Masters Thesis

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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 7 th May, 2015 Supervisor Antonella De Santo

description

Masters thesis

Transcript of Masters Thesis

  • 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

  • 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.

  • 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

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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

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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

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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.

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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.

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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

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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.

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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++

    9

  • 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

    10

  • 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)

    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 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.

    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 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.

    15

  • 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.

    16

  • 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

    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 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.

    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 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,

    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, 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.

    20

  • 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

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    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

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    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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