su.diva-portal.orgsu.diva-portal.org/smash/get/diva2:753514/fulltext01.pdf · abstract the large...

Maja Tylmad

Search for Weakly Produced Supersymmetric Particles in theATLAS Experiment

Department of Physics

Stockholm University

2014

Doctoral Dissertation 2014FysikumStockholm UniversityRoslagstullsbacken 21106 91 Stockholm

c©Maja Tylmad 2014ISBN 978-91-7447-992-8Printed by Universitetsservice US AB, Stockholm 2014

Cover image: A three-year-old’s impression of a particle collision. With special thanksto Tilde Tylmad.

Abstract

The Large Hadron Collider located at CERN is currently the most powerful particleaccelerator and ATLAS is an experiment designed to exploit the high energy proton-proton collisions provided by the LHC. It opens a unique window to search for newphysics at very high energy, such as supersymmetry, a postulated symmetry betweenfermions and bosons.

Supersymmetry can provide a solution to the hierarchy problem and a candidate forDark Matter. It also predicts the existence of new particles with masses around 1 TeV, thusreachable with the LHC. This thesis presents a new search for supersymmetry in a pre-viously unexplored search channel, namely the production of charginos and neutralinosdirectly decaying to electroweak on-shell gauge bosons, with two leptons, jets, and miss-ing transverse momentum in the final state. The search is performed with proton-protoncollision data at a center of mass energy of

√s = 8 TeV recorded with the ATLAS exper-

iment in 2012. The design of a signal region sensitive to the new signal is presented anda data driven technique to estimate the Z + jets background is developed.

Precise measurements of hadronic jet energies are crucial to search for new physicswith ATLAS. A precise energy measurement of hadronic jets requires detailed knowledgeof the pulse-shapes from the hadron calorimeter signals. Performance of the ATLAS TileCalorimeter in this respect is presented using both pion test-beams and proton–protoncollision data.

Sammanfattning

Partikelfysikens standardmodell är en teori som beskriver materiens minsta byggste-nar samt hur dessa växelverkar. Standardmodellen har med framgång förutsagt ett stortantal fenomen som kunnat påvisas i experiment. Trots teorins framgångar finns indika-tioner på att den inte är komplett. Till exempel saknas i standardmodellen en kandidat tillMörk Materia. En möjlig lösning på några av standardmodellens problem är supersym-metri (SUSY), en postulerad utökning av standardmodellen som bland annat förutsäger attett antal hittills oupptäckta partiklar existerar. Några av dessa nya partiklar skulle kunnautgöra Mörk Materia.

För att utföra precisionsmätningar av standardmodellen och söka efter nya partiklaranvänds partikelacceleratorer. Den i dagsläget mest kraftfulla acceleratorn är LHC vidfysiklaboratoriet CERN. Protoner accelereras till en energi av 4 TeV i två strålar medmotsatt riktning. Vid fyra så kallade interaktionspunkter kolliderar protoner från de tvåstrålarna. Vid en av dessa interaktionspunkter finns ATLAS-detektorn, designad både föratt studera redan kända processer och för att upptäcka nya.

SUSY förutspår partiklar som har massor i storleksordningen 1 TeV, vilket är inomräckhåll för LHC. Om dessa partiklar existerar kan de skapas i proton-proton-kollisionerna.Att hitta dessa partiklar kan liknas vid att leta efter en nål i en höstack. En gedigen kun-skap om bakgrunden krävs för att SUSY-signalen ska kunna hittas, eller uteslutas. Detkrävs också att sökområdet avgränsas på ett effektivt sätt, så att bakgrunden avlägsnasmen den sökta signalen blir kvar. Ett sådant sökområde kallas för signalregion. Signalre-gionen beror på vilken SUSY-signatur som söks.

Denna avhandling presenterar en studie där supersymmetriska partiklar söks i en hit-tills outforskad sökkanal, nämligen produktion av gauginos vilka omedelbart sönderfallertill W - och Z-bosoner på sina respektive mass-skal. I sluttillståndet finns två leptoner,två hadroniska skurar och en obalans i den uppmätta transversella rörelsemängden. Stu-dien genomförs med data från proton-proton-kollisioner med energin 8 TeV, insamladmed ATLAS-detektorn. Optimeringen av signalregionen presenteras, tillsammans meden metod, baserad på data, för att uppskatta bakgrunden från produktion av Z + jets.

Att mäta energin hos hadroniska skurar är mycket viktigt, både för precisionsmät-ningar av standardmodellen och för att upptäcka ny fysik. För att rekonstruera energinhos en hadronisk skur på ett tillförlitligt sätt krävs kunskap om puls-formerna från denhadroniska kalorimetern, TileCal. I denna avhandling presenteras även studier av puls-former från TileCal, och deras möjliga påverkan på energirekonstruktionen diskuteras.

Contents

Acknowledgments 1

Preface 3About this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Author’s contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

I Theoretical Overview 7

1 The Standard Model of Particle Physics 91.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Fundamental Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.1 The Strong Nuclear Interaction . . . . . . . . . . . . . . . . . . . 111.2.2 The Electromagnetic Interaction . . . . . . . . . . . . . . . . . . 111.2.3 The Weak Nuclear Interaction . . . . . . . . . . . . . . . . . . . 11

1.3 The Higgs Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Problems of the Standard Model . . . . . . . . . . . . . . . . . . . . . . 13

1.4.1 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4.2 The Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Supersymmetry 152.1 The Basics of Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Supersymmetry Breaking . . . . . . . . . . . . . . . . . . . . . . 152.1.2 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 The Minimally Supersymmetric Standard Model . . . . . . . . . . . . . 162.2.1 The Phenomenological MSSM . . . . . . . . . . . . . . . . . . . 17

II Experimental Facilities 19

3 The Large Hadron Collider 213.1 The Accelerator Complex . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 The Main Experiments at the LHC . . . . . . . . . . . . . . . . . . . . . 22

4 The ATLAS Detector 254.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 The ATLAS Coordinate System . . . . . . . . . . . . . . . . . . . . . . 254.3 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.4 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.5 The Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . 284.6 Data Acquisition and Trigger Systems . . . . . . . . . . . . . . . . . . . 284.7 Particle Identification and Event Wide Variables . . . . . . . . . . . . . . 30

4.7.1 Primary Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.7.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.7.3 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.7.4 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.7.5 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.7.6 Missing Transverse Momentum . . . . . . . . . . . . . . . . . . 32

5 The Tile Calorimeter 335.1 The Physics of Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.1.1 Particle Showers . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 The Tile Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2.1 Mechanical Structure . . . . . . . . . . . . . . . . . . . . . . . . 355.2.2 TileCal Readout . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 TileCal Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.3.1 Test-Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Sources of Uncertainty on the Energy Reconstruction . . . . . . . . . . . 41

III Search for Weakly Produced Supersymmetry 43

6 Weakly Produced Supersymmetry 456.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.2 Overview of Search Channels . . . . . . . . . . . . . . . . . . . . . . . . 45

6.2.1 Intermediate Slepton Scenario . . . . . . . . . . . . . . . . . . . 456.2.2 Heavy Slepton Scenario . . . . . . . . . . . . . . . . . . . . . . 46

6.3 Signal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.4 Standard Model Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . 48

6.4.1 ZW , ZZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4.2 Top Background . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4.3 WW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4.4 Z + jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4.5 Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.4.6 Non-Prompt Leptons and Fake Leptons . . . . . . . . . . . . . . 516.5 Observables for Signal Selection . . . . . . . . . . . . . . . . . . . . . . 51

6.5.1 Jet Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.5.2 Lepton Observables . . . . . . . . . . . . . . . . . . . . . . . . 526.5.3 Relative Missing Transverse Momentum . . . . . . . . . . . . . 52

6.6 ATLAS Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7 Choice of Signal Region 557.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.2.1 Figure of Merit for Sensitivity . . . . . . . . . . . . . . . . . . . 567.2.2 Signal Region Cut Optimization . . . . . . . . . . . . . . . . . . 587.2.3 Validation and Final Selection of Cuts . . . . . . . . . . . . . . . 60

7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8 Standard Model Background Estimate 698.1 Diboson production, ZW and ZZ . . . . . . . . . . . . . . . . . . . . . . 698.2 Top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.3 Fake Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.4 Other Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708.5 Z + jets Background with the Jet Smearing Method . . . . . . . . . . . . 70

9 Data Driven Z + jets Background Estimation 719.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719.2 Missing Transverse Momentum in Photon Control Regions . . . . . . . . 73

9.2.1 Diphoton Control Region . . . . . . . . . . . . . . . . . . . . . . 739.2.2 Single Photon Control Region . . . . . . . . . . . . . . . . . . . 74

9.3 Control Region Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 759.4 The ABCD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769.5 Sample Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

9.5.1 γ + jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789.5.2 γγ + jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789.5.3 W/Z +0γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799.5.4 W/Z +1γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809.5.5 W/Z +2γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809.5.6 Top+X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809.5.7 Diboson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819.5.8 Multijet QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829.5.9 Summary of Processes with Real Emiss,rel

T . . . . . . . . . . . . . 829.6 Validation of Normalization of real Emiss rel

T Processes . . . . . . . . . . . 829.7 Photon Template Comparison with Dilepton Data . . . . . . . . . . . . . 839.8 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 86

9.8.1 Theoretical Uncertainty on Cross Sections . . . . . . . . . . . . . 889.8.2 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889.8.3 Unidentified Energy Deposits . . . . . . . . . . . . . . . . . . . 899.8.4 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899.8.5 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899.8.6 Pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899.8.7 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

9.9 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909.10 Statistical Combination of the Control Regions . . . . . . . . . . . . . . 91

9.10.1 The BLUE Method . . . . . . . . . . . . . . . . . . . . . . . . . 919.10.2 Result of the Statistical Combination . . . . . . . . . . . . . . . 92

9.11 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929.11.1 Comparison to the Jet Smearing Method . . . . . . . . . . . . . . 93

10 Exclusion Limits 9510.1 The CLS Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9510.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

11 Conclusions 99

List of figures 100

List of tables 106

Bibliography 108

Acknowledgments

This thesis would never have come into being without my advisor Christophe Clément,who has provided me with inspiration and ideas. Thank you for your support, encourage-ment, and enthusiasm. I have really enjoyed working with you. Thanks also to my secondadvisor, Barbro Åsman.

My many thanks to the past and present members of the Stockholm particle physicsgroup. Working with you for the last few years has been a pleasure. Sten Hellman hasgiven me comments on the thesis, David Milstead has helped with proofreading of thethesis and has been invaluable for various physics discussions over the years, and AndreasPetridis has offered most helpful advice in matters of SR optimization and getting cutflowsright. I appreciate your help.

My fellow PhD students have made life in physics fun. Special thanks to Kattis, Olleand Paweł for good times in the office, discussions on matters great and small, for sharedcode, and not least for keeping my spirits up. It would not have been the same withoutyou. Thanks to Gustav, Henrik, Matthias and Anna for being good office mates.

I am grateful to Christian Ohm for providing me with LaTeX templates and variousother help, and to Johan Lundberg for statistics advice, for encouragement and moralsupport, and much more. Thank you for everything!

Finally, my most sincere thanks to my family, Micke and Tilde. Thank you for yourendless support.

Preface

The Standard Model of particle physics describes the fundamental building blocks ofmatter and their interactions. The model has successfully predicted a range of phenomena,such as the existence of charm and top quarks and the W , Z, and Higgs bosons. Howeverthere are several theoretical arguments indicating that the Standard Model is only a lowenergy approximation of a more fundamental theory, the arguments behind this belief aredeveloped in chapter 1.

The field of experimental particle physics is dedicated to perform precision tests andmeasurements of the Standard Model processes and searches into what may lie beyond.Particle colliders are essential tools in experimental particle physics. When highly en-ergetic particles collide, new particles are produced thanks to the equivalence betweenenergy and mass, and their properties can be measured in detectors located around orclose to the collision point.

The most powerful accelerator today is the Large Hadron Collider (LHC), locatedat CERN near Geneva in Switzerland. During 2012 the accelerator produced proton-proton collisions at a center of mass energy of

√s = 8 TeV. With a center of mass energy

more than three times higher than previous colliders, the LHC has opened a windowto a new energy regime, allowing to test the existence of new hypothetical particles withmasses of several TeV. This thesis presents a search for supersymmetry, a possible theoryof physics beyond the standard model, in a previously unexplored search channel, withATLAS experiment.

The ATLAS detector used in this work is the largest of four experiments located at theinteraction points of the LHC. Together with the CMS experiment, ATLAS is a generalpurpose detector designed to provide precision measurements of the physics processesproduced in the collisions. The detector consists of several subsystems, responsible fortracking, energy and momentum measurements, and particle identification. This thesispresents a study of the energy measurement in one of these subdetectors, namely thehadronic Tile Calorimeter.

About this thesis

The thesis is divided into three parts, and four papers are included. Part I gives a briefintroduction to the particle physics theory. The particles and interactions of the StandardModel of particle physics are described, and the shortcomings of this model are discussed.

4

One possible extension to the Standard Model, Supersymmetry (SUSY), is described.Part II introduces the Tile Calorimeter and the work presented in Paper I and Paper II

and describes the experimental setup: the LHC accelerator and the ATLAS detector.The hadronic calorimeter of ATLAS, the Tile Calorimeter, is described in more detailas it is the focus of part of the work presented in this thesis. The included Paper I andPaper II concern the energy reconstruction in the Tile Calorimeter.

Part III describes a search for weakly produced supersymmetric particles in the ATLASdetector, with emphasis on data driven background techniques. In chapter 7 the signal re-gion optimization used in Paper III is developed. Chapter 9 describes in detail one of twomethods developed to compute the Z + jets background in Paper III. Paper IV presentswork I have carried out to evaluate a technique to determine so called non-prompt leptonbackgrounds, similar to the technique used in Paper III.

This thesis is an extension of my licentiate thesis. The chapters 1-5 are, with somealterations, taken from the licentiate.

The attached papers are:

Paper I: I. Jen-La Plante and M. Tylmad. Pulse shapes for signal reconstruction in theATLAS Tile Calorimeter. Nuclear Instruments and Methods in Physics ResearchSection A617, (2010), 96-98, January 2010.

Paper II: C. Clément and M. Tylmad. Measurement of the ATLAS Tile Calorime-ter Pulse-Shapes with

√s = 7 TeV Collision Data. Technical Report ATL-COM-

TILECAL-2010-026, CERN, Geneva, Dec 2010.

Paper III: The ATLAS Collaboration. Search for direct production of charginos, neu-tralinos and sleptons in final states with two leptons and missing transverse mo-mentum in pp collisions at

√s = 8 TeV with the ATLAS detector. JHEP, 1405:071,

2014.

Paper IV: B. Åsman, C. Clément, P. Hansson, J. Sjölin, M. Tylmad. Fake Isolated MuonBackgrounds in Searches for Supersymmetry with two Muons in the Final State.Technical Report ATL-PHYS-INT-2010-015, CERN, Geneva, Jan 2010.

The author's contribution

My first task when I started my work as PhD student on the ATLAS experiment concerneda study of fake isolated muon backgrounds to supersymmetry. A data-driven method todetermine the background from fake isolated muons in events with two muons in the finalstate was developed and a range of systematic effects were studied. I am main contributorto the study which was internally reviewed by a referee appointed by ATLAS physicscoordination. The internal note is included in this thesis as Paper IV.

5

For my qualification work on ATLAS I worked on the Tile Calorimeter. At first, whenthe accelerator was not yet operational, I worked with pulse-shapes in test-beam data. Us-ing the data collected from a full slice of the calorimeter exposed to pion beams, I studiedthe amplitude and channel-to-channel variation of the pulse-shapes, and investigated theimplication of these fluctuations on the energy reconstruction. This work is published ina conference proceeding included as Paper I and is described in more detail in an internalreviewed ATLAS note:

T. Carli, N. Gollub, I. Jen-LaPlante, M. Tylmad. Effect of Pulse-Shape Variations onthe Energy Reconstruction in the ATLAS Tile Calorimeter. Technical Report ATL-TILECAL-INT-2010-005, CERN, Geneva, Aug 2010.

When LHC delivered the first collisions, I expanded the pulse-shape study to includethe entire Tile Calorimeter. I investigated deviations between the measured pulse-shapesand the pulse-shape used for reconstruction, and estimated the possible bias on the energyreconstruction caused by these deviations. The work resulted in an internal reviewedATLAS note included in this thesis as Paper II. My study of TileCal pulse-shapes hasalso entered as contributions in the public papers:

K. J. Anderson at al. Calibration of ATLAS Tile Calorimeter at Electromagnetic Scale.Technical Report ATL-TILECAL-PUB-2009-001, CERN, Geneva, Jan 2009.

The ATLAS Collaboration. Readiness of the ATLAS Tile Calorimeter for LHC colli-sions. European Physical Journal C70, (2010), 1193-1236, Dec 2010.

As more data was collected my focus shifted back to searches for supersymmetry.One of the largest background sources to SUSY is top pair production. To estimate thisbackground a kinematic reconstruction of top pairs can be used. I worked with validationof the performance of the method used for the kinematic reconstruction. I used the methodto perform a cross check of the tt background for the SUSY search published in:

The ATLAS Collaboration. Searches for supersymmetry with the ATLAS detector us-ing final states with two leptons and missing transverse momentum in

√s = 7 TeV

proton proton collisions. Physics Letters B709, (2012) 137-157, March 2012.

and was also presented in an internal communication to which I was main contributor:

C. Clément, J. Lundberg, J. Sjölin, M. Tylmad. A Package for Kinematic Reconstructionof Top Pair Dilepton Events. Technical Report ATL-COM-PHYS-2011-335, March2011.

Part III of this thesis is dedicated to a new search for weakly produced supersym-metry in a channel previously unexplored, namely in the channel pp → χ0

2 + χ±1 →

Zχ01 +W χ0

1 → ``χ01 +qq′χ0

1 , where the gauge bosons are produced on-shell. The search

6

for pp→ χ02 + χ

±1 has previously focused on final states with three leptons. I performed

the first ATLAS study showing that the addition of this channel would be beneficial.Chapter 7 presents the signal region optimization for this new signal labeled SR-Zjets

in Paper III. Due to the presence of an on-shell Z-boson in the signal region the Z +jets background which could leak into the signal region must be well understood. Chap-ter 9 presents one of two methods developed to compute the Z + jets background inPaper III. It is important in previously unexplored signal regions to cross check resultsfrom several methods. The method presented in this thesis has been developed by meand relies on photon plus jets control regions. The weakness and strength of the proposedphoton plus jets control regions are analysed.

Part I

Theoretical Overview

1 The Standard Model of Particle

Physics

The Standard Model (SM) of elementary particle physics [1, 2, 3] is a quantum field theorywhich successfully describes a vast range of observed particle physics phenomena. Thetheory has great predictive power and has been extensively tested at various experimentsduring the last half century [4]. The elementary particles are divided into two groups:fermions and bosons. According to the Standard Model, matter is built of fermions whilethe vector bosons are responsible for mediating the fundamental forces.

A general description of the particle content and fundamental forces of the StandardModel is given in the sections 1.1 and 1.2 respectively. Section 1.3 gives a short intro-duction to mass generation in the Standard Model. The motivation for hitherto unob-served physics processes is discussed in section 1.4 and possible extensions to the Stan-dard Model in section 1.5.

1.1 Matter

Matter in the Standard Model consists of point-like particles of spin-1/2 called fermions.The fermions are divided into quarks and leptons. Furthermore, the fermions are groupedinto three generations of leptons and quarks. One quark generation comprises two quarks,and a lepton generation comprises one charged and one neutral lepton usually called neu-trino. All stable matter is built of fermions from the first generation [5]. Higher gener-ation fermions rapidly decay into lighter particles1). The quarks and leptons are listedin Tab. 1.1. Each fermion has an antiparticle, denoted by a bar, for example t is the an-tiparticle of the top quark. Free quarks have never been observed, they appear in boundstates known as hadrons [7]. Hadrons are categorized into mesons which are made up ofa quark-antiquark pair, and baryons which consist of three quarks or anti-quarks.

1.2 Fundamental Interactions

The Standard Model describes three fundamental interactions: the electromagnetic, thestrong, and the weak interactions. Gravity, the dominating force in the macroscopic

1)Neutrinos do not decay. Observations indicate that neutrinos oscillate between the three generations[6].

10 The Standard Model of Particle Physics

Generation ElectricI II III charge

up, u charm, c top, t+2

3 eQuarks (2.3 ·10−3) (1.28) (173.1)

(mass, GeV) down, d strange, s bottom, b−1

3 e(4.8 ·10−3) (0.95) (4.18)electron, e− muon, µ− tau, τ− −1 e

Leptons (5.11 ·10−4) (0.106) (1.78)(mass, GeV) e neutrino, νe µ neutrino, νµ τ neutrino, ντ 0 e

(< 2 ·10−9) (< 0.19 ·10−3) (< 18.2 ·10−3)

Table 1.1: The fermion flavors of the Standard Model. The particle masses are taken fromreference [8].

world, is not included in the Standard Model. The effect of gravity on elementary par-ticles is negligible compared to that of the other forces and becomes important only atthe Planck scale, MP = 2.4×1018 GeV. This energy scale is far beyond the reach of cur-rent experiments. Nevertheless precision measurements at current accelerators could byextrapolation help understanding physics at much higher energies. Within the StandardModel the fundamental interactions are mediated by spin-1 bosons. The bosons and theirproperties are briefly summarized in Tab. 1.2.

Interaction MediatorElectric Masscharge ( GeV)

Electro- γ0 e 0

magnetic photon

WeakW± ±1 e 80.4Z0 0 e 91.2

Strongg

0 e 0gluon

Table 1.2: The force mediators, vector bosons, of the Standard Model. The boson massesare taken from reference [8].

1.2 Fundamental Interactions 11

1.2.1 The Strong Nuclear Interaction

The strong interaction acts upon particles carrying color charge, that is the quarks andgluons. The mediating bosons of the strong interaction are eight gluons: massless, elec-trically neutral particles which themselves carry color charge, thus being able to inter-act directly with each other. The strong interaction is described by the theory QuantumChromo Dynamics, QCD. The strength of the strong force does not diminish with in-creased distance. Measurements indicate that the strength increases up to a distance ap-proximately the size of a hadron (1 fm). A single particle carrying color charge has neverbeen observed; the strong interaction forces these particles to form bound states, hadrons.The phenomenon is known as color confinement. Quarks and gluons produced in colli-sions hadronize in the detector and produce a shower of particles known as a jet. Thestrong force binds the quarks in hadrons and is also responsible for binding the protonsand neutrons within atomic nuclei.

The coupling constant of the strong interaction at distances λ > 1 fm is of the orderone. This prevents the use of perturbation theory for calculating the interactions at thatscale. Instead other approaches such as lattice QCD or phenomenological models mustbe used. For small distances and high energies the coupling constant is smaller and thusperturbation theory can be used. For small distances the quarks and gluons behave asquasi-free particles. This phenomenon is known as asymptotic freedom.

1.2.2 The Electromagnetic Interaction

The electromagnetic interaction is mediated by the photon, a massless vector boson. Allparticles with electric charge couple to the electromagnetic interaction. The quantumfield theory describing electromagnetic interactions is quantum electrodynamics, QED.Arguably the most successful physics theory, QED withstands experimental tests whichhave been made with experimental precision as small as 1 part in 10−12 [9]. The interac-tion is responsible for binding electrons to the atomic nucleus and it allows molecules toform.

The range of the electromagnetic interaction is infinite. The coupling constant or finestructure constant of the interaction is α ≈ 1/137. Since α � 1 the interactions can becalculated precisely to a given order of α with perturbation theory.

1.2.3 The Weak Nuclear Interaction

Three vector bosons mediate the weak interaction: the Z0, the W+ and the W− particleswhich represent the neutral (Z0) and charged (W±) weak currents. These bosons aremassive particles (80–90 GeV) thus shortening the range of the interaction to 10−18 m.All fermions couple to the weak interaction, which is the only interaction coupling toneutrinos.

The weak interaction is unique in several aspects. It is the only interaction in theStandard Model in which parity and charge conjugation is violated. A P-symmetric inter-


action must couple equally to a left-handed2) lepton and its P-conjugate, a right-handedlepton. Equivalently, a C-symmetric interaction must couple equally to a left-handed lep-ton and its C-conjugate, the left-handed antilepton. The weak interaction couples only toleft-handed particles and right-handed antiparticles, thus violating C and P.

Although the C- and P-symmetries are violated separately, the combined CP-symmetryis preserved in most weak processes. In certain rare weak processes in the quark sectorCP-violation has been observed. In the Standard Model only the weak interaction isCP-violating. The weak interaction is also the only Standard Model interaction allowingflavor-changing interactions, enabling processes such as:

d→ u+W−→ u+ e−+ νe (1.1)

which yields the nuclear reaction called β -decay:

n→ p+ e−+ νe (1.2)

in which a down quark in the neutron is converted to an up quark. The CP-violationand flavor-changing are both parametrized in the CKM matrix.

1.3 The Higgs Boson

The electroweak theory contains four electroweak gauge boson fields and a Higgs field.Gauge invariance of the Standard Model Lagrangian does not allow mass terms for theW± and Z0 bosons and the photon. Therefore a different approach is needed to providemasses to the W± and Z0 bosons.

It is postulated that spontaneous symmetry breaking leads to a non-zero vacuum ex-pectation value for the Higgs, early in the history of the Universe. The symmetry break-ing produces three massless Goldstone bosons which have the same quantum numbers asthree of the Standard Model gauge bosons. Through the Higgs mechanism, the Goldstonebosons are integrated with three of the electroweak gauge boson fields which in this wayacquire mass. These massive bosons are the Z0 and W± bosons [10, 11, 12]. The fourthelectroweak gauge boson remains massless and is identified as the photon. The theoryalso predicts the existence of a scalar particle associated with the Higgs field, the Higgsboson [13, 14].

Thus the electroweak theory unifies the electromagnetic and the weak interactionsand at the same time provides a mechanism that can generate mass. The theory hassuccessfully predicted among other things the mass of the massive gauge bosons. TheHiggs boson evaded discovery through several decades of extensive search at colliderexperiments [15]. In July 2012 the ATLAS and CMS experiments at CERN announced

2)Particles with spin and momentum in opposite directions are left-handed, particles with parallel spinand momentum are right-handed. See reference [5].

1.4 Problems of the Standard Model 13

the discovery of a new boson with mass 125 GeV [16, 17]. At the time of writing of thisthesis all measurements of this boson are consistent with a Standard Model Higgs boson[18, 19].

1.4 Problems of the Standard Model

Although there is to date no disagreement between the Standard Model and a large bodyof experimental measurements, there are reasons to believe that it is only a low energyeffective theory. Several questions remain unanswered. There is no explanation in themodel for why three generations of fermions are preferred. The CP-violation is not un-derstood, it is parametrized in the CKM matrix. The CP-violation in the Standard Modelis not large enough to explain the matter–antimatter imbalance observed in the Universe.The Standard Model neutrinos are massless. During the last decade several experimentshave established that neutrinos in fact have masses, albeit very small [6]. To account forthis a number of extra free parameters must be introduced in the Standard Model. Al-though neutrino masses can be incorporated in the Standard Model, it is desirable that acomplete theory has as few free parameters as possible. Perhaps the most obvious short-coming of the Standard Model is that gravity is not included. In the following subsectionsfurther problems are outlined.

1.4.1 Dark Matter

Astronomical observations have shown that the visible matter only explains a fractionof the matter in the Universe. At present, 4.9% of the total energy content of the Uni-verse is thought to be Standard Model particles and 26.8% is thought to be Dark Matter,non-luminous and non-absorbing matter only detectable indirectly through gravitationaleffects. One possible candidate for Dark Matter is the existence of electrically neutral,Weakly Interacting, Massive Particles (WIMPs). However, the Standard Model does notinclude such a particle. The neutrinos alone cannot account for the vast quantities of DarkMatter in the universe. The remaining 68.3% of the energy of the Universe is referred toas Dark Energy, the properties and origins of which are even more mysterious [20, 21].

1.4.2 The Hierarchy Problem

H

f

Figure 1.1: One-loop quantum correction to the Higgs mass.


The Standard Model Higgs mass is of the order mH = 125 GeV. However the Higgsmass term receives enormous quantum corrections from every particle coupling to theHiggs field. A fermion loop such as Fig. 1.1 yields a correction ∆m2

H to the Higgs mass:

∆m2H =|λ f |2

8π2 Λ2UV + ... (1.3)

where λ f is the coupling constant between the fermion and the Higgs field and ΛUVis an ultraviolet momentum cutoff. The interpretation of ΛUV is the energy scale at whichnew physics enters the theory. If the ultraviolet cutoff is set to the Planck scale3), MP =2.4×1018 GeV, the corrections produce a Higgs mass 15 orders of magnitude larger thanthe mass required by the Standard Model.

It is conceivable that all quantum corrections to the Higgs mass could cancel eachother, although this cancellation would have to be as perfect as one part in 1030. This isconsidered unnatural by many theorists. The problem is often referred to as the hierarchyproblem or the fine tuning problem [5, 10, 22]. It is believed that the fine tuning is sup-pressed by some yet unknown symmetry, such as supersymmetry described in chapter 2.

1.5 Beyond the Standard Model

In order to solve the problems discussed in section 1.4 the Standard Model must be ex-tended. Numerous candidate theories exist, among the more famous are Supersymmetryand theories with Extra Dimensions. Supersymmetry imposes a new symmetry whichleads to a new set of particles. These new particles cancel the infinities in the Higgsmass. The new spectrum of particles can provide candidates for Dark Matter. Supersym-metry and its implications are described in more detail in chapter 2. Extra Dimensionsproposes that some of the Standard Model particles are confined to a four-dimensionalbrane whereas other particles may propagate in additional spatial dimensions. This couldexplain why gravity is so much weaker than the other fundamental forces. If the extradimensions are large enough there could be phenomenological implications already at theTeV energy scale which can be explored at the LHC. Extra Dimensions could solve thehierarchy problem by lowering the ultraviolet cutoff, ΛUV [23]. Other models beyondthe Standard Model include the Little Higgs Model [24] in which the Higgs boson is apseudo-Goldstone boson from the breaking of a new global symmetry; and compositness,where some Standard Model particles themselves have a substructure. Gaining under-standing of the origin of mass and other new physics beyond the Standard Model is themain purpose of the experiments at the Large Hadron Collider, LHC.

3)The Planck scale is defined as the scale where gravity becomes comparable in strength to the otherinteractions.

2 Supersymmetry

A symmetry of fermions and bosons was first postulated in the early 1970s [25, 26]. In1981 the Minimal Supersymmetric Standard Model (MSSM) was introduced and pro-vided a solution to the hierarchy problem [27].

2.1 The Basics of Supersymmetry

Supersymmetry (SUSY) is a symmetry relating fermions and bosons. When acting ona particle of half-integer spin, SUSY transforms the particle to one of integer spin. Inthe same way particles of integer spin are transformed into half-integer spin particles.In SUSY every Standard Model particle has a supersymmetric partner particle, a su-perpartner or superparticle. All quantum numbers except spin of the superpartners arethe same as for the Standard Model particles. The spin of the superpartner differs fromthe spin of the Standard Model particle by 1/2. Thus the superpartners of the StandardModel fermions are spin-0 bosons and the superpartners of the gauge bosons are spin-1/2fermions.

The naming convention of superpartners adds a prefix “s” to the name of a StandardModel fermion and adds a suffix “ino” to the names of Standard Model bosons. Forinstance, the superpartners of leptons are called sleptons (e.g. selectron, sneutrino), thesuperpartners of quarks are squarks (e.g. sup, sdown, stop) and the superpartners of thegauge bosons are gauginos (e.g. gluino) [12].

If supersymmetry is unbroken Standard Model particles and their superpartners havethe same mass. Therefore the superpartners contribute to the loop-diagrams (see Fig. 1.1)in the exact same way as the Standard Model particles with the difference only of a sign.This provides a solution to the hierarchy problem as the quantum corrections from thesuperpartners exactly cancel those from Standard Model particles, removing the need forfine tuning.

2.1.1 Supersymmetry Breaking

Unbroken supersymmetry postulates the existence of a large number of new supersym-metric particles with the same mass and quantum numbers as Standard Model particles.Clearly this cannot be true as no such particles have ever been detected experimentally.Therefore supersymmetry, if it exists, must be broken and the mass of the superpartnershas to be larger than the mass of Standard Model particles.

16 Supersymmetry

The experimental absence of detected superpartners to date allows to derive a lowerlimit on their masses. If the masses of the supersymmetric particles are around 1–2 TeV,supersymmetry can still solve the hierarchy problem. The need for fine tuning still existsbut the degree is much relaxed. Breaking of supersymmetry on this scale is called softsupersymmetry breaking [8].

It is difficult to construct a model of spontaneously broken supersymmetry where thebreaking is due to interactions between supersymmetric particles. One way to introducebreaking of supersymmetry is the addition of a new sector to the model. This sectorwould be completely neutral with respect to the Standard Model gauge group, and wouldthus be a hidden sector. The supersymmetry breaking occurs in the hidden sector and istransmitted to the MSSM or visible sector. The transmission may involve a third sector,the messenger sector [8]. There are several scenarios for the mediation of supersymmetrybreaking: gravity-mediated, gauge-mediated and anomaly-mediated.

2.1.2 R-parity

In the Standard Model lepton number L and baryon number B must be conserved, whichprevents the proton from decaying. In Supersymmetry L- and B-violating processes canoccur. As no such processes have been observed experimentally, a new conserved multi-plicative quantum number is introduced:

R = (−1)3(B−L)+2S (2.1)

where S is the spin of the particle [28]. R-parity is even for Standard Model parti-cles and odd for superparticles. The conservation of R-parity has important implicationsfor the phenomenology. At a collider experiment where two Standard Model particlescollide, supersymmetric particles can only be produced in pairs. The production of onesingle superparticle would violate R-parity conservation. Supersymmetric particles arelikely to be highly unstable, rapidly decaying into lighter particles. Again due to R-parityconservation, a superparticle cannot decay into only Standard Model particles. This willproduce a decay chain with ever lighter supersymmetric particles and Standard Modelparticles.

When the decay chain reaches the lightest supersymmetric particle (LSP) no furtherdecays are possible. This implies that if R-parity is conserved, the LSP is completelystable. Cosmological observations show that the LSP must be neutral of electrical andcolor charge. In many supersymmetric models the LSP will therefore be a WIMP, andthus provides an excellent candidate for Dark Matter [29, 30].

2.2 The Minimally Supersymmetric Standard Model

The simplest supersymmetric model encompassing the Standard Model is the MinimalSupersymmetric extension to the Standard Model (MSSM). It consists of exactly one su-

2.2 The Minimally Supersymmetric Standard Model 17

perpartner per Standard Model particle. However the Higgs sector must be modified. OneHiggs doublet cannot generate mass for all fermions in a way consistent with supersym-metry; therefore the Higgs sector is extended to two Higgs doublets. The MSSM doesnot provide for a model of how Supersymmetry is broken. Therefore the number of freeparameters of the MSSM is large. Apart from the free parameters of the Standard Modelthe MSSM requires more than 100 new parameters [22].

The particle content of the MSSM is summarized in Tab. 2.1. In addition to the Stan-dard Model particles, there are four Higgs bosons, two electrically neutral and two elec-trically charged. Left- and right-handed quarks and leptons have separate superpartners.The superpartner of the gluon is the gluino. The gauginos are combinations of the su-perpartners of the electroweak gauge bosons and Higgs bosons. The neutral gauginos arecalled neutralinos, denoted χ0

1−4, where the indices 1–4 indicate increasing mass. Thecharged gauginos are called charginos, χ±

1,2. In this thesis the lightest supersymmetric

particle is assumed to be the lightest neutralino, χ01 .

MSSM mass eigenstates SpinHiggs sector h0,H0,A0,H± 0Squarks uL, uR, dL, dR sL, sR, cL, cR b1, b2, t1, t2 0Sleptons eL, eR, νe, µL, µR, νµ , τ1, τ2, ντ 0Gluino g 1/2Gauginos χ0

1 , χ02 , χ

03 , χ

04 (neutralinos), χ

±1 , χ

±2 (charginos) 1/2

Table 2.1: Particle content of the MSSM.

2.2.1 The Phenomenological MSSM

In its most general form, the MSSM has 124 free parameters. However, many of theseparameters have to be constrained in order to form a phenomenologically viable theory.Without constraints, MSSM models may exhibit non-conservation of lepton numbers,unsuppressed flavor changing neutral currents, or sources of CP-violation inconsistentwith experimental results. Given the experimental constraints, the parameter space of theMSSM can be strongly constrained.

Several attempts to theoretically describe the breaking of supersymmetry, and thus settheoretical constraints compatible with observational constraints on the parameter spaceof the MSSM, have been made. The mechanism chosen to break the supersymmetryhas implications on the resulting supersymmetric particle spectrum. However, in lack ofexperimental evidence, it is impossible to say which of these models is the more favorable.

In order to allow efficient and general searches for SUSY a more model-independentway of constraining the MSSM is preferred and therefore the phenomenological MSSM,or pMSSM, is introduced. In this framework the experimental observations are used to put

18 Supersymmetry

phenomenological constraints on the MSSM. A pMSSM model must fulfill the followingrequirements:

• Conserved quark and lepton flavor in the SUSY sector.

• Suppressed flavor changing neutral currents.

• No additional CP-violation compared to the Standard Model.

In addition mass degenerate 1st and 2nd generation sfermions may be required. In thisway the parameter space is reduced to 19–24 free parameters in addition to the StandardModel parameters. These additional parameters include gaugino and higgsino mass pa-rameters, Higgs sector parameters, squark and slepton mass parameters, and the trilinearcouplings between sfermions and Higgs. The much reduced number of parameters en-ables scans of the parameter space that would not be possible in a theory with more than100 parameters.

Although the CP-violation of Standard Model alone cannot explain the observedmatter-antimatter imbalance in the universe, there are still heavy constraints on the amountof CP-violation present. Therefore requiring no additional CP-violation is a good approx-imation for most direct searches for Supersymmetry.

A search for supersymmetric particles in the framework of the pMSSM is presentedin part III.

Part II

Experimental Facilities

3 The Large Hadron Collider

The Large Hadron Collider (LHC) [31] is an accelerator located at the European Organi-zation for Nuclear Research (CERN), on the Swiss–French border close to Geneva. TheLHC is mainly a proton–proton collider which during 2012 operated at a center of massenergy

√s = 8 TeV. Collisions at

√s = 13 GeV are scheduled for 2015 and the design

energy is√

s = 14 TeV. With a peak recorded luminosity of 7.7 ·1033 cm−2s−1 [32], theLHC is the most powerful particle collider in terms of both collision energy and numberof collisions.

3.1 The Accelerator Complex

The accelerator is housed in the tunnel originally used for the Large Electron PositronCollider, LEP. This is a circular tunnel located approximately 100 meters underground.The circumference is nearly 27 km. Figure 3.1 shows a schematic view of the acceleratorand the four main experiments.

The LHC is provided with protons from a chain of injectors where the proton energyis successively increased. The protons are accelerated to 50 MeV in the linear acceleratorcalled LINAC2 before being injected into the Booster where the energy is increased to1.4 GeV. Thereafter follows the Proton Synchrotron (PS) which accelerates the protonsto 25 GeV. The final step is the Super Proton Synchrotron (SPS) where the protons reachthe LHC injection energy 450 GeV. A sketch of the accelerator chain is shown in Fig. 3.2.

The LHC itself consists of two adjacent beam pipes in which the protons are acceler-ated. Around 1200 superconducting dipole magnets providing a magnetic field of 8.3 Tkeep the protons in a circular path and nearly 400 quadrupole magnets keep the beamsfocused. The magnets are cooled by liquid helium to the operating temperature of 1.9Kelvin. The protons are accelerated in a Radio Frequency (RF) cavity. When fully ac-celerated, the protons travel at nearly the speed of light, completing one full circle inapproximately 90 µs, equivalent to about 11000 laps per second. The two beam pipes in-tersect at four points, called Interaction Points, allowing the protons to collide. To observethe collisions detectors are placed at the interaction points. The protons are prepared inbunches, meaning the interactions take place at discrete time intervals. When the LHCis fully operational, the number of bunches will be nearly 3000 and the interactions willtake place every 25 ns. In the 2010–2012 runs the LHC was operated with about 1500bunches separated by 50 ns.

22 The Large Hadron Collider

Figure 3.1: A schematic view of the LHC and the major experiments.

Although mainly a proton–proton collider, the LHC also collides heavy ions at arecord center of mass energy. In shorter runs of approximately one month per year, theLHC has accelerated Pb82+ ions to collide at energies of

√s = 2.76 TeV per nucleon.

3.2 The Main Experiments at the LHC

In order to be able to study a wide range of physics at the LHC four large detectors havebeen built. Two of these, ATLAS [33] and CMS [34], are multi-purpose experimentsdesigned to be sensitive to any new physics. LHCb [35] is designed to study CP-violationand other phenomena in the decay of B-hadrons1). Finally, ALICE [36] is designed tostudy the states of extremely high energy density, known as quark–gluon plasma whichcan be produced in heavy ion collisions. The ATLAS experiment is described in moredetail in chapter 4

1)Hadrons containing b quarks.

3.2 The Main Experiments at the LHC 23

Figure 3.2: The injection chain of the LHC and other CERN beam lines.

4 The ATLAS Detector

4.1 Introduction

The ATLAS detector [33] is an approximately cylindrical detector located at InteractionPoint 1 of the LHC. The detector is 44 m long and 25 m in diameter. In order to accuratelydetermine what happens in a proton-proton collision ATLAS is divided into three maincomponents: the Inner Detector which provides charged particle tracking and momen-tum measurement; the calorimeters which measure the energy; and the muon spectrom-eter which provides tracking and momentum information of the muons. A sketch of theATLAS detector is seen in Fig. 4.1. The ATLAS detector is forward–backward symmetricand also approximately symmetrical in the azimuthal angle φ around the beam line. Thesubsystems of ATLAS are described in the following sections.

Different types of particles leave different signatures in the detector. All chargedparticles are visible to the Inner Detector (ID) whereas electrically neutral particles suchas photons pass unnoticed. Photons and electrons cause electromagnetic showers in theinnermost part of the calorimeter called the electromagnetic calorimeter. Hadrons producehadronic showers in the outermost part of the calorimeter called the hadron calorimeter.Most particles are stopped in the calorimeter, which allows a precise determination oftheir energy. Only very highly energetic jets can punch through the calorimeter and reachthe muon system. Muons and neutrinos are the only Standard Model particles whichalways pass through the calorimeter. The muons leave tracks in the Muon Spectrometer;the neutrinos escape undetected but lead to an apparent non-conservation of momentum.Hypothetical particles such as the χ0

1 would lead to the same signature. Figure 4.2 showsa schematic end view of the ATLAS detector with the interaction of different types ofparticles indicated.

4.2 The ATLAS Coordinate System

The coordinate system of ATLAS is a right-handed coordinate system with the x-axisin the horizontal plane pointing towards the center of the LHC ring; the y-axis pointsupwards; and the z-axis is parallel to the beam axis. The polar angle θ is measured withrespect to the beam axis and φ is the azimuthal angle. In addition to these coordinatespseudorapidity is often used. The pseudorapidity η is defined as η = − ln(tan(θ/2)).This gives η = 0 perpendicular to the beam axis and η = ±∞ in the ±z directions. The


Figure 4.1: Overview of ATLAS and its main subdetector components.

pseudorapidity–azimuthal space angle ∆R =√

∆η2 +∆φ 2 is often used to define distancebetween particles in the detector.

When two protons collide, the z-component of the momentum of the interacting par-tons can vary greatly. Therefore events are boosted in the z-direction. Since the mo-mentum of the colliding partons is unknown it is important to look at variables that areinvariant under the boost. The pseudorapidity is invariant under Lorentz transformationsand is therefore preferred over the polar angle. The colliding partons have negligible mo-mentum in the x,y plane, perpendicular to the beamline. The transverse momentum isconserved in the collision, therefore only the transverse component of an objects momen-tum, pT, is used for most purposes. The sum of the transverse momentum of all outgoingparticles must be zero.

4.3 The Inner Detector

The Inner Detector is designed to provide pattern recognition capacity, high resolutionmomentum measurement, and primary and secondary vertex measurements. It coversthe range |η | < 2.5. The ID consists of three subsystems: the pixel detector, the siliconmicrostrip tracker, and the transition radiation tracker (TRT). The TRT reaches to |η | <2.0 and provides discrimination between electrons and π-mesons. The three subsystems

4.4 Calorimetry 27

Figure 4.2: Schematic end view of the ATLAS detector, showing different types of parti-cles and where they interact in the detector.

are immersed in a solenoidal magnetic field of 2 T which allows momentum measurementin conjunction with the radius of curvature of the tracks. Located just centimeters awayfrom the beam pipe, the ID must operate in a high radiation environment. Excellentspatial resolution is crucial to discriminate physics from noise hits in the high-occupancyenvironment. High radiation levels cause the detector components to deteriorate and theinnermost layers will need to be replaced in the future [33, 37].

4.4 Calorimetry

The ATLAS calorimeter [38] consists of several subsystems: the Liquid Argon Calorime-ter (LAr) [39] which measures the energy of electromagnetic showers from electrons andphotons and the EM components of jets, the Forward Calorimeter (FCAL), the HadronicEnd Cap (HEC), and the Tile Calorimeter (TileCal) [40] which measure the energy of


hadronic showers. In the forward region liquid argon detectors are used for both electro-magnetic and hadronic calorimetry due to the high radiation environment.

The barrel Liquid Argon calorimeter covers the range |η |< 2.5. The end-cap calorime-ters extend the range to cover the region 2.5 < |η | < 4.9. The LAr calorimeter has anaccordion geometry which provides full coverage in φ and a fast extraction of the signal.The absorbing material is lead reinforced with stainless steel. The gaps between the ab-sorbers contain liquid argon, the active medium of the calorimeter, and readout electrodes.The liquid argon calorimeters are housed in three cryostats: one for the barrel and two forthe end-cap calorimeters [33, 38, 39].

The work described in the attached Paper I and Paper II has been performed as part ofthe calibration of the Hadronic Tile Calorimeter. Chapter 5 is dedicated to a more detaileddescription of this subdetector.

4.5 The Muon Spectrometer

The outermost subdetector of ATLAS is the Muon Spectrometer. A toroidal magnet sys-tem (one barrel and two end-cap magnets) provides a magnetic field in the muon system.The air-core toroidal structure ensures a strong field in a large volume with a minimalamount of dead material in the detector, thus minimizing the effect of multiple scattering.In the barrel region the tracks are measured by three cylindrical layers of tracking cham-bers. In the end-cap regions the tracking chambers are arranged in three planes perpen-dicular to the beam axis. Most of the muon chambers are Monitored Drift Tubes (MDTs).In the end-caps, Cathode Strip Chambers (CSCs) are used for the innermost plane. Ded-icated chambers are used for the muon triggers, Resistive Plate Chambers (RPCs) in thebarrel and Thin Gap Chambers (TGCs) in the end-caps. The Muon Spectrometer coversthe range |η |< 2.7 for tracking and |η |< 2.4 for the trigger. The momentum resolutionis of the order 2–4% for muons of momentum in the range 10–100 GeV [33, 41, 42].

4.6 Data Acquisition and Trigger Systems

The LHC proton-proton bunch crossing frequency is 40 MHz, which gives a very highcollision rate. Due to limited resources in readout bandwidth, data storage, and process-ing, only a small fraction of the events can be stored for further analysis. To ensure thatthe most important events are saved, a sophisticated trigger and data Acquisition (TDAQ)system is required. The trigger system must provide rapid decisions and the rate must bereduced to about 200 Hz for the final stage. The trigger system of ATLAS is divided intothree levels: Level-1 (L1), Level-2 (L2), and the Event Filter (EF). Figure 4.3 shows aschematic overview of the ATLAS trigger system [43].

The L1 trigger is achieved by hardware custom electronics and searches for objectswith high transverse momentum, pT , which indicates a large momentum transfer in thecollision, and large missing and total transverse energy. The trigger uses informationwith reduced granularity from the calorimeter and muon system. The highest accept rate

4.6 Data Acquisition and Trigger Systems 29

ATLAS Technical Design ReportLevel-1 Trigger 24 June 1998

2 General description of the level-1 trigger system 3

2 General description of the level-1 trigger system

2.1 ATLAS trigger and data-acquisition system overview

The ATLAS trigger and data-acquisition system is based on three levels of online event selection[2-1]. Each trigger level refines the decisions made at the previous level and, where necessary,applies additional selection criteria. Starting from an initial bunch-crossing rate of 40 MHz(interaction rate ~109 Hz at a luminosity of 1034 cm–2s–1), the rate of selected events must bereduced to ~100 Hz for permanent storage. While this requires an overall rejection factor of 107

against ‘minimum-bias’ processes, excellent efficiency must be retained for the rare newphysics, such as Higgs boson decays, that is sought in ATLAS.

Figure 2-1 shows a simplified functional view of the Trigger/DAQ system. In the following, abrief description is given of some of the key aspects of the event-selection process.

The level-1 (LVL1) trigger described in this TDR makes an initial selection based on reduced-granularity information from a subset of detectors. High transverse-momentum (high-pT)muons are identified using only the so-called Trigger chambers, resistive-plate chambers (RPCs)in the barrel, and thin-gap chambers (TGCs) in the endcaps [2-2]. The calorimeter selections arebased on reduced-granularity information from all the ATLAS calorimeters (electromagneticand hadronic; barrel, endcap and forward) [2-3], [2-4]. Objects searched for by the calorimetertrigger are high-pT electrons and photons, jets, and taus decaying into hadrons, as well as largemissing and total transverse energy. In the case of the electron/photon and hadron/tautriggers, isolation can be required. Information is available for a number of sets of pT thresholds(generally 6–8 sets of thresholds per object type).

Figure 2-1 Block diagram of the Trigger/DAQ system.

LEVEL 2TRIGGER

LEVEL 1TRIGGER

CALO MUON TRACKING

Event builder

Pipelinememories

Derandomizers

Readout buffers(ROBs)

EVENT FILTER

Bunch crossingrate 40 MHz

< 75 (100) kHz

~ 1 kHz

~ 100 Hz

Interaction rate~1 GHz

Regions of Interest Readout drivers(RODs)

Full-event buffersand

processor sub-farms

Data recording

ATLAS Technical Design ReportLevel-1 Trigger 24 June 1998

2 General description of the level-1 trigger system 3

2 General description of the level-1 trigger system

2.1 ATLAS trigger and data-acquisition system overview

The ATLAS trigger and data-acquisition system is based on three levels of online event selection[2-1]. Each trigger level refines the decisions made at the previous level and, where necessary,applies additional selection criteria. Starting from an initial bunch-crossing rate of 40 MHz(interaction rate ~109 Hz at a luminosity of 1034 cm–2s–1), the rate of selected events must bereduced to ~100 Hz for permanent storage. While this requires an overall rejection factor of 107

against ‘minimum-bias’ processes, excellent efficiency must be retained for the rare newphysics, such as Higgs boson decays, that is sought in ATLAS.

Figure 2-1 shows a simplified functional view of the Trigger/DAQ system. In the following, abrief description is given of some of the key aspects of the event-selection process.

The level-1 (LVL1) trigger described in this TDR makes an initial selection based on reduced-granularity information from a subset of detectors. High transverse-momentum (high-pT)muons are identified using only the so-called Trigger chambers, resistive-plate chambers (RPCs)in the barrel, and thin-gap chambers (TGCs) in the endcaps [2-2]. The calorimeter selections arebased on reduced-granularity information from all the ATLAS calorimeters (electromagneticand hadronic; barrel, endcap and forward) [2-3], [2-4]. Objects searched for by the calorimetertrigger are high-pT electrons and photons, jets, and taus decaying into hadrons, as well as largemissing and total transverse energy. In the case of the electron/photon and hadron/tautriggers, isolation can be required. Information is available for a number of sets of pT thresholds(generally 6–8 sets of thresholds per object type).

Figure 2-1 Block diagram of the Trigger/DAQ system.

LEVEL 2TRIGGER

LEVEL 1TRIGGER

CALO MUON TRACKING

Event builder

Pipelinememories

Derandomizers

Readout buffers(ROBs)

EVENT FILTER

Bunch crossingrate 40 MHz

< 75 (100) kHz

~ 1 kHz

~ 100 Hz

Interaction rate~1 GHz

Regions of Interest Readout drivers(RODs)

Full-event buffersand

processor sub-farms

Data recording

Figure 4.3: An overview of the ATLAS trigger and data acquisition system.

allowed from the L1 trigger is 100 kHz. The trigger decision must be made within 2.5 µsafter the bunch-crossing.

After a L1 trigger accept the data leaves the detector front-end electronics and is sentto the Read Out Drivers (RODs) located in underground counting rooms 100 m awayfrom ATLAS. The RODs perform some calculations on the data before it is passed alongto the Read Out Buffer (ROB) where it is stored awaiting a L2 trigger decision. TheTileCal RODs calculate the amplitude and time of pulses with the optimal filtering methoddescribed in more detail in chapter 5 and Paper II.

The L2 trigger uses as input regions-of-interest (RoIs), detector regions where theL1 trigger has identified possible trigger objects. The L2 trigger has access to the fullgranularity and tracking of ATLAS in the RoIs. Using information on coordinates, energyand signatures, the L2 trigger reduces the event rate to below 3.5 kHz. The average eventprocessing time is approximately 40 ms.

The event filter uses offline analysis algorithms to further reduce the event rate andclassify the events by signature. The output event rate from the event filter is approxi-mately 200 Hz and the average processing time is of the order four seconds. The eventfilter has access to full ATLAS data at full granularity.

The events that survive the event filter are saved to different data streams depending ontheir signature. There are physics data streams for events containing a muon, an electronor a photon, a jet, or high missing energy. In addition to the physics streams eventsmay also be written to calibration and express streams. The express stream is used formonitoring of the detector and data quality; the calibration streams provide the necessary


amount of data needed for detector calibration [33, 44].

4.7 Particle Identi�cation and Event Wide Variables

This section describes a few key objects and observables to carry out the analysis of datain part III.

4.7.1 Primary Vertex

The point where two protons from the colliding beams interact is called the primary inter-action point or Primary Vertex, (PV). When running at high luminosity many protons mayinteract in the same bunch crossing, leading to several primary vertices in the same event.In order to obtain an accurate measurement of the four-vectors of particles emerging fromone collision it is important to know which primary vertex is the origin of every identifiedparticle, as well as the location of each primary vertex. This is known as pile-up.

To reconstruct the primary vertices of a bunch crossing a vertex finding algorithmis applied. It uses track information from the inner detector to extrapolate tracks to theinteraction point. In the analysis described in part III of this thesis at least five chargedtracks per primary vertex are required.

4.7.2 Electrons

A cluster of EM calorimeter cells with significant energy deposits which in η , φ spacematch a charged track in the inner detector is referred to as an electron candidate. Forthe electron candidates used in the analysis of this thesis the energy of the cluster and thetrack must fulfill the criteria pT > 10 GeV and |η |< 2.47. Additional cuts on the qualityof the electron candidate are applied. Three different levels of quality are available, calledloose, medium and tight, with increasing rejection power against background and jetsfaking electrons. The variables on which the quality cuts are applied include leakage intothe hadronic calorimeter, width and shape of the EM shower and number of hits on theinner detector track [45]. The number of hits in the TRT is used to distinguish electronsfrom charged hadrons. For the analysis described in Part III of this thesis the electrons arerequired to satisfy the tightest criteria.

To select electrons coming from the decay of gauge bosons or sleptons as opposed toelectrons produced in jets, isolation criteria are applied. The sum of the pT of the tracksabove 400 MeV in with in a cone of size ∆R = 0.3 around the electron candidate must notexceed 16% of the electron pT. The electron must also be isolated in the calorimeter. Theisolation is defined as the sum of the ET in the calorimeter clusters within ∆R = 0.3 fromthe electron which must be less than 18% of the electron pT.

4.7 Particle Identi�cation and Event Wide Variables 31

4.7.3 Photons

For photon identification two types of photons must be considered: converted photonswhich have been converted into an electron-positron pair, and unconverted photons. Inthe case of unconverted photons no ID track will be associated with the energy deposit,while in the case of converted photons typically two tracks matching the energy depositwill be present. If the conversion is asymmetric and one of the e+e− has momentumunder the reconstruction threshold, or if the separation between electron and positron islow, only one track will be reconstructed leading to a single track matching the energydeposit [46].

The energy reconstruction of photons is similar to that of electrons. The shower shapesof photons and electrons are very similar; nevertheless the shower shape selections havebeen optimized for photons. Due to the similarities between electrons and photons acertain ambiguity between the two is unavoidable.

The photons used in the analysis in part III of this thesis are required to be isolated.The energy deposited in a cone of size ∆R = 0.2 around the photon candidate must notexceed 5 GeV.

4.7.4 Muons

Muons are reconstructed using the statistical combination algorithm. This requires amatch in η , φ space between a track in the inner detector and a track in the muon spec-trometer. The muon track parameters are obtained by combining both systems and theyare required to have pT > 10 GeV and |η | < 2.4. Also a minimum number of hits in thedifferent layers of the inner detector is required [47]. The sum of the pT of the tracksabove 400 MeV in with in a cone of size ∆R = 0.3 around the muon candidate must notexceed 15% of the muon pT.

4.7.5 Jets

Jet candidates are reconstructed using the anti-kt jet clustering algorithm with the distanceparameter ∆R = 0.4. The jet candidates are required to have pT > 20 GeV and |η |< 4.5.If the probability that a jet candidate may arise from detector problems or cosmic rays ishigh, the event is rejected. The energy of the jets is also corrected for inhomogeneities ofthe detector and pile-up interactions [48].

B-tagging

Jets containing a b-hadron decay are identified using a b-jet identification algorithm alsocalled b-tagging. A jet which is considered likely to contain a b-hadron decay is calledb-tagged. b-jet identification algorithms typically use the fact that b- and c-hadrons arelong lived, thus traveling some distance before decaying which causes the origin of the jetto be displaced from the primary vertex. In order for this displacement to be measurable


the decay must occur within the silicon detector volume. Therefore b-tagging can only beperformed within the range of the inner detector, that is for |η |< 2.4 [49].

Jet Vertex Fraction

With increasing luminosity the amount of pile-up per event increases. To reduce thebackground from pile-up jets and increase the resolution of jet energy measurements thevariable Jet Vertex Fraction (JVF) is introduced. The JVF is determined per jet and vertex.The JVF of a single jet with respect to a vertex is defined as:

JV F =∑k ptrkk

T (jeti,PVj)

∑n ∑l ptrklT (jeti,PVn)

(4.1)

The numerator is the sum of pT of all tracks coming from primary vertex PVj andpointing into jeti. The denominator is the sum of the pT of all tracks pointing to the jetindependently of the PV from which they arise.

4.7.6 Missing Transverse Momentum

Undetectable particles, such as neutrinos or hypothetical weakly interacting massive par-ticles, can be produced in the proton collisions and subsequent decays. The presence ofsuch particles can be inferred from an apparent non-conservation of transverse momen-tum.

The missing transverse momentum vector pmissT , a two-vector in the plane transverse

to the beam axis, is defined as the negative sum of the transverse momentum of all objectsin the event:

pmissT =−∑pe

T−∑pµ

T −∑pγ

T−∑pjetT −∑punidentified

T (4.2)

The electrons, muons and photons are required to have pT > 10 GeV and the jetspT > 20 GeV. The term ∑punidentified

T refers to the sum of all calorimeter clusters with|η | < 4.7 not already associated to leptons, photons or jets. The magnitude of pmiss

T iscalled the missing transverse energy and is denoted Emiss

T .In the presence of a neutrino in the final state, pmiss

T will be approximately the mo-mentum of the neutrino within experimental uncertainties on the momenta in Eq. 4.2. Ingeneral pmiss

T is the vector sum of all invisible particles.

5 The Tile Calorimeter

This chapter introduces the physics of calorimetry and describes the ATLAS Tile Calorime-ter. Studies of the signal reconstruction of the Tile Calorimeter are the focus of the at-tached Paper I and Paper II.

5.1 The Physics of Calorimetry

5.1.1 Particle Showers

When a particle passes through matter it interacts with the surrounding matter and losespart of or all its energy. The processes involved in the interaction depend on the energyand type of particle. The shower processes are divided into two categories defined by theinteractions: electromagnetic showers which involve electromagnetic interactions; andhadronic showers which involve strong interactions [50].

Electromagnetic Showers

The main process of energy loss for high energy electrons and positrons traversing amedium is bremsstrahlung. The charged particles radiate photons as a result of Coulombinteractions with atomic nuclei in the medium. For charged particles of lower energythe dominating process is ionization. The dominating photon interactions are electron–positron pair production, photoelectric effect, Rayleigh scattering, and Compton scat-tering. A high energy electron or photon entering matter will induce a chain reactionproducing a shower of electrons, positrons, and photons of ever lower energy via pairproduction and brehmsstrahlung.

Hadronic Showers

Hadronic showers are more complex than electromagnetic showers. A hadron of highenergy traversing a dense medium interacts by ionization. The hadron is likely to in-teract strongly with atomic nuclei in the matter. The incoming hadron and the nucleiinteract inelastically via strong interaction and produce a number of new hadrons. Theparticles created in the interactions will continue to interact with the matter, producinga shower of particles. These are often neutral hadrons decaying into photons which cre-ate an electromagnetic shower component inside the hadronic shower. Figure 4.2 showselectromagnetic and hadronic showers in the calorimeters of ATLAS.


5.1.2 Calorimeters

Calorimeters are devices in which incident particles are absorbed and their energy mea-sured. The calorimeter must enhance and absorb the particle showers and produce a mea-surable electric or light signal proportional to the number of particles in the shower. Adense absorber enhances and absorbs the shower and an active material produces a signalwhen particles pass through it. There are two basic types of calorimeters: homogeneouscalorimeters and sampling calorimeters. A homogeneous calorimeter consists of only onematerial, acting both as absorber and active material. The electromagnetic calorimeter ofCMS [34] is a homogeneous calorimeter. Sampling calorimeters alternate layers of ab-sorbing dense materials such as lead, iron or uranium with layers of active material [51].The electromagnetic and hadronic calorimeters of ATLAS are sampling calorimeters.

Energy Resolution of Calorimeters

The relative energy resolution of a calorimeter improves with higher energy and can bewritten generally as

σ

E=

a√E⊕ b

E⊕ c (5.1)

The first term, a, is called the stochastic term and gets contributions from all stochas-tic processes contributing to the energy resolution, including fluctuations in the physicaldevelopment of a shower. Generally homogeneous calorimeters have small stochasticterms as the entire shower is absorbed in active material. The stochastic term of samplingcalorimeters is larger because of the fraction of energy deposited in the active materialvaries from one shower to another. This effect can be reduced by reducing the thicknessof the absorbing layers.

The second term is the noise term. This depends on the noise of the readout chain.Scintillating calorimeters typically have lower noise terms than detectors based on chargecollection. Energy reconstruction methods such as the optimal filtering method used in thehadronic calorimeter of ATLAS can reduce the noise further. The noise term dominatesat low energies when signals are small.

The last term is a constant term summarizing all contributions that do not dependon particle energy, such as material or calibration non-uniformity, radiation damage andother instrumental effects. This is the dominant term at high energy [51].

5.2 The Tile Calorimeter

The ATLAS Hadronic Tile Calorimeter [40] is a sampling calorimeter made of alternatinglayers of iron absorber and scintillating plastic tiles. When a particle passes through thescintillating tiles, light is emitted and transported to photomultiplier tubes via wavelengthshifting fibers. The main task of TileCal is to identify jets and measure their energy and

5.2 The Tile Calorimeter 35

direction. TileCal is also important in measuring the missing transverse energy. Theenergy resolution requirement for jets is σ/E = 50%/

√E⊕3% [40]. TileCal covers the

range |η |< 1.6.

5.2.1 Mechanical Structure

The calorimeter consists of four mechanically distinct cylinders or partitions: two longbarrel segments (called LBA and LBC) and two smaller extended barrels (called EBAand EBC). Each barrel is divided into 64 independent azimuthal wedges called modules.Figure 5.1 shows the layout of the Tile Calorimeter partitions. The space between thelong and extended barrels is instrumented with gap and crack scintillators. These providecorrections for energy losses in dead material in the crack region.

Figure 5.1: Layout of the Tile Calorimeter partitions.

EBALBA

LBCEBC

The TileCal modules are built of many layers of absorbing iron and scintillating plastictiles. The ultraviolet light produced in the plastic tiles is collected at the edges of eachtile in wavelength shifting (WLS) fibers, two for each tile. The fibers are bundled andcoupled to photomultiplier tubes (PMTs). The grouping of the fibers defines the readoutgranularity. The PMTs are housed in a steel girder at the outer edge of each module.The girders provide both the volume in which TileCal front-end readout electronics arecontained and the flux return yoke of the solenoidal field. Source tubes used for calibrationpurposes pass through every tile. Figure 5.2 [33] shows a schematic of a TileCal module.

The grouping of the fibers is done in such a way that a three dimensional cell structureis defined, each cell being read out by two PMTs. There are three radial layers of cells,referred to as the “A”, “BC”, and “D” layers, “A” corresponding to the innermost layer.


Photomultiplier

Wavelength-shifting fibre

Scintillator Steel

Source

tubes

Figure 5.2: A schematic of the mechanical assembly and optical readout of a TileCalmodule.

x

yz

The depth of these layers is 1.5, 4.1, and 1.8 interaction lengths1) respectively at η = 0.The cells of two innermost layers have the dimensions ∆η×∆φ = 0.1×0.1 and the out-ermost layer ∆η ×∆φ = 0.2×0.1. Figure 5.3 [33] shows the depth and η-segmentationof the long barrel and extended barrel in the positive z region in the r, z plane. The TileCalorimeter is symmetric under the symmetry z→−z.

5.2.2 TileCal Readout

Each barrel (extended barrel) module is read out by 45 (32) channels, summing to a totalof 9856 readout channels for the entire Tile Calorimeter. Signals from the PMTs areshaped and thereafter amplified. Each PMT is read out by two analogue paths differingby an amplification ratio of 64, called low gain and high gain. The shaped and amplifiedsignals are sampled at the LHC bunch crossing frequency, 40 MHz, using a 10-bit analog

1)One interaction length is the average distance a hadron will travel in the absorber before a nuclearinteraction occurs.


500 1000 1500 mm0

A3 A4 A5 A6 A7 A8 A9 A10A1 A2

BC1 BC2 BC3 BC5 BC6 BC7 BC8BC4

D0 D1 D2 D3

A13 A14 A15 A16

B9

B12 B14 B15

D5 D6

D4

C10

0,7 1,0 1,1

1,3

1,4

1,5

1,6

B11 B13

A12

E4

E3

E2

E1

beam axis

0,1 0,2 0,3 0,4 0,5 0,6 0,8 0,9 1,2

2280 mm

3865 mm=0,0η

~~

Figure 5.3: Segmentation in depth and η of the Tile Calorimeter.

to digital converter (ADC). Seven samples are read out by the front-end electronics. Theseven digitized samples are transferred to the back-end electronics, readout drivers located100 m away in an underground counting room. The RODs compute the time and energyof the signal [52].

5.2.3 Energy Reconstruction

The amplitude A of the reconstructed pulse is related to the energy E by

E = FADC→MeV · (A−P) (5.2)

where P is the pedestal and FADC→MeV is a conversion factor between ADC-counts andMeV. The factors have been determined using a Charge Injection System (CIS) whichinjects a calibrated charge, the cesium calibration system which uses a Cs source, andelectron test-beams [52]. The calibration of TileCal is described in more detail in sec-tion 5.3.

Several methods of energy reconstruction have been developed in TileCal, two ofwhich are the fit method and the optimal filtering method [52, 53]. The energy reconstruc-tion can be performed offline on recorded data, or online by the RODs. If the L1 triggerrate is beyond 30 kHz the energy reconstruction must be performed by the RODs.

The Fit Method

The fit method uses a predefined pulse-shape to reduce the bias on the reconstructedamplitude introduced by electronic noise. For each channel a three parameter fit of the


function f (t) to the measured signals is performed:

f (t) = Afit ·g(t− tfit)+Pfit, (5.3)

where g(t− tfit) is a predefined pulse-shape function normalized to unit amplitude. Thefit determines the peak amplitude Afit, the time of the peak amplitude tfit and the pedestalPfit. The fit minimizes the expression:

χ2 =

7

∑i=1

(Si− (Afit ·g(ti− tfit)+Pfit)

σi

)2

(5.4)

where Si is each measured sample of the signal pulse in ADC-counts and σi is the un-certainty on each sample, the electronic noise. For high gain the noise is estimated to1.5 ADC-counts and for low gain 0.6 ADC-counts. For events with very small energydepositions the time parameter tfit is fixed to tfit = 0 ns and only a two parameter fit isperformed. The decision whether two or three parameters should be fitted is based onwhich method gives the smallest χ2/ndo f [53].

The method uses separate pulse-shapes for the low and high gain fits. Figure 5.4shows the predefined pulse-shape functions currently used in the energy reconstruction inlow and high gain. Since the autumn 2008 the fit method is used only for Charge InjectionSystem (CIS) calibration data [52]. The fit method is used as reconstruction technique inPaper I and as a cross check in Paper II.

Optimal Filtering

The optimal filtering algorithm [54] is the default energy reconstruction method of Tile-Cal. The method obtains the amplitude of the pulse using linear combinations of thesignal samples:

Aopt =7

∑i=1

ai ·Si (5.5a)

topt =1

Aopt

7

∑i=1

bi ·Si (5.5b)

where Aopt is the reconstructed amplitude and topt is the reconstructed time. Theweights ai and bi are chosen to minimize the impact of the noise on the reconstructionand are dependent on the peak time. The sum runs over all seven samples. The pulse-shapes in Fig. 5.4 must be known beforehand to be able determine the weights. Thepedestal Popt is estimated as the first measured sample. The algorithm can be performedonline with one iteration for L1 trigger rates < 75 kHz. For higher trigger rates no itera-tions are possible. If the energy reconstruction is performed offline there is no limit to the


Time [ns]60 40 20 0 20 40 60 80 100 120

No

rma

lize

d a

mp

litu

de

[a

.u.]

0

0.2

0.4

0.6

0.8

1Low gain

High gain

Figure 5.4: The predefined pulse-shape functions used for energy reconstruction in low(solid line) and high (dashed line) gain.

number of iterations used. The first iteration of the optimal filtering algorithm assumestopt ≈ 0 ns, thereafter using the previously determined topt for the following iterations.The procedure is terminated when convergence in the fitted time is obtained or after thepredefined number of iterations. To quantify the agreement between the measured sam-ples and the predefined pulse-shape a quality factor QF is defined. This quality factor isused to determine which pulses need to be stored for further analysis offline; a large QFindicates bad agreement and the samples Si are stored for further analysis. The qualityfactor of the reconstruction is given by the expression:

QF =7

∑i=1

(Si− (Aoptgi +Popt))2

Si(5.6)

The optimal filtering algorithm is described in more detail in references [52, 54]. Op-timal filtering is the main method used for energy reconstruction in Paper II.

Paper I describes a study performed on test-beam data where the effect of pulse-shapevariations on the energy reconstruction is investigated. Channel-by-channel and energydependencies of the pulse-shapes are studied. It is concluded that the observed variationsintroduce a bias on the reconstructed energy smaller than 1%.

Paper II describes a systematic measurement of pulse-shapes from the entire TileCalorimeter performed on

√s = 7 TeV proton–proton collision data. This study also con-

cludes that the energy bias introduced by pulse-shape variations is smaller than 1%.


5.3 TileCal Calibration

The TileCal calibration system consists of the charge injection system (CIS), the cesiumsystem (Cs), and the laser system. Apart from calibration with these systems TileCal hasalso undergone extensive testing and calibration in the test-beam and in cosmic runs. Thegoal of the calibration is:

• to establish the electromagnetic energy scale of TileCal. The EM scale conversionfactors relate the calorimeter signals measured in pC to the energy deposited byelectrons,

• to obtain understanding of cell-to-cell variations of the EM scale,

• to measure the average time offset between signal detection and collision time forevery TileCal channel,

• to monitor the time evolution of these quantities.

Figure 5.5 shows a flow diagram of readout path of the TileCal calibration systems.

Figure 5.5: Diagram of the TileCal calibration systems, illustrating the signal path forparticles and from the various calibration systems [52].

The charge injection system is a part of the front-end electronics. It is used to measurethe conversion factor between pC and ADC-counts for the readout of physics data andlaser calibration. CIS calibration runs are taken frequently. The constants are stable withrespect to time and are updated twice per year. Data from CIS can be used to identify badchannels and these calibration data are therefore taken several times per week betweenphysics runs.

The cesium system uses a hydraulic system to drive capsules containing cesium sourcesalong the z-axis through every scintillating tile in every TileCal module, see Fig. 5.2. As

5.4 Sources of Uncertainty on the Energy Reconstruction 41

the Cs source passes through a cell the signal in the PMT is continuously read out. TheCs source scans provide measurement of the response of individual cells and result inupdates in the constants that adjust the global EM scale. As Cs scans are time consumingthey are only performed between beam periods with a periodicity varying with the LHCschedules. [52, 55, 56, 57]

The laser system provides monitoring and calibration of the PMT gain and linearity. Alaser located in the ATLAS underground counting room emits pulses resembling physicspulses which are transported to the PMTs via optical fibers. Prior to beam, the lasersystem was also used for timing calibration [52, 58].

5.3.1 Test-Beam

To establish a thorough understanding of the response of the final TileCal modules, ap-proximately 11% [53] of the TileCal modules were exposed to test-beams of muons, elec-trons and hadrons with momentum from 3 to 350 GeV. The test-beam setup was installedin the H8 beam line at the SPS accelerator. The detector parts were stacked on a scan-ning table capable of x, y, θ and φ motion, mimicking the same particle-calorimeter entryconfiguration as in ATLAS. For the combined test-beam runs in 2004 a full slice of theATLAS barrel was exposed to the test-beam. More details on the test-beam setup andresults are found in references [53, 55, 59].

The attached Paper I uses data from the 2004 combined test-beam to quantify theenergy dependence of the TileCal pulse-shapes.

5.4 Sources of Uncertainty on the Energy Reconstruction

The uncertainty on the energy reconstruction in TileCal has three main sources as seen inEq. 5.1, the stochastic term, the noise term, and the constant term.

The stochastic term a in Eq. 5.1 arises from the randomness of the hadronic showerdevelopment. For instance, low energy neutrons are produced in showers and carry awaya part of the energy, which remains unmeasured. TileCal is a sampling calorimeter and theenergy deposited in the absorber is not measured. The exact amount of energy absorbedin the absorber or lost via undetected hadrons varies from shower to shower. The size ofthe stochastic term for jet resolution is 50%/

√E. The noise term b in Eq. 5.1 is due to

noise in the readout chain. In TileCal this term is smaller than 1%/E and is considerednegligible. The constant term c in Eq. 5.1 takes contributions from effects that are notenergy dependent, e.g. non-uniformity of the detector response. Wrong timing of pulses(in the case of non-iterative optimal filtering) and channel-to-channel variations of signalpulse-shapes can contribute to the constant term. In ATLAS the constant term of the jetresolution is required to be c < 3%.

For low energy jets, the stochastic term is the dominating source of uncertainty. How-ever, as the energy of the jet increases, the constant term becomes more important. For jetenergies of the order 300 GeV or more the constant term is the dominating source of uncer-


tainty. Precise jet energy measurement is crucial to many physics studies in ATLAS andit is therefore important to understand the contributions to the constant term.

The energy reconstruction in TileCal relies on predefined pulse-shapes for the energyreconstruction. If these reference pulse-shapes deviate from the actual pulse-shapes of theTileCal channels, a bias on the energy reconstruction can be introduced. Figure 5.6 showsthe bias on the energy reconstruction as a function of the actual pulse-shape width relativeto the reference pulse-shape, obtained using simulated data. It is noted that a pulse-shape10% narrower than the reference pulse-shape would cause a bias of the order 1.5% on theenergy reconstruction. This is not negligible compared to the 3% constant term and it istherefore important to investigate the actual pulse-shapes of the TileCal channels.

Relative pulse width (%)10 5 0 5 10

En

erg

y b

ias (

%)

1.5

1

0.5

0

0.5Optimal Filtering, Low gain

15 GeV

30 GeV

45 GeV

Figure 5.6: Bias on the energy reconstruction as a function of the actual pulse-shape widthrelative to the reference pulse-shape taken from Paper II. The estimated bias is obtainedusing simulated data.

In the attached Paper I and Paper II, studies of the TileCal pulse-shapes are presented.The study presented in Paper I was performed on three TileCal modules which wereexposed to pion test-beams in 2004. The energy dependence of the pulse-shapes wasinvestigated. A slight energy dependence, especially in the tail region, was observed.Paper II presents a study where channel-by-channel variations of all TileCal channels ismeasured using collision data taken in 2010. It was found that the pulse-shapes in lowgain are slightly narrower than the reference pulse-shape. However the bias on the energyreconstruction caused by this discrepancy is very small.

Part III

Search for Weakly Produced

Supersymmetry

6 Weakly Produced

Supersymmetry

One of the major goals of the ATLAS experiment is to search for new physics at theTeV scale. Supersymmetry, described in chapter 2, is one of the theories that needs to betested. In this chapter weakly produced supersymmetry is introduced.

6.1 Motivation

The production cross section of SUSY particles at the LHC depends on their mass andcouplings. Colored sparticles, such as squarks and gluinos, have significantly higher pro-duction cross sections than weakly interacting sparticles, such as gauginos and sleptons,of equal mass. If the colored supersymmetric particles are very massive and the weaklyinteracting sparticles are relatively light, direct production of gauginos and sleptons coulddominate the SUSY production at the LHC, as seen in Fig 6.1 which shows the productioncross section as function of particle mass. The cross sections are calculated at next to lead-ing order (NLO) with PROSPINO [60]. This mass hierarchy is possible in the frameworksof MSSM and pMSSM.

6.2 Overview of Search Channels

The preferred decay channels of the supersymmetric particles depends on the SUSY masshierarchy. The models concerned here have conserved R-parity, thus providing a candi-date for Dark Matter. In these models the lightest supersymmetric particle is a stableneutralino denoted χ0

1 and a pair of LSPs always end the supersymmetric decay chains.

6.2.1 Intermediate Slepton Scenario

In SUSY models where mχ0

2 ,χ±1>m ˜>m

χ01, the only kinematically allowed slepton decay

is ˜→ `+ χ01 . Final states containing leptons provide a better signal to background ratio

than those containing only strongly interacting particles. Therefore models with interme-diate sleptons were the focus of early searches at the LHC. So far no excess over StandardModel expectations has been observed. For models with a massless χ0

1 , chargino massesbetween 140 GeV and 465 GeV have been excluded, see Fig. 6.2(a) and Ref. [61].

46 Weakly Produced Supersymmetry

10-3

10-2

10-1

1

10

200 400 600 800 1000 1200 1400 1600

νeν

e* l

ele*

t1t1*

qq

qq*

gg

qg

χ2ogχ

2oχ

1+

maverage

[GeV]

σtot

[pb]: pp → SUSY

√S = 8 TeV

Figure 6.1: Production cross section as a function of sparticle mass for SUSY processesat√

8 TeV pp collisions, calculated at NLO with PROSPINO [60].

σ[p

b]

6.2.2 Heavy Slepton Scenario

In the analysis presented in this thesis a mass hierarchy where mχ0

2= m

χ±1

and m ˜� mχ0

2is considered, see Fig 6.3 (a). The sleptons are decoupled from the phenomenology understudy here due to their large mass. A mass gap m

χ02 ,χ±1−m

χ01> mZ enables the production

of on-shell W - and Z-bosons.Searches for this scenario are limited by the branching ratio of the gauge bosons de-

caying leptonically and therefore require more data than the intermediate slepton case.However, it is important to perform an exhaustive search for supersymmetric models andalso the scenario with more massive sleptons and on-shell gauge bosons must be consid-ered.

Searches for weakly produced supersymmetry with on-shell bosons have previouslybeen performed in the channel where both vector bosons decay leptonically, producingthree final state leptons and one neutrino. No significant excess of events above StandardModel expectations was found in 20.3 fb−1of

√s = 8 TeV proton-proton collision data.

Limits on neutralino and chargino masses are set and reproduced in Fig. 6.2(b). For sim-plified supersymmetric models with gauge boson decays, degenerate χ

±1 and χ0

2 massesup to 345 GeV are excluded [62].

If the Z-boson decays leptonically and the W -boson decays hadronically the final state

6.3 Signal Models 47

[GeV]±

1χ∼

m100 200 300 400 500 600

[G

eV

]0 1χ∼

m

0

50

100

150

200

250

300

350

400

)theory

SUSYσ1 ±Observed limit (

)expσ1 ±Expected limit (

= 7 TeVs, 1ATLAS 4.7 fb (103.5 GeV)

±

1χ∼LEP2

ATLAS

= 8 TeVs, 1 Ldt = 20.3 fb∫

All limits at 95% CL

0

1χ∼ν l× 2 →l) ν∼(νl

~ × 2 →

1χ∼

+

1χ∼

)/2 0

1χ∼

+m±

1χ∼

= (ml~,ν∼

m

)0

1χ∼

) < m

(

±1χ∼

m(

(a)

[GeV]1

±χ∼, 2

0χ∼m

100 150 200 250 300 350 400 [G

eV

]0 1χ∼

m0

50

100

150

200

250

300

01χ∼

< m

0

2χ∼m

Z

= m

1

0

χ∼

m

2

0

χ∼m

1

0χ∼

= 2m

2

0χ∼m

0

2χ∼

= m±

1χ∼m

1

0χ∼

(*) Z

1

0χ∼

(*) W→

0

2χ∼

±

1χ∼

ATLAS

=8 TeVs, 1

L dt = 20.3 fb∫ =8 TeVs, 1

L dt = 20.3 fb∫)

theory

SUSYσ1 ±Observed limit (

)expσ1 ±Expected limit (

= 7 TeVs, 1ATLAS 4.7 fb

All limits at 95% CL

(b)

Figure 6.2: Observed and expected 95% CL exclusion contours for (a) chargino pairproduction in the simplified model scenario with intermediate sleptons and two leptonsin the final state [61], and (b) chargino and neutralino production in the simplified modelscenario with decay via gauge bosons and three leptons in the final state [62].

contains two same flavor leptons of opposite sign, two jets, and missing transverse energydue to the LSPs which escape the detector undetected. A diagram depicting this decay isshown in Fig 6.3 (b). This channel is the focus of this thesis. Although the productioncross section and the branching ratio to dilepton final states are low, a study first performedby the author of this thesis showed that the ATLAS detector does have sensitivity in thischannel.

6.3 Signal Models

The signal models considered in chapters 7 and 9 of this thesis are so-called simplifiedmodels. A simplified model is defined by a set of particles and their modes of productionand decay. From these parameters and the couplings the production cross section as afunction of particle mass is determined. In simplified models the branching ratio can beset to any value, often to 100% for a studied decay. The final exclusion plots can thenbe scaled to any branching ratio. The simplified model is independent of the underlyingtheory; it merely states the production cross section and branching ratios given a set ofparameters. If the parameters are chosen to be consistent with for instance pMSSM,exclusion limits set on the simplified models can be interpreted in terms that framework.

The models considered here are direct gaugino production, pp→ χ±1 χ0

2 . The χ±1 and


0

1χ∼

±

1χ∼

, 0

2χ∼

± l~

Mass

(a) (b)

Figure 6.3: (a) The mass hierarchy of the SUSY models considered in this work. (b)Diagram showing a chargino and a neutralino decaying to the LSP via W - and Z-bosons.The W decays hadronically and the Z leptonically, giving a final state with two same flavorleptons of opposite charge.

the χ02 are assumed to be pure wino states1) and mass degenerate. Pure wino states yield

the largest production cross sections. It is possible to scale the result to obtain exclusionlimits for any other desired scenario, that is pure bino states or a combination of the two.

A number of signal points with different chargino and neutralino masses are gener-ated by Monte Carlo simulation, forming a grid in the m

χ02 ,χ±1

, mχ0

1plane. The next to

leading order production cross section of the models is shown in Fig. 6.4. All signal sam-ples are generated with HERWIG++2.5.2 [63] and normalized to NLO cross section fromPROSPINO.

6.4 Standard Model Backgrounds

In order to discriminate supersymmetry signals from Standard Model backgrounds a sig-nature with low background must be chosen. In the LHC, the background arising frommultijet production is particularly high. In the ATLAS detector these backgrounds areseen as a large number of jets. A signal including leptons2) is therefore an efficient ap-proach to reduce the Standard Model background. Requiring a high missing transversemomentum further reduces the number of background events.

The main backgrounds to the supersymmetric process χ±1 + χ0

2 → W χ01 + Zχ0

1 →qq′χ0

1 + ``χ01 , with two opposite sign final state leptons, high missing transverse momen-

1)Pure wino states means that the bino and higgsinos do not mix with the wino to form the lightestchargino and second lightest neutralino.

2)Lepton in this analysis refers to electron or muon.

6.4 Standard Model Backgrounds 49

[GeV]±

1χ∼,

0

2χ∼m

100 150 200 250 300 350 400 450 500

Pro

duction c

ross s

ection [pb]

-210

-110

1

10

Figure 6.4: Production cross section of the signal models at√

s = 8 GeV as function ofm

χ02 ,χ±1

, where χ02 and χ

±1 are pure wino states, calculated at NLO with PROSPINO [64].

tum, and two high momentum jets are Standard Model processes with the same signature.These backgrounds are referred to as irreducible backgrounds and are detailed below.Processes with fake leptons and/or fake missing transverse momentum contribute to thebackground to some extent. The main Standard Model backgrounds are described in thefollowing sections.

p

p

q

q

q

q

Z

Z

+l

-l

ν

ν

(a)

p

p

q

q

g

tb

-W

-l

ν

tb

+W

+l

ν

(b)

p

p

q

q

Z

g

+l

-l

q

q

(c)

Figure 6.5: Three of the Standard Model backgrounds with a final state similar to that ofthe sought supersymmetric signal. (a) shows the ZZ background, (b) is the tt backgroundand (c) is the Z + jets background.


6.4.1 ZW , ZZ

Pair production of bosons is the largest background to the signal shown in Fig. 6.3. Theprocesses ZW → ``+ τν and ZZ→ ``+νν (see Fig. 6.5 (a)) both have real leptons andmissing transverse momentum, and jets can be produced in initial state radiation (ISR).The invariant mass of the two leptons will be close to the mass of the Z-boson, hencefurther mimicking the signature of the supersymmetry model under study.

6.4.2 Top Background

Top quarks exclusively decay into a W -boson and a b-quark. Therefore top quark pairproduction and the production of a single top and a W -boson have very similar signatures.In the case of top pair production, two high momentum jets arising from the b-quarks,so called b-jets, are present. Single top production Wt contains one b-jet. If the W -bosons decay leptonically, W+W− → `+ν + `−ν , both real opposite sign leptons andmissing transverse momentum will be observed. However the invariant mass of the twoleptons will be unrelated to the mass of the Z-boson, allowing distinction from the SUSYsignature. A diagram of top pair production and decay is shown in Fig. 6.5 (b).

6.4.3 WW

This background closely resembles the top background, however missing the b-jets. Anyjets present arise from ISR.

6.4.4 Z + jets

Z + jets is a collective name for processes where a Z-boson and one or more stronglyinteracting particles are produced in the proton-proton collision. The Z-boson may de-cay leptonically, producing a pair of leptons with invariant mass near the mass of theZ-boson, and the strongly interacting particle will produce jets. If the energy of the jetsis mismeasured, fake missing transverse momentum is artificially introduced followingEq. 4.2. Therefore these events resemble the signature of the supersymmetric process un-der study. An example of a Z+ jets process is shown in Fig. 6.5 (c). Chapter 9 is dedicatedto the estimation of the Z + jets background.

6.4.5 Higgs

In this analysis Higgs production represents a background. This process group comprisesboth Higgs decay channels such as H→ ZZ and Higgs production with associated vectorboson production, such as pp→HZ, where the decay products include leptons, neutrinosand jets. Although these backgrounds are irreducible, their cross sections are low andgive a very small contribution to the total background.

6.5 Observables for Signal Selection 51

6.4.6 Non-Prompt Leptons and Fake Leptons

The non-prompt and fake lepton backgrounds are processes where one or more objectsin the detector are misidentified as isolated leptons. The fake leptons are objects that arenot leptons at all, such as jets, which are misidentified as leptons. Non-prompt leptons areleptons that do not directly arise from vector boson decays. For example, a kaon producedin a jet is likely to decay into a muon. If the energy deposits in the calorimeter aroundthis muon are sufficiently small, the muon will appear isolated and the event may bemisinterpreted as a leptonic decay. Processes that contribute to the fake lepton backgroundare s- and t-channel single top, tt, W+jets and bb. Hereinafter the term fake leptons is usedcollectively for fake leptons and non-prompt leptons.

All contributions to the fake lepton backgrounds are estimated simultaneously, basedon the statistical probability that a lepton should pass certain isolation criteria. A similarmethod for data driven estimation of the fake isolated muon background was developedby the author in Paper IV.

6.5 Observables for Signal Selection

6.5.1 Jet Observables

Number of Jets and Jet Categories

As the supersymmetric decay under study has two quarks in its final state, the number ofjets is an important observable. The jets from the signal are from u, d, c, and s quarkswhile b-quarks can arise in the background, mainly from top quark decays. The observ-able NB20 is the number of b-tagged jets with p jet

T > 20 GeV. A veto is placed on thisobservable in order to reduce the top background.

b-tagging is only possible in the central part of the detector, where |η | < 2.4. Afterthe veto on NB20, b-jets in the forward region (|η | > 2.4) can remain. Therefore a vetois also placed on the observable NF30, the number jets with p jet

T > 30 GeV in the forwardregion, |η | > 2.4. The observable NC20 is the number of jets with p jet

T > 20 GeV in thecentral region of the detector, |η |< 2.4. At least two such jets must be present.

Dijet Invariant Mass, m j j

As the two jets in the signal originate in a W -boson decay, the invariant mass of the twojets peaks at the mass of the W -boson. The invariant mass m j j of the two leading jets cantherefore be used to suppress backgrounds.

m j j =((

E jet1 +E jet2)2−∣∣p jet1 +p jet2∣∣2)1/2

(6.1)


6.5.2 Lepton Observables

Transverse Momentum of the Lepton System, p``T

The transverse momentum of the dilepton system is defined as follows:

p``T =

((p`

+

x + p`−

x

)2+(

p`+

y + p`−

y

)2)1/2

(6.2)

and is shown in chapter 7 to be a useful variable.

Dilepton Invariant Mass, m``

In the sought signal, the leptons come from a decaying Z-boson. Therefore the mass ofthe dilepton system, m``, is expected to be close to the mass of the Z-boson.

m`` =

((E`+ +E`−

)2−∣∣∣p`+ +p`−

∣∣∣2)1/2

(6.3)

∆R(``)

The angle ∆R(``) between the two leptons is defined in terms of η and φ :

∆R(``) =((η`+−η`−)

2 +(φ`+−φ`−)2)1/2

(6.4)

and is shown in chapter 7 to be a useful variable.

6.5.3 Relative Missing Transverse Momentum

The observable EmissT , missing transverse momentum, is defined in section 4.7.6 as the

negative sum of the transverse momentum of all objects in the event. If the momentum ofone or more objects is badly measured, the Emiss

T will be affected so that the direction ofthe Emiss

T will be aligned with that of the badly reconstructed object. To reduce the effectof such mismeasurements the observable relative missing transverse momentum, Emiss,rel

T ,is introduced [65]. If the angle between the direction of the Emiss

T and the nearest leptonor jet is small, only the Emiss

T component perpendicular to this object is considered:

Emiss,relT =

{Emiss

T if ∆φ`, j ≥ π/2Emiss

T × sin∆φ`, j if ∆φ`, j < π/2(6.5)

∆φ`, j is the angular distance between the direction of the EmissT and the nearest lepton

or jet.

6.6 ATLAS Data Set 53

6.6 ATLAS Data Set

The analysis presented in this thesis is based on the data from proton-proton collisions at√s = 8 TeV collected in 2012. Due to the technical limitation on event readout, band-

width, recording, and storage capacity, only the most useful proton-proton collisions canbe recorded. As the number of events with a single low-pT lepton is large, the singlelepton triggers have relatively high pT thresholds on the leptons in order to keep an event.The thresholds are 24 GeV for the single electron trigger and 20 GeV for the single muontrigger. Since this analysis is looking for events with final states containing two leptonsdilepton triggers can also be used. Due to the presence of a second lepton the event rateis lower and the energy threshold can be lowered. Hence a dilepton trigger with threshold12 GeV is used in combination with the single lepton triggers.

After removing data taking periods flagged as bad by detector experts, the remainingintegrated luminosity that can be used in this analysis is 20.3 fb−1[66].

7 Choice of Signal Region

A signal region is defined by a set of cuts selected to optimize statistical sensitivity tothe new physics signal. In SUSY searches where the model parameters are unknown thesignal region must be sensitive to a large number of signal points with slightly differentsignatures. In the search presented in Paper III, the signal region has been optimizedto obtain the largest exclusion reach with respect to the signal models described in theprevious chapter. The steps of the optimization of the signal region called SR-Zjets inPaper III are described in this chapter.

7.1 Preselection

From the kinematic characteristics of the signal a minimum set of selections, or baseselections, for the signal region are determined. As the signal contains a hadronically de-caying W -boson, at least two jets must be present. In order to distinguish the signal fromthe tt background a veto on b-jets is applied. However, since the b-tagging requires track-ing information from the inner detector, no b-tagging is available for |η |> 2.4. Thereforea different approach must be used to suppress the tt background in events with jets inthe forward region. A veto on forward jets with pT > 30 GeV is applied. This removestt events with high-pT jets but leaves jets from the signal, since the signal is expected tohave more central jets than the background

The signal contains two leptons from the decay of a Z-boson. These leptons musthave same flavor and opposite sign. The sensitivity to the signal does not exhibit anysignificant dependence on the momentum of the leptons, therefore cuts on p`1T > 35 GeVand p`2T > 25 GeV are applied to ensure uniformity with other signal regions [61]. Sincethe leptons are the result of the decay of an on-shell Z-boson, the invariant mass m`` of thetwo leptons is required to lie within a 10 GeV window around the Z-boson mass. Thesecuts are referred to as the base cuts and are defined in Tab. 7.1.

7.2 Method

The signal region optimization is performed on Monte Carlo simulation. The optimizationof cuts is a complex process which may require many iterations to arrive at the final cuts.The systematic errors and errors on Monte Carlo statistics depend on the selections andtherefore change with each cut. The variables are correlated and cutting on one variable


Variable ValueNC20 ≥ 2NB20 +NF30 = 0N` = 2p`1T > 35 GeVp`2T > 20 GeV|mZ−m``| < 10 GeV

Table 7.1: The base cuts defining the region within which the signal region optimizationis performed. The two leptons must have same flavor and opposite sign.

may change the optimal cut on another.In Sec. 7.2.2 the important variables are described and suggestions for cut values are

given. The main goal of the selection is to maximize the exclusion range in the gridof signal points, but other factors such as background calculation must also be takeninto account. At this stage of the analysis the backgrounds are estimated using MonteCarlo simulated data but in later stages data driven methods are developed for several ofthe background processes. In Sec. 7.2.3 the effect of the cuts proposed is validated byapplying all cuts except one and checking the the optimal cut value.

7.2.1 Figure of Merit for Sensitivity

In order to evaluate different selections a figure of merit p is introduced. The expectednumber of background events in the signal region is b±σb, where σb is the quadratic sumof the statistical errors from Monte Carlo and the systematic errors. The expected numberof signal events in the same region is s. Assuming a signal plus background hypothesisand no uncertainty on b or s, the observed event count N in the signal region is expectedto follow a Poisson distribution, P(N|s+ b), with central value s+ b. This is illustratedby the dashed curve in Fig. 7.1.

However b does have an uncertainty σb, and to obtain the correct probability distribu-tion of the number of events the function P(N|s+b) must be convoluted with a Gaussianfunction G(B|b,σb) with central value b and standard deviation σb. G(B|b,σb) gives aweight to each possible value B of the number of background events. The resulting prob-ability density function F(N|s+b,σb) is given by:

F(N|s+b,σb) =

∫∞

0P(N|s+b)G(B|b,σb)dB∫

∞

0G(B|b,σb)dB

(7.1)

This is illustrated by the solid curve in Fig. 7.1. The black area p under the curve isthe probability of the signal plus background to yield an observed number of events of

7.2 Method 57

b or less. This probability is obtained by summing the probability density function fromzero to b:

p =

∫∞

0

b

∑N=0

P(N|s+b)G(B|b,σb)dB∫∞

0G(B|b,σb)dB

(7.2)

Lower p-values correspond to higher sensitivity to the signal in the signal region. Ifp < 0.05 the probability of observing b events under the signal plus background hypoth-esis is less than 5%, and if no excess over Standard Model background expectation isobserved, that hypothesis can be excluded with 95% confidence level.

Number of events

-10 35-0.1

1.1

s+bb

p

Figure 7.1: Illustration of the probability density function for the signal plus background(s+ b) hypothesis with no uncertainty (dashed curve) and convoluted with a Gaussianfunction to include the uncertainty on the background (solid curve). The area of the filledsurface under the graph corresponds to the probability p of observing only the expectedbackground b under the s+b hypothesis. Lower p-values correspond to higher sensitivityto the signal. p is used as figure of merit to evaluate the effect of different signal regionselections.

The error on p is obtained by varying the expected b by one σb up and down andcomparing the resulting p with the nominal value. Thus the effect of variations in thebackground are translated to an error on the probability p. In the following sections thestatistical error and a flat systematic error of 20% on the expected background yield isused. The p-values are numerically calculated with the function BinomialExpP from theROOFIT package [67].


7.2.2 Signal Region Cut Optimization

Missing Transverse Momentum

Due to the two χ01 that escape detection, the supersymmetric signal is expected to contain

a large amount of missing transverse momentum compared to the Standard Model back-ground. Figure 7.2(a) shows the distribution of relative missing transverse momentum(Emiss,rel

T ) after the base cuts in Monte Carlo simulation. The stacked histograms show thedifferent components of the background and the overlaid dashed lines show the distribu-tion for three different signal points. As expected the background process Z/γ∗→ `` isdominating at low Emiss,rel

T . Fig 7.2(a) also illustrates the need of a data driven method toestimate the Z/γ∗→ `` background as the Monte Carlo quickly runs out of statistics athigh Emiss,rel

T , which indicates that the background suffers from low statistics.Fig 7.2(b) shows the p-value described in the previous section for different cuts on

Emiss,relT for a few selected signal points. The errors on p are determined using the method

described in section 7.2.1. The signal points have been chosen to represent low, mediumand high mass difference between the gauginos. For the signal points with low gauginomass difference, where ∆m. 100 GeV, the sensitivity is low throughout the Emiss,rel

T spec-trum. These models are so called “compressed spectra” models and are in general verychallenging at the LHC. For the points with higher gaugino mass difference it is clear thatthe sensitivity to the signal increases as the cut on Emiss,rel

T is tightened. However othercuts will be applied and it is desired to retain sufficient Monte Carlo statistics for theanalysis. Also, systematic errors can increase significantly at high Emiss,rel

T . Therefore arelatively loose cut is chosen at this point. As an increase in sensitivity compared to loosercuts is observed at Emiss,rel

T > 80 GeV this cut level is chosen. After other cuts have beenapplied the cut is validated and may be adjusted if necessary. The value of the Emiss,rel

T cutis reevaluated after all other cuts have been applied, see discussion in Sec. 7.2.3.

Momentum and Invariant Mass of Leading Jets

In the sought signal two jets come from the decay of an on-shell W -boson, whereas jetsin the Z + jets, WW and ZZ background processes originate mainly from initial stateradiation. Therefore the pT of the two leading jets in the signal is expected to be higherthan in the backgrounds. In Fig 7.3 the distribution of the pT of the leading (a) and secondleading (b) jets after preselection and the cut on Emiss,rel

T > 80 GeV are applied are shown.Figure 7.3(c) shows the p-value for different combinations of cuts on the two jets. The

sensitivity does not exhibit much improvement after [40,40] GeV. The background calcu-lation (described in chapter 8) benefits from cuts on p jet1

T > 45 GeV and p jet2T > 45 GeV.

Since these cuts do not affect the sensitivity negatively the cut [45,45] GeV is selected forthe signal region.

Although other jets may arise from ISR, it is likely that the two jets from the W -decay will have higher pT. Therefore the invariant mass (m j j) of the two leading jets is

7.2 Method 59

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400

Events

/ 1

0 G

eV

110

1

10

210

310

410

510

610

710

Base

1

L dt = 20.3 fb∫µµ ee,→Z

ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(a)

[GeV]miss, rel

TCut value E

>50 >60 >70 >80 >90 >100 >110 >120 >130 >140p

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(b)

Figure 7.2: (a) Distribution of the relative missing transverse momentum after the basecuts are applied. The stacked histograms show the different components of the back-ground and the overlaid dashed lines show the distribution for three different signal points.The error band represents the quadratic sum of the error on Monte Carlo statistics and aflat systematic error of 20%. (b) Sensitivity to different signal points, measured with thep-value described in section 7.2.1, after different cuts. Lower p-value means higher sen-sitivity. The error on p is determined by shifting the background estimate by its totaluncertainty.

expected to be close to the mass of the W -boson. Figure 7.4(a) shows the distributionof the invariant mass of the two leading jets after the preselection and additional cuts onEmiss,rel

T > 80 GeV and p jet1,2T > 45 GeV are applied. In the region 50 < m j j < 100 GeV

an increase of the number of events is observed for the signal points.A clear improvement in sensitivity is observed in the regions 50 < m j j < 100 GeV

and 0 < m j j < 100 GeV for signal points with higher gaugino mass difference, as seen inFig. 7.4(b). The sensitivity to signal points with low gaugino mass difference is low for allinvestigated cuts on m j j. Since the jets in the signal are known to arise from the W -decay,it is more natural to place a selection close to the mass of the W -boson. Therefore the cut50 < m j j < 100 GeV is selected for the signal region.

Kinematics of Dilepton System

The transverse momentum of the system of leptons, p``T , and the angle between them,∆R(``), are also useful variables to discriminate the signal from the background. In thesignal, the initial gauginos are massive and are produced approximately at rest. The pT of


the χ02 therefore is approximately close to zero. As it decays the pT of the Z-boson must

balance that of the χ01 . If the mass difference m

χ02− (m

χ01+mZ) is large, the Z-boson and

the χ01 will receive high pT. The lepton pair from the Z-boson decay will be boosted,

making the angle between the two leptons small and the pT of the system of leptons high.For the Z + jets background most Z-bosons are produced with low pT. Therefore the

angle between the resulting leptons will be large and the pT of the dilepton system willbe low. In tt events the two leptons arise from the decay of two separate bosons and thedirection of the leptons therefore will be uncorrelated. Thus the angle between the leptonsand the pT of the dilepton system can assume any value.

These differences in kinematics can be seen in Fig 7.5, which shows the distributionof p``T (a) and ∆R(``) (b) after the preselection and additional cuts on Emiss,rel

T > 80 GeV,p jet1,2

T > 45 GeV and 50 < m j j < 100 GeV are applied. Fig 7.5(c) and (d) show the p-values for different cuts on p``T and ∆R(``) respectively.

At this stage very few events remain. In Fig 7.5(a) no tt events are present in theregion 60 < p``T < 80 GeV, which is reflected in the lower p-values for the cut values onp``T > 60 GeV and p``T > 70 GeV in Fig 7.5(c). However it is probable that this is the effectof the low remaining Monte Carlo statistics rather than an effect of physics. Thereforea slightly higher cut, p``T > 80 GeV is selected for the signal region. The lack of MonteCarlo statistics clearly shows the need for a data driven estimate for the tt background.

Similarly the ∆R(``) suffers from low remaining statistics, especially for the tt back-ground. The region 1.6 < ∆R(``) < 2.0 has very low background resulting in seeminglylow p-value in the three rightmost bins in Fig 7.5(d). Considering that this is likely to bean effect of the low statistics the more conservative cut 0.3 < ∆R(``)< 1.5 is chosen forthe signal region.

7.2.3 Validation and Final Selection of Cuts

The cuts selected in the previous section are summarized in Tab. 7.2. To validate the cutvalues chosen the sensitivity to signal models is studied for each cut separately. After allcuts in Tab. 7.2 are applied, one cut at a time is removed and the p-value for differentcut values on the removed cut is calculated. In Fig. 7.6 this is shown for all variablesreviewed in the previous section. The sensitivity to the two signal points with gauginomass difference of 50 GeV and 100 GeV is low for all investigated cuts and the discussionis therefore focused on models with higher mass difference.

Figure 7.6(a) shows p-values for different cuts on Emiss,relT after all other cuts are

applied. The behavior of the sensitivity varies with the mass difference between the gaug-inos in the signal models. For medium mass difference the sensitivity displays a clearimprovement for cuts around Emiss,rel

T > 70 GeV. For high mass differences however, thesensitivity continues to increase as the cut is tightened. Therefore the benefits on the twotypes of events must be weighed against each other; a loose cut benefits the first type anda tight cut benefits the latter. As a compromise Emiss,rel

T > 80 GeV is suitable and is chosen

7.2 Method 61

Variable Value Variable ValueNC20 ≥ 2 p`1T > 35 GeVNB20 +NF30 = 0 p`2T > 20 GeVp jet1

T > 45 GeV |mZ−m``| < 10 GeVp jet2

T > 45 GeV p``T > 80 GeVm j j [50,100] GeV ∆R(``) [0.3,1.5]Emiss,rel

T > 80 GeV

Table 7.2: Definition of the Z + jets signal region.

for the signal region selection.In Fig. 7.6(b) all cuts except the cuts on p jet1,2

T > 45 GeV are applied. The figure showsthat beyond [40,40] GeV this cut does not greatly affect the sensitivity and therefore thecut p jet1,2

T > 45 GeV, which is preferred for the background calculation, can be used. Asseen in Fig. 7.6(c) the cut 50 < m j j < 100 GeV is a natural choice for the invariant massof the jets.

Figure 7.6(d) shows no effect on the sensitivity for different cuts on p``T below 100 GeV.However, a cut on p``T > 80 GeV enables the use of photon control regions for the Z +jets background estimate (see chapter 9), and therefore a cut is placed on p``T > 80 GeV.In Fig. 7.6(e) it is seen that 0.3 < ∆R(``) < 1.5 gives the lowest p-value and this cut istherefore selected.


[GeV]jet1

Tp

0 50 100150200250300350400450500

Events

/ 2

0 G

eV

110

1

10

210

310

410

>80 GeVmiss, rel

TBase, E

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(a)

[GeV]jet2

Tp

0 50 100150200250300350400450500E

vents

/ 2

0 G

eV

110

1

10

210

310

410

>80 GeVmiss, rel

TBase, E

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(b)

] [GeV]jet2

T,p

jet1

TCut value [p

[20,20] [30,30] [35,25] [35,35] [40,35] [40,40] [45,40] [45,45] [50,45] [50,50]

p

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(c)

Figure 7.3: Distribution of the transverse momentum of the leading (a) and second leading(b) jets, after the base cuts and Emiss,rel

T > 80 GeV are applied. The stacked histogramsshow the different components of the background and the overlaid dashed lines show thedistribution for three different signal points. The error band represents the quadratic sumof the error on Monte Carlo statistics and a flat systematic error of 20%. (c) Sensitivityto different signal points, measured with the p-value described in section 7.2.1, afterdifferent combinations of cuts on the pT of the two leading jets. Lower p-value meanshigher sensitivity. The error on p is determined by shifting the background estimate byits total uncertainty. [45,45] GeV is selected for the signal region.

7.2 Method 63

[GeV]jjM

0 100 200 300 400 500 600 700 800 900

Events

/ 5

0 G

eV

110

1

10

210

310

>45 GeVj1,2

T>80 GeV, p

miss, rel

TBase, E

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(a)

[GeV]jj

Cut value M

[0,100] [0,150] [0,200] [50,100] [50,150] [50,200]

p

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(b)

Figure 7.4: (a) Distribution of the invariant mass of the two leading jets after the basecuts, Emiss,rel

T > 80 GeV and p jet1,2T > 45 GeV are applied. The stacked histograms show

the different components of the background and the overlaid dashed lines show the dis-tribution for three different signal points. The error band represents the error on MonteCarlo statistics and a flat systematic error of 20%. (b) Sensitivity to different signal points,measured with the p-value described in section 7.2.1, after different cuts on m j j. Lowerp-value means higher sensitivity. The error on p is determined by shifting the backgroundestimate by its total uncertainty. The cut 50 < m j j < 100 GeV is selected for the signalregion.


[GeV]ll

Tp

0 50 100150200250300350400450500

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eV

110

1

10

210

>45 GeVj1,2

T=[50,100] GeV, p

jj>80 GeV, M

miss, rel

TBase, E

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

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=350 GeV, m±

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0

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m

(a)

R(ll)∆

0 1 2 3 4 5 6E

vents

/ b

in

110

1

10

210

>45 GeVj1,2

T=[50,100] GeV, p

jj>80 GeV, M

miss, rel

TBase, E

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(b)

[GeV]ll

TCut value p

>60 >70 >80 >90 >100 >120 >140 >160 >180 >200

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(c)

R(ll)∆Cut value

[0.3,0.9] [0.3,1.1] [0.3,1.3] [0.3,1.5] [0.3,1.7] [0.3,1.9] [0.3,2.1]

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼

m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(d)

Figure 7.5: Distribution of the transverse momentum of the dilepton system (a) and theangle between the leptons (b) after the base cuts, Emiss,rel

T > 80 GeV, p jet1,2T > 45 GeV and

50 < m j j < 100 GeV are applied. The stacked histograms show the different componentsof the background and the overlaid dashed lines show the distribution for three differentsignal points. The error band represents the error on Monte Carlo statistics and a flatsystematic error of 20%. (c) and (d) Sensitivity to different signal points, measured withthe p-value described in section 7.2.1, after different cuts on p``T and ∆R(``) respectively.Lower p-value means higher sensitivity. The error on p is determined by shifting the back-ground estimate by its total uncertainty. The cuts p``T > 80 GeV and 0.3 < ∆R(``)< 1.5are selected for the signal region.

7.2 Method 65

[GeV]miss, rel

TCut value E

>50 >60 >70 >80 >90 >100 >110 >120 >130 >140

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(a)

] [GeV]jet2

T,p

jet1

TCut value [p

[20,20] [30,30] [35,25] [35,35] [40,35] [40,40] [45,40] [45,45] [50,45] [50,50]

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(b)

[GeV]jj

Cut value M

[0,100] [0,150] [0,200] [50,100] [50,150] [50,200]

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(c)

[GeV]ll

TCut value p

>60 >70 >80 >90 >100 >120 >140 >160 >180 >200

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼m

(d)

R(ll)∆Cut value

[0.3,0.9] [0.3,1.1] [0.3,1.3] [0.3,1.5] [0.3,1.7] [0.3,1.9] [0.3,2.1]

p

210

110

1

10 =150 GeV0

1χ∼

=200 GeV, m±

1χ∼,

0

2χ∼

m

=150 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

(e)

Figure 7.6: After all cuts are in place one cut at a time is removed and the sensitivity fordifferent cuts on each variable is studied. The figure of merit is the p-value defined insection 7.2.1. The variables shown are (a) Emiss,rel

T , (b) p jet1,2T , (c) m j j, (d) p``T and (e)

∆R(``).


7.3 Results

The signal region is now fixed to the selections of Tab. 7.2. Table 7.3 shows the numberof Monte Carlo events in the signal region for each background source. Also the expectednumber of events for three signal points are shown. After all cuts have been appliedthe expected sensitivity is calculated for supersymmetric models with pp→ χ0

2 + χ±1 →

W±χ01 + Zχ0

1 . In Fig. 7.7 the p-value (see Sec. 7.2.1) for each signal point is plottedas color scale in the m

χ02 ,χ±1,m

χ01

plane. A flat systematic error of 20% on the expectednumber of background events is used. p < 0.05 means that the probability of the signalplus background fluctuating to the expected b is less than 5%. If no excess over theexpected Standard Model background is observed in the signal region that signal modelcan be excluded with 95% confidence level.

Source ee µµ ee+µµ

ZW, ZZ 0.59±0.15 0.39±0.11 0.99±0.17WW 0.00±0.00 0.04±0.03 0.04±0.03Top 0.02±0.01 0.01±0.01 0.03±0.01Higgs 0.00±0.00 0.00±0.00 0.00±0.00Z→ ττ 0.00±0.00 0.00±0.00 0.00±0.00Z+jets 0.00±0.00 0.00±0.00 0.00±0.00Total MC background 0.62±0.15 0.45±0.11 1.07±0.17m

χ02 ,χ±1= 250 GeV, m

χ01= 100 GeV 1.20±0.20 1.46±0.21 2.66±0.29

mχ0

2 ,χ±1= 300 GeV, m

χ01= 100 GeV 1.70±0.16 1.79±0.16 3.50±0.23

mχ0

2 ,χ±1= 350 GeV, m

χ01= 50 GeV 1.94±0.12 1.77±0.11 3.71±0.16

Table 7.3: Background composition of the signal region based on Monte Carlo simulation.The given errors are purely statistical.

The contour in Fig. 7.7 indicates the area where p < 0.05 and shows the expected ex-clusion reach of this analysis for a 20% systematic uncertainty. Compared to Fig. 6.2(b),which shows the area previously excluded by searches in the trilepton channel, the ex-clusion reach is improved. Chargino and neutralino masses up to m

χ02 ,χ±1= 410 GeV are

within reach for a massless χ01 .

The actual observed limit from measurements on collision data can be expected tochange with respect to the limit in Fig. 7.7. The systematic uncertainties in this chapterare taken to be 20%, a number estimated from previous studies. The exact size of thesystematic uncertainties is dependent on signal region definition and not fully known untilthe analysis is complete. At later stages of the analysis the systematic error on the signalregion is fully determined and this number is used in the final calculation of actual limits.Also the observed number of events in the signal region may a priori fluctuate from the

7.3 Results 67

background estimate even under a background only scenario.

[GeV]±

1χ∼,

0

2χ∼

m

100 150 200 250 300 350 400 450 500

[G

eV

]0 1χ∼

m

0

50

100

150

200

250

300

350

400

450 p

0

0.05

0.1

0.15

0.2

0.25

0.31

L dt = 20.3 fb∫ = 8 TeVs

µµee + 01χ∼

< m

±1χ∼,0

2χ∼m

Z

= m

01χ∼

m

0

2χ∼m

Figure 7.7: Expected sensitivity for different gaugino masses in the mχ0

2 ,χ±1,m

χ01

plane.The figure of merit on the color z-axis is the probability p defined in section 7.2.1. A flatsystematic error of 20% on the expected number of background events is used in the sen-sitivity calculation. The contour indicates the limit where p < 0.05 which is the expectedexclusion reach. Each black cross indicates one signal point that has been simulated.

8 Standard Model Background

Estimate

A large number of Standard Model processes can enter the signal region established inchapter 7. The processes are grouped in several categories described below. In this chapterthe techniques used to derive these backgrounds are briefly described for each group andmore details are given in Paper III. The measurement of the Z + jets background is thefocus of chapter 9 of this thesis.

8.1 Diboson production, ZW and ZZEvents contributing to this background come from the processes ZZ→ ``νν and ZW →```ν where one lepton fails to be reconstructed. The jets come essentially from ISR.Triboson processes are added to this category. As seen in Tab. 7.3, this is the largestexpected background.

It is difficult to find a control region similar to the signal region and sufficiently purein ZZ and ZW . Therefore the background is estimated from Monte Carlo simulated data.Special control samples with three and four reconstructed leptons, enriched in ZZ→ ````and ZW → ```ν respectively, are used to validate the shape and scale of the simulateddata. An additional uncertainty is assigned to the estimated background to account fordiscrepancies between simulated and collision data.

8.2 Top

The tt and Wt backgrounds have very similar Emiss,relT shapes and are therefore estimated

together. For this background a data driven method is used. A control region is identifiedwith events with two leptons outside the Z-window and with one b-tagged jet. The numberof events at high Emiss,rel

T is extracted and compared to the simulation. The ratio betweendata and simulation is then used to scale the top Monte Carlo in the signal region.

8.3 Fake Leptons

Fake leptons are leptons that originate from hadron decays, misidentified jets, or electronsfrom photon conversions. These leptons can be misidentified as real, isolated leptons that

70 Standard Model Background Estimate

normally arise from the decay of W and Z bosons. If a jet or photon is misidentifiedas a lepton, processes with one or no real lepton can appear to have two leptons, thuscontributing to the background in the signal region. Processes contributing to this orfake lepton background are s- and t-channel single top, tt where at least one W decayshadronically, W + jets, bb, and multijet QCD production.

All background processes with fake leptons are estimated collectively using a datadriven method known as the matrix method. This method uses the real efficiency, i.e.the probability of a real lepton passing the selections criteria, and the fake rate, i.e. theprobability of a fake lepton passing the same criteria, to statistically predict the number offake leptons in the signal region. The real efficiency and fake rate are measured in data. Asimilar method was applied by the author in an earlier work and is described in Paper IV.

8.4 Other Backgrounds

In this category are included electroweak backgrounds that lead to small contributions:WW , Higgs and Z→ ττ . All these processes are determined with simulation and normal-ized using theoretical cross sections at NLO or higher.

8.5 Z + jets Background with the Jet Smearing Method

For the estimation of the (Z/γ∗→ ``)+ jets background, two methods were developed forPaper III. The Emiss,rel

T in this background is fake Emiss,relT , mainly due to the jet resolution

rather than the presence of high pT invisible particles. It is desirable to use a data driventechnique, since Monte Carlo simulations run out of statistics and it is nearly impossiblesimulate the statistics necessary. Another reason to rely on data is that the Z+ jets processhas a large cross section, thus a low rate of events with high calorimeter noise could lead toa significant number of Z+ jets events migrating towards the signal region. Two methodshave been developed in support of Paper III, the method relying on photon control regionsdeveloped by the author described in chapter 9, and the jet smearing method describedbelow which is used for the final numbers in Paper III.

The jet smearing method uses a sample enriched in Z+ jets events with well measuredjets to define seed events. This is implemented by requiring Emiss

T /√

EsumT < 1.5 GeV1/2.

Each seed event is smeared multiple times by multiplying the four-momentum of each jetwith a random number from a jet response function. The jet response function is obtainedfrom simulation and adjusted to data in a control sample. The smearing is repeated 10,000times for each seed event. Thus pseudo-data with jet resolution following the adjusted jetresponse is obtained. The pseudo-data is normalized to data in the low Emiss,rel

T region andthe number of Z + jets events is evaluated in the high Emiss,rel

T region.

9 Data Driven Z + jets

Background Estimation

This chapter presents one of two methods developed for the estimation of the Z+jets back-ground in the search for supersymmetry described in Paper III. In a previously unexploredsignal region it is important to cross check results with different methods, and at the endof the chapter the two methods are compared and the strong and weak points of each arediscussed.

9.1 Motivation

Although simulations indicate that the number of Z+ jets events in the high Emiss,relT region

is low, it is important to confirm this point using a data driven method. The Emiss,relT can

schematically be seen as coming from two sources: real Emiss,relT and fake Emiss,rel

T .

• Real Emiss,relT arises when neutrinos or other weakly interacting neutral particles

such as hypothetical neutralinos pass through the detector, carrying away momen-tum that cannot be detected.

• Fake Emiss,relT is due to instrumental effects, such as the resolution of leptons and

jets. The fake Emiss,relT is difficult to model in simulations.

(Z/γ∗→ ``)+ jets where both leptons have been identified do not have true Emiss,relT ,

since no particles invisible to the detector are present. The missing energy in these eventsarises mainly from the limited resolution of the jet energy. In ATLAS the jet energyresolution is approximately 7 GeV for a jet with pT = 45 GeV [68], while the uncertaintyfor leptons with pT around 30 GeV is close to 2% or 0.6 GeV per lepton [69, 42].

Figure 9.1 shows the distribution of Emiss,relT in the signal region for different back-

ground processes and signal models. The sharp drop of the Z → ``+ jets backgroundat Emiss,rel

T = 70 GeV is the result of too low Monte Carlo statistics. The low numberof predicted events causes large statistical errors and it is not time efficient to producethe number of simulated events required for an accurate background estimate. Thereforea data driven background estimate is preferred. Using a data driven technique shouldcapture detector effects that could lead to a low rate of events with high mismeasuredEmiss,rel

T contributing to the signal region.

72 Data Driven Z + jets Background Estimation

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400

Events

/ 1

0 G

eV

110

1

10

210

310

410

510

µµSignal Region, ee +

1


ZW, ZZ

WW

τ τZ

top

Higgs

=100 GeV0

1χ∼

=250 GeV, m±

1χ∼,

0

2χ∼

m

=100 GeV0

1χ∼

=300 GeV, m±

1χ∼,

0

2χ∼

m

=50 GeV0

1χ∼

=350 GeV, m±

1χ∼,

0

2χ∼

m

Figure 9.1: Distribution of the relative missing transverse momentum within the signalregion without the cut on Emiss,rel

T > 80 GeV. The band on the total background is theerror from Monte Carlo statistics and a flat systematic error of 20%. The dashed linesshow the Emiss,rel

T distribution from three benchmark signal models.

This chapter presents a data driven estimate of the Z + jets background using controlregions selected with one or two photons plus jets. The Z + jets background events sur-viving to the signal region must be characterized by a high pT Z-boson recoiling against ajet system that sets the missing energy; the single photon and diphoton regions are charac-terized by a high pT photon or diphoton system recoiling against a jet system, as depictedin Fig. 9.2.

Jet

Jet

l

l

Z

(a)

Jet

Jet

γ

(b)

Jet

Jet γ

γ

(c)

Figure 9.2: Sketch of the event topology for (a) a Z + jets event, (b) a single photon plusjets event, and (c) a diphoton plus jets event

9.2 Missing Transverse Momentum in Photon Control Regions 73

9.2 Missing Transverse Momentum in Photon Control Regions

In order to perform a data driven background estimate in a signal region, a control region,completely orthogonal to the signal region and with similar kinematic properties, must bedefined. If the shape of the Emiss,rel

T distribution in the control region is close enough tothat in the signal region, the number of background events can be extracted from collisiondata in the control region and transferred to the signal region. In the present case photoncontrol regions are chosen. Since photon energy resolution is similar to that of electronsthe missing energy in such regions is dominated by jet effects and presents the same jetresolution effects. This chapter investigates two different photon control regions and theadvantages and disadvantages for each are discussed.

9.2.1 Diphoton Control Region

Photons and electrons are measured via electromagnetic showers in the EM calorimeterand contribute in the same way to the Emiss

T resolution. Also the muons have a comparableresolution. In all three cases the Emiss,rel

T spectrum will be dominated by the jet energyresolution. The distribution of fake Emiss

T is therefore expected to be similar in the signalregion and in a control region with cuts mimicking the signal region but with the twoleptons replaced by two photons. Since the two photons exactly match the number ofleptons, the total number of objects present in the detector is the same in the control andsignal regions, and the Emiss,rel

T (defined in Eq. 6.5.3) distribution is also expected to besimilar in the two regions. Figure 9.3(a) shows the Emiss,rel

T distribution in simulation,normalized to unit area, from simulation in the diphoton control region (black circles)and in the electron (red triangles) and muon (green squares) channels of the signal region.The error band represents the error on Monte Carlo statistics and systematic uncertaintiescombined.

As seen in Fig. 9.3(a), the core of the Emiss,relT distribution in the diphoton control

region agrees well within errors with the distributions from the signal region. However itis again clear that the simulation runs out of statistics with increasing Emiss,rel

T . Thereforeit is important to check the shapes also in collision data. In Sec. 9.7 the shape of thediphoton Emiss,rel

T template from data is compared to the shape of the Emiss,relT in the signal

region. The agreement is good in data and it is concluded that the Emiss,relT distribution in

control region can be used to estimate the number of Z + jets events with high Emiss,relT in

the signal region.The choice of a diphoton region however has the disadvantage of low statistics. No

simulated events survive the hard cuts of the signal region. To circumvent this problemit is investigated whether some cuts can be relaxed to increase the number of events, asdescribed in further detail later in this chapter. The shape of the Emiss,rel

T distributionis unaffected by changes to the cuts on mγγ , ∆R(γγ), m j j, and p jet2

T . Therefore slightlyrelaxed cuts in the control region can be used. The selections defining the diphoton control

74 Data Driven Z + jets Background EstimationA

rbitra

ry u

nits

510

410

310

210

110

1γγ

ee

µµ

>80 GeV)T

γγ

Diphoton Control Region (p

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400

γγ

ll/

10123

(a)

Arb

itra

ry u

nits

510

410

310

210

110

1

80γ1

ee

µµ

>80 GeV)T

γ

Single Photon Control Region (p

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400 8

0

γll/

110123

(b)

Figure 9.3: The Emiss,relT distribution from simulation in (a) the diphoton control region

(γγ) and (b) the single photon control region (1γ80), see Tab. 9.1. The Emiss,relT distribu-

tion in the control regions is marked by black circles, and that of the electron and muonchannels of the signal region are marked by red triangles and green squares respectively.The error band represents the error on Monte Carlo statistics, theoretical uncertainties andsystematic uncertainties combined. For the distribution in (b) the correction discussed inSec. 9.2.2 is applied.

region are given in Tab. 9.1. The looser control region cuts are used in Fig. 9.3(a). Evenafter the looser cuts of the control region are applied few events remain, causing a largestatistical error.

9.2.2 Single Photon Control Region

A different approach for a control region is to use γ + jets events. Photons and Z-bosonsare both vector bosons and are produced via similar processes. If the photon in a γ +jets event has high pT, the jet activity balancing the event is expected to be similar to thatin a Z+ jets event. Since the Emiss,rel

T mostly arises from jet activity, the Emiss,relT spectrum

should be similar in high-pT γ + jets events and in Z + jets events.

The cuts in the single photon control region closely mimic those in the signal regionexcept the lepton selections. The signal region cut on the dilepton momentum p``T istranslated into a cut on the pT of the single photon, and the cut on pT of the secondleading jet is relaxed in order to gain statistics. The selections of the control and signalregions are defined in Tab. 9.1.

9.3 Control Region De�nitions 75

Correction for Emiss,relT

The single photon control region exhibits a slightly harder Emiss,relT spectrum than the

signal region. The explanation for this lies in the definition of Emiss,relT given in Eq. 6.5.31).

If the angle ∆φγ, j between a reconstructed object and the direction of the EmissT is small

(∆φγ, j < π/2), only the component of EmissT perpendicular to the object is considered,

defining the variable Emiss,relT . If the number of reconstructed objects in the detector is

larger, the probability that ∆φγ, j < π/2 increases giving a smaller Emiss,relT .

In the single photon control region only one photon is required instead of two as inthe diphoton control region. Also in the signal region two particles (e/µ) are present.Therefore the number of objects potentially close to the direction of the Emiss

T is lower inthe single photon control region, which translates into a harder Emiss,rel

T spectrum.Since the background estimate requires close agreement between the Emiss,rel

T distri-butions in the control and signal regions, the Emiss,rel

T in the single photon control regionmust be treated equivalently to that of the dilepton and diphoton regions. For each event,a direction is randomly chosen so that it does not overlap with electrons, muons, jets, orphotons in the detector. This direction defines a so called pseudo photon. When calcu-lating the Emiss,rel

T the direction of this pseudo photon is considered along with the otherobjects, giving the same number of objects in the control and signal regions.

Figure 9.3(b) shows the Emiss,relT distribution after the correction is applied. The agree-

ment between the control and signal regions is within errors in the core of the distribution.The low Monte Carlo statistics in the signal region prevents a comparison in the highEmiss,rel

T region. In Sec. 9.7 the single photon Emiss,relT template from data is compared to

the shape of the Emiss,relT in dilepton data and the agreement is good.

Compared to the diphoton control region the single photon control region benefitsfrom higher statistics, which is reflected in smaller statistical errors.

9.3 Control Region De�nitions

The cuts of the control regions are chosen to correspond to those of the signal region.However some modifications are necessary to increase statistics. The signal region cutson variables related to leptons are translated into corresponding cuts on photon variables.For the diphoton control region the cuts on m j j, ∆R(``), and |mZ−m``| are removed andthe cut on the pT of the second leading jet is lowered from 45 GeV to 20 GeV in orderto increase statistics. The diphoton control region uses a diphoton trigger where bothphotons are required to pass a pT > 20 GeV threshold.

For the single photon control region all cuts involving the second leading leptonare ignored, since only one photon is present. The cut on m j j has been relaxed tom j j < 600 GeV, which increases statistics while still reducing the amount of QCD con-

1)For photon events the term ∆φl, j in Eq. 6.5.3 is substituted by ∆φγ, j.


tamination in the region. For the single photon control region a combination of threephoton triggers are used, requiring photon pT larger than 40, 80, and 120 GeV respec-tively. The cuts defining the control regions are detailed in Tab. 9.1.

Signal region 1γ80 γγ

NC20 ≥ 2 ≥ 2 ≥ 2NB20 +NF30 = 0 = 0 = 0p jet1

T > 45 GeV > 45 GeV > 45 GeVp jet2

T > 45 GeV > 20 GeV > 20 GeVm j j [50,100] GeV < 600 GeV —N` = 2 = 0 = 0Nγ — = 1 = 2

pγ1/`1T > 35 GeV > 80 GeV > 35 GeV

pγ2/`2T > 20 GeV — > 20 GeV

pγγ/``T > 80 GeV — > 80 GeV

∆R(γγ/``) [0.3,1.5] — —|mZ−m``| < 10 GeV — —

Table 9.1: Definition of the single photon and diphoton control regions, with the signalregion definition as comparison. N` denotes the number of tight electrons or muons, andNγ denotes the number of tight photons whose definition are outlined in chapter 4. pγ1/`1

T ,pγ2/`2

T , and pγγ/``T denote the pT of the photons in the control regions and the pT of the

leptons in the signal region. ∆R(γγ/``) denotes the distance between the photons orleptons in the control and signal regions respectively.

9.4 The ABCD Method

If the shape of the Emiss,relT spectrum in the control region is approximately the same as

in the signal region, a template Emiss,relT spectrum from the control region can be used to

obtain the number of events with Emiss,relT > 80 GeV in the signal region. However, the

Emiss,relT templates from single photon, diphoton, and dilepton data can be contaminated

by processes with true Emiss,relT which contribute to a high tail of Emiss,rel

T . The events withtrue Emiss,rel

T must be subtracted from the photon templates before the templates can beused as a model for the fake Emiss,rel

T in the signal region. The number of such events isobtained from simulation and is the focus of section 9.5.

9.4 The ABCD Method 77

The number of Z + jets events in the high Emiss,relT region is predicted following these

steps:

1. Extract the shape of a Emiss,relT template in the photon control region in collision

data.

2. Validate the normalization of real Emiss,relT processes by comparing Monte Carlo

simulations to data in the photon control regions.

3. Subtract (using Monte Carlo simulation) processes with real Emiss,relT from data to

obtain a fake Emiss,relT template.

4. Use dilepton events with Emiss,relT < 40 GeV, which are dominated by Z + jets, to

normalize the fake Emiss,relT template.

5. Finally use the normalized fake Emiss,relT template to predict the number of Z + jets

events with Emiss,relT > 80 GeV in the signal region.

[GeV]miss, rel

TE

0 20 40 60 80 100 120 140 160 180 2000

1

A

NR

B

Signal Region

C

NR

D

Control Region

ll

γ /1γγ

Figure 9.4: Schematic picture showing the signal region, control region and normalizationregions (NR) used to estimate the Z + jets background.

A schematic picture of the control region, signal region and normalization regionsis shown in Fig. 9.4. Agreement between the shape of the Emiss,rel

T distribution in thecontrol and signal regions translates into the relation B/A = D/C, were A, B, C, and Dare the number of Z + jets events in the regions defined in Fig. 9.4. The number of fake


Emiss,relT events is obtained by subtracting the number of real Emiss,rel

T events, denoted bysubscript ’MC’, from the number of events from data, denoted by subscript ’data’, in eachregion:

Bdata−BMC

Adata−AMC=

Ddata−DMC

Cdata−CMC(9.1)

The sought number of Z+ jets events, N(Z+ jets), in the signal region is Bdata−BMC.From Eq. 9.1 this number is obtained from

N(Z + jets) =[

Adata−AMC

Cdata−CMC

]× (Ddata−DMC) (9.2)

An important aspect to determining the number of Z + jets events is the ability topredict the number of events with real Emiss,rel

T in the photon control regions, as detailedin Sec. 9.5.

9.5 Sample Composition

From Eq. 9.2 it appears crucial to be able to subtract the processes with real Emiss,relT from

the control regions to get an accurate estimate of the number of Z + jets events. The goalof this section is to determine which processes should be included in the real Emiss,rel

T tem-plate for the two control regions. The Monte Carlo samples used to simulate the processesare described and the theoretical uncertainties on the cross sections are stated. These un-certainties are later propagated to the final fake Emiss,rel

T template.

9.5.1 γ + jets

In the single photon control region the goal is to extract the Emiss,relT template for the

process γ + jets from data. Therefore it is not included in the real Emiss,relT contribution

which is subtracted from data.In the diphoton control region γ + jets events can enter if a fake prompt photon arises.

The Emiss,relT in these events is fake and the process is therefore not included in the real

Emiss,relT template. Monte Carlo samples generated with Pythia8 [70, 71] are used to

validate the agreement between simulation and collision data in the control regions but donot enter in any of the terms in Eq. 9.2.

9.5.2 γγ + jets

This group of processes dominates the low Emiss,relT region in the diphoton control region.

Events of this process group that pass into the diphoton control region do not have anyreal Emiss,rel

T and are therefore not included in the real Emiss,relT template.

9.5 Sample Composition 79

If one photon fails reconstruction the process will contribute significantly to the singlephoton control region. However, in this case the non-reconstructed photon will contributeto the Emiss,rel

T . This contribution is much larger than the Emiss,relT from resolution effects

and has no corresponding contribution in the signal region. Therefore the process groupis subtracted from the fake Emiss,rel

T template.The diphoton Monte Carlo sample is generated with Pythia8 and contains processes

of two types: processes with two prompt photons produced by hard scattering and pro-cesses with one prompt photon and one photon from initial state radiation. The eventswith two prompt photons are weighted with a k-factor of 8 to normalize the cross sectionto NLO. The cross section on both types of processes are assigned an uncertainty of 30%.The k-factor and the uncertainty thereupon are estimated using DIPHOX [72].

9.5.3 W/Z +0γ

This class of processes contains the processes (Z → ``) + jets, (Z → νν) + jets, and(W → `ν)+ jets. Any observed photons are misidentified electrons or jets. (Z→ νν)+

jets and (W → `ν) events always have real Emiss,relT due to the neutrinos and are subtracted

from the fake Emiss,relT template for both single photon and diphoton control regions.

In the control regions a veto on electrons and muons is applied which means no lep-tons have been reconstructed. Z→ `` events do not normally have real Emiss,rel

T . However,in order for a Z→ `` event to pass into the single photon control region where electron andmuon vetoes are applied, one lepton must be misidentified as a photon and the other lep-ton must fail reconstruction entirely. The lepton that is not reconstructed will contributeits entire transverse momentum to the Emiss,rel

T , causing a much higher Emiss,relT than ex-

pected from resolution effects. There is no equivalent contribution in the signal regionand therefore the process is subtracted from the fake Emiss,rel

T template.In the diphoton region a distinction must be made between Z → ee and Z → µµ

events. A Z→ ee event passing into the diphoton control region will have two electronsmisidentified as photons. In such an event no objects have completely failed reconstruc-tion. The energy resolution and energy scale are very similar for electrons and photonsand the Emiss,rel

T is not affected by the misidentification of the electrons. Therefore theprocess is not included in the Emiss,rel

T template.Muons have a different signature and cannot be misidentified as photons. Photons

can be produced in a Z → µµ event either by bremsstrahlung from a muon or from ajet. In order for the event to pass the control region criteria, the muons must entirely failreconstruction. If the photons are radiated from the muons and carry a large part of themomentum the muons would be lost and the pT of the muon would be replaced by thepT of the photon in Eq. 4.2. It is however very unlikely that a radiated photon would carryall of the muon momentum. Instead the muons are not reconstructed for other reasons, forinstance by falling out of the muon system acceptance. No such contribution is present inthe signal region since two leptons are required. Therefore the process is subtracted from


the fake Emiss,relT template for both single photon and diphoton control regions.

In the signal region the Z→ ττ background has been estimated with Monte Carlo. Inorder not to double count this background the process is included in the real Emiss,rel

T pro-cesses to be subtracted from the photon control regions. It is however a very small contri-bution.

The samples are generated with Alpgen [73] and the parton showering is modeledwith Pythia. The cross sections are calculated with FEWZ [74] at NNLO and have atheoretical uncertainty of 5%.

9.5.4 W/Z +1γ

This group contains the processes (W → `ν)+ γ + jets, (Z → ``)+ γ + jets, and (Z →νν)+ γ + jets. The (W → `ν)+ γ and (Z→ νν)+ γ events always have real Emiss,rel

T dueto the neutrinos and are subtracted from the fake Emiss,rel

T template for both single pho-ton and diphoton control regions. In order for the (Z → ``) + γ events to pass to oneof the control regions at least one lepton must fail to be reconstructed. This gives realEmiss,rel

T and the process must be subtracted from the fake Emiss,relT template since no cor-

responding contribution is present in the signal region which requires two leptons.The W + γ events are generated with Alpgen and the parton showering is performed

by HERWIG/JIMMY [75, 76]. The cross sections are calculated at NLO with MCFM [77]. Ak-factor of k = 1.4 is applied and a theoretical uncertainty of 50% is used [78].

The Z + γ events are modeled with Sherpa [79]. The cross sections are calculated atNLO with MCFM. The theoretical uncertainty is 15% [78].

9.5.5 W/Z +2γ

The group comprises the processes (W → `ν)+ γγ , (Z→ ``)+ γγ , and (Z→ νν)+ γγ .The latter has real Emiss,rel

T due to the neutrinos and is therefore included in the realEmiss,rel

T processes to be subtracted from the photon control regions. In order for the otherprocesses to pass the control region criteria one or more lepton must completely fail re-construction and the process group is therefore subtracted from the fake Emiss,rel

T template.The Z samples are generated with Sherpa, and the W samples are generated with Alpgen

with hadronic showering provided by HERWIG/JIMMY. The cross sections are calculatedat leading order and a NLO k-factor is applied. The uncertainty on the k-factor is 15% forthe Sherpa samples [80] and 100% for the Alpgen samples [81].

9.5.6 Top+X

This group contains all processes that include top quarks. Leptonic top quark decays areassociated with real Emiss,rel

T these processes are included in the real Emiss,relT processes

to be subtracted from the photon control regions. Hadronic top quark decays enteringthe signal region are estimated by the matrix method and are therefore subtracted from

9.5 Sample Composition 81

the photon control regions in order to avoid double counting. The samples used for theTop+X processes are described below.

Top Pair Production

The top quark pair production sample is generated with MC@NLO [82] and the hadronicshowering is modeled with Jimmy. The cross section is calculated to approximatelyNNLO with a theoretical uncertainty of 6% [83].

Single Top

Three different subprocesses contribute to the production of single top quarks at the LHC:the t-channel, the s-channel, and the Wt-channel. The t-channel processes are generatedusing AcerMC [84] with the hadronic showering modeled by Pythia. The s- and Wt-channels are generated using MC@NLO with hadronic showering modeled by Jimmy. Thecross sections are calculated at approximately NNLO [85, 86, 87]. The theoretical uncer-tainty on the cross sections is of the order 3–4% for the t- and s-channels and 7% for theWt-channel.

Top Pair + Bosons

The production of top quark pairs in association with electroweak bosons is modeled atleading order with MadGraph [88] with parton showering by Pythia. A k-factor is appliedto normalize the events to NLO. The uncertainty of the k-factor is 30% for tt+W and 50%for tt +Z and tt +WW [89, 90].

Top Pair + γ

The production of top quark pairs with an associated photon is generated using MadGraph

and the parton showering is modeled by Pythia. The cross section has been measuredin ATLAS and was in good agreement with the Standard Model expectation [91]. Theuncertainty of the measurement was 25% and this uncertainty is assumed for the crosssection of the process.

9.5.7 Diboson

This group of processes contains electroweak boson pair production: WW , ZZ, and ZW .Also the triboson processes ZWW , ZZZ, and WWW are included in the group. Dueto neutrinos or undetected leptons all processes in this group have real Emiss,rel

T and aretherefore subtracted from the fake Emiss,rel

T template.The diboson processes are generated using a combination of the Monte Carlo gen-

erators Sherpa, gg2WW [92], and gg2ZZ [93], where the latter two provide correctionsfor gluon induced QCD loop processes producing pairs of W and Z bosons respectively.The parton showering for the processes generated with gg2WW and gg2ZZ is performed


by HERWIG/JIMMY. The cross sections are calculated with MCFM to NLO with a theoret-ical uncertainty of 5–7%. The gluon induced QCD corrections have larger theoreticaluncertainties but contribute only about 5% of the diboson background.

The triboson samples are generated with MadGraph interfaced with Pythia for had-ronic showering. The cross sections are calculated at leading order and a k-factor isapplied to normalize the samples to NLO. However the k-factor varies over the phasespace and therefore a conservative theoretical uncertainty of 100% is applied [94].

9.5.8 Multijet QCD

This process group contains pure multijet QCD processes. No real Emiss,relT is present so

the processes are not subtracted from the fake Emiss,relT template; the Monte Carlo samples

generated with Pythia8 are only used to evaluate the agreement between simulation andcollision data in the following sections. Since the processes are not subtracted from thefake Emiss,rel

T template, they do not enter any term of Eq. 9.2 and the theoretical uncertaintyon the cross section does not affect the final uncertainty on the number of Z + jets eventsin the signal region. Therefore no theoretical uncertainty is applied.

9.5.9 Summary of Processes with Real Emiss,relT

A summary of which process groups are subtracted from the photon control regions isfound in Tab. 9.2. All the processes contributing to real Emiss,rel

T are subtracted fromthe data in the single photon and diphoton control regions. The uncertainties from thetheoretical cross sections are propagated as well as the detector systematic uncertaintieson the fake Emiss,rel

T template.

9.6 Validation of Normalization of real Emiss relT Processes

For the subtraction of real Emiss,relT processes it is important to verify that the simulated

samples and theoretical cross sections provide an accurate model. For this purpose colli-sion data and simulated data in the control regions are compared.

Figure 9.5 shows the EmissT (a) and Emiss,rel

T (b) spectra in the diphoton control region,(c) and (d) show the Emiss

T and Emiss,relT spectra in the single photon control region. The

lower part of the figure shows the ratio between collision data and the prediction. Theerror band incorporates the error from Monte Carlo statistics, theoretical uncertaintiesfrom real Emiss,rel

T processes, luminosity uncertainty and systematic uncertainties. Thestatistics in the diphoton control region is low in the high Emiss,rel

T region. Therefore asingle wide bin is used in the region where Emiss,rel

T > 80 GeV. In both control regionsthe simulated and collision data agree well within errors, which indicates that the realEmiss,rel

T estimate is at the right level.Figure 9.6 shows a comparison between collision and simulated data for (a) the pT of

9.7 Photon Template Comparison with Dilepton Data 83

Diphoton Control Region Single Photon Control regionγ + jets Not subtracted Not subtractedγγ Not subtracted SubtractedW +0γ Subtracted Subtracted(Z→ ee)+0γ Not subtracted Subtracted(Z→ µµ)+0γ Subtracted Subtracted(Z→ νν)+0γ Subtracted SubtractedW/Z +1γ Subtracted SubtractedW/Z +2γ Subtracted SubtractedTop + X Subtracted SubtractedDiboson Subtracted SubtractedQCD Not subtracted Not subtracted

Table 9.2: Summary of process groups are subtracted from the photon control regions toobtain the fake Emiss,rel

T template.

the diphoton system in the control region, and (b) the pT of the photon in the single pho-ton control region. The error band incorporates the error on Monte Carlo statistics, the-oretical uncertainties from real Emiss,rel

T processes, luminosity uncertainty and systematicuncertainties. Also in these variables excellent agreement is observed.

9.7 Photon Template Comparison with Dilepton Data

As discussed in previous sections, it is important for the ABCD method that the shape ofthe Emiss,rel

T spectra of the signal and control regions are the same. The real Emiss,relT con-

tribution can now be subtracted from the data, enabling a comparison between the fakeEmiss,rel

T in ee/µµ and photon data. Some caution is necessary at this point to avoidunblinding the signal region, thus contaminating the shape with signal. Two differentapproaches are possible.

The first approach consists in comparing the fake Emiss,relT template from the photon

control regions to a subset of dilepton data. Although this check involves the signal regionitself, unblinding is avoided by limiting the data set size. Previous studies have shown thatfor 5 fb−1 there is no sensitivity to pp→ χ0

2 χ±1 → Zχ0

1W χ01 in the signal region.

Figure 9.7 shows photon fake Emiss,relT templates from data, with real Emiss,rel

T pro-cesses subtracted, normalized to unit area in (a) the diphoton region and (b) the singlephoton region. The photon templates are marked by black circles and the electron andmuon channels of the signal region are marked by red triangles and green squares respec-tively. In this figure 5 fb−1of data is used for the dilepton distributions. The core of thedistribution is shown in logarithmic scale and the high Emiss,rel

T region, which becomes

84 Data Driven Z + jets Background EstimationE

ve

nts

/ 2

0 G

eV

110

1

10

210

310

410

510

610

710

>80 GeV)T

γγDiphoton Control Region (p

+ jetγγγ

νν→ZγW/Z + 0 γW/Z + 1

γ 2 ≥W/Z + top + XDibosonQCDMonte Carlo

=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]Tmiss

E0 50 100 150 200 250 300 350 400d

ata

/ p

red

.

0

1

2

(a)

Eve

nts

/ b

in

110

1

10

210

310

410

510

610

710

>80 GeV)T


+ jetγγγ



=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400da

ta /

pre

d.

0

1

2

(b)

Eve

nts

/ 2

0 G

eV

110

1

10

210

310

410

510

610

710

810

>80 GeV)T

γSingle Photon Control Region (p

+ jetγγγ



=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]Tmiss

E0 50 100 150 200 250 300 350 400d

ata

/ p

red

.

0

1

2

(c)

Eve

nts

/ 2

0 G

eV

110

1

10

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310

410

510

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710

810

910

>80 GeV)T


+ jetγγγ



=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]T

miss, relE

0 50 100 150 200 250 300 350 400da

ta /

pre

d.

0

1

2

(d)

Figure 9.5: Comparison between simulated and collision data in the control regions. (a)shows Emiss

T and (b) shows Emiss,relT in the diphoton control region, (c) shows Emiss

T and(d) shows Emiss,rel

T in the single photon control region. The lower panel of the figureshows the ratio between collision data and the prediction. The error band incorporates theerror on Monte Carlo statistics, theoretical uncertainties on the real Emiss,rel

T processes,luminosity uncertainty and systematic uncertainties.

slightly negative after the subtraction of real Emiss,relT , is inset in linear scale.

The other approach utilizes a relaxed dilepton signal region where the signal is so di-

9.7 Photon Template Comparison with Dilepton Data 85E

ve

nts

/ 4

0 G

eV

110

1

10

210

310

410

510

610

710

>80 GeV)T


+ jetγγγ



=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]2γ

1γ

TP

0 100 200 300 400 500 600 700 800 900 1000da

ta /

pre

d.

0

1

2

(a)

Eve

nts

/ 4

0 G

eV

110

1

10

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310

410

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710

810

>80 GeV)T


+ jetγγγ



=8 TeV)sData (

1

L dt = 20.3 fb∫

[GeV]1γ

Tp

0 100 200 300 400 500 600 700 800 900 1000da

ta /

pre

d.

0

1

2

(b)

Figure 9.6: Comparison between simulated and collision data. (a) shows the pT of thediphoton system in the diphoton control region, and (b) the pT of the photon in the singlephoton control region. The lower panel of the figure shows the ratio between collisiondata and the prediction. The error band incorporates the error on Monte Carlo statis-tics, theoretical uncertainties on the real Emiss,rel

T processes, luminosity uncertainty andsystematic uncertainties.

luted that the effect of the signal on the Emiss,relT shape becomes negligible. This method

requires that the relaxation of cuts itself does not affect the Emiss,relT shape. Removing the

cuts on m j j and ∆R(``) dilutes the signal sufficiently to effectively eliminate all sensitiv-ity to the signal. Figure 9.8 shows photon fake Emiss,rel

T templates from data, with realEmiss,rel

T processes subtracted, normalized to unit area in (a) the diphoton region and (b)the single photon region. The relaxed and diluted signal region is used for the dileptondistributions.

In the case of the relaxed signal region, Fig. 9.8, the shape of the two lepton Emiss,relT dis-

tributions are very similar. Both single photon and diphoton control regions exhibitEmiss,rel

T shapes within errors of the dilepton shapes for most of the Emiss,relT range. In

the case where the full signal region selection is used for the comparison, Fig. 9.7, theEmiss,rel

T shape in the control regions closely follow that in the electron channel. In themuon channel a small deviation is noted around Emiss,rel

T = 50 GeV.In spite of these deviations between the Emiss,rel

T shape in the control regions and thatin the muon channel it is concluded that agreement is sufficient. The deviation is largestin the region Emiss,rel

T = 40–80 GeV, which is not used in the ABCD-method. In the nor-malization region (Emiss,rel

T < 40 GeV) and the high Emiss,relT region (Emiss,rel

T > 80 GeV)


[GeV]miss, rel

TE

0 50 100 150 200 250 300 350 400

Arb

itra

ry u

nits

410

310

210

110

1>80 GeV)

γγ

TDiphoton template (p

0 50 100 150 200 250 300 3500.005

0

0.005

0.01

0.015 γγ

1ee, 5 fb1, 5 fbµµ

(a)

[GeV]miss, rel

TE

0 50 100 150 200 250 300 350 400A

rbitra

ry u

nits

410

310

210

110

1>80 GeV)

γ

TSingle photon template (p

0 50 100 150 200 250 300 3500.005

0

0.005

0.01

0.015 80γ11ee, 5 fb1, 5 fbµµ

(b)

Figure 9.7: Photon fake Emiss,relT templates from data, with real Emiss,rel

T processes sub-tracted, normalized to unit area in (a) the diphoton (γγ) control region and (b) the singlephoton (1γ80) control region. The photon templates are marked by black circles, and theelectron and muon channels of the signal region are marked by red triangles and greensquares respectively. For the dilepton distributions only 5 fb−1 of data is used for blindingpurposes. The error band incorporates the statistical, theoretical, and systematic uncer-tainties from the real Emiss,rel

T processes.

the agreement is within errors. The deviation could be taken into account as a systematicuncertainty. This uncertainty would however be negligible compared to the much largeruncertainties on Monte Carlo statistics and jet energy resolution, which are discussed inthe following sections.

9.8 Systematic Uncertainties

Following Eq. 9.2, the number of Z + jets events in the signal region is estimated using aphoton template constructed by subtracting Monte Carlo simulated real Emiss,rel

T processesfrom collision data in the one or two photon control regions. The simulated processes thatmodel the real Emiss,rel

T are affected by a number of systematic uncertainties which mustbe propagated into a final uncertainty on the number of Z + jets events.

The missing transverse momentum is the negative sum of the energy of all jets, lep-tons, photons, and unidentified energy deposits. Therefore uncertainties on any of thesequantities will be propagated into a total uncertainty on the Emiss,rel

T .

The impact on the Emiss,relT shape is investigated separately for the various sources of

9.8 Systematic Uncertainties 87

[GeV]miss, rel

TE

0 50 100 150 200 250 300 350 400

Arb

itra

ry u

nits

410

310

210

110

1>80 GeV)

γγ

TDiphoton template (p

0 50 100 150 200 250 300 3500.005

0

0.005

0.01

0.015 γγ

ee, relaxed SR

, relaxed SRµµ

(a)

[GeV]miss, rel

TE

0 50 100 150 200 250 300 350 400A

rbitra

ry u

nits

410

310

210

110

1>80 GeV)

γ

TSingle photon template (p

0 50 100 150 200 250 300 3500.005

0

0.005

0.01

0.015 80γ1

ee, relaxed SR

, relaxed SRµµ

(b)

Figure 9.8: Photon fake Emiss,relT templates from data, with real Emiss,rel

T processes sub-tracted, normalized to unit area in (a) the diphoton (γγ) control region and (b) the singlephoton (1γ80) control region. The photon templates are marked by black circles, and theelectron and muon channels of the signal region are marked by red triangles and greensquares respectively. For the dilepton distributions a relaxed version of the signal region isused. The error band incorporates the statistical, theoretical, and systematic uncertaintiesfrom the real Emiss,rel

T processes.

uncertainty. The Emiss,relT shape is determined using nominal values for all parameters.

This is the nominal distribution marked by circles in the sketch in Fig. 9.9. The shape ofthe Emiss,rel

T is reevaluated separately for each source of systematic uncertainty. A singlesource of systematic uncertainty is applied, entering as a shift of one standard deviation,±1σ , in a parameter. Thus two additional Emiss,rel

T shapes are produced, marked in thesketch by N for the +1σ and H for the −1σ . For each bin, the deviation between thenominal and shifted distributions is determined. Thus the impact of that specific sourceof uncertainty is obtained.

This procedure is repeated for all sources of systematic uncertainties. The impacts ofall sources of systematic uncertainties are added in quadrature in each bin to give the totalsystematic uncertainty of the Emiss,rel

T shape.

When the real Emiss,relT processes are subtracted from data, the systematic uncertainties

are added to the statistical error from data, thereby giving the total uncertainty on theEmiss,rel

T template to be used to model Z + jets.

The sources of systematic uncertainties are described in the following sections.


miss,rel

TE

0 50 100 150 200 250 300 350 400

Arb

itra

ry u

nits

0

20

40

60

80

100Nominal

σSyst +1

σSyst -1

Figure 9.9: Sketch showing a nominal Emiss,relT shape, and Emiss,rel

T shapes where a param-eter has been shifted by ±1σ .

9.8.1 Theoretical Uncertainty on Cross Sections

Each process contributing to the real Emiss,relT is normalized with its theoretical cross sec-

tion before it is subtracted from the measured Emiss,relT template in the control regions. The

cross section of each process is varied independently. The uncertainties on the theoreticalcross sections are stated in Sec. 9.5.

9.8.2 Jets

The jet energies in simulation must be scaled to match the energy scale in data. Theamount by which the jets must be scaled is called the jet energy scale, JES. The JES hasan uncertainty due to pile-up and near-by jets and varies with jet pT and η . The jet energyresolution (JER) in simulation would be slightly better than in data if it was not smeared.The amount of smearing is not perfectly known.

The uncertainties on the jet energy scale and resolution have been determined usingboth test beam and collision data [95]. To determine the impact of the uncertainty on thejet energy resolution, the pT of jets is smeared according to a Gaussian with unit meanand width from a pT dependent resolution function.

The uncertainty on jet measurement is the largest source of systematic uncertaintiesfor both diphoton and single photon control regions.

9.8 Systematic Uncertainties 89

9.8.3 Unidenti�ed Energy Deposits

Unidentified energy deposits are significant energy deposits in the calorimeter that arenot included in any of the identified particles. The energy scale and energy resolution forthese energy deposits are not perfectly known but do affect the Emiss,rel

T [96]. The impact ofthe unidentified energy scale and resolution uncertainties on the shape of the Emiss,rel

T dis-tribution is determined by varying an unidentified jet energy scale and resolution. It isone of the largest sources of systematic uncertainties in both diphoton and single photoncontrol regions.

9.8.4 Leptons

In the control regions a lepton veto is applied, and changes in lepton momentum or energyaffects the number of events passing the control region selection and may also affect theshape of the Emiss,rel

T distribution. Changes in the electron energy may also affect theoverlap removal between jets and electrons.

The sources of uncertainty on electron energy considered are the electron energy scale,the electron energy resolution, the electron trigger efficiency, and the electron reconstruc-tion efficiency.

Previous ATLAS analyses have shown that the systematic uncertainty from muons issimilar in size as that from electrons. Therefore the muon contribution is set to equal theelectron contribution in this analysis.

9.8.5 Photons

In order to compensate for discrepancies in photon shower shape variables between sim-ulation and collision data, so called fudge factors are applied on the simulation. As thefudge factors are applied to variables used for photon identification, this gives an uncer-tainty on the photon identification efficiency.

The uncertainty depends on the type of photon and on the energy and η of the photon.For unconverted photons the uncertainty is 2.5% for ET < 40 GeV, 1.5% for ET > 40 GeVand |η | < 1.81, and 2.5% for ET > 40 GeV and |η | > 1.81. For converted photons theuncertainty is 2.5% for ET < 40 GeV and 1.5% for ET > 40 GeV [97].

Also uncertainties on photon identification efficiency, photon resolution, and photonscale make slight contributions to the total systematic uncertainty.

9.8.6 Pile-up

The amount of pile-up, i.e. the expected number µ of interactions per bunch crossing,varies with the instantaneous luminosity and beam parameters. After a data run an aver-age 〈µ〉 is calculated for each lumi-block2) of that run. Monte Carlo simulations on the

2)A lumi-block is an approximately two-minute interval of a run.


other hand, are often prepared before the actual data runs. The Monte Carlo samples aregenerated using an anticipated distribution of 〈µ〉, necessarily different from the actualdistribution. The Monte Carlo events are reweighted at the analysis level to correct fordiscrepancies between the simulated 〈µ〉 distribution and that measured in data.

The correction factor by which the Monte Carlo pile-up is reweighted is associatedwith an uncertainty 2.8%. In order to quantify the effect of this uncertainty on theEmiss,rel

T shape, the correction factor is shifted up and down by one standard deviationand the resulting Emiss,rel

T distributions are compared to the nominal distribution.

9.8.7 Luminosity

The simulation entering the real Emiss,relT processes is normalized to the integrated lumi-

nosity of the collision data. The integrated luminosity has an uncertainty, which is addedto the other systematic uncertainties. The uncertainty on the integrated luminosity is 2.8%.It is derived, following the same methodology as that detailed in Ref. [66], from a prelim-inary calibration of the luminosity scale derived from beam-separation scans performedin November 2012.

9.9 Results

The method described in section 9.4 is used to estimate the number of Z + jets events inthe signal region. A Emiss,rel

T template is extracted from collision data in the control re-gions. Real Emiss,rel

T processes are subtracted from the template as described in section 9.5.This fake Emiss,rel

T template is normalized to the dilepton sample in the Emiss,relT < 40 GeV

region. Integrating the normalized template above Emiss,relT = 80 GeV gives N(Z+ jets) as

seen in Eq. 9.2.

The systematic errors on the real Emiss,relT template described in the previous section

are added in quadrature to the statistical errors from Monte Carlo and data control re-gion statistics. This gives an uncertainty on the expected N(Z + jets). Table 9.3 lists theexpected N(Z + jets) as predicted with the diphoton and single photon control regionswith total systematic and statistical uncertainties. The lower part of the table shows abreakdown of the uncertainties. Due to the subtraction of the real Emiss,rel

T processes thepredicted N(Z + jets) is negative but consistent with zero.

The Emiss,relT in Z+ jets events is fake, arising from instrumentation effects. The domi-

nating source of Emiss,relT is the jet energy resolution. This is reflected in a large systematic

uncertainty due to the jets.

The single photon control region globally gives the more precise estimate. This isdue to the much higher statistics in the control region, reflected in the significantly lowerstatistical errors compared to the diphoton control region.

9.10 Statistical Combination of the Control Regions 91

γγ 1γ80e+e− µ+µ− e+e− µ+µ−

Prediction −1.75 −2.03 −0.02 −0.03Total uncertainty ±1.75 ±2.04 ±0.88 ±1.02Data statistics ±0.53 ±0.61 ±0.04 ±0.05MC statistics ±1.12 ±1.30 ±0.08 ±0.09Theory ±0.20 ±0.23 ±0.03 ±0.04Jets ±1.15 ±1.34 ±0.86 ±1.00Unidentified energy ±0.35 ±0.41 ±0.08 ±0.09Leptons ±0.04 ±0.06 ±0.17 ±0.20Photons ±0.06 ±0.07 ±0.01 ±0.01Pile-up ±0.06 ±0.07 ±0.01 ±0.01Luminosity ±0.05 ±0.05 ±0.01 ±0.01

Table 9.3: Predicted number of Z + jets event in the signal region with breakdown ofsystematic errors.

9.10 Statistical Combination of the Control Regions

As the single photon and diphoton control regions are orthogonal it is natural to statisti-cally combine the results from the two regions. This allows for a more precise estimatewith a smaller impact of systematic errors. One of the most commonly used approachesfor statistical combination of results is the Best Linear Unbiased Estimate method, knownas the BLUE method [98].

9.10.1 The BLUE Method

Assuming a measurement of a parameter with true value ytrue has been performed n timeswith the result y1,...,n, and each measurement is associated with a weight w1,...,n, the com-bined estimate y is a linear combination of the available measurements:

y =n

∑i=1

wiyi (9.3)

If the individual estimates are unbiased, the combined estimate is unbiased as well.Therefore the expectation value of the combination and the individual measurements areequal, 〈y〉= 〈yi〉= ytrue, which constrains the linear coefficients to:

n

∑i=0

wi = 1. (9.4)


The set of coefficients which minimizes the combined variance is chosen. The coeffi-cients are given by the following equation, where E is the covariance matrix:

wi =∑ j E−1

i j

∑i ∑ j E−1i j

(9.5)

This reduces to the usual wi = 1/σ2i/

∑1/σ2j for uncorrelated errors. If a high positive

correlation of uncertainties is present the linear coefficients can assume negative values,see discussion in Ref. [99, 100]. In the case of the combination of the diphoton and singlephoton control regions, the uncertainties are highly positively correlated because of thejet uncertainty. Therefore some negative BLUE coefficients are expected.

9.10.2 Result of the Statistical Combination

In order to construct a covariance matrix for the two control regions, it is necessary to dis-tinguish between correlated and uncorrelated uncertainties. The systematic uncertaintiesdue to detector effects are treated as correlated, while the uncertainties on data and MonteCarlo statistics are uncorrelated. The uncertainties on theoretical cross sections are par-tially correlated, but since the two control regions are dominated by different processesand thus different theoretical uncertainties, this contribution is considered uncorrelated.

Applying the BLUE method to the estimates from the single photon and diphotoncontrol regions gives the weights wγγ = −0.137 and w

γ+jets = 1.137 for the dielectronchannel, and wγγ = −0.139 and w

γ+jets = 1.139 for the dimuon channel. As expectedsome of the weights become negative. As an effect of the negative weights, the combinedestimate becomes positive, N(Z+ jets) = 0.22±0.87 in the ee channel and N(Z+ jets) =0.25±1.01 in the µµ channel. A breakdown of the combined systematic errors is foundin Tab. 9.4. The uncorrelated uncertainties appear twice as they enter separately for thetwo control regions.

9.11 Discussion

In this chapter a new approach for a data driven estimate of the number of Z+ jets events ina dilepton signal region using photon data is presented. It utilizes the similarities betweensingle photons and diphoton systems recoiling against jets and Z-bosons recoiling againstjets. Two control regions are defined, based on single photon and diphoton data.

Both control regions are shown to be useful, as they within errors reproduce theEmiss,rel

T spectrum of the signal region. The predicted number of Z + jets events in thesignal region is consistent with zero for both control regions.

For the diphoton control region the low statistics is a concern as the statistical uncer-tainty on the predicted number of events is very large. The statistical uncertainties arelarger than the systematic uncertainties. The single photon region does better in this as-

9.11 Discussion 93

e+e− µ+µ−

Prediction 0.22 0.25Total uncertainty ±0.87 ±1.01Data statistics γγ ±0.073 ±0.085Data statistics γ + jets ±0.045 ±0.057MC statistics γγ ±0.153 ±0.181MC statistics γ + jets ±0.091 ±0.103Theory γγ ±0.027 ±0.032Theory γ + jets ±0.034 ±0.046Jets ±0.820 ±0.953Unidentified energy ±0.043 ±0.045Leptons ±0.188 ±0.219Photons ±0.003 ±0.002Pile-up ±0.003 ±0.002Luminosity ±0.005 ±0.004

Table 9.4: Predicted number of Z+ jets event in the signal region with breakdown of sys-tematic errors, determined using a BLUE combination of the single photon and diphotoncontrol regions.

pect. The dominating systematic uncertainty for both control regions is that due to jetenergy scale and resolution.

The two control regions are completely orthogonal and can therefore be statisticallycombined. The combination is performed using the BLUE method. The high positive cor-relation of the systematic uncertainties gives negative weights, and the resulting combinedestimate is compatible with zero.

9.11.1 Comparison to the Jet Smearing Method

The jet smearing method uses seed events which are smeared to obtain pseudo-data with aEmiss,rel

T spectrum similar to that of the signal region. This way an arbitrarily large samplecan be produced and the statistical uncertainties are small. However, this method arguablyloses part of the benefit of a data driven method since only the well known resolutioneffects are taken into account in the smearing. It is possible that a low rate unknowndetector problem causing mismeasurement of jets could produce events entering into thesignal region. These events would not be reproduced by the jet smearing method.

The background estimate using photon control regions on the other hand is sensitiveto this type of mismeasurement. The Emiss,rel

T template is derived in events with simi-lar topology to that of the signal region and therefore any unknown detector problems


would affect the control region to the same extent. The photon control regions, especiallythe diphoton control region, instead suffer from large statistical uncertainties, which isreflected in a larger overall uncertainty compared to the jet smearing method.

Both methods of background estimation produce compatible results. The jet smear-ing estimate is 0.3± 0.2 and the photon control region estimate is 0.47± 1.87 for thecombined ee and µµ channels.

10 Exclusion Limits

In this chapter results from unblinded data in the signal region is compared to the expectedsum of Standard Model backgrounds. The backgrounds are determined with the methodsdescribed in the previous chapters. Since no excess over background is observed, upperlimits on the gaugino masses are derived.

10.1 The CLS Method

In order to exclude signal models, a signal plus background hypothesis is assumed. Con-sidering an expected background b and a signal model with expectation s, a p-value formeasuring Ndata under the hypothesis s+ b is calculated, ps+b = P(Ndata|s+ b). If theresulting p-value is smaller than a predefined α , ps+b < α , the model is excluded withconfidence level 1−α . For instance, if ps+b < 0.05, the model is excluded with 95%confidence level.

In high energy physics, when dealing with models with very low cross sections towhich the experiment has low sensitivity, this method can encounter problems. A down-ward fluctuation of the observed number of events in data (i.e. when fewer events areobserved than the expected background b) will produce a low p-value and a signal modelcan be excluded despite the lack of sensitivity of the experiment.

To circumvent this problem, the CLS method assigns a weight to the p-value. Thisweight is constructed so that it decreases with decreasing sensitivity:

CLS =ps+b

1− pb(10.1)

where pb is the probability of observing Ndata under a background only hypothe-sis: pb = P(Ndata|b). In the case of low sensitivity the numerator and denominator bothdecrease, thus preventing the condition CLS < α from being fulfilled. Since the denom-inator by construction is always less than or equal to unity, the CLS method will producelimits that are more conservative than the nominal 1−α confidence level [101, 102].

The systematic uncertainties are modeled with nuisance parameters which are ran-dom variables added to the nominal background estimates. Each independent source ofsystematic uncertainty is model-led by its own nuisance parameter. The p-value pb isevaluated for the set of nuisance parameters that best best fits the data in the backgroundonly hypothesis. This is referred to as a background only fit.

96 Exclusion Limits

The CLS method is commonly used for setting exclusion limits in high energy physicsexperiments and it is the method used to set limits in this analysis.

10.2 Results

Table 10.1 summarizes the predicted Standard Model backgrounds and the measurednumber of events in data for the ee and µµ channels. The third column shows the sum ofthe two channels.

ee µµ ee+µµ

ZW, ZZ 0.56±0.36 0.41±0.30 0.98±0.62WW 0.00±0.00 0.07+0.09

−0.07 0.07+0.09−0.07

Top 0.02±0.02 0.01±0.01 0.03±0.02Z + jets 0.22±0.87 0.25±1.01 0.47±1.87Other 0.00+0.12

−0.00 0.00+0.09−0.00 0.00+0.15

−0.00

Total SM 0.81±0.81 0.75±0.95 1.56±1.68Data 0 1 1

Table 10.1: Composition of the signal region using expected background yields obtainedwith the techniques described in chapter 8 and after a background only fit to the data.

Exclusion limits determined with the CLS method are shown in Fig. 10.1(a). Fig-ure 10.1(b) shows exclusion limits obtained by combining the dilepton limit from Paper IIIwith the three-lepton search [62]. In both (a) and (b) the dashed black line marks the ex-pected limit and the solid red line represents the observed limit. The yellow band aroundthe expected limit indicates the±1σ limit where all experimental uncertainties, statisticaland systematic, are considered. The dashed red lines around the observed limit representthe ±1σ contours which are obtained by shifting the cross section of the signal modelsby ±1σ . The limits are shown in the m

χ02 ,χ±1,m

χ01

plane. The limits stated in the textcorrespond to the observed limit where the signal cross sections have been reduced by1σ .

Using the background estimate from Tab. 10.1 degenerate χ02 and χ

±1 masses between

170 GeV and 330 GeV are excluded at 95% confidence level for models with a masslessχ0

1 . This limit is slightly lower than the expected sensitivity estimated in Sec. 7.3. Severalfactors contribute to this difference. First, the result in Sec. 7.3 was obtained using a 20%flat systematic uncertainty on the background whereas the final result uses the propersystematic uncertainty which is higher. Second, the sensitivity quoted in Sec. 7.3 wasestimated by the p-value of the signal plus background, ps+b, while Fig. 10.1(a) uses theCLS method. The CLS method gives a more conservative limit.

The exclusion limits obtained in the analysis of Paper III have been combined withresults from the ATLAS search for weakly produced supersymmetry in the three-lepton

10.2 Results 97

[GeV]±

1χ∼,

0

2χ∼

m

100 150 200 250 300 350 400 450 500

[G

eV

]0 1χ∼

m

0

50

100

150

200

250

300

350

[GeV]±

1χ∼,

0

2χ∼

m

100 150 200 250 300 350 400 450 500

[G

eV

]0 1χ∼

m

0

50

100

150

200

250

300

350

-1 L dt = 20.3 fb∫ = 8 TeVs

µµee + 0

1χ∼

< m

±1χ∼,0

2χ∼m

Z

= m

0

1χ∼

- m

0

2χ∼m

0

1χ∼

= 2m

0

2χ∼m

)SUSYtheoryσ 1±Obs limit (

)expσ 1±Exp limit (

(a) (b)

Figure 10.1: (a) Observed and expected 95% confidence level limit contours for charginoand neutralino production in the simplified model scenario with decay via gauge bosonsand two leptons in the final state; and (b) exclusion limits obtained by combining thedilepton limit from Paper III with the three-lepton search [62].

channel, see chapter 6. The fit is performed on the combined likelihood function usingall signal regions. For models with a massless χ0

1 degenerate χ02 and χ

±1 masses between

100 GeV and 415 GeV are excluded with 95% confidence level. The combination shows asignificant improvement compared to the results obtained from either of the two searches.

The dotted lines in Fig. 10.1(a) and (b) indicate relations in the mass hierarchy thathave implications on the preferred decay channels of the supersymmetric particles. On-shell Z bosons are allowed below the line marked m

χ02−m

χ01= mZ . Models close to

the diagonal are called compressed spectra models, for which special signal regions arerequired due to the much lower pT of the particles produced in the gaugino decays.

11 Conclusions

A precise energy reconstruction of hadronic jets is important both for measurements ofStandard Model processes and searches for physics beyond the Standard Model. TheATLAS Tile Calorimeter uses a predefined pulse-shape to obtain a precise and rapid en-ergy reconstruction. Variations of the actual pulse-shapes of the TileCal cells with respectto the reference pulse-shape could cause an energy bias which would enter in the constantterm of the energy resolution.

Paper I presents the pulse-shape energy dependence observed in test-beam data. Smallvariations with energy is observed, especially in the tail region. The implication on energyreconstruction is investigated and it is concluded that the bias introduced is less than 1%.

Paper II presents a study of pulse-shapes in collision data. Here the channel-by-channel variations of the pulse-shapes are investigated for all TileCal channels. A de-viation between the actual pulse-shapes and the reference pulse-shape is found in lowgain; the measured pulse-shapes are slightly narrower than the reference pulse-shape.The bias on the energy reconstruction due to the pulse-shape variations is investigatedand are found to be small. Only 1 channel in low gain and 4 channels in high gain areexpected to have an energy bias larger than 1%. This should be compared to the totalnumber of TileCal channels, which is 9856 in each gain.

The work presented in this thesis has shown that the ATLAS detector can be sensitiveto weakly produced supersymmetry in a previously unexplored search channel, namelypp→ χ

±1 + χ0

2 → χ01W±+ χ0

1 Z → χ01 qq′+ χ0

1``. It is demonstrated how to construct asignal region sensitive to this signal, which is used in Paper III.

It is also shown that it is possible to construct control regions with topologies similarto the signal region using single photon and diphoton data. Such control regions cancatch a possible low rate of events with mismeasured Emiss,rel

T entering into the signalregion. Both single photon and diphoton control regions are proven useful. The diphotoncontrol region suffers from high statistical uncertainties; the single photon control regionis better in this aspect. However, it is meaningful to use both control regions since theyare orthogonal and therefore can be statistically combined, producing a better overallestimate. The jet uncertainty is the largest systematic uncertainty for both control regionsand is the largest uncertainty on the combined background estimate.

Although the uncertainties are large, the background estimate from the photon controlregions is precise enough to produce competitive exclusion limits. The future ATLAS datataking will produce more events in this region, thus enabling further improvement ofexclusion limits.

List of Figures

1.1 One-loop quantum correction to the Higgs mass. . . . . . . . . . . . . . 13

3.1 A schematic view of the LHC and the major experiments. . . . . . . . . 223.2 The injection chain of the LHC and other CERN beam lines. . . . . . . . 23

4.1 Overview of ATLAS and its main subdetector components. . . . . . . . 264.2 Schematic end view of the ATLAS detector, showing different types of

particles and where they interact in the detector. . . . . . . . . . . . . . 274.3 An overview of the ATLAS trigger and data acquisition system. . . . . . 29

5.1 Layout of the Tile Calorimeter partitions. . . . . . . . . . . . . . . . . . 355.2 A schematic of the mechanical assembly and optical readout of a TileCal

module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3 Segmentation in depth and η of the Tile Calorimeter. . . . . . . . . . . . 375.4 The predefined pulse-shape functions used for energy reconstruction. . . . 395.5 Diagram of the TileCal calibration systems, illustrating the signal path for

particles and from the various calibration systems [52]. . . . . . . . . . . 405.6 Bias on the energy reconstruction as a function of the actual pulse-shape

width relative to the reference pulse-shape taken from Paper II. The esti-mated bias is obtained using simulated data. . . . . . . . . . . . . . . . . 42

6.1 Production cross section as a function of sparticle mass for SUSY pro-cesses at

√8 TeV pp collisions, calculated at NLO with PROSPINO [60]. . 46

6.2 Observed and expected 95% CL exclusion contours for (a) chargino pairproduction in the simplified model scenario with intermediate sleptonsand two leptons in the final state [61], and (b) chargino and neutralinoproduction in the simplified model scenario with decay via gauge bosonsand three leptons in the final state [62]. . . . . . . . . . . . . . . . . . . . 47

6.3 (a) The mass hierarchy of the SUSY models considered in this work. (b)Diagram showing a chargino and a neutralino decaying to the LSP via W -and Z-bosons. The W decays hadronically and the Z leptonically, givinga final state with two same flavor leptons of opposite charge. . . . . . . . 48

102 LIST OF FIGURES

6.4 Production cross section of the signal models at√

s = 8GeV as functionof m

χ02 ,χ±1

, where χ02 and χ

±1 are pure wino states, calculated at NLO with

PROSPINO [64]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.5 Three of the Standard Model backgrounds with a final state similar to thatof the sought supersymmetric signal. (a) shows the ZZ background, (b) isthe tt background and (c) is the Z + jets background. . . . . . . . . . . . 49

7.1 Illustration of the probability density function for the signal plus back-ground (s+ b) hypothesis with no uncertainty (dashed curve) and con-voluted with a Gaussian function to include the uncertainty on the back-ground (solid curve). The area of the filled surface under the graph cor-responds to the probability p of observing only the expected backgroundb under the s+ b hypothesis. Lower p-values correspond to higher sen-sitivity to the signal. p is used as figure of merit to evaluate the effect ofdifferent signal region selections. . . . . . . . . . . . . . . . . . . . . . . 57

7.2 (a) Distribution of the relative missing transverse momentum after thebase cuts are applied. The stacked histograms show the different com-ponents of the background and the overlaid dashed lines show the dis-tribution for three different signal points. The error band represents thequadratic sum of the error on Monte Carlo statistics and a flat systematicerror of 20%. (b) Sensitivity to different signal points, measured withthe p-value described in section 7.2.1, after different cuts. Lower p-valuemeans higher sensitivity. The error on p is determined by shifting thebackground estimate by its total uncertainty. . . . . . . . . . . . . . . . . 59

7.3 Distribution of the transverse momentum of the leading (a) and secondleading (b) jets, after the base cuts and Emiss,rel

T > 80GeV are applied. Thestacked histograms show the different components of the background andthe overlaid dashed lines show the distribution for three different signalpoints. The error band represents the quadratic sum of the error on MonteCarlo statistics and a flat systematic error of 20%. (c) Sensitivity to dif-ferent signal points, measured with the p-value described in section 7.2.1,after different combinations of cuts on the pT of the two leading jets.Lower p-value means higher sensitivity. The error on p is determined byshifting the background estimate by its total uncertainty. [45,45]GeV isselected for the signal region. . . . . . . . . . . . . . . . . . . . . . . . . 62

LIST OF FIGURES 103

7.4 (a) Distribution of the invariant mass of the two leading jets after the basecuts, Emiss,rel

T > 80GeV and p jet1,2T > 45GeV are applied. The stacked his-

tograms show the different components of the background and the over-laid dashed lines show the distribution for three different signal points.The error band represents the error on Monte Carlo statistics and a flatsystematic error of 20%. (b) Sensitivity to different signal points, mea-sured with the p-value described in section 7.2.1, after different cuts onm j j. Lower p-value means higher sensitivity. The error on p is deter-mined by shifting the background estimate by its total uncertainty. Thecut 50 < m j j < 100GeV is selected for the signal region. . . . . . . . . . 63

7.5 Distribution of the transverse momentum of the dilepton system (a) andthe angle between the leptons (b) after the base cuts, Emiss,rel

T > 80GeV,p jet1,2

T > 45GeV and 50 < m j j < 100GeV are applied. The stacked his-tograms show the different components of the background and the over-laid dashed lines show the distribution for three different signal points.The error band represents the error on Monte Carlo statistics and a flatsystematic error of 20%. (c) and (d) Sensitivity to different signal points,measured with the p-value described in section 7.2.1, after different cutson p``T and ∆R(``) respectively. Lower p-value means higher sensitiv-ity. The error on p is determined by shifting the background estimate byits total uncertainty. The cuts p``T > 80GeV and 0.3 < ∆R(``)< 1.5 areselected for the signal region. . . . . . . . . . . . . . . . . . . . . . . . . 64

7.6 After all cuts are in place one cut at a time is removed and the sensitivityfor different cuts on each variable is studied. The figure of merit is thep-value defined in section 7.2.1. The variables shown are (a) Emiss,rel

T , (b)p jet1,2

T , (c) m j j, (d) p``T and (e) ∆R(``). . . . . . . . . . . . . . . . . . . . 65

7.7 Expected sensitivity for different gaugino masses in the mχ0

2 ,χ±1,m

χ01

plane.The figure of merit on the color z-axis is the probability p defined in sec-tion 7.2.1. A flat systematic error of 20% on the expected number ofbackground events is used in the sensitivity calculation. The contour in-dicates the limit where p < 0.05 which is the expected exclusion reach.Each black cross indicates one signal point that has been simulated. . . . 67

9.1 Distribution of the relative missing transverse momentum within the sig-nal region without the cut on Emiss,rel

T > 80GeV. The band on the totalbackground is the error from Monte Carlo statistics and a flat systematicerror of 20%. The dashed lines show the Emiss,rel

T distribution from threebenchmark signal models. . . . . . . . . . . . . . . . . . . . . . . . . . 72

9.2 Sketch of the event topology for (a) a Z + jets event, (b) a single photonplus jets event, and (c) a diphoton plus jets event . . . . . . . . . . . . . . 72

104 LIST OF FIGURES

9.3 The Emiss,relT distribution from simulation in (a) the diphoton control re-

gion (γγ) and (b) the single photon control region (1γ80), see Tab. 9.1.The Emiss,rel

T distribution in the control regions is marked by black cir-cles, and that of the electron and muon channels of the signal region aremarked by red triangles and green squares respectively. The error bandrepresents the error on Monte Carlo statistics, theoretical uncertaintiesand systematic uncertainties combined. For the distribution in (b) the cor-rection discussed in Sec. 9.2.2 is applied. . . . . . . . . . . . . . . . . . . 74

9.4 Schematic picture showing the signal region, control region and normal-ization regions (NR) used to estimate the Z + jets background. . . . . . . 77

9.5 Comparison between simulated and collision data in the control regions.(a) shows Emiss

T and (b) shows Emiss,relT in the diphoton control region,

(c) shows EmissT and (d) shows Emiss,rel

T in the single photon control re-gion. The lower panel of the figure shows the ratio between collision dataand the prediction. The error band incorporates the error on Monte Carlostatistics, theoretical uncertainties on the real Emiss,rel

T processes, luminos-ity uncertainty and systematic uncertainties. . . . . . . . . . . . . . . . . 84

9.6 Comparison between simulated and collision data. (a) shows the pT ofthe diphoton system in the diphoton control region, and (b) the pT of thephoton in the single photon control region. The lower panel of the figureshows the ratio between collision data and the prediction. The error bandincorporates the error on Monte Carlo statistics, theoretical uncertaintieson the real Emiss,rel

T processes, luminosity uncertainty and systematic un-certainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

9.7 Photon fake Emiss,relT templates from data, with real Emiss,rel

T processes sub-tracted, normalized to unit area in (a) the diphoton (γγ) control regionand (b) the single photon (1γ80) control region. The photon templates aremarked by black circles, and the electron and muon channels of the signalregion are marked by red triangles and green squares respectively. For thedilepton distributions only 5 fb−1 of data is used for blinding purposes.The error band incorporates the statistical, theoretical, and systematic un-certainties from the real Emiss,rel

T processes. . . . . . . . . . . . . . . . . 86

9.8 Photon fake Emiss,relT templates from data, with real Emiss,rel

T processes sub-tracted, normalized to unit area in (a) the diphoton (γγ) control regionand (b) the single photon (1γ80) control region. The photon templates aremarked by black circles, and the electron and muon channels of the signalregion are marked by red triangles and green squares respectively. For thedilepton distributions a relaxed version of the signal region is used. Theerror band incorporates the statistical, theoretical, and systematic uncer-tainties from the real Emiss,rel

T processes. . . . . . . . . . . . . . . . . . . 87

LIST OF FIGURES 105

9.9 Sketch showing a nominal Emiss,relT shape, and Emiss,rel

T shapes where aparameter has been shifted by ±1σ . . . . . . . . . . . . . . . . . . . . . 88

10.1 (a) Observed and expected 95% confidence level limit contours for char-gino and neutralino production in the simplified model scenario with de-cay via gauge bosons and two leptons in the final state; and (b) exclusionlimits obtained by combining the dilepton limit from Paper III with thethree-lepton search [62]. . . . . . . . . . . . . . . . . . . . . . . . . . . 97

List of Tables

1.1 The fermion flavors of the Standard Model. The particle masses are takenfrom reference [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2 The force mediators, vector bosons, of the Standard Model. The bosonmasses are taken from reference [8]. . . . . . . . . . . . . . . . . . . . . 10

2.1 Particle content of the MSSM. . . . . . . . . . . . . . . . . . . . . . . . 17

7.1 The base cuts defining the region within which the signal region optimiza-tion is performed. The two leptons must have same flavor and oppositesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.2 Definition of the Z + jets signal region. . . . . . . . . . . . . . . . . . . . 617.3 Background composition of the signal region based on Monte Carlo sim-

ulation. The given errors are purely statistical. . . . . . . . . . . . . . . . 66

9.1 Definition of the single photon and diphoton control regions, with thesignal region definition as comparison. N` denotes the number of tightelectrons or muons, and Nγ denotes the number of tight photons whosedefinition are outlined in chapter 4. pγ1/`1

T , pγ2/`2T , and pγγ/``

T denote thepT of the photons in the control regions and the pT of the leptons in thesignal region. ∆R(γγ/``) denotes the distance between the photons orleptons in the control and signal regions respectively. . . . . . . . . . . . 76

9.2 Summary of process groups are subtracted from the photon control re-gions to obtain the fake Emiss,rel

T template. . . . . . . . . . . . . . . . . . 839.3 Predicted number of Z+ jets event in the signal region with breakdown of

systematic errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919.4 Predicted number of Z + jets event in the signal region with breakdown

of systematic errors, determined using a BLUE combination of the singlephoton and diphoton control regions. . . . . . . . . . . . . . . . . . . . . 93

10.1 Composition of the signal region using expected background yields ob-tained with the techniques described in chapter 8 and after a backgroundonly fit to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

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