauge symmetry SU(2)L U(1)Y has the gaugebosons W+, W 0, W, and B0
associated with it. The corresponding sparticles are the W+, W 0,
W,and B0. These are the winos and binos respectively. After
electroweak symmetry breaking, W 0 andB0 gauge eigenstates mix to
form the photon, , and the Z0 bosons. The Supersymmetric versionsof
these, mixing the W 0 and B0, give the Zino, Z0, and photino, . A
list of the particles within theminimal Supersymmetric extension to
the Standard Model (MSSM) is in table 2.1.
Names Spin 0 Spin 1/2
Mass Sector
squarks, quarks (uL, dL) (uL, dL)
3 families uR, dR uR, dRsleptons, leptons lL lL3 families lR
lR
sneutrinos, neutrinos L L
Higgs Sector
Higgs, Higgsinos (H+u , H0u) (H
+u , H0u)
(H0d , Hd ) (H
0d , H
d )
Gauge sector Spin 1 Spin 1/2
gluons, gluinos g g
W bosons, Winos W, W 0 W, W 0
B bosons, Binos B0 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(BL)+2S , (1)
where B is the baryon number, L the lepton number, and S is the
particles spin. R-parity is+1 for the SM, -1 for SUSY particles,
and is multiplicative. The implications of this parity are thatthe
lightest Supersymmetric particle (LSP) is going to be stable, and
that when SUSY particles arethe result of a decay they must be
produced in pairs. R-parity conservation is suggested by
protonstability. If baryon and lepton numbers are not conserved, as
can happen in many grand unifyingtheories (GUT), then, considering
the first order couplings of R-parity violating couplings, the
protoncould decay in approximately 102s. Since this is not the case
and the proton lifetime, if it doesdecay, 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. Itis minimal as it only includes the
minimal number of particles and interactions that are is
consistentwith current phenomenology. Included are corresponding
sparticles for each particle in the SM, and
6
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two Higgs doublets. Table 2.1 gives the Standard Model and the
corresponding sparticles, howeverthere are more that are relevant
to this analysis. Each of the sleptons and gauginos, apart fromthe
gluino, can mix, resulting in mass eigenstates different to table
2.1. The neutral higgsino andgauginos (H0, W 0, B0) mix to form the
neutralinos 01,2,3,4, and the charged higgsinos and winos
(H, W) from the charginos 1,2. The subscript number denotes the
mass hierarchy, so 01 is the
lightest neutralino, and 02 the second-to-lightest. The lightest
neutralino is expected to have a massof 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 energyrange.
2.3 Solutions with the Minimal Supersymmetric Extension to the
Standard Model
2.3.1 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.
Whenparticles interact they can have a number of quantum loop
corrections to the interaction, see figure2.1a. These can occur
because for a short amount of time, virtual particles can
spontaneously beproduced before annihilating. The time frames and
energies of these particles exist within the limitsof the
Heisenberg Uncertainty Principle, and can happen under quantum
fluctuations. These loopsare higher order interactions, and usually
have a asymptotic affect on interactions, and after one ortwo extra
orders, are negligible. However, with the Higgs interactions, this
is not the case. Particlescouple to the Higgs field via the Yukawa
term, f , with the Lagrangian interaction term
LY ukawa = f H, (2)
where is the Dirac field, and H the Higgs field. The Yukawa
term, and therefore the couplingstrength, is proportional to the
particles mass, so the Higgs will couple strongest to the most
massiveparticle, which is the t quark.
Quantum mass corrections to the Higgs mass squared are given
by
m2H = |f |28pi2
[2UV + . . . ]. (3)
The term 2UV 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 divergingLagrangian, which
results in an infinite correction to the Higgs mass. A solution to
this is offered bySUSY. According to spin statistics theorem[9],
the loop corrections due to fermions is negative, andbosons
positive. Therefore if there is a bosonic superpartner for each
fermion and vice versa, everyterm will cancel, and there will be no
correction to the Higgs mass. The calculation using SUSYcorresponds
with the experimentally confirmed Higgs mass of mH = 125 GeV, and
is further evidencein support of Supersymmetry.
7
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(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) dueto 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.
Whenastronomers plotted the rotational velocities of galaxies, they
found that the rotations were muchfaster 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 representsthe rotational velocities
expected due to the visible matter, but the data shows that this is
not thecase. There is more mass present causing the rotational
velocities to remain relatively constant as afunction 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 moremass 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 notinteract with photons or by
electromagnetism, otherwise it would be seen. There are a few
candi-dates 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 detectionof dark matter from
LUX and similar poor results from the LHC to find SUSY, some doubt
has beencast on its existence.
2.3.3 Grand Unified Theory
A Grand Unified Theory (GUT) is a theory postulating that, above
a certain energy, GUT , believedto be the Planck scale, the three
fundamental forces, electromagnetic, weak, and strong, become
equalin strength and merge into a single, unified force. By merging
gravity also, this would become a theory
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of everything (TOE); a GUT is considered a good first step to
this. If the Standard Model alone isused, at GUT , the three forces
almost meet, though they miss by a small amount. With the
additionof the MSSM, they do, and unify conveniently at the Planck
scale. Figure 2.3 shows how the forcesnearly 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 thethree colours
of quarks and gluons, SU(2) the weak interaction and the up and
down doublet of leptons and quarks, andU(1) the single photon and
electromagnetism. The green shows how the forces nearly meet with
the SM, and the orangeshows the unification with the MSSM. The
yellow line at 1TeV represents a kink in the lines, where the lines
will nowmeet at 1016GeV, or the Planck scale, as expected. This is
further evidence for SUSY as this is the energy scale it isexpected
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 ofthis project, MC generators
have been used to generate SM processes and SUSY signals instead
ofusing real data from ATLAS. This is favourable over real data at
this point because each signal canbe attributed to a certain
process, which makes cuts and selections on the data much more
compre-hensive, because it explicitly shows how each process is
affected. The signals have been generated tobehave exactly as they
would in the detector, including all the specifications and errors
that comewith it. It is generated to be as similar to ATLAS
collision data as possible. The following processesare used in the
analysis:[ZZ,WW,WZ], diboson (V V ),[WWW,ZWW,ZZZ], triboson (V V V
),ttVsingle ttVZ+JetsW+JetsHiggsSUSY Signals
Each of these signals represent data from specific products in
p-p collisions. If a ZZ pair is pro-duced, all the possible decays
and their final states can be described with the signals generated
bythat MC generator. A number of different MC generators are used,
as some generators are bet-ter at producing different signals, for
example the SUSY signals are produced with the Herwig++
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generator, and tt with the Powheg+Pythia generator.
2.5 Simplified Models
Multiple simplified Supersymmetric model (simplified models) are
used, which impose physical con-straints, such as a conservation of
R-parity or a mass hierarchy on certain sparticles. The MSSMhas
105+19 free parameters, and in order to perform any analyses, some
of these parameters mustbe constrained. Simplified models will set
the masses of experimentally relevant particles to certainvalues,
and set the masses of irrelevant particles to either infinity, high
enough that they could notbe produced in collisions at a given
energy. In this model, R-parity is conserved, and the
lightestchargino, 1 , is set to be mass degenerate with the
second-to-lightest neutralino,
02. Their actual
masses are dependent on the signal region. Sleptons and
sneutrinos are heavy, and the lightestneutralino, 01, will have a
mass similar to the mass degenerate chargino/neutralino pairs. This
massdifference 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 analysispossible, these cross
sections and branching ratios are set. The scenarios used involve
SUSY decaysvia mediating W and Z bosons to three leptons, with no
intermediate sleptons or sneutrinos, as theyare sufficiently heavy.
The feynman diagram for this process is described in figure 2.4. In
this scenariothe branching ratio to this process is 100%. The only
possible decays are
02 Z + 01,and
1 W + 01.The scenarios explored are those when 01 1 . When these
masses are similar, the scenarios are saidto be compressed. Now
only the masses and decay modes of (01,
02) are the remaining free parameters.
The 02 and 1 are assumed to be entirely of the wino component,
while the
01 is entirely of the bino
component, which affects the branching ratios of possible
decays. This is motivated by unsuccessfullab searches for
sparticles at LEP[6].
Figure 2.4: Decay of 1 02 via W and Z bosons. From [7]
2.7 Initial State Radiation
If an initial (pre-collision) state is energetic enough, it can
produce a virtual gluon which will thenscatter inside the detector.
After scattering it will form more gluons quark-antiquark pairs,
which willin turn form more. This chain reaction of coloured
particle production is called hadronisation, and
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will appear in the detector as a burst of energy in an effective
cone from the initial gluon. This showerof 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 ofthe pair produced
chargino/neutralino pair. With little kinetic energy, their decay
products will havea similar mass to their progenitors. The
selection of events with ISR chooses events where the massof 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 sectionat 8 TeV at the LHC. Three
leptons are chosen because they represent a large portion of the
possiblefinal states of the sparticles, and tri-lepton events have
little SM background. This project exploresthe scenarios where the
mass of the LSP, 01, is similar to that of the lightest
chargino,
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 01 =
1 /
02 have not yet been excluded,
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, WZ-mediated[7].The yellow band
is the 1 variation of the expected limit, and the red dotted line
is the 1 variations of theoreticallimits. These uncertainties
include all uncertainties except theoretical uncertainties on the
signal cross-section. The bluelines are from the 7TeV limit from
ATLAS three-lepton analysis. From [13].
1 , 02 has the largest cross section that results in three
leptons, figure 2.6a, so this project focusses
is on these scenarios. 2.6b shows that, once the LHC increases
its energy to 14 TeV, the cross sectionwill go up considerably,
whilst still remaining the largest relative cross section at these
masses. Thissupports this line of analysis to continue, and
increases the likelihood of obtaining better results oncethe LHC
energy upgrade has commenced.
3 CERN, the LHC, and ATLAS
3.1 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 aroundnuclear
research and specifically on the use of large particle accelerators
for high energy physics (HEP)
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(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 meettowards common goals.
Because of the accelerators on site a large number of HEP
experiments havebeen performed at CERN. It is home to a collection
of accelerators, notably the linear acceleratorsLinac2 and Linac3,
and formerly LEP[15], the Large Electron-Positron collider. CERN is
also hometo the Large Hadron Collider[16].
3.2 The LHC
The Large Hadron Collider is currently the worlds largest
scientific experimental facility, and theworlds largest particle
collider. It went live briefly in 2008 then again in 2009 and has
subsequentlyrun tests at 3.5 TeV (2010,11) and 4 TeV (2012). It is
currently upgrading its energy to 6.5TeV andhas already begun
circulating the beams in the former beam tunnel for LEP. The
collider sits in a27km circumference tunnel up to 175 meters below
the ground. The LHC is designed for proton-proton collisions, but
can also accelerate lead (Pb) nuclei, and it contains two beam
pipes that meetat four different locations.
3.2.1 Accelerator Complex
The beam reaches its target energy by a series of accelerators
in the accelerator complex[17]. Theproton 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 injectsthem into the Proton
Synchrotron Booster (PSB), which accelerates them to 1.4 GeV. The
ProtonSynchrotron (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,
andLHCb. In order to accelerate Pb nuclei the lead is vapourised
and fed from Linac3, to the LowEnergy Ion Ring (LEIR) before
following the same route as the protons. The LHC has a
designluminosity of 32cm2s1.
3.3 ATLAS
ATLAS [19] is a multi-purpose detector built at CERN coaxially
along the main beam pipe. It isone of a number of experiments and
detectors there, including CMS, ALICE, and LHCb. It is builtwith
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
asix substage detection system.
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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 beamaxis. It is defined as
ln[tan
(
2
)], (4)
where is the angle between the particles three momentum compared
to the positive direction of thebeam axis. In order to visually
understand how relates to the angle, see figure 3.3.
Pseudorapidityis preferred over the angle for particle physics
because particle production is constant as a functionof , and not
of . Differences is pseudorapidity are also Lorentz invariant, and
so a measurement of 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, asemiconductor tracker, and a
semiconductor radiation detector. It is surrounded by a 2T axial
solenoidand has a detective pseudorapidity of ||
-
Figure 3.3: A graph representing the connection between and .
From [21]
per track. The SCT contributes to the measurements of the
particles momentum, impact parameterand 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
radiationphotons created by particles between them.
3.3.3 Electromagnetic Calorimeter
The second stage consists of a high-granularity
lead/liquid-Argon (LAr) calorimeter for measuringthe energy and
position of electromagnetic showers, caused by electrons or
photons, within || < 3.2.Similar LAr calorimeters detect
hadronic showers in the front and end caps in the (3.1 < ||
-
detector contains a barrel region coaxial to the beam pipe, and
two end caps. Within the barrel regionthe tracks are measured in
three cylindrical layers. In the cap regions, the chambers are
planal andperpendicular 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 hadroniccalorimeter, and
the muon system. The green lines represent the tracks made in the
ID by charged particles. Theblue line is a detected muon. There are
energy deposits in the EM and hadronic calorimeters and the red
dotted linerepresents 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 32cm2s1 is
around 1GHz[19] (events/s).The data recording is limited to around
200Hz (events/s) due to current technologies and
storagecapabilities. This means there is a rejection factor of 5
106. The LHC uses a three levelled triggerand filter in order to
make sure as much relevant data is being kept as possible while
reaching therequired 200Hz rate. The level-1 (L1) trigger cuts down
the data to around 75kHz, whilst the finaltwo, 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 and
-leptons withhigh transverse-momentum decaying into hadrons,
alongside large EmissT and
EtotalT . The triggers
makes these decisions based on information from the muon
spectrometer and calorimeters. The L1trigger is able to define
Regions-of-Interest (RoIs), 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 isdesigned to reduce the data
rate to around 3.5kHz. A hypothesis algorithm determines whether
thefeatures defined meet the criteria of triggering, like an ET
threshold or shower shape. If an eventpasses the L2 trigger, the
event fragments from all RoIs combined are sent to the event
builder, andthen 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 ATLASsoine event reconstruction[24]. It
is designed to reject events after 1s in order to restrict its
eventoutput. The EF reduces the data rate to the required
200Hz.
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3.3.10 Missing Transverse Energy Detection at ATLAS
Missing transverse momentum is very important in understanding a
collision, as not all particles willbe detected by ATLAS. There is
no way of directly measuring MET, as the total transverse
momentumisnt known, but it can be calculated by understanding the
momentum imbalance. Because momentumis conserved, and the
transverse momentum can be considered zero at the time of the
collision, if thetotal vector sum of the detected momentum is not
zero, some must be missing. MET is thereforecalculated as the
negative of the vector sum of the detected transverse momentum.
EmissT = Ni
~pT i (5)
The detected transverse momentum is only counted if ATLAS
reconstructs it to originate from theprimary vertex, or if the the
impact parameter d0, is within a small enough range. MET will
bedetected when particles like neutrinos or the LSP are present in
a process. These particles will notreact 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 hadroniccalorimeters, some MET
may arise because of them. The detector may also have some hot or
deadzones within the calorimeters which over or understate the
amount of momentum in an area. Thiscan 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 smalldistance from the primary
vertex, because of its non-negligible lifetime. This decay will
result inhadronisation and a jet, detected in the hadronic
calorimeter. The small distance, the impact param-eter, that the b
decays from the primary vertex can be detected by ATLAS, which will
then markthe resultant jet as having derived from a b-quark. This
is called b-tagging. The process behindb-tagging is not perfect
however, and many b-jets can be overlooked, as well as many normal
jetsbeing mis-tagged as having derived from b-quarks.
4 Analysis
4.1 Technical Framework
The ATLAS framework contains a large repository of libraries and
codes in order to perform the tasksrequired for the analysis, from
plotting, tabulating, or selecting datasets. The framework resides
inthe file repositories of the Feynman HPC cluster at the
university, and this cluster performs allthe computational tasks.
The Monte Carlo simulation data is stored as ROOT[25] NTuples,
eachcontaining information regarding each events final states, for
example the momenta, energies anddirections of particles. These
pieces of information can be tabulated or plotted in order to get
arepresentation of how the distributions of these variables look
for the data. There is one NTuple foreach process, e.g ZZ 4e and a
script can take each of these background processes and combinethem
into a single NTuple, for example ZZ, or Z+Jets. The framework was
copied from anotherusers file repositories and was relevant to
their analyses. Although this was sufficient for some ofthe initial
analysis, many extensive edits had to be made, and in order to do
them, a capability inC++, ROOT, and Python was required, as these
are what the framework is based upon. In order tomake 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 beexplored to
gain further insight into the project. The plots seen in this
report are created using ascript already used within the ATLAS
framework. It stacks the histograms of each of the backgroundsand
superimposes the SUSY signals. The significance plots are created
with an algorithm sent to meby Yusufu Shehu.
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4.2 Pre-selection
Each event must first pass the pre-selection defined by the
ATLAS framework, which selects eventsbased on their quality and on
trigger requirements. This occurs on each of the datasets before
anyanalysis 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 fluctuationcould not cause the
seen effects. Significance is the confidence that an effect is not
due to one of theserandom fluctuations. A higher significance
across as many signal regions as possible is what eachcut or
selection tries to achieve, up to the point of exclusion, which is
after a significance of =1.64. After exclusion it is within reason
to believe that the signal points are not due to any
statisticalfluctuations, and the data can be described by new
physics. A discovery in particle physics requires5, which is a 1 in
3.5 million chance of a statistical anomaly, a standard set
purposefully very highby organisations such as CERN. A significance
of 1.64 corresponds to a 90% confidence interval, a1 in 10 chance
of the results being randomly caused. Significance can be simply
formulated as thestrength of the signal over the square root of the
background.
=Signal
Background. (6)
This form works generally, but it has some limitations. Firstly,
it does not take into account anystatistical fluctuations that the
background or signal may have, and, when the background
approacheszero, it becomes unnaturally large, which is problematic.
Instead, ZN is used. This takes into accountmore of the statistical
nature of the signals and background and is able to return a far
more accuratevalue. The algorithm plotting significance within the
framework uses
ZN = 1(1 p0(S,B,B)), (7)
where 1 is the cumulative distribution of the standard Gaussian
and S and B are the numberof events for signal and background. B is
the systematic uncertainty of the background signal, andfor this
analysis it is 30%. This uncertainty comes from the fact that a
Monte Carlo simulation willnot be able to replicate real data
perfectly, and this formula accounts for this. p0 is the p-value,
whichis the probability that the data is more signal-like than
signal and background together. In order todeal with infinities and
negatives, the algorithm will set all negative values to zero, and
will truncateZN at 8. The ZN algorithm returns plots for each
explored variable, and how the significance wouldchange given a
certain cut location. Figure 4.1 shows how significance depends
where a left-handedcut is made for five different signals.
Figure 4.1 is how the framework originally displayed
significance plots. I found that, because thesignificance only
ranges between around 0 and 3, a logarithmic y-axis is unnecessary,
and much betterresolution 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 thedatasets, which chooses to
keep or remove all events above or below a certain threshold. A cut
canbe made on any measurable variable from the NTuples, for example
missing transverse momentumor jet multiplicity. The cuts are chosen
in order to isolate data specific to our analysis and to removeas
much of the background as possible. The Monte Carlo simulations
will show how each cut affectseach background signal type
individually, which is impossible using real data. Because of the
differentnature of the SUSY signals and their decays compared to
the SM background, the cuts will havedifferent effects on each
distribution. For example, processes with SUSY in their final
states willhave high missing transverse momentum so a cut, removing
all events with low MET, will removebackground whilst keeping the
bulk of the SUSY signal. There are two types of cut, left-handed
or
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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 theinvariant mass
of three leptons, and each of the different coloured lines
represents a different signal region. This plotis from data that
has already been cut a number of times previously. The best cut
would be one which maximises thesignificance 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
madewithout affecting the SUSY signal at all. These are dubbed free
cuts and are very useful because ofhow 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 binnedvariable. Events with low MET may, for example,
have high jet momenta. A cut removing the lowMET events will
therefore mean the remainder all have lower jet momenta. Each cut
will have adifferent effect depending on which point in the
analysis it is made. For this reason it is important tocheck each
variables distributions at each point. The aim of these cuts is to
increase the significanceof the signal. This gives a set of
criteria. They should make a cut relevant to the analysis,
significantlyreduce 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 comparedto the signal. Reducible
backgrounds end in final states with at least one fake lepton, and
can be easilyexcluded from the data with a few cuts. For example,
almost all (183,476,7466) of the W+Jetsevents are removed by asking
for exactly three Leptons. The remaining six events will be due
tomisidentified fake leptons. Irreducible backgrounds are more
troublesome, and are when a processhas three genuine leptons in the
final state. Dealing with this background is the real challenge of
thisproject.
WZ/, triboson (V V V ) and tt + V/V V are the main irreducible
backgrounds for this analysis, asthey can all end in three leptons,
while tt, tV , Z+jets and WW are the main reducible
backgrounds.
4.6 Important SM Backgrounds
4.6.1 WZ
Because the SUSY signal has a 100% branching ratio to be
mediated with WZ bosons, the biggestirreducible background will be
the WZ processes. A differentiator between the WZ and SUSY
finalstates is the larger EmissT due to the undetected neutralinos.
The WZ signals are produced by thePowheg+Pythia8 MC generators.
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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 withoutaffecting the SUSY
signal. On the right, there is no obvious place to cut, and a
compromise will have to be made, orthis 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 thirdfake lepton in the jets. These
jets will have a low MET compared to the SUSY signals, and a
fairlylow MET cut will deal with this background. Z+jet signals are
produced by the Alpgen+PythiaGenerators.
4.6.3 tt
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
shouldremove 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 anevent selection. It is
important to tailor this event selection to exclude specific
regions, as one selectioncannot exclude every point. Not all
regions can be excluded at all with the current level of
statistics,
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-
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, sixwere chosen,
representing the regions where m1 m01. These were chosen to have a
wide range ofmasses along the diagonal so as to represent as many
signal regions as possible. These initial pointsare stated in table
5.1. A preliminary event selection is designed that endeavours to
obtain the highestsignificance for the six regions. The following
section will lightly explain the reasoning behind eachof the
preliminary cuts, the sequence of which is called a cutflow.
However, most of the detail will becovered in section 6, as that
represents a more full analysis.
m1 m01
100 75100 87.5
150 125150 137.5
200 175200 187.5
Table 5.1: The initial signal regions chosen for the preliminary
event selection. These points best represent a wide massrange along
the diagonal m1 m01.
5.1 Initial Cuts
The following cuts represent the basis of the analysis. This
project focusses on events with threeleptons and with ISR, so the
first cuts ask for three leptons, and at least one jet. A request
is alsomade for a SFOS pair. SFOS means Same Flavour, Opposite
Sign, and refers to pair produced lightleptons like e+, e or +, .
Light in this contexts means non -leptons. This request is required
fora cut later on, and since a SFOS pair will be produced by the Z
boson in the WZ mediated SUSYdecays, this will not affect the
signals strongly.
Initial Cuts
3 Leptonshas a SFOS pair
1 Jet
Table 5.2: The initial cuts for the preliminary event selection.
These reflect the basis of the analysis.
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5.2 Baseline
The baseline is a series of cuts selected to reduce a large
quantity of background, and remove some ofthe specific signals.
Cuts are made on the leading lepton momentum, the MET, and whether
or not ab-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
theSUSY final states, events with b-jets were also removed with a b
veto. The b veto is specifically toremove tt events. These cuts are
able to remove most of the background signals, but the majorityof
the remaining background is from the WZ processes, as their final
states are very similar to theSUSY signals.
Baseline Cuts
1st Lepton Momentum < 40 GeVMET > 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 thesignificance for as many of the
signal regions as possible. The aim of this preliminary cutflow is
tosee which signal regions are viable to exclude, but not
necessarily to exclude any. Cuts are madeon 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 themissing energy, and another cut
on the MET. Each of these aims to increase the significance of
eachof the selected signal regions. These cuts were chosen by
finding the variables in which the largestdifference in
distribution between signal and background could be found, then
specifically optimisingfor significance each time.
Optimisation Cuts
Invariant Mass of SFOS pair < 20 GeV1st Jet Momentum > 110
GeV
between 1st Jet and MET > 2.9MET > 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
theselected 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 howthey affected the signal
distributions. Before this selection was established, the angles
between thetwo SFOS leptons, the momenta of the 2nd and 3rd leptons
and jets, and the transverse mass were allconsidered. The angles ()
between many of the variables were usually very uniform for both
signaland background and did not favour any direction, so did not
offer any places to cut, as shown in figure4.3 earlier. 5 GeV
slices were taken of mSFOS between 0 GeV and 30 GeV and
investigated. I wantedto know how the distributions of other
variables depended on mSFOS. Some of the regions, especiallylow
energy, had high proportions of diboson events and offered insight
into how small differencesin cuts would affect different signals
but, unfortunately, no particular method of reducing the
WZbackground. The aim of using the transverse mass, mT , was to try
and veto events with an on-shellW boson, in an attempt to reduce
the prominent WZ background. The transverse mass is calculated
21
-
using the EmissT and the lepton that is not part of the SFOS
pair, as this lepton would have originatedfrom the W decay. It has
the form
mT =
2plTEmissT 2~p lT ~p missl , [7] (8)
where plT is the lepton momentum, and ~pmissT 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 thereforedid 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, butis 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 excludeanother. A 2D significance plot
shows how the preliminary event selection affected a wider range
ofsignal 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 torepresent
which of the SUSY signals are likely to be excludable.
Mass of 01 [GeV] Mass of 1 /
02 [GeV]
75 10075 125
87.5 100100 125125 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 theanalysis are in table 5.5. It is
important to note that these are not the only signal regions that
canbe 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
isalso worth noting that some of the signal regions may however,
not be possible to exclude at all withthe current statistics and
centre of mass energy, which unfortunately can not be avoided. The
finalcutflows for the preliminary event selection can be found in
tables 5.6 and 5.7. The cutflow showsthe affect that each cut has
on each signal, and the significance as a result. Parts of the
cutflowdenoted by 0.0 do not necessarily mean zero events or
significance. Those points are considered zeroin accordance with
the precision, which was one decimal place for the preliminary
work, and increasedto two for the final analysis.
24
-
Sam
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Table
5.6
:P
relim
inary
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ion,
resu
ltin
gin
the
excl
usi
on
of
two
poin
ts.
This
even
tse
lect
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isuse
dto
choose
whic
hsi
gnals
touse
inth
efu
llanaly
sis.a
25
-
Sam
ple
b-v
eto
mS
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Table
5.7
:P
relim
inary
even
tse
lect
ion,
resu
ltin
gin
the
excl
usi
on
of
two
poin
ts.
This
even
tse
lect
ion
isuse
dto
choose
whic
hsi
gnals
touse
inth
efu
llanaly
sis.(b)
26
-
6 Event Selection
The final event selection is designed with the five specifically
chosen signal regions in mind, insteadof 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 verysimilar. During the
analysis it became clear that some of the points can not be
excluded at thesame time as each other. Although high significances
can be reached for many of the points at thesame 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 SRaand SRb. The two
event selections share a common baseline before they take different
paths. Thefollowing section outlines the sequence of cuts; each one
is made in succession and the plots representdata 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 largeamount 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 difficultyresolving high
multiplicities of leptons from a single event, and because of the
harsh triggering it hason leptons, many of the SUSY events are
incorrectly recorded as having less than three. Because ofthis,
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) isthe
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 invariantmass, and therefore an
indication of which process they originate from. Although it does
not greatlyreduce the background, this cut is necessary, as some of
the cuts later ask for a limit on the invariantmass of the SFOS
pair. This requires that all the data have a pair of which can be
cut. Plots havenot 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 SUSYprocess (see the feynman
diagram in figure 2.4) does not result in any jets in the final
state, anyremaining events after this will have at least one jet,
due to ISR. This cut acts mainly as a selectionon the SUSY signals
for the analysis, and not specifically to reduce background. Just
like the SUSYsignals, 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. Thesame follows for their decay
products, and the three leptons. These SUSY events have soft
leptonsmeaning they do not have much energy, whereas background
events will have a wider distribution inthe lepton momentum. An
upper-cut can be made, removing all events in which the leading
leptonsmomentum 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
positionwould 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-handedcut
location (meaning cutting all events above a certain limit). A cut
at 30 GeV increases the significance to a non zerovalues 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 beinferred by the MET. If the LSP
is present, the events will show significant MET, more than for
mostSM processes. A preliminary cut is made, removing all events
with < 50 GeV, figure 6.4. This cutis not with the intent to
directly increase significance, although it does, it is done to
remove eventswith 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 WZ mediated SUSY process, there is no b-quark production,
and because of ATLAS capabil-ities regarding b-tagging, a request
can be made to remove any events which contain b-jets. This is
ab-veto, and is useful in removing the tt background, as those
events will almost always result in oneor more b-jets. This
successfully removes 75% of the tt background, while leaving the
SUSY signalsrelatively untouched. There is a small reduction in
signal strength, but that is due to the ISR beingfalsely tagged as
b-jets, because they do not originate from the primary vertex. This
also applies tothe background signals other than tt. The remaining
tt signal is due to the opposite, where b-jetshave 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 ttsignal.
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 signalscan be excluded with just a
few more cuts, however the points m1 , m
01 = (100 GeV, 87.5 GeV)
and m1 , m01 = (125 GeV, 75 GeV) can not be excluded at the same
time. Realising that they
are mutually exclusive is important because previously, each cut
tried to optimise for as many of thesignals as possible. Now,
depending on which region is being focussed on, the others
significance canbe disregarded so as to not make any unnecessary
compromises on the first. The two event selections,SRa and SRb, aim
to exclude the points m1 , m
01 = (100 GeV, 87.5 GeV) and m
1 , m
01 =
(125 GeV, 75 GeV) respectively. These are the target regions of
these selections. Table 6.1 displaysthe two cutflows, and how they
differ past the baseline.
Baseline
3 Leptonshas SFOS pair1 Jet
Lepton Pt 50 GeV
b-jet veto
SRa SRb
5 GeV< mSFOS
-
trying to exclude m1 , m01 = (100 GeV, 87.5 GeV) (Red line in
figure 6.6b) and not m
1 , m
01 =
(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 cutlocation.
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
pointmost of the background signal events have relatively low MET
compared to the SUSY signals andcome from WZ processes. These will
have some MET due to the neutrinos in W e + /, butthere will not be
as much as with the SUSY signals, as they are less massive. A
left-handed cut ismade at 130 GeV even though this compromises the
points (125, 100) and (100, 75), because thetarget 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 markedlyincrease 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 ismade to maximise
significance with (100, 87.5) as priority. Figure (b) shows that,
for optimising SRa, a cut at 130 GeVwill 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 apseudorapidity of 2.8.
This removes some of the SUSY events as well, but the priority is
to excludethe target region, so this is a considered compromise.
This is the last selection in the SRa cutflow, asit 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 =2.8 increasesthe
significance of (100, 87.5) desirably. Although this removes some
SUSY signals, because the priority is to excludethe target region
this compromise is made.
6.9 Signal Region SRb
6.9.1 Invariant Mass of SFOS Pair
Similar to SRa, the first variable cut is mSFOS, as there is a
great difference between the distributionsof the signal to the
background. Because the point (100 GeV, 87.5 GeV) now does not have
to be takeninto account, this cut can be different. The best
significance can be found by cutting a slice between15 GeV and 45
GeV. With this cut alone, the significance for the three target
signals increases aboveexclusion, so no further action is required.
Further cuts on MET and on the leading jet momentumwill 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 proneto statistical fluctuations. Because of this the
choice has been made to make no further cuts on thesesignal
regions.
34
-
Figure 6.9: Invariant Mass distribution for mSFOS after the
baseline. A slice between 15 GeV and 45 GeV will be takenin order
to optimise for (125, 100). This shaves off background events at
the start and end of the distribution, namelythe WZ 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 onmSFOS
after the baseline. The cuts at 15 GeV and 45 GeV are chosen to
optimise for the point (125, 100), the dashedblack, while keeping
the brown and cyan above ZN =1.64.
35
-
7 Results
7.1 Baseline
The baseline for the two event selections is a development on
the preliminary, as that was found tobest increase the significance
for a broad range of signals. It is chosen to have all five of the
selectedsignal regions reach as close to exclusion as possible,
without compromising on any of the pointsin particular. The
preliminary event selection was only able to exclude one point
(100, 75) withZN=1.86, though a second, (125, 100) with ZN=1.54
comes close. The event selection returned poorsignificances on many
of the regions because of their poor statistics. There are not
enough eventsto 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
1.3108 backgroundevents and it is clear that resolving these
signals will be difficult. Because of this, many of the
signalpoints likely can not be excluded with any event selection.
The full cutflow for the baseline is almostidentical to the
preliminary event selection except for two differences: The lepton
momentum cut is30 GeV instead of 40 GeV and the first MET cut is
raised to 50 GeV instead of 20 GeV, because thesehave a much
greater effect on the significance. The two cuts now raise every
points significance to anon zero value and increase the point (100,
75) to ZN=1.24, whereas before, the highest significanceat this
point in the cutflow was 0.3 for the same region. At the end of the
baseline, that same pointhas been excluded, and two others are
around ZN= 1. The full cutflow for the baseline follows intables
7.1 and 7.2.
36
-
Sam
ple
init
ial
3L
has
SF
OS
1Jet
Lep
ton
Pt
50G
eVb
-vet
o
ttb
ar26
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W2.
80
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Z0.
30.
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+Jet
s0.
10.
10.
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ibos
on0.
10.
00.10
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bar
+B
oson
1.0
0.2
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on0.
50.
10.10
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s0.
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iggs
0.70
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otal
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oun
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eV]
18.92
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(30%
SM
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MC
1,M
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eV]
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(30%
SM
)0.
320.
51
MC
1,M
N2
=10
0;M
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[GeV
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.0Zn
(30%
SM
)1.
241.7
2M
C1,
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(30%
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721.
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1,M
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(30%
SM
)0.
180.3
4
Table
7.2
:B
ase
line
cutfl
owb
efore
the
analy
sis
splits
into
SR
aand
SR
b(b)
38
-
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 01 [GeV] Mass of 1 /
02 [GeV] Event Selection Significance
75 100 SRa, SRb 1.79, 2.6675 125 SRb 2.12
87.5 100 SRa 1.67100 125 SRb 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 0.50.1 background
events remaining. The final significancesof the signal regions are
in table 7.4. This cutflow is able to exclude two of the five
points, and almosta third. SRa successfully excludes two regions
where m1 =100 GeV raises the significance of someadjacent points to
reasonable levels.
Figure 7.1 shows how all the surrounding signal regions are
affected by SRa.
Mass of 01 [GeV] Mass of 1 /
02 [GeV] ZN
75 100 1.7975 125 0.91
87.5 100 1.67100 125 1.53125 150 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 WZ
mediated SUSY signal regions, at the end of SRa.
Sample Baseline 5 2.8
ttbar 6.51.3 1.60.6 0.40.3 0.00.0WW 2.50.1 1.50.1 0.00.0
0.00.0ZZ 0.20.1 0.10.0 0.00.0 0.00.0WZ 28.41.2 16.80.9 0.60.2
0.50.1
Z+Jets 0.10.1 0.00.0 0.00.0 0.00.0triboson 0.10.0 0.00.0 0.00.0
0.00.0
ttbar+Boson 0.10.1 0.10.1 0.00.0 0.00.0t+Boson 0.10.0 0.00.0
0.00.0 0.00.0W+Jets 0.00.0 0.00.0 0.00.0 0.00.0
Higgs 0.40.0 0.10.0 0.00.0 0.00.0Total Background 38.51.8
20.21.1 1.10.4 0.50.1
MC1,MN2 = 125; MN1 = 100[GeV] 16.62.0 14.01.8 1.80.6 1.80.6Zn
(30% SM) 0.95 1.40 1.12 1.53
MC1,MN2 = 150; MN1 = 125[GeV] 9.90.9 9.10.9 1.60.4 1.40.3Zn (30%
SM) 0.51 0.89 0.94 1.11
MC1,MN2 = 100; MN1 = 75[GeV] 29.84.0 25.63.7 3.31.2 2.21.1Zn
(30% SM) 1.72 2.47 1.99 1.79
MC1,MN2 = 125; MN1 = 75[GeV] 19.62.1 5.51.1 .10.5 1.10.5Zn (30%
SM) 1.13 0.48 0.62 0.91
MC1,MN2 = 100; MN1 = 87.5[GeV] 7.31.1 6.21.0 2.20.6 2.00.6Zn
(30% SM) 0.47 0.57 1.35 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
issuccessfully excluded alongside another.
40
- Sample Baseline 15 GeV
-
Figure 7.2: 2D significance plot, showing ZN for all available
WZ 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 theevent selections would
exclude a wide area surrounding the target point and the outcome
would statethat points up to a certain mass range were successfully
excluded. However, due to the widely varyingstatistics between each
signal region this is not the case. This would occur if nearby
points exhibiteda similar signal shape or a similar number of
events. To an extent they do, but an adjacent point maydiffer
wildly on both these counts. This is the case with the points (100,
75) and (100, 87.5), whichare adjacent, yet have 7881.53 and 2454.9
events respectively. When reducing the background to suchlow levels
and making cuts for small increases in significance, the
statistical nature of the events meanthat the event selection may
have a completely different effect when transferred to real data
than onMC simulations. The cuts are chosen on data with random
statistical fluctuations, and will not actidentically on another
similar sample. Many of the signals also have high proportional
errors, somealmost 50%, and although the significance algorithm
takes these uncertainties into account, it is theresults on events
like these that will likely not replicate with real data. With more
time, the signalscould be normalised to 300fb1 integrated
luminosity in order to boost the weaker signals. Althoughthe SM
background would also increase, since the ZN algorithm is not
linear this should still givebetter results, and potentially
exclude more regions. This is especially relevant to the regions
wherem=12.5 GeV, near the diagonal, as these regions have very few
events and cannot be excludedbecause of it; a re-normalisation
could solve this problem.
The selection SRa manages to exclude two points, both with m1
=100 GeV. These points are atthe edge of the range of data that the
analysis has access to, and none of the signal regions havem1
-
The selection SRb only adds a single cut to the baseline and
still retains a relatively large num-ber of events, it can
therefore likely be developed on, as another baseline for different
points. Figure7.2 suggests the points (112.5, 50) and (150, 100)
are close to exclusion, and with one or two morecuts perhaps could
be so. Although excluding more points is beneficial, it detracts
from the aim ofthis project, which is looking to specifically
exclude points near the diagonal, and these points are atthe 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
notpossible. The highest significance it reaches is in SRa with
ZN=1.11. This is a confidence interval of73%, which is reasonable,
however it is not excluded. Given more time I would develop a
drasticallydifferent 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 theintegrated
luminosity this line of analysis becomes more viable.
9 Conclusion and Outlook
This projects analysis uses Monte Carlo simulated data based on
20.3fb1 integrated luminosityats =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 toexclude with a 90%
confidence interval. The signals are mediated by gauge bosons, have
initial stateradiation, no intermediate sleptons, and result in
three lepton final states. Four signal regions close tothe
diagonal, where m01 m1 , are successfully excluded, with two event
different selections, (m01,m1 /m
02)=(100, 75), (125, 75) (100, 87.5) (125, 100) where the masses
are in GeV. Further signal
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 datafrom 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 buton MC data generated at the
upgraded energies, and at an increase (300fb1) integrated
luminosity.This would develop a greater understanding of what to
expect with new data, and possibly exclude thelow event signals
near the diagonal. I believe, due to the increased cross section at
14 TeV, the signalswould be better resolved against the background
and more signal regions, specifically compressedregions, 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 thankthe PhD students Zara Grout and Yusufu Shehu for guiding me
through the (at first) complicatedframework, and for their
advice.
43
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