Maja ylmad Search for Weakly Produced Supersymmetric Particles in the ALAS Experiment Department of Physics Stockholm University 204
Doctoral Dissertation 204 Fysikum Stockholm University Roslagstullsbacken 2 06 9 Stockholm c Maja ylmad 204 ISBN 978-9-7447-992-8 Printed by Universitetsservice US AB, Stockholm 204 Cover image: A three-year-old s impression of a particle collision. With special thanks to ilde ylmad.
Abstract he Large Hadron Collider located at CERN is currently the most powerful particle accelerator and ALAS is an experiment designed to exploit the high energy protonproton collisions provided by the LHC. It opens a unique window to search for new physics at very high energy, such as supersymmetry, a postulated symmetry between fermions and bosons. Supersymmetry can provide a solution to the hierarchy problem and a candidate for Dark Matter. It also predicts the existence of new particles with masses around ev, thus reachable with the LHC. his thesis presents a new search for supersymmetry in a previously unexplored search channel, namely the production of charginos and neutralinos directly decaying to electroweak on-shell gauge bosons, with two leptons, jets, and missing transverse momentum in the final state. he search is performed with proton-proton collision data at a center of mass energy of s = 8 ev recorded with the ALAS experiment in 202. he design of a signal region sensitive to the new signal is presented and a data driven technique to estimate the Z + jets background is developed. Precise measurements of hadronic jet energies are crucial to search for new physics with ALAS. A precise energy measurement of hadronic jets requires detailed knowledge of the pulse-shapes from the hadron calorimeter signals. Performance of the ALAS ile Calorimeter in this respect is presented using both pion test-beams and proton proton collision data.
Sammanfattning Partikelfysikens standardmodell är en teori som beskriver materiens minsta byggstenar samt hur dessa växelverkar. Standardmodellen har med framgång förutsagt ett stort antal fenomen som kunnat påvisas i experiment. rots teorins framgångar finns indikationer på att den inte är komplett. ill exempel saknas i standardmodellen en kandidat till Mörk Materia. En möjlig lösning på några av standardmodellens problem är supersymmetri (SUSY), en postulerad utökning av standardmodellen som bland annat förutsäger att ett antal hittills oupptäckta partiklar existerar. Några av dessa nya partiklar skulle kunna utgöra Mörk Materia. För att utföra precisionsmätningar av standardmodellen och söka efter nya partiklar används partikelacceleratorer. Den i dagsläget mest kraftfulla acceleratorn är LHC vid fysiklaboratoriet CERN. Protoner accelereras till en energi av 4 ev i två strålar med motsatt riktning. Vid fyra så kallade interaktionspunkter kolliderar protoner från de två strålarna. Vid en av dessa interaktionspunkter finns ALAS-detektorn, designad både för att studera redan kända processer och för att upptäcka nya. SUSY förutspår partiklar som har massor i storleksordningen ev, vilket är inom räckhåll 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 kunskap om bakgrunden krävs för att SUSY-signalen ska kunna hittas, eller uteslutas. Det krävs också att sökområdet avgränsas på ett effektivt sätt, så att bakgrunden avlägsnas men den sökta signalen blir kvar. Ett sådant sökområde kallas för signalregion. Signalregionen beror på vilken SUSY-signatur som söks. Denna avhandling presenterar en studie där supersymmetriska partiklar söks i en hittills outforskad sökkanal, nämligen produktion av gauginos vilka omedelbart sönderfaller till 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. Studien genomförs med data från proton-proton-kollisioner med energin 8 ev, insamlad med ALAS-detektorn. Optimeringen av signalregionen presenteras, tillsammans med en metod, baserad på data, för att uppskatta bakgrunden från produktion av Z + jets. Att mäta energin hos hadroniska skurar är mycket viktigt, både för precisionsmätningar av standardmodellen och för att upptäcka ny fysik. För att rekonstruera energin hos en hadronisk skur på ett tillförlitligt sätt krävs kunskap om puls-formerna från den hadroniska kalorimetern, ilecal. I denna avhandling presenteras även studier av pulsformer från ilecal, och deras möjliga påverkan på energirekonstruktionen diskuteras.
Contents Acknowledgments Preface 3 About this thesis.................................. 3 Author s contribution............................... 4 I heoretical Overview 7 he Standard Model of Particle Physics 9. Matter.................................... 9.2 Fundamental Interactions.......................... 9.2. he Strong Nuclear Interaction....................2.2 he Electromagnetic Interaction...................2.3 he Weak Nuclear Interaction....................3 he Higgs Boson.............................. 2.4 Problems of the Standard Model...................... 3.4. Dark Matter............................. 3.4.2 he Hierarchy Problem....................... 3.5 Beyond the Standard Model........................ 4 2 Supersymmetry 5 2. he Basics of Supersymmetry....................... 5 2.. Supersymmetry Breaking...................... 5 2..2 R-parity............................... 6 2.2 he Minimally Supersymmetric Standard Model............. 6 2.2. he Phenomenological MSSM................... 7 II Experimental Facilities 9 3 he Large Hadron Collider 2 3. he Accelerator Complex.......................... 2 3.2 he Main Experiments at the LHC..................... 22
4 he ALAS Detector 25 4. Introduction................................. 25 4.2 he ALAS Coordinate System...................... 25 4.3 he Inner Detector............................. 26 4.4 Calorimetry................................. 27 4.5 he Muon Spectrometer.......................... 28 4.6 Data Acquisition and rigger Systems................... 28 4.7 Particle Identification and Event Wide Variables.............. 30 4.7. Primary Vertex........................... 30 4.7.2 Electrons.............................. 30 4.7.3 Photons............................... 3 4.7.4 Muons............................... 3 4.7.5 Jets................................. 3 4.7.6 Missing ransverse Momentum.................. 32 5 he ile Calorimeter 33 5. he Physics of Calorimetry......................... 33 5.. Particle Showers.......................... 33 5..2 Calorimeters............................ 34 5.2 he ile Calorimeter............................ 34 5.2. Mechanical Structure........................ 35 5.2.2 ilecal Readout.......................... 36 5.2.3 Energy Reconstruction....................... 37 5.3 ilecal Calibration............................. 40 5.3. est-beam............................. 4 5.4 Sources of Uncertainty on the Energy Reconstruction........... 4 III Search for Weakly Produced Supersymmetry 43 6 Weakly Produced Supersymmetry 45 6. Motivation.................................. 45 6.2 Overview of Search Channels........................ 45 6.2. Intermediate Slepton Scenario................... 45 6.2.2 Heavy Slepton Scenario...................... 46 6.3 Signal Models................................ 47 6.4 Standard Model Backgrounds........................ 48 6.4. ZW, ZZ............................... 50 6.4.2 op Background.......................... 50 6.4.3 WW................................. 50 6.4.4 Z + jets............................... 50 6.4.5 Higgs................................ 50
6.4.6 Non-Prompt Leptons and Fake Leptons.............. 5 6.5 Observables for Signal Selection...................... 5 6.5. Jet Observables........................... 5 6.5.2 Lepton Observables........................ 52 6.5.3 Relative Missing ransverse Momentum............. 52 6.6 ALAS Data Set.............................. 53 7 Choice of Signal Region 55 7. Preselection................................. 55 7.2 Method................................... 55 7.2. Figure of Merit for Sensitivity................... 56 7.2.2 Signal Region Cut Optimization.................. 58 7.2.3 Validation and Final Selection of Cuts............... 60 7.3 Results.................................... 66 8 Standard Model Background Estimate 69 8. Diboson production, ZW and ZZ...................... 69 8.2 op..................................... 69 8.3 Fake Leptons................................ 69 8.4 Other Backgrounds............................. 70 8.5 Z + jets Background with the Jet Smearing Method............ 70 9 Data Driven Z + jets Background Estimation 7 9. Motivation.................................. 7 9.2 Missing ransverse Momentum in Photon Control Regions........ 73 9.2. Diphoton Control Region...................... 73 9.2.2 Single Photon Control Region................... 74 9.3 Control Region Definitions......................... 75 9.4 he ABCD Method............................. 76 9.5 Sample Composition............................ 78 9.5. γ + jets............................... 78 9.5.2 γγ + jets............................... 78 9.5.3 W/Z + 0γ.............................. 79 9.5.4 W/Z + γ.............................. 80 9.5.5 W/Z + 2γ.............................. 80 9.5.6 op + X............................... 80 9.5.7 Diboson............................... 8 9.5.8 Multijet QCD............................ 82 9.5.9 Summary of Processes with Real E miss,rel............. 82 9.6 Validation of Normalization of real Emiss rel Processes........... 82 9.7 Photon emplate Comparison with Dilepton Data............. 83 9.8 Systematic Uncertainties.......................... 86
9.8. heoretical Uncertainty on Cross Sections............. 88 9.8.2 Jets................................. 88 9.8.3 Unidentified Energy Deposits................... 89 9.8.4 Leptons............................... 89 9.8.5 Photons............................... 89 9.8.6 Pile-up............................... 89 9.8.7 Luminosity............................. 90 9.9 Results.................................... 90 9.0 Statistical Combination of the Control Regions.............. 9 9.0. he BLUE Method......................... 9 9.0.2 Result of the Statistical Combination............... 92 9. Discussion.................................. 92 9.. Comparison to the Jet Smearing Method.............. 93 0 Exclusion Limits 95 0. he CL S Method.............................. 95 0.2 Results.................................... 96 Conclusions 99 List of figures 00 List of tables 06 Bibliography 08
Acknowledgments his thesis would never have come into being without my advisor Christophe Clément, who has provided me with inspiration and ideas. hank you for your support, encouragement, and enthusiasm. I have really enjoyed working with you. hanks also to my second advisor, Barbro Åsman. My many thanks to the past and present members of the Stockholm particle physics group. Working with you for the last few years has been a pleasure. Sten Hellman has given me comments on the thesis, David Milstead has helped with proofreading of the thesis and has been invaluable for various physics discussions over the years, and Andreas Petridis has offered most helpful advice in matters of SR optimization and getting cutflows right. I appreciate your help. My fellow PhD students have made life in physics fun. Special thanks to Kattis, Olle and Paweł for good times in the office, discussions on matters great and small, for shared code, and not least for keeping my spirits up. It would not have been the same without you. hanks to Gustav, Henrik, Matthias and Anna for being good office mates. I am grateful to Christian Ohm for providing me with LaeX templates and various other help, and to Johan Lundberg for statistics advice, for encouragement and moral support, and much more. hank you for everything! Finally, my most sincere thanks to my family, Micke and ilde. hank you for your endless support.
Preface he Standard Model of particle physics describes the fundamental building blocks of matter and their interactions. he model has successfully predicted a range of phenomena, such as the existence of charm and top quarks and the W, Z, and Higgs bosons. However there are several theoretical arguments indicating that the Standard Model is only a low energy approximation of a more fundamental theory, the arguments behind this belief are developed in chapter. he field of experimental particle physics is dedicated to perform precision tests and measurements of the Standard Model processes and searches into what may lie beyond. Particle colliders are essential tools in experimental particle physics. When highly energetic particles collide, new particles are produced thanks to the equivalence between energy and mass, and their properties can be measured in detectors located around or close to the collision point. he most powerful accelerator today is the Large Hadron Collider (LHC), located at CERN near Geneva in Switzerland. During 202 the accelerator produced protonproton collisions at a center of mass energy of s = 8 ev. With a center of mass energy more than three times higher than previous colliders, the LHC has opened a window to a new energy regime, allowing to test the existence of new hypothetical particles with masses of several ev. his thesis presents a search for supersymmetry, a possible theory of physics beyond the standard model, in a previously unexplored search channel, with ALAS experiment. he ALAS detector used in this work is the largest of four experiments located at the interaction points of the LHC. ogether with the CMS experiment, ALAS is a general purpose detector designed to provide precision measurements of the physics processes produced in the collisions. he detector consists of several subsystems, responsible for tracking, energy and momentum measurements, and particle identification. his thesis presents a study of the energy measurement in one of these subdetectors, namely the hadronic ile Calorimeter. About this thesis he thesis is divided into three parts, and four papers are included. Part I gives a brief introduction to the particle physics theory. he particles and interactions of the Standard Model 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 ile Calorimeter and the work presented in Paper I and Paper II and describes the experimental setup: the LHC accelerator and the ALAS detector. he hadronic calorimeter of ALAS, the ile Calorimeter, is described in more detail as it is the focus of part of the work presented in this thesis. he included Paper I and Paper II concern the energy reconstruction in the ile Calorimeter. Part III describes a search for weakly produced supersymmetric particles in the ALAS detector, with emphasis on data driven background techniques. In chapter 7 the signal region optimization used in Paper III is developed. Chapter 9 describes in detail one of two methods developed to compute the Z + jets background in Paper III. Paper IV presents work I have carried out to evaluate a technique to determine so called non-prompt lepton backgrounds, similar to the technique used in Paper III. his thesis is an extension of my licentiate thesis. he chapters -5 are, with some alterations, taken from the licentiate. he attached papers are: Paper I: I. Jen-La Plante and M. ylmad. Pulse shapes for signal reconstruction in the ALAS ile Calorimeter. Nuclear Instruments and Methods in Physics Research Section A67, (200), 96-98, January 200. Paper II: C. Clément and M. ylmad. Measurement of the ALAS ile Calorimeter Pulse-Shapes with s = 7 ev Collision Data. echnical Report AL-COM- ILECAL-200-026, CERN, Geneva, Dec 200. Paper III: he ALAS Collaboration. Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at s = 8 ev with the ALAS detector. JHEP, 405:07, 204. Paper IV: B. Åsman, C. Clément, P. Hansson, J. Sjölin, M. ylmad. Fake Isolated Muon Backgrounds in Searches for Supersymmetry with two Muons in the Final State. echnical Report AL-PHYS-IN-200-05, CERN, Geneva, Jan 200. he author's contribution My first task when I started my work as PhD student on the ALAS experiment concerned a study of fake isolated muon backgrounds to supersymmetry. A data-driven method to determine the background from fake isolated muons in events with two muons in the final state was developed and a range of systematic effects were studied. I am main contributor to the study which was internally reviewed by a referee appointed by ALAS physics coordination. he internal note is included in this thesis as Paper IV.
5 For my qualification work on ALAS I worked on the ile Calorimeter. At first, when the accelerator was not yet operational, I worked with pulse-shapes in test-beam data. Using the data collected from a full slice of the calorimeter exposed to pion beams, I studied the amplitude and channel-to-channel variation of the pulse-shapes, and investigated the implication of these fluctuations on the energy reconstruction. his work is published in a conference proceeding included as Paper I and is described in more detail in an internal reviewed ALAS note:. Carli, N. Gollub, I. Jen-LaPlante, M. ylmad. Effect of Pulse-Shape Variations on the Energy Reconstruction in the ALAS ile Calorimeter. echnical Report AL- ILECAL-IN-200-005, CERN, Geneva, Aug 200. When LHC delivered the first collisions, I expanded the pulse-shape study to include the entire ile Calorimeter. I investigated deviations between the measured pulse-shapes and the pulse-shape used for reconstruction, and estimated the possible bias on the energy reconstruction caused by these deviations. he work resulted in an internal reviewed ALAS note included in this thesis as Paper II. My study of ilecal pulse-shapes has also entered as contributions in the public papers: K. J. Anderson at al. Calibration of ALAS ile Calorimeter at Electromagnetic Scale. echnical Report AL-ILECAL-PUB-2009-00, CERN, Geneva, Jan 2009. he ALAS Collaboration. Readiness of the ALAS ile Calorimeter for LHC collisions. European Physical Journal C70, (200), 93-236, Dec 200. 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. o estimate this background a kinematic reconstruction of top pairs can be used. I worked with validation of the performance of the method used for the kinematic reconstruction. I used the method to perform a cross check of the t t background for the SUSY search published in: he ALAS Collaboration. Searches for supersymmetry with the ALAS detector using final states with two leptons and missing transverse momentum in s = 7 ev proton proton collisions. Physics Letters B709, (202) 37-57, March 202. and was also presented in an internal communication to which I was main contributor: C. Clément, J. Lundberg, J. Sjölin, M. ylmad. A Package for Kinematic Reconstruction of op Pair Dilepton Events. echnical Report AL-COM-PHYS-20-335, March 20. Part III of this thesis is dedicated to a new search for weakly produced supersymmetry in a channel previously unexplored, namely in the channel pp χ 2 0 + χ ± Z χ 0 +W χ 0 ll χ 0 + q q χ, 0 where the gauge bosons are produced on-shell. he search
6 for pp χ 2 0 + χ ± has previously focused on final states with three leptons. I performed the first ALAS 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. Chapter 9 presents one of two methods developed to compute the Z + jets background in Paper III. It is important in previously unexplored signal regions to cross check results from several methods. he method presented in this thesis has been developed by me and relies on photon plus jets control regions. he weakness and strength of the proposed photon plus jets control regions are analysed.
Part I heoretical Overview
he Standard Model of Particle Physics he Standard Model (SM) of elementary particle physics [, 2, 3] is a quantum field theory which successfully describes a vast range of observed particle physics phenomena. he theory has great predictive power and has been extensively tested at various experiments during the last half century [4]. he elementary particles are divided into two groups: fermions and bosons. According to the Standard Model, matter is built of fermions while the vector bosons are responsible for mediating the fundamental forces. A general description of the particle content and fundamental forces of the Standard Model is given in the sections. and.2 respectively. Section.3 gives a short introduction to mass generation in the Standard Model. he motivation for hitherto unobserved physics processes is discussed in section.4 and possible extensions to the Standard Model in section.5.. Matter Matter in the Standard Model consists of point-like particles of spin-/2 called fermions. he fermions are divided into quarks and leptons. Furthermore, the fermions are grouped into 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 neutrino. All stable matter is built of fermions from the first generation [5]. Higher generation fermions rapidly decay into lighter particles ). he quarks and leptons are listed in ab... Each fermion has an antiparticle, denoted by a bar, for example t is the antiparticle of the top quark. Free quarks have never been observed, they appear in bound states known as hadrons [7]. Hadrons are categorized into mesons which are made up of a quark-antiquark pair, and baryons which consist of three quarks or anti-quarks..2 Fundamental Interactions he Standard Model describes three fundamental interactions: the electromagnetic, the strong, and the weak interactions. Gravity, the dominating force in the macroscopic [6]. ) Neutrinos do not decay. Observations indicate that neutrinos oscillate between the three generations
0 he Standard Model of Particle Physics Generation Electric I II III charge up, u charm, c top, t Quarks (2.3 0 3 ) (.28) (73.) (mass, GeV) down, d strange, s bottom, b (4.8 0 3 ) (0.95) (4.8) + 2 3 e 3 e electron, e muon, µ tau, τ e Leptons (5. 0 4 ) (0.06) (.78) (mass, GeV) e neutrino, ν e µ neutrino, ν µ τ neutrino, ν τ 0 e (< 2 0 9 ) (< 0.9 0 3 ) (< 8.2 0 3 ) able.: he fermion flavors of the Standard Model. he particle masses are taken from reference [8]. world, is not included in the Standard Model. he effect of gravity on elementary particles is negligible compared to that of the other forces and becomes important only at the Planck scale, M P = 2.4 0 8 GeV. his energy scale is far beyond the reach of current experiments. Nevertheless precision measurements at current accelerators could by extrapolation help understanding physics at much higher energies. Within the Standard Model the fundamental interactions are mediated by spin- bosons. he bosons and their properties are briefly summarized in ab..2. Interaction Mediator Electric charge Mass ( GeV) Electro- magnetic γ photon 0 e 0 Weak W ± ± e 80.4 Z 0 0 e 9.2 Strong g gluon 0 e 0 able.2: he force mediators, vector bosons, of the Standard Model. he boson masses are taken from reference [8].
.2 Fundamental Interactions.2. he Strong Nuclear Interaction he strong interaction acts upon particles carrying color charge, that is the quarks and gluons. he mediating bosons of the strong interaction are eight gluons: massless, electrically neutral particles which themselves carry color charge, thus being able to interact directly with each other. he strong interaction is described by the theory Quantum Chromo Dynamics, QCD. he strength of the strong force does not diminish with increased distance. Measurements indicate that the strength increases up to a distance approximately the size of a hadron ( fm). A single particle carrying color charge has never been observed; the strong interaction forces these particles to form bound states, hadrons. he phenomenon is known as color confinement. Quarks and gluons produced in collisions hadronize in the detector and produce a shower of particles known as a jet. he strong force binds the quarks in hadrons and is also responsible for binding the protons and neutrons within atomic nuclei. he coupling constant of the strong interaction at distances λ > fm is of the order one. his prevents the use of perturbation theory for calculating the interactions at that scale. Instead other approaches such as lattice QCD or phenomenological models must be used. For small distances and high energies the coupling constant is smaller and thus perturbation theory can be used. For small distances the quarks and gluons behave as quasi-free particles. his phenomenon is known as asymptotic freedom..2.2 he Electromagnetic Interaction he electromagnetic interaction is mediated by the photon, a massless vector boson. All particles with electric charge couple to the electromagnetic interaction. he quantum field theory describing electromagnetic interactions is quantum electrodynamics, QED. Arguably the most successful physics theory, QED withstands experimental tests which have been made with experimental precision as small as part in 0 2 [9]. he interaction is responsible for binding electrons to the atomic nucleus and it allows molecules to form. he range of the electromagnetic interaction is infinite. he coupling constant or fine structure constant of the interaction is α /37. Since α the interactions can be calculated precisely to a given order of α with perturbation theory..2.3 he Weak Nuclear Interaction hree vector bosons mediate the weak interaction: the Z 0, the W + and the W particles which represent the neutral (Z 0 ) and charged (W ± ) weak currents. hese bosons are massive particles (80 90 GeV) thus shortening the range of the interaction to 0 8 m. All fermions couple to the weak interaction, which is the only interaction coupling to neutrinos. he weak interaction is unique in several aspects. It is the only interaction in the Standard Model in which parity and charge conjugation is violated. A P-symmetric inter-
2 he Standard Model of Particle Physics action must couple equally to a left-handed 2) lepton and its P-conjugate, a right-handed lepton. Equivalently, a C-symmetric interaction must couple equally to a left-handed lepton and its C-conjugate, the left-handed antilepton. he weak interaction couples only to left-handed particles and right-handed antiparticles, thus violating C and P. Although the C- and P-symmetries are violated separately, the combined CP-symmetry is preserved in most weak processes. In certain rare weak processes in the quark sector CP-violation has been observed. In the Standard Model only the weak interaction is CP-violating. he weak interaction is also the only Standard Model interaction allowing flavor-changing interactions, enabling processes such as: d u +W u + e + ν e (.) which yields the nuclear reaction called β-decay: n p + e + ν e (.2) in which a down quark in the neutron is converted to an up quark. he CP-violation and flavor-changing are both parametrized in the CKM matrix..3 he Higgs Boson he 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 the W ± and Z 0 bosons and the photon. herefore a different approach is needed to provide masses to the W ± and Z 0 bosons. It is postulated that spontaneous symmetry breaking leads to a non-zero vacuum expectation value for the Higgs, early in the history of the Universe. he symmetry breaking produces three massless Goldstone bosons which have the same quantum numbers as three of the Standard Model gauge bosons. hrough the Higgs mechanism, the Goldstone bosons are integrated with three of the electroweak gauge boson fields which in this way acquire mass. hese massive bosons are the Z 0 and W ± bosons [0,, 2]. he fourth electroweak gauge boson remains massless and is identified as the photon. he theory also predicts the existence of a scalar particle associated with the Higgs field, the Higgs boson [3, 4]. hus the electroweak theory unifies the electromagnetic and the weak interactions and at the same time provides a mechanism that can generate mass. he theory has successfully predicted among other things the mass of the massive gauge bosons. he Higgs boson evaded discovery through several decades of extensive search at collider experiments [5]. In July 202 the ALAS and CMS experiments at CERN announced 2) Particles with spin and momentum in opposite directions are left-handed, particles with parallel spin and momentum are right-handed. See reference [5].
.4 Problems of the Standard Model 3 the discovery of a new boson with mass 25 GeV [6, 7]. At the time of writing of this thesis all measurements of this boson are consistent with a Standard Model Higgs boson [8, 9]..4 Problems of the Standard Model Although there is to date no disagreement between the Standard Model and a large body of experimental measurements, there are reasons to believe that it is only a low energy effective theory. Several questions remain unanswered. here is no explanation in the model for why three generations of fermions are preferred. he CP-violation is not understood, it is parametrized in the CKM matrix. he CP-violation in the Standard Model is not large enough to explain the matter antimatter imbalance observed in the Universe. he Standard Model neutrinos are massless. During the last decade several experiments have established that neutrinos in fact have masses, albeit very small [6]. o account for this a number of extra free parameters must be introduced in the Standard Model. Although neutrino masses can be incorporated in the Standard Model, it is desirable that a complete theory has as few free parameters as possible. Perhaps the most obvious shortcoming of the Standard Model is that gravity is not included. In the following subsections further problems are outlined..4. Dark Matter Astronomical observations have shown that the visible matter only explains a fraction of the matter in the Universe. At present, 4.9% of the total energy content of the Universe 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 gravitational effects. One possible candidate for Dark Matter is the existence of electrically neutral, Weakly Interacting, Massive Particles (WIMPs). However, the Standard Model does not include such a particle. he neutrinos alone cannot account for the vast quantities of Dark Matter in the universe. he remaining 68.3% of the energy of the Universe is referred to as Dark Energy, the properties and origins of which are even more mysterious [20, 2]..4.2 he Hierarchy Problem H f Figure.: One-loop quantum correction to the Higgs mass.
4 he Standard Model of Particle Physics he Standard Model Higgs mass is of the order m H = 25 GeV. However the Higgs mass term receives enormous quantum corrections from every particle coupling to the Higgs field. A fermion loop such as Fig.. yields a correction m 2 H to the Higgs mass: m 2 H = λ f 2 8π 2 Λ2 UV +... (.3) where λ f is the coupling constant between the fermion and the Higgs field and Λ UV is an ultraviolet momentum cutoff. he interpretation of Λ UV is the energy scale at which new physics enters the theory. If the ultraviolet cutoff is set to the Planck scale 3), M P = 2.4 0 8 GeV, the corrections produce a Higgs mass 5 orders of magnitude larger than the mass required by the Standard Model. It is conceivable that all quantum corrections to the Higgs mass could cancel each other, although this cancellation would have to be as perfect as one part in 0 30. his is considered unnatural by many theorists. he problem is often referred to as the hierarchy problem or the fine tuning problem [5, 0, 22]. It is believed that the fine tuning is suppressed by some yet unknown symmetry, such as supersymmetry described in chapter 2..5 Beyond the Standard Model In order to solve the problems discussed in section.4 the Standard Model must be extended. Numerous candidate theories exist, among the more famous are Supersymmetry and theories with Extra Dimensions. Supersymmetry imposes a new symmetry which leads to a new set of particles. hese new particles cancel the infinities in the Higgs mass. he new spectrum of particles can provide candidates for Dark Matter. Supersymmetry and its implications are described in more detail in chapter 2. Extra Dimensions proposes that some of the Standard Model particles are confined to a four-dimensional brane whereas other particles may propagate in additional spatial dimensions. his could explain why gravity is so much weaker than the other fundamental forces. If the extra dimensions are large enough there could be phenomenological implications already at the ev energy scale which can be explored at the LHC. Extra Dimensions could solve the hierarchy problem by lowering the ultraviolet cutoff, Λ UV [23]. Other models beyond the Standard Model include the Little Higgs Model [24] in which the Higgs boson is a pseudo-goldstone boson from the breaking of a new global symmetry; and compositness, where some Standard Model particles themselves have a substructure. Gaining understanding of the origin of mass and other new physics beyond the Standard Model is the main purpose of the experiments at the Large Hadron Collider, LHC. 3) he Planck scale is defined as the scale where gravity becomes comparable in strength to the other interactions.
2 Supersymmetry A symmetry of fermions and bosons was first postulated in the early 970s [25, 26]. In 98 the Minimal Supersymmetric Standard Model (MSSM) was introduced and provided a solution to the hierarchy problem [27]. 2. he Basics of Supersymmetry Supersymmetry (SUSY) is a symmetry relating fermions and bosons. When acting on a particle of half-integer spin, SUSY transforms the particle to one of integer spin. In the 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 superpartner or superparticle. All quantum numbers except spin of the superpartners are the same as for the Standard Model particles. he spin of the superpartner differs from the spin of the Standard Model particle by /2. hus the superpartners of the Standard Model fermions are spin-0 bosons and the superpartners of the gauge bosons are spin-/2 fermions. he naming convention of superpartners adds a prefix s to the name of a Standard Model fermion and adds a suffix ino to the names of Standard Model bosons. For instance, the superpartners of leptons are called sleptons (e.g. selectron, sneutrino), the superpartners of quarks are squarks (e.g. sup, sdown, stop) and the superpartners of the gauge bosons are gauginos (e.g. gluino) [2]. If supersymmetry is unbroken Standard Model particles and their superpartners have the same mass. herefore the superpartners contribute to the loop-diagrams (see Fig..) in the exact same way as the Standard Model particles with the difference only of a sign. his provides a solution to the hierarchy problem as the quantum corrections from the superpartners exactly cancel those from Standard Model particles, removing the need for fine tuning. 2.. Supersymmetry Breaking Unbroken supersymmetry postulates the existence of a large number of new supersymmetric 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. herefore supersymmetry, if it exists, must be broken and the mass of the superpartners has to be larger than the mass of Standard Model particles.
6 Supersymmetry he experimental absence of detected superpartners to date allows to derive a lower limit on their masses. If the masses of the supersymmetric particles are around 2 ev, supersymmetry can still solve the hierarchy problem. he need for fine tuning still exists but the degree is much relaxed. Breaking of supersymmetry on this scale is called soft supersymmetry breaking [8]. It is difficult to construct a model of spontaneously broken supersymmetry where the breaking is due to interactions between supersymmetric particles. One way to introduce breaking of supersymmetry is the addition of a new sector to the model. his sector would be completely neutral with respect to the Standard Model gauge group, and would thus be a hidden sector. he supersymmetry breaking occurs in the hidden sector and is transmitted to the MSSM or visible sector. he transmission may involve a third sector, the messenger sector [8]. here are several scenarios for the mediation of supersymmetry breaking: gravity-mediated, gauge-mediated and anomaly-mediated. 2..2 R-parity In the Standard Model lepton number L and baryon number B must be conserved, which prevents the proton from decaying. In Supersymmetry L- and B-violating processes can occur. As no such processes have been observed experimentally, a new conserved multiplicative quantum number is introduced: R = ( ) 3(B L)+2S (2.) where S is the spin of the particle [28]. R-parity is even for Standard Model particles and odd for superparticles. he conservation of R-parity has important implications for the phenomenology. At a collider experiment where two Standard Model particles collide, supersymmetric particles can only be produced in pairs. he production of one single superparticle would violate R-parity conservation. Supersymmetric particles are likely to be highly unstable, rapidly decaying into lighter particles. Again due to R-parity conservation, a superparticle cannot decay into only Standard Model particles. his will produce a decay chain with ever lighter supersymmetric particles and Standard Model particles. When the decay chain reaches the lightest supersymmetric particle (LSP) no further decays are possible. his implies that if R-parity is conserved, the LSP is completely stable. Cosmological observations show that the LSP must be neutral of electrical and color charge. In many supersymmetric models the LSP will therefore be a WIMP, and thus provides an excellent candidate for Dark Matter [29, 30]. 2.2 he Minimally Supersymmetric Standard Model he simplest supersymmetric model encompassing the Standard Model is the Minimal Supersymmetric extension to the Standard Model (MSSM). It consists of exactly one su-
2.2 he Minimally Supersymmetric Standard Model 7 perpartner per Standard Model particle. However the Higgs sector must be modified. One Higgs doublet cannot generate mass for all fermions in a way consistent with supersymmetry; therefore the Higgs sector is extended to two Higgs doublets. he MSSM does not provide for a model of how Supersymmetry is broken. herefore the number of free parameters of the MSSM is large. Apart from the free parameters of the Standard Model the MSSM requires more than 00 new parameters [22]. he particle content of the MSSM is summarized in ab. 2.. In addition to the Standard Model particles, there are four Higgs bosons, two electrically neutral and two electrically charged. Left- and right-handed quarks and leptons have separate superpartners. he superpartner of the gluon is the gluino. he gauginos are combinations of the superpartners of the electroweak gauge bosons and Higgs bosons. he neutral gauginos are called neutralinos, denoted χ0 4, where the indices 4 indicate increasing mass. he charged gauginos are called charginos, χ ±,2. In this thesis the lightest supersymmetric particle is assumed to be the lightest neutralino, χ. 0 MSSM mass eigenstates Spin Higgs sector h 0,H 0,A 0,H ± 0 Squarks ũ L, ũ R, d L, d R s L, s R, c L, c R b, b 2, t, t 2 0 Sleptons ẽ L, ẽ R, ν e, µ L, µ R, ν µ, τ, τ 2, ν τ 0 Gluino g /2 Gauginos χ 0, χ 0 2, χ 0 3, χ 0 4 (neutralinos), χ ±, χ ± 2 (charginos) /2 able 2.: Particle content of the MSSM. 2.2. he Phenomenological MSSM In its most general form, the MSSM has 24 free parameters. However, many of these parameters 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 inconsistent with experimental results. Given the experimental constraints, the parameter space of the MSSM can be strongly constrained. Several attempts to theoretically describe the breaking of supersymmetry, and thus set theoretical constraints compatible with observational constraints on the parameter space of the MSSM, have been made. he mechanism chosen to break the supersymmetry has implications on the resulting supersymmetric particle spectrum. However, in lack of experimental 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-independent way 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
8 Supersymmetry phenomenological constraints on the MSSM. A pmssm model must fulfill the following requirements: 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 st and 2nd generation sfermions may be required. In this way the parameter space is reduced to 9 24 free parameters in addition to the Standard Model parameters. hese additional parameters include gaugino and higgsino mass parameters, Higgs sector parameters, squark and slepton mass parameters, and the trilinear couplings between sfermions and Higgs. he much reduced number of parameters enables scans of the parameter space that would not be possible in a theory with more than 00 parameters. Although the CP-violation of Standard Model alone cannot explain the observed matter-antimatter imbalance in the universe, there are still heavy constraints on the amount of CP-violation present. herefore requiring no additional CP-violation is a good approximation for most direct searches for Supersymmetry. A search for supersymmetric particles in the framework of the pmssm is presented in part III.
Part II Experimental Facilities
3 he Large Hadron Collider he Large Hadron Collider (LHC) [3] is an accelerator located at the European Organization for Nuclear Research (CERN), on the Swiss French border close to Geneva. he LHC is mainly a proton proton collider which during 202 operated at a center of mass energy s = 8 ev. Collisions at s = 3 GeV are scheduled for 205 and the design energy is s = 4 ev. With a peak recorded luminosity of 7.7 0 33 cm 2 s [32], the LHC is the most powerful particle collider in terms of both collision energy and number of collisions. 3. he Accelerator Complex he accelerator is housed in the tunnel originally used for the Large Electron Positron Collider, LEP. his is a circular tunnel located approximately 00 meters underground. he circumference is nearly 27 km. Figure 3. shows a schematic view of the accelerator and the four main experiments. he LHC is provided with protons from a chain of injectors where the proton energy is successively increased. he protons are accelerated to 50 MeV in the linear accelerator called LINAC2 before being injected into the Booster where the energy is increased to.4 GeV. hereafter follows the Proton Synchrotron (PS) which accelerates the protons to 25 GeV. he final step is the Super Proton Synchrotron (SPS) where the protons reach the LHC injection energy 450 GeV. A sketch of the accelerator chain is shown in Fig. 3.2. he LHC itself consists of two adjacent beam pipes in which the protons are accelerated. Around 200 superconducting dipole magnets providing a magnetic field of 8.3 keep the protons in a circular path and nearly 400 quadrupole magnets keep the beams focused. he magnets are cooled by liquid helium to the operating temperature of.9 Kelvin. he protons are accelerated in a Radio Frequency (RF) cavity. When fully accelerated, the protons travel at nearly the speed of light, completing one full circle in approximately 90 µs, equivalent to about 000 laps per second. he two beam pipes intersect at four points, called Interaction Points, allowing the protons to collide. o observe the collisions detectors are placed at the interaction points. he protons are prepared in bunches, meaning the interactions take place at discrete time intervals. When the LHC is fully operational, the number of bunches will be nearly 3000 and the interactions will take place every 25 ns. In the 200 202 runs the LHC was operated with about 500 bunches separated by 50 ns.
22 he Large Hadron Collider Figure 3.: A schematic view of the LHC and the major experiments. Although mainly a proton proton collider, the LHC also collides heavy ions at a record center of mass energy. In shorter runs of approximately one month per year, the LHC has accelerated Pb 82+ ions to collide at energies of s = 2.76 ev per nucleon. 3.2 he Main Experiments at the LHC In order to be able to study a wide range of physics at the LHC four large detectors have been built. wo of these, ALAS [33] and CMS [34], are multi-purpose experiments designed to be sensitive to any new physics. LHCb [35] is designed to study CP-violation and other phenomena in the decay of B-hadrons ). Finally, ALICE [36] is designed to study the states of extremely high energy density, known as quark gluon plasma which can be produced in heavy ion collisions. he ALAS experiment is described in more detail in chapter 4 ) Hadrons containing b quarks.
3.2 he Main Experiments at the LHC 23 Figure 3.2: he injection chain of the LHC and other CERN beam lines.
4 he ALAS Detector 4. Introduction he ALAS detector [33] is an approximately cylindrical detector located at Interaction Point of the LHC. he detector is 44 m long and 25 m in diameter. In order to accurately determine what happens in a proton-proton collision ALAS is divided into three main components: the Inner Detector which provides charged particle tracking and momentum measurement; the calorimeters which measure the energy; and the muon spectrometer which provides tracking and momentum information of the muons. A sketch of the ALAS detector is seen in Fig. 4.. he ALAS detector is forward backward symmetric and also approximately symmetrical in the azimuthal angle φ around the beam line. he subsystems of ALAS are described in the following sections. Different types of particles leave different signatures in the detector. All charged particles are visible to the Inner Detector (ID) whereas electrically neutral particles such as photons pass unnoticed. Photons and electrons cause electromagnetic showers in the innermost part of the calorimeter called the electromagnetic calorimeter. Hadrons produce hadronic showers in the outermost part of the calorimeter called the hadron calorimeter. Most particles are stopped in the calorimeter, which allows a precise determination of their energy. Only very highly energetic jets can punch through the calorimeter and reach the muon system. Muons and neutrinos are the only Standard Model particles which always pass through the calorimeter. he 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 χ 0 would lead to the same signature. Figure 4.2 shows a schematic end view of the ALAS detector with the interaction of different types of particles indicated. 4.2 he ALAS Coordinate System he coordinate system of ALAS is a right-handed coordinate system with the x-axis in the horizontal plane pointing towards the center of the LHC ring; the y-axis points upwards; and the z-axis is parallel to the beam axis. he polar angle θ is measured with respect to the beam axis and φ is the azimuthal angle. In addition to these coordinates pseudorapidity is often used. he pseudorapidity η is defined as η = ln(tan(θ/2)). his gives η = 0 perpendicular to the beam axis and η = ± in the ±z directions. he
26 he ALAS Detector Figure 4.: Overview of ALAS and its main subdetector components. p pseudorapidity azimuthal space angle R = η 2 + φ 2 is often used to define distance between particles in the detector. When two protons collide, the z-component of the momentum of the interacting partons can vary greatly. herefore events are boosted in the z-direction. Since the momentum of the colliding partons is unknown it is important to look at variables that are invariant under the boost. he pseudorapidity is invariant under Lorentz transformations and is therefore preferred over the polar angle. he colliding partons have negligible momentum in the x, y plane, perpendicular to the beamline. he transverse momentum is conserved in the collision, therefore only the transverse component of an objects momentum, p, is used for most purposes. he sum of the transverse momentum of all outgoing particles must be zero. 4.3 he Inner Detector he Inner Detector is designed to provide pattern recognition capacity, high resolution momentum measurement, and primary and secondary vertex measurements. It covers the range η < 2.5. he ID consists of three subsystems: the pixel detector, the silicon microstrip tracker, and the transition radiation tracker (R). he R reaches to η < 2.0 and provides discrimination between electrons and π-mesons. he three subsystems
4.4 Calorimetry 27 Figure 4.2: Schematic end view of the ALAS detector, showing different types of particles and where they interact in the detector. are immersed in a solenoidal magnetic field of 2 which allows momentum measurement in conjunction with the radius of curvature of the tracks. Located just centimeters away from the beam pipe, the ID must operate in a high radiation environment. Excellent spatial resolution is crucial to discriminate physics from noise hits in the high-occupancy environment. High radiation levels cause the detector components to deteriorate and the innermost layers will need to be replaced in the future [33, 37]. 4.4 Calorimetry he ALAS calorimeter [38] consists of several subsystems: the Liquid Argon Calorimeter (LAr) [39] which measures the energy of electromagnetic showers from electrons and photons and the EM components of jets, the Forward Calorimeter (FCAL), the Hadronic End Cap (HEC), and the ile Calorimeter (ilecal) [40] which measure the energy of
28 he ALAS Detector hadronic showers. In the forward region liquid argon detectors are used for both electromagnetic and hadronic calorimetry due to the high radiation environment. he barrel Liquid Argon calorimeter covers the range η < 2.5. he end-cap calorimeters extend the range to cover the region 2.5 < η < 4.9. he LAr calorimeter has an accordion geometry which provides full coverage in φ and a fast extraction of the signal. he absorbing material is lead reinforced with stainless steel. he gaps between the absorbers contain liquid argon, the active medium of the calorimeter, and readout electrodes. he liquid argon calorimeters are housed in three cryostats: one for the barrel and two for the end-cap calorimeters [33, 38, 39]. he work described in the attached Paper I and Paper II has been performed as part of the calibration of the Hadronic ile Calorimeter. Chapter 5 is dedicated to a more detailed description of this subdetector. 4.5 he Muon Spectrometer he outermost subdetector of ALAS is the Muon Spectrometer. A toroidal magnet system (one barrel and two end-cap magnets) provides a magnetic field in the muon system. he air-core toroidal structure ensures a strong field in a large volume with a minimal amount 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 chambers. In the end-cap regions the tracking chambers are arranged in three planes perpendicular to the beam axis. Most of the muon chambers are Monitored Drift ubes (MDs). In the end-caps, Cathode Strip Chambers (CSCs) are used for the innermost plane. Dedicated chambers are used for the muon triggers, Resistive Plate Chambers (RPCs) in the barrel and hin Gap Chambers (GCs) in the end-caps. he Muon Spectrometer covers the range η < 2.7 for tracking and η < 2.4 for the trigger. he momentum resolution is of the order 2 4% for muons of momentum in the range 0 00 GeV [33, 4, 42]. 4.6 Data Acquisition and rigger Systems he LHC proton-proton bunch crossing frequency is 40 MHz, which gives a very high collision rate. Due to limited resources in readout bandwidth, data storage, and processing, only a small fraction of the events can be stored for further analysis. o ensure that the most important events are saved, a sophisticated trigger and data Acquisition (DAQ) system is required. he trigger system must provide rapid decisions and the rate must be reduced to about 200 Hz for the final stage. he trigger system of ALAS is divided into three levels: Level- (L), Level-2 (L2), and the Event Filter (EF). Figure 4.3 shows a schematic overview of the ALAS trigger system [43]. he L trigger is achieved by hardware custom electronics and searches for objects with high transverse momentum, p, which indicates a large momentum transfer in the collision, and large missing and total transverse energy. he trigger uses information with reduced granularity from the calorimeter and muon system. he highest accept rate
4.6 Data Acquisition and rigger Systems 29 Interaction rate ~ GHz Bunch crossing rate 40 MHz LEVEL RIGGER < 75 (00) khz Regions of Interest LEVEL 2 RIGGER ~ khz EVEN FILER ~ 00 Hz CALO MUON RACKING Event builder Pipeline memories Readout drivers (RODs) Readout buffers (ROBs) Full-event buffers and processor sub-farms Data recording Figure 4.3: An overview of the ALAS trigger and data acquisition system. allowed from the L trigger is 00 khz. he trigger decision must be made within 2.5 µs after the bunch-crossing. After a L trigger accept the data leaves the detector front-end electronics and is sent to the Read Out Drivers (RODs) located in underground counting rooms 00 m away from ALAS. he RODs perform some calculations on the data before it is passed along to the Read Out Buffer (ROB) where it is stored awaiting a L2 trigger decision. he ilecal RODs calculate the amplitude and time of pulses with the optimal filtering method described in more detail in chapter 5 and Paper II. he L2 trigger uses as input regions-of-interest (RoIs), detector regions where the L trigger has identified possible trigger objects. he L2 trigger has access to the full granularity and tracking of ALAS in the RoIs. Using information on coordinates, energy and signatures, the L2 trigger reduces the event rate to below 3.5 khz. he average event processing time is approximately 40 ms. he event filter uses offline analysis algorithms to further reduce the event rate and classify the events by signature. he output event rate from the event filter is approximately 200 Hz and the average processing time is of the order four seconds. he event filter has access to full ALAS data at full granularity. he events that survive the event filter are saved to different data streams depending on their signature. here are physics data streams for events containing a muon, an electron or a photon, a jet, or high missing energy. In addition to the physics streams events may also be written to calibration and express streams. he express stream is used for monitoring of the detector and data quality; the calibration streams provide the necessary
30 he ALAS Detector amount of data needed for detector calibration [33, 44]. 4.7 Particle Identication and Event Wide Variables his section describes a few key objects and observables to carry out the analysis of data in part III. 4.7. Primary Vertex he point where two protons from the colliding beams interact is called the primary interaction point or Primary Vertex, (PV). When running at high luminosity many protons may interact 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 from one collision it is important to know which primary vertex is the origin of every identified particle, as well as the location of each primary vertex. his is known as pile-up. o reconstruct the primary vertices of a bunch crossing a vertex finding algorithm is applied. It uses track information from the inner detector to extrapolate tracks to the interaction point. In the analysis described in part III of this thesis at least five charged tracks per primary vertex are required. 4.7.2 Electrons A cluster of EM calorimeter cells with significant energy deposits which in η, φ space match a charged track in the inner detector is referred to as an electron candidate. For the electron candidates used in the analysis of this thesis the energy of the cluster and the track must fulfill the criteria p > 0 GeV and η < 2.47. Additional cuts on the quality of the electron candidate are applied. hree different levels of quality are available, called loose, medium and tight, with increasing rejection power against background and jets faking electrons. he variables on which the quality cuts are applied include leakage into the hadronic calorimeter, width and shape of the EM shower and number of hits on the inner detector track [45]. he number of hits in the R is used to distinguish electrons from charged hadrons. For the analysis described in Part III of this thesis the electrons are required to satisfy the tightest criteria. o select electrons coming from the decay of gauge bosons or sleptons as opposed to electrons produced in jets, isolation criteria are applied. he sum of the p of the tracks above 400 MeV in with in a cone of size R = 0.3 around the electron candidate must not exceed 6% of the electron p. he electron must also be isolated in the calorimeter. he isolation is defined as the sum of the E in the calorimeter clusters within R = 0.3 from the electron which must be less than 8% of the electron p.
4.7 Particle Identication and Event Wide Variables 3 4.7.3 Photons For photon identification two types of photons must be considered: converted photons which have been converted into an electron-positron pair, and unconverted photons. In the 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 deposit will be present. If the conversion is asymmetric and one of the e + e has momentum under the reconstruction threshold, or if the separation between electron and positron is low, only one track will be reconstructed leading to a single track matching the energy deposit [46]. he energy reconstruction of photons is similar to that of electrons. he shower shapes of photons and electrons are very similar; nevertheless the shower shape selections have been optimized for photons. Due to the similarities between electrons and photons a certain ambiguity between the two is unavoidable. he photons used in the analysis in part III of this thesis are required to be isolated. he energy deposited in a cone of size R = 0.2 around the photon candidate must not exceed 5 GeV. 4.7.4 Muons Muons are reconstructed using the statistical combination algorithm. his requires a match in η, φ space between a track in the inner detector and a track in the muon spectrometer. he muon track parameters are obtained by combining both systems and they are required to have p > 0 GeV and η < 2.4. Also a minimum number of hits in the different layers of the inner detector is required [47]. he sum of the p of the tracks above 400 MeV in with in a cone of size R = 0.3 around the muon candidate must not exceed 5% of the muon p. 4.7.5 Jets Jet candidates are reconstructed using the anti-k t jet clustering algorithm with the distance parameter R = 0.4. he jet candidates are required to have p > 20 GeV and η < 4.5. If the probability that a jet candidate may arise from detector problems or cosmic rays is high, the event is rejected. he energy of the jets is also corrected for inhomogeneities of the detector and pile-up interactions [48]. B-tagging Jets containing a b-hadron decay are identified using a b-jet identification algorithm also called b-tagging. A jet which is considered likely to contain a b-hadron decay is called b-tagged. b-jet identification algorithms typically use the fact that b- and c-hadrons are long lived, thus traveling some distance before decaying which causes the origin of the jet to be displaced from the primary vertex. In order for this displacement to be measurable
32 he ALAS Detector the decay must occur within the silicon detector volume. herefore b-tagging can only be performed 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. o reduce the background from pile-up jets and increase the resolution of jet energy measurements the variable Jet Vertex Fraction (JVF) is introduced. he JVF is determined per jet and vertex. he JVF of a single jet with respect to a vertex is defined as: JV F = k p trk k (jet i,pv j) n l p trk l (jet i,pv n) (4.) he numerator is the sum of p of all tracks coming from primary vertex PV j and pointing into jet i. he denominator is the sum of the p of all tracks pointing to the jet independently of the PV from which they arise. 4.7.6 Missing ransverse Momentum Undetectable particles, such as neutrinos or hypothetical weakly interacting massive particles, can be produced in the proton collisions and subsequent decays. he presence of such particles can be inferred from an apparent non-conservation of transverse momentum. he missing transverse momentum vector p miss, a two-vector in the plane transverse to the beam axis, is defined as the negative sum of the transverse momentum of all objects in the event: p miss = p e p µ p γ p jet p unidentified (4.2) he electrons, muons and photons are required to have p > 0 GeV and the jets p > 20 GeV. he term p unidentified refers to the sum of all calorimeter clusters with η < 4.7 not already associated to leptons, photons or jets. he magnitude of p miss is called the missing transverse energy and is denoted E miss. In the presence of a neutrino in the final state, p miss will be approximately the momentum of the neutrino within experimental uncertainties on the momenta in Eq. 4.2. In general p miss is the vector sum of all invisible particles.
5 he ile Calorimeter his chapter introduces the physics of calorimetry and describes the ALAS ile Calorimeter. Studies of the signal reconstruction of the ile Calorimeter are the focus of the attached Paper I and Paper II. 5. he Physics of Calorimetry 5.. Particle Showers When a particle passes through matter it interacts with the surrounding matter and loses part of or all its energy. he processes involved in the interaction depend on the energy and type of particle. he shower processes are divided into two categories defined by the interactions: electromagnetic showers which involve electromagnetic interactions; and hadronic showers which involve strong interactions [50]. Electromagnetic Showers he main process of energy loss for high energy electrons and positrons traversing a medium is bremsstrahlung. he charged particles radiate photons as a result of Coulomb interactions with atomic nuclei in the medium. For charged particles of lower energy the dominating process is ionization. he dominating photon interactions are electron positron pair production, photoelectric effect, Rayleigh scattering, and Compton scattering. A high energy electron or photon entering matter will induce a chain reaction producing a shower of electrons, positrons, and photons of ever lower energy via pair production and brehmsstrahlung. Hadronic Showers Hadronic showers are more complex than electromagnetic showers. A hadron of high energy traversing a dense medium interacts by ionization. he hadron is likely to interact strongly with atomic nuclei in the matter. he incoming hadron and the nuclei interact inelastically via strong interaction and produce a number of new hadrons. he particles created in the interactions will continue to interact with the matter, producing a shower of particles. hese are often neutral hadrons decaying into photons which create an electromagnetic shower component inside the hadronic shower. Figure 4.2 shows electromagnetic and hadronic showers in the calorimeters of ALAS.
34 he ile Calorimeter 5..2 Calorimeters Calorimeters are devices in which incident particles are absorbed and their energy measured. he calorimeter must enhance and absorb the particle showers and produce a measurable electric or light signal proportional to the number of particles in the shower. A dense absorber enhances and absorbs the shower and an active material produces a signal when particles pass through it. here are two basic types of calorimeters: homogeneous calorimeters and sampling calorimeters. A homogeneous calorimeter consists of only one material, acting both as absorber and active material. he electromagnetic calorimeter of CMS [34] is a homogeneous calorimeter. Sampling calorimeters alternate layers of absorbing dense materials such as lead, iron or uranium with layers of active material [5]. he electromagnetic and hadronic calorimeters of ALAS are sampling calorimeters. Energy Resolution of Calorimeters he relative energy resolution of a calorimeter improves with higher energy and can be written generally as σ E = a b E E c (5.) he first term, a, is called the stochastic term and gets contributions from all stochastic processes contributing to the energy resolution, including fluctuations in the physical development of a shower. Generally homogeneous calorimeters have small stochastic terms as the entire shower is absorbed in active material. he stochastic term of sampling calorimeters is larger because of the fraction of energy deposited in the active material varies from one shower to another. his effect can be reduced by reducing the thickness of the absorbing layers. he second term is the noise term. his depends on the noise of the readout chain. Scintillating calorimeters typically have lower noise terms than detectors based on charge collection. Energy reconstruction methods such as the optimal filtering method used in the hadronic calorimeter of ALAS can reduce the noise further. he noise term dominates at low energies when signals are small. he last term is a constant term summarizing all contributions that do not depend on particle energy, such as material or calibration non-uniformity, radiation damage and other instrumental effects. his is the dominant term at high energy [5]. 5.2 he ile Calorimeter he ALAS Hadronic ile Calorimeter [40] is a sampling calorimeter made of alternating layers of iron absorber and scintillating plastic tiles. When a particle passes through the scintillating tiles, light is emitted and transported to photomultiplier tubes via wavelength shifting fibers. he main task of ilecal is to identify jets and measure their energy and
5.2 he ile Calorimeter 35 direction. ilecal is also important in measuring the missing transverse energy. he energy resolution requirement for jets is σ/e = 50%/ E 3% [40]. ilecal covers the range η <.6. 5.2. Mechanical Structure he calorimeter consists of four mechanically distinct cylinders or partitions: two long barrel segments (called LBA and LBC) and two smaller extended barrels (called EBA and EBC). Each barrel is divided into 64 independent azimuthal wedges called modules. Figure 5. shows the layout of the ile Calorimeter partitions. he space between the long and extended barrels is instrumented with gap and crack scintillators. hese provide corrections for energy losses in dead material in the crack region. EBA LBA LBC EBC Figure 5.: Layout of the ile Calorimeter partitions. he ilecal modules are built of many layers of absorbing iron and scintillating plastic tiles. he ultraviolet light produced in the plastic tiles is collected at the edges of each tile in wavelength shifting (WLS) fibers, two for each tile. he fibers are bundled and coupled to photomultiplier tubes (PMs). he grouping of the fibers defines the readout granularity. he PMs are housed in a steel girder at the outer edge of each module. he girders provide both the volume in which ilecal front-end readout electronics are contained and the flux return yoke of the solenoidal field. Source tubes used for calibration purposes pass through every tile. Figure 5.2 [33] shows a schematic of a ilecal module. he grouping of the fibers is done in such a way that a three dimensional cell structure is defined, each cell being read out by two PMs. here are three radial layers of cells, referred to as the A, BC, and D layers, A corresponding to the innermost layer.
36 he ile Calorimeter Photomultiplier Wavelength-shifting fibre Scintillator Steel y x z Source tubes Figure 5.2: A schematic of the mechanical assembly and optical readout of a ilecal module. he depth of these layers is.5, 4., and.8 interaction lengths ) respectively at η = 0. he cells of two innermost layers have the dimensions η φ = 0. 0. and the outermost layer η φ = 0.2 0.. Figure 5.3 [33] shows the depth and η-segmentation of the long barrel and extended barrel in the positive z region in the r, z plane. he ile Calorimeter is symmetric under the symmetry z z. 5.2.2 ilecal Readout Each barrel (extended barrel) module is read out by 45 (32) channels, summing to a total of 9856 readout channels for the entire ile Calorimeter. Signals from the PMs are shaped and thereafter amplified. Each PM is read out by two analogue paths differing by an amplification ratio of 64, called low gain and high gain. he shaped and amplified signals are sampled at the LHC bunch crossing frequency, 40 MHz, using a 0-bit analog ) One interaction length is the average distance a hadron will travel in the absorber before a nuclear interaction occurs.
5.2 he ile Calorimeter 37 3865 mm η=0,0 2280 mm 0 ~ D0 D D2 D3 BC BC2 BC3 BC4 BC5 BC6 BC7 BC8 A 0, 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9,0,,2 A2 A3 A4 A5 A6 A7 A8 A9 A0 500 000 500 mm B9 E E2 E3 E4 D4 C0 B D5 D6 B2 B3 B4 B5 A2 A3 A4 A5 A6,3,4,5,6 beam axis Figure 5.3: Segmentation in depth and η of the ile Calorimeter. to digital converter (ADC). Seven samples are read out by the front-end electronics. he seven digitized samples are transferred to the back-end electronics, readout drivers located 00 m away in an underground counting room. he RODs compute the time and energy of the signal [52]. 5.2.3 Energy Reconstruction he amplitude A of the reconstructed pulse is related to the energy E by E = F ADC MeV (A P) (5.2) where P is the pedestal and F ADC MeV is a conversion factor between ADC-counts and MeV. he factors have been determined using a Charge Injection System (CIS) which injects a calibrated charge, the cesium calibration system which uses a Cs source, and electron test-beams [52]. he calibration of ilecal is described in more detail in section 5.3. Several methods of energy reconstruction have been developed in ilecal, two of which are the fit method and the optimal filtering method [52, 53]. he energy reconstruction can be performed offline on recorded data, or online by the RODs. If the L trigger rate is beyond 30 khz the energy reconstruction must be performed by the RODs. he Fit Method he fit method uses a predefined pulse-shape to reduce the bias on the reconstructed amplitude introduced by electronic noise. For each channel a three parameter fit of the
38 he ile Calorimeter function f (t) to the measured signals is performed: f (t) = A fit g(t t fit ) + P fit, (5.3) where g(t t fit ) is a predefined pulse-shape function normalized to unit amplitude. he fit determines the peak amplitude A fit, the time of the peak amplitude t fit and the pedestal P fit. he fit minimizes the expression: χ 2 = 7 i= ( ) Si (A fit g(t i t fit ) + P fit ) 2 (5.4) σ i where S i is each measured sample of the signal pulse in ADC-counts and σ i is the uncertainty on each sample, the electronic noise. For high gain the noise is estimated to.5 ADC-counts and for low gain 0.6 ADC-counts. For events with very small energy depositions the time parameter t fit is fixed to t fit = 0 ns and only a two parameter fit is performed. he decision whether two or three parameters should be fitted is based on which method gives the smallest χ 2 /n do f [53]. he method uses separate pulse-shapes for the low and high gain fits. Figure 5.4 shows the predefined pulse-shape functions currently used in the energy reconstruction in low and high gain. Since the autumn 2008 the fit method is used only for Charge Injection System (CIS) calibration data [52]. he fit method is used as reconstruction technique in Paper I and as a cross check in Paper II. Optimal Filtering he optimal filtering algorithm [54] is the default energy reconstruction method of ile- Cal. he method obtains the amplitude of the pulse using linear combinations of the signal samples: A opt = 7 i= t opt = A opt a i S i 7 i= b i S i (5.5a) (5.5b) where A opt is the reconstructed amplitude and t opt is the reconstructed time. he weights a i and b i are chosen to minimize the impact of the noise on the reconstruction and are dependent on the peak time. he sum runs over all seven samples. he pulseshapes in Fig. 5.4 must be known beforehand to be able determine the weights. he pedestal P opt is estimated as the first measured sample. he algorithm can be performed online with one iteration for L trigger rates < 75 khz. For higher trigger rates no iterations are possible. If the energy reconstruction is performed offline there is no limit to the
5.2 he ile Calorimeter 39 Normalized amplitude [a.u.] 0.8 0.6 0.4 0.2 Low gain High gain 0 60 40 20 0 20 40 60 80 00 20 ime [ns] Figure 5.4: he predefined pulse-shape functions used for energy reconstruction in low (solid line) and high (dashed line) gain. number of iterations used. he first iteration of the optimal filtering algorithm assumes t opt 0 ns, thereafter using the previously determined t opt for the following iterations. he procedure is terminated when convergence in the fitted time is obtained or after the predefined number of iterations. o quantify the agreement between the measured samples and the predefined pulse-shape a quality factor Q F is defined. his quality factor is used to determine which pulses need to be stored for further analysis offline; a large Q F indicates bad agreement and the samples S i are stored for further analysis. he quality factor of the reconstruction is given by the expression: Q F = 7 (S i (A opt g i + P opt )) 2 (5.6) i= S i he optimal filtering algorithm is described in more detail in references [52, 54]. Optimal 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-shape variations on the energy reconstruction is investigated. Channel-by-channel and energy dependencies of the pulse-shapes are studied. It is concluded that the observed variations introduce a bias on the reconstructed energy smaller than %. Paper II describes a systematic measurement of pulse-shapes from the entire ile Calorimeter performed on s = 7 ev proton proton collision data. his study also concludes that the energy bias introduced by pulse-shape variations is smaller than %.
40 he ile Calorimeter 5.3 ilecal Calibration he ilecal calibration system consists of the charge injection system (CIS), the cesium system (Cs), and the laser system. Apart from calibration with these systems ilecal has also undergone extensive testing and calibration in the test-beam and in cosmic runs. he goal of the calibration is: to establish the electromagnetic energy scale of ilecal. he EM scale conversion factors relate the calorimeter signals measured in pc to the energy deposited by electrons, to obtain understanding of cell-to-cell variations of the EM scale, to measure the average time offset between signal detection and collision time for every ilecal channel, to monitor the time evolution of these quantities. Figure 5.5 shows a flow diagram of readout path of the ilecal calibration systems. Figure 5.5: Diagram of the ilecal calibration systems, illustrating the signal path for particles and from the various calibration systems [52]. he charge injection system is a part of the front-end electronics. It is used to measure the conversion factor between pc and ADC-counts for the readout of physics data and laser calibration. CIS calibration runs are taken frequently. he constants are stable with respect to time and are updated twice per year. Data from CIS can be used to identify bad channels and these calibration data are therefore taken several times per week between physics runs. he cesium system uses a hydraulic system to drive capsules containing cesium sources along the z-axis through every scintillating tile in every ilecal module, see Fig. 5.2. As
5.4 Sources of Uncertainty on the Energy Reconstruction 4 the Cs source passes through a cell the signal in the PM is continuously read out. he Cs source scans provide measurement of the response of individual cells and result in updates in the constants that adjust the global EM scale. As Cs scans are time consuming they are only performed between beam periods with a periodicity varying with the LHC schedules. [52, 55, 56, 57] he laser system provides monitoring and calibration of the PM gain and linearity. A laser located in the ALAS underground counting room emits pulses resembling physics pulses which are transported to the PMs via optical fibers. Prior to beam, the laser system was also used for timing calibration [52, 58]. 5.3. est-beam o establish a thorough understanding of the response of the final ilecal modules, approximately % [53] of the ilecal modules were exposed to test-beams of muons, electrons and hadrons with momentum from 3 to 350 GeV. he test-beam setup was installed in the H8 beam line at the SPS accelerator. he detector parts were stacked on a scanning table capable of x, y, θ and φ motion, mimicking the same particle-calorimeter entry configuration as in ALAS. For the combined test-beam runs in 2004 a full slice of the ALAS barrel was exposed to the test-beam. More details on the test-beam setup and results are found in references [53, 55, 59]. he attached Paper I uses data from the 2004 combined test-beam to quantify the energy dependence of the ilecal pulse-shapes. 5.4 Sources of Uncertainty on the Energy Reconstruction he uncertainty on the energy reconstruction in ilecal has three main sources as seen in Eq. 5., the stochastic term, the noise term, and the constant term. he stochastic term a in Eq. 5. arises from the randomness of the hadronic shower development. For instance, low energy neutrons are produced in showers and carry away a part of the energy, which remains unmeasured. ilecal is a sampling calorimeter and the energy deposited in the absorber is not measured. he exact amount of energy absorbed in the absorber or lost via undetected hadrons varies from shower to shower. he size of the stochastic term for jet resolution is 50%/ E. he noise term b in Eq. 5. is due to noise in the readout chain. In ilecal this term is smaller than %/E and is considered negligible. he constant term c in Eq. 5. takes contributions from effects that are not energy 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 signal pulse-shapes can contribute to the constant term. In ALAS the constant term of the jet resolution is required to be c < 3%. For low energy jets, the stochastic term is the dominating source of uncertainty. However, as the energy of the jet increases, the constant term becomes more important. For jet energies of the order 300 GeV or more the constant term is the dominating source of uncer-
42 he ile Calorimeter tainty. Precise jet energy measurement is crucial to many physics studies in ALAS and it is therefore important to understand the contributions to the constant term. he energy reconstruction in ilecal relies on predefined pulse-shapes for the energy reconstruction. If these reference pulse-shapes deviate from the actual pulse-shapes of the ilecal channels, a bias on the energy reconstruction can be introduced. Figure 5.6 shows the bias on the energy reconstruction as a function of the actual pulse-shape width relative to the reference pulse-shape, obtained using simulated data. It is noted that a pulse-shape 0% narrower than the reference pulse-shape would cause a bias of the order.5% on the energy reconstruction. his is not negligible compared to the 3% constant term and it is therefore important to investigate the actual pulse-shapes of the ilecal channels. Energy bias (%) 0.5 0 0.5 Optimal Filtering, Low gain 5 GeV 30 GeV 45 GeV.5 0 5 0 5 0 Relative pulse width (%) Figure 5.6: Bias on the energy reconstruction as a function of the actual pulse-shape width relative to the reference pulse-shape taken from Paper II. he estimated bias is obtained using simulated data. In the attached Paper I and Paper II, studies of the ilecal pulse-shapes are presented. he study presented in Paper I was performed on three ilecal modules which were exposed to pion test-beams in 2004. he energy dependence of the pulse-shapes was investigated. A slight energy dependence, especially in the tail region, was observed. Paper II presents a study where channel-by-channel variations of all ilecal channels is measured using collision data taken in 200. It was found that the pulse-shapes in low gain are slightly narrower than the reference pulse-shape. However the bias on the energy reconstruction 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 ALAS experiment is to search for new physics at the ev scale. Supersymmetry, described in chapter 2, is one of the theories that needs to be tested. In this chapter weakly produced supersymmetry is introduced. 6. Motivation he production cross section of SUSY particles at the LHC depends on their mass and couplings. Colored sparticles, such as squarks and gluinos, have significantly higher production cross sections than weakly interacting sparticles, such as gauginos and sleptons, of equal mass. If the colored supersymmetric particles are very massive and the weakly interacting sparticles are relatively light, direct production of gauginos and sleptons could dominate the SUSY production at the LHC, as seen in Fig 6. which shows the production cross section as function of particle mass. he cross sections are calculated at next to leading order (NLO) with PROSPINO [60]. his mass hierarchy is possible in the frameworks of MSSM and pmssm. 6.2 Overview of Search Channels he preferred decay channels of the supersymmetric particles depends on the SUSY mass hierarchy. he models concerned here have conserved R-parity, thus providing a candidate for Dark Matter. In these models the lightest supersymmetric particle is a stable neutralino denoted χ 0 and a pair of LSPs always end the supersymmetric decay chains. 6.2. Intermediate Slepton Scenario In SUSY models where m χ 0 2, χ ± > m l > m χ 0, the only kinematically allowed slepton decay is l l + χ. 0 Final states containing leptons provide a better signal to background ratio than those containing only strongly interacting particles. herefore models with intermediate sleptons were the focus of early searches at the LHC. So far no excess over Standard Model expectations has been observed. For models with a massless χ, 0 chargino masses between 40 GeV and 465 GeV have been excluded, see Fig. 6.2(a) and Ref. [6].
46 Weakly Produced Supersymmetry σ [pb] 0 σ tot [pb]: pp SUSY S = 8 ev 0 - q g q q q q * 0-2 χ 2o χ + χ 2o g t t * g g 0-3 ν eν e* l el e* 200 400 600 800 000 200 400 600 m average [GeV] Figure 6.: Production cross section as a function of sparticle mass for SUSY processes at 8 ev pp collisions, calculated at NLO with PROSPINO [60]. 6.2.2 Heavy Slepton Scenario In the analysis presented in this thesis a mass hierarchy where m χ 0 2 = m χ ± and m l m χ 0 2 is considered, see Fig 6.3 (a). he sleptons are decoupled from the phenomenology under study here due to their large mass. A mass gap m χ 0 2, χ ± m χ 0 > m Z enables the production of on-shell W- and Z-bosons. Searches for this scenario are limited by the branching ratio of the gauge bosons decaying leptonically and therefore require more data than the intermediate slepton case. However, it is important to perform an exhaustive search for supersymmetric models and also the scenario with more massive sleptons and on-shell gauge bosons must be considered. Searches for weakly produced supersymmetry with on-shell bosons have previously been performed in the channel where both vector bosons decay leptonically, producing three final state leptons and one neutrino. No significant excess of events above Standard Model expectations was found in 20.3 fb of s = 8 ev proton-proton collision data. Limits on neutralino and chargino masses are set and reproduced in Fig. 6.2(b). For simplified supersymmetric models with gauge boson decays, degenerate χ ± and χ 0 2 masses up to 345 GeV are excluded [62]. If the Z-boson decays leptonically and the W-boson decays hadronically the final state
0 0 6.3 Signal Models 47 [GeV] m χ 400 350 300 250 200 ALAS Ldt = 20.3 fb, s = 8 ev ~ 0 χ + χ 2 lν(ν l) 2 lνχ m ~ = +m 0)/2 ν, l ± (mχ χ ± 0 m( χ ) < m(χ ) SUSY Observed limit (± σ ) theory Expected limit (± σ exp ) ALAS 4.7 fb, s = 7 ev ± LEP2 χ (03.5 GeV) All limits at 95% CL [GeV] m χ 300 250 200 50 ALAS L dt = 20.3 fb, s=8 ev ± 0 (*) 0 (*) 0 χ χ W χ Z χ 2 m ± = m 0 χ χ m 0 χ 2 0 < m χ 2 m χ 0 2 m χ 0 = m Z SUSY Observed limit (± σ ) theory Expected limit (± σ exp ) ALAS 4.7 fb, All limits at 95% CL m 0 χ 2 = 2m s = 7 ev 0 χ 50 00 00 50 50 0 00 200 300 400 500 600 [GeV] ± (a) m χ 0 00 50 200 250 300 350 400 0 [GeV] ± (b) m χ, χ 2 Figure 6.2: Observed and expected 95% CL exclusion contours for (a) chargino pair production in the simplified model scenario with intermediate sleptons and two leptons in the final state [6], and (b) chargino and neutralino production in the simplified model scenario 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 energy due to the LSPs which escape the detector undetected. A diagram depicting this decay is shown in Fig 6.3 (b). his channel is the focus of this thesis. Although the production cross section and the branching ratio to dilepton final states are low, a study first performed by the author of this thesis showed that the ALAS detector does have sensitivity in this channel. 6.3 Signal Models he signal models considered in chapters 7 and 9 of this thesis are so-called simplified models. A simplified model is defined by a set of particles and their modes of production and decay. From these parameters and the couplings the production cross section as a function of particle mass is determined. In simplified models the branching ratio can be set to any value, often to 00% for a studied decay. he final exclusion plots can then be scaled to any branching ratio. he simplified model is independent of the underlying theory; it merely states the production cross section and branching ratios given a set of parameters. 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. he models considered here are direct gaugino production, pp χ ± χ0 2. he χ ± and
48 Weakly Produced Supersymmetry Mass ~ l ± 0 χ, χ 2 ± χ 0 (a) (b) Figure 6.3: (a) he 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. he W decays hadronically and the Z leptonically, giving a final state with two same flavor leptons of opposite charge. the χ 2 0 are assumed to be pure wino states ) and mass degenerate. Pure wino states yield the largest production cross sections. It is possible to scale the result to obtain exclusion limits 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 generated by Monte Carlo simulation, forming a grid in the m χ 0 2, χ ±, m χ 0 plane. he next to leading order production cross section of the models is shown in Fig. 6.4. All signal samples are generated with HERWIG++2.5.2 [63] and normalized to NLO cross section from PROSPINO. 6.4 Standard Model Backgrounds In order to discriminate supersymmetry signals from Standard Model backgrounds a signature with low background must be chosen. In the LHC, the background arising from multijet production is particularly high. In the ALAS detector these backgrounds are seen as a large number of jets. A signal including leptons 2) is therefore an efficient approach to reduce the Standard Model background. Requiring a high missing transverse momentum further reduces the number of background events. he main backgrounds to the supersymmetric process χ ± + χ 0 2 W χ 0 + Z χ 0 q q χ 0 + ll χ 0, with two opposite sign final state leptons, high missing transverse momen- ) Pure wino states means that the bino and higgsinos do not mix with the wino to form the lightest chargino and second lightest neutralino. 2) Lepton in this analysis refers to electron or muon.
6.4 Standard Model Backgrounds 49 Production cross section [pb] 0 0 - -2 0 00 50 200 250 300 350 400 450 500 0 ± [GeV] m χ, χ Figure 6.4: Production cross section of the signal models at s = 8 GeV as function of m χ 0 2, χ ±, where χ 0 2 and χ ± are pure wino states, calculated at NLO with PROSPINO [64]. 2 tum, and two high momentum jets are Standard Model processes with the same signature. hese backgrounds are referred to as irreducible backgrounds and are detailed below. Processes with fake leptons and/or fake missing transverse momentum contribute to the background to some extent. he main Standard Model backgrounds are described in the following sections. p p q q Z Z q q + l - l ν ν p p q q g t t - W W + b b - l ν + l ν p p q q Z g + l - l q q (a) (b) (c) Figure 6.5: hree of the Standard Model backgrounds with a final state similar to that of the sought supersymmetric signal. (a) shows the ZZ background, (b) is the t t background and (c) is the Z + jets background.
50 Weakly Produced Supersymmetry 6.4. ZW, ZZ Pair production of bosons is the largest background to the signal shown in Fig. 6.3. he processes ZW ll + τν and ZZ ll + νν (see Fig. 6.5 (a)) both have real leptons and missing transverse momentum, and jets can be produced in initial state radiation (ISR). he invariant mass of the two leptons will be close to the mass of the Z-boson, hence further mimicking the signature of the supersymmetry model under study. 6.4.2 op Background op quarks exclusively decay into a W-boson and a b-quark. herefore top quark pair production 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 l + ν + l ν, both real opposite sign leptons and missing transverse momentum will be observed. However the invariant mass of the two leptons will be unrelated to the mass of the Z-boson, allowing distinction from the SUSY signature. A diagram of top pair production and decay is shown in Fig. 6.5 (b). 6.4.3 WW his background closely resembles the top background, however missing the b-jets. Any jets 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 strongly interacting particles are produced in the proton-proton collision. he Z-boson may decay leptonically, producing a pair of leptons with invariant mass near the mass of the Z-boson, and the strongly interacting particle will produce jets. If the energy of the jets is mismeasured, fake missing transverse momentum is artificially introduced following Eq. 4.2. herefore these events resemble the signature of the supersymmetric process under study. An example of a Z +jets process is shown in Fig. 6.5 (c). Chapter 9 is dedicated to the estimation of the Z + jets background. 6.4.5 Higgs In this analysis Higgs production represents a background. his process group comprises both Higgs decay channels such as H ZZ and Higgs production with associated vector boson production, such as pp HZ, where the decay products include leptons, neutrinos and jets. Although these backgrounds are irreducible, their cross sections are low and give a very small contribution to the total background.
6.5 Observables for Signal Selection 5 6.4.6 Non-Prompt Leptons and Fake Leptons he non-prompt and fake lepton backgrounds are processes where one or more objects in the detector are misidentified as isolated leptons. he fake leptons are objects that are not leptons at all, such as jets, which are misidentified as leptons. Non-prompt leptons are leptons that do not directly arise from vector boson decays. For example, a kaon produced in a jet is likely to decay into a muon. If the energy deposits in the calorimeter around this muon are sufficiently small, the muon will appear isolated and the event may be misinterpreted as a leptonic decay. Processes that contribute to the fake lepton background are s- and t-channel single top, t t, W+jets and b b. Hereinafter the term fake leptons is used collectively for fake leptons and non-prompt leptons. All contributions to the fake lepton backgrounds are estimated simultaneously, based on the statistical probability that a lepton should pass certain isolation criteria. A similar method for data driven estimation of the fake isolated muon background was developed by the author in Paper IV. 6.5 Observables for Signal Selection 6.5. Jet Observables Number of Jets and Jet Categories As the supersymmetric decay under study has two quarks in its final state, the number of jets is an important observable. he jets from the signal are from u, d, c, and s quarks while b-quarks can arise in the background, mainly from top quark decays. he observable N B20 is the number of b-tagged jets with p jet > 20 GeV. A veto is placed on this observable in order to reduce the top background. b-tagging is only possible in the central part of the detector, where η < 2.4. After the veto on N B20, b-jets in the forward region ( η > 2.4) can remain. herefore a veto is also placed on the observable N F30, the number jets with p jet > 30 GeV in the forward region, η > 2.4. he observable N C20 is the number of jets with p jet > 20 GeV in the central 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 two jets peaks at the mass of the W-boson. he invariant mass m j j of the two leading jets can therefore be used to suppress backgrounds. ( (E m j j = jet + E jet2) 2 p jet + p jet2 2) /2 (6.)
52 Weakly Produced Supersymmetry 6.5.2 Lepton Observables ransverse Momentum of the Lepton System, p ll he transverse momentum of the dilepton system is defined as follows: ( ( p ll = p l+ x ) 2 ( + p l x + p l+ y and is shown in chapter 7 to be a useful variable. ) ) 2 /2 + p l y (6.2) Dilepton Invariant Mass, m ll In the sought signal, the leptons come from a decaying Z-boson. herefore the mass of the dilepton system, m ll, is expected to be close to the mass of the Z-boson. ( ( m ll = E l+ + E l ) 2 p l + + p l ) 2 /2 (6.3) R(ll) he angle R(ll) between the two leptons is defined in terms of η and φ: R(ll) = ( (η l + η l ) 2 + (φ l + φ l ) 2) /2 (6.4) and is shown in chapter 7 to be a useful variable. 6.5.3 Relative Missing ransverse Momentum he observable E miss, 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 of one or more objects is badly measured, the E miss will be affected so that the direction of the E miss will be aligned with that of the badly reconstructed object. o reduce the effect of such mismeasurements the observable relative missing transverse momentum, E miss,rel, is introduced [65]. If the angle between the direction of the E miss and the nearest lepton or jet is small, only the E miss component perpendicular to this object is considered: E miss,rel = { E miss if φ l, j π/2 E miss sin φ l, j if φ l, j < π/2 (6.5) φ l, j is the angular distance between the direction of the E miss and the nearest lepton or jet.
6.6 ALAS Data Set 53 6.6 ALAS Data Set he analysis presented in this thesis is based on the data from proton-proton collisions at s = 8 ev collected in 202. Due to the technical limitation on event readout, bandwidth, recording, and storage capacity, only the most useful proton-proton collisions can be recorded. As the number of events with a single low-p lepton is large, the single lepton triggers have relatively high p thresholds on the leptons in order to keep an event. he thresholds are 24 GeV for the single electron trigger and 20 GeV for the single muon trigger. Since this analysis is looking for events with final states containing two leptons dilepton triggers can also be used. Due to the presence of a second lepton the event rate is lower and the energy threshold can be lowered. Hence a dilepton trigger with threshold 2 GeV is used in combination with the single lepton triggers. After removing data taking periods flagged as bad by detector experts, the remaining integrated luminosity that can be used in this analysis is 20.3 fb [66].
7 Choice of Signal Region A signal region is defined by a set of cuts selected to optimize statistical sensitivity to the new physics signal. In SUSY searches where the model parameters are unknown the signal region must be sensitive to a large number of signal points with slightly different signatures. In the search presented in Paper III, the signal region has been optimized to obtain the largest exclusion reach with respect to the signal models described in the previous chapter. he steps of the optimization of the signal region called SR-Zjets in Paper III are described in this chapter. 7. Preselection From the kinematic characteristics of the signal a minimum set of selections, or base selections, for the signal region are determined. As the signal contains a hadronically decaying W-boson, at least two jets must be present. In order to distinguish the signal from the t t background a veto on b-jets is applied. However, since the b-tagging requires tracking information from the inner detector, no b-tagging is available for η > 2.4. herefore a different approach must be used to suppress the t t background in events with jets in the forward region. A veto on forward jets with p > 30 GeV is applied. his removes t t events with high-p jets but leaves jets from the signal, since the signal is expected to have more central jets than the background he signal contains two leptons from the decay of a Z-boson. hese leptons must have same flavor and opposite sign. he sensitivity to the signal does not exhibit any significant dependence on the momentum of the leptons, therefore cuts on p l > 35 GeV and p l2 > 25 GeV are applied to ensure uniformity with other signal regions [6]. Since the leptons are the result of the decay of an on-shell Z-boson, the invariant mass m ll of the two leptons is required to lie within a 0 GeV window around the Z-boson mass. hese cuts are referred to as the base cuts and are defined in ab. 7.. 7.2 Method he signal region optimization is performed on Monte Carlo simulation. he optimization of cuts is a complex process which may require many iterations to arrive at the final cuts. he systematic errors and errors on Monte Carlo statistics depend on the selections and therefore change with each cut. he variables are correlated and cutting on one variable
56 Choice of Signal Region Variable Value N C20 2 N B20 + N F30 = 0 N l = 2 p l p l2 > 35 GeV > 20 GeV m Z m ll < 0 GeV able 7.: he base cuts defining the region within which the signal region optimization is performed. he 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. he main goal of the selection is to maximize the exclusion range in the grid of signal points, but other factors such as background calculation must also be taken into account. At this stage of the analysis the backgrounds are estimated using Monte Carlo simulated data but in later stages data driven methods are developed for several of the background processes. In Sec. 7.2.3 the effect of the cuts proposed is validated by applying all cuts except one and checking the the optimal cut value. 7.2. Figure of Merit for Sensitivity In order to evaluate different selections a figure of merit p is introduced. he expected number of background events in the signal region is b±σ b, where σ b is the quadratic sum of the statistical errors from Monte Carlo and the systematic errors. he expected number of signal events in the same region is s. Assuming a signal plus background hypothesis and no uncertainty on b or s, the observed event count N in the signal region is expected to follow a Poisson distribution, P(N s + b), with central value s + b. his is illustrated by the dashed curve in Fig. 7.. However b does have an uncertainty σ b, and to obtain the correct probability distribution of the number of events the function P(N s + b) must be convoluted with a Gaussian function G(B b,σ b ) with central value b and standard deviation σ b. G(B b,σ b ) gives a weight to each possible value B of the number of background events. he resulting probability density function F(N s + b,σ b ) is given by: F(N s + b,σ b ) = 0 P(N s + b)g(b b,σ b )db G(B b,σ b )db 0 (7.) his is illustrated by the solid curve in Fig. 7.. he black area p under the curve is the probability of the signal plus background to yield an observed number of events of
7.2 Method 57 b or less. his probability is obtained by summing the probability density function from zero to b: p = 0 b N=0 P(N s + b)g(b b,σ b )db 0 G(B b,σ b )db (7.2) Lower p-values correspond to higher sensitivity to the signal in the signal region. If p < 0.05 the probability of observing b events under the signal plus background hypothesis is less than 5%, and if no excess over Standard Model background expectation is observed, that hypothesis can be excluded with 95% confidence level.. p -0. -0 b s+b 35 Number of events Figure 7.: Illustration of the probability density function for the signal plus background (s + b) hypothesis with no uncertainty (dashed curve) and convoluted with a Gaussian function to include the uncertainty on the background (solid curve). he area of the filled surface under the graph corresponds to the probability p of observing only the expected background b under the s + b hypothesis. Lower p-values correspond to higher sensitivity to the signal. p is used as figure of merit to evaluate the effect of different signal region selections. he error on p is obtained by varying the expected b by one σ b up and down and comparing the resulting p with the nominal value. hus the effect of variations in the background are translated to an error on the probability p. In the following sections the statistical error and a flat systematic error of 20% on the expected background yield is used. he p-values are numerically calculated with the function BinomialExpP from the ROOFI package [67].
58 Choice of Signal Region 7.2.2 Signal Region Cut Optimization Missing ransverse Momentum Due to the two χ 0 that escape detection, the supersymmetric signal is expected to contain a large amount of missing transverse momentum compared to the Standard Model background. Figure 7.2(a) shows the distribution of relative missing transverse momentum (E miss,rel ) after the base cuts in Monte Carlo simulation. he stacked histograms show the different components of the background and the overlaid dashed lines show the distribution for three different signal points. As expected the background process Z/γ ll is dominating at low E miss,rel. Fig 7.2(a) also illustrates the need of a data driven method to estimate the Z/γ ll background as the Monte Carlo quickly runs out of statistics at high E miss,rel, 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 E miss,rel for a few selected signal points. he errors on p are determined using the method described in section 7.2.. he signal points have been chosen to represent low, medium and high mass difference between the gauginos. For the signal points with low gaugino mass difference, where m 00 GeV, the sensitivity is low throughout the E miss,rel spectrum. hese models are so called compressed spectra models and are in general very challenging at the LHC. For the points with higher gaugino mass difference it is clear that the sensitivity to the signal increases as the cut on E miss,rel is tightened. However other cuts will be applied and it is desired to retain sufficient Monte Carlo statistics for the analysis. Also, systematic errors can increase significantly at high E miss,rel. herefore a relatively loose cut is chosen at this point. As an increase in sensitivity compared to looser cuts is observed at E miss,rel > 80 GeV this cut level is chosen. After other cuts have been applied the cut is validated and may be adjusted if necessary. he value of the E miss,rel cut is 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 jets in the Z + jets, WW and ZZ background processes originate mainly from initial state radiation. herefore the p of the two leading jets in the signal is expected to be higher than in the backgrounds. In Fig 7.3 the distribution of the p of the leading (a) and second leading (b) jets after preselection and the cut on E miss,rel > 80 GeV are applied are shown. Figure 7.3(c) shows the p-value for different combinations of cuts on the two jets. he sensitivity does not exhibit much improvement after [40, 40] GeV. he background calculation (described in chapter 8) benefits from cuts on p jet > 45 GeV and p jet2 > 45 GeV. Since these cuts do not affect the sensitivity negatively the cut [45, 45] GeV is selected for the signal region. Although other jets may arise from ISR, it is likely that the two jets from the W- decay will have higher p. herefore the invariant mass (m j j ) of the two leading jets is
7.2 Method 59 Events / 0 GeV 7 0 6 0 5 0 4 0 3 0 2 0 0 0 Base L dt = 20.3 fb Z ee,µµ ZW, ZZ WW Z τ τ top Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 0 50 00 50 200 250 300 350 400 (a) E χ ±=350 GeV, m 0=50 GeV χ miss, rel [GeV] p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 0 2 m 0 χ,χ 2 m 0 χ,χ 2 m 0 χ,χ 2 ±=250 GeV, m =00 GeV 0 χ ±=300 GeV, =00 GeV 0 mχ ±=350 GeV, =50 GeV 0 mχ >50 >60 >70 >80 >90 >00 >0 >20 >30 >40 miss, rel Cut value E [GeV] Figure 7.2: (a) Distribution of the relative missing transverse momentum after the base cuts are applied. he stacked histograms show the different components of the background and the overlaid dashed lines show the distribution for three different signal points. he error band represents the quadratic sum of the error on Monte Carlo statistics and a flat systematic error of 20%. (b) Sensitivity to different signal points, measured with the p-value described in section 7.2., after different cuts. Lower p-value means higher sensitivity. he error on p is determined by shifting the background estimate by its total uncertainty. (b) expected to be close to the mass of the W-boson. Figure 7.4(a) shows the distribution of the invariant mass of the two leading jets after the preselection and additional cuts on E miss,rel > 80 GeV and p jet,2 > 45 GeV are applied. In the region 50 < m j j < 00 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 < 00 GeV and 0 < m j j < 00 GeV for signal points with higher gaugino mass difference, as seen in Fig. 7.4(b). he sensitivity to signal points with low gaugino mass difference is low for all investigated 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. herefore the cut 50 < m j j < 00 GeV is selected for the signal region. Kinematics of Dilepton System he transverse momentum of the system of leptons, p ll, and the angle between them, R(ll), are also useful variables to discriminate the signal from the background. In the signal, the initial gauginos are massive and are produced approximately at rest. he p of
60 Choice of Signal Region the χ 0 2 therefore is approximately close to zero. As it decays the p of the Z-boson must balance that of the χ 0. If the mass difference m χ 0 2 (m χ 0 + m Z ) is large, the Z-boson and the χ 0 will receive high p. he lepton pair from the Z-boson decay will be boosted, making the angle between the two leptons small and the p of the system of leptons high. For the Z + jets background most Z-bosons are produced with low p. herefore the angle between the resulting leptons will be large and the p of the dilepton system will be low. In t t events the two leptons arise from the decay of two separate bosons and the direction of the leptons therefore will be uncorrelated. hus the angle between the leptons and the p of the dilepton system can assume any value. hese differences in kinematics can be seen in Fig 7.5, which shows the distribution of p ll (a) and R(ll) (b) after the preselection and additional cuts on Emiss,rel > 80 GeV, > 45 GeV and 50 < m j j < 00 GeV are applied. Fig 7.5(c) and (d) show the p- p jet,2 values for different cuts on p ll and R(ll) respectively. At this stage very few events remain. In Fig 7.5(a) no t t events are present in the region 60 < p ll < 80 GeV, which is reflected in the lower p-values for the cut values on p ll > 60 GeV and pll > 70 GeV in Fig 7.5(c). However it is probable that this is the effect of the low remaining Monte Carlo statistics rather than an effect of physics. herefore a slightly higher cut, p ll > 80 GeV is selected for the signal region. he lack of Monte Carlo statistics clearly shows the need for a data driven estimate for the t t background. Similarly the R(ll) suffers from low remaining statistics, especially for the t t background. he region.6 < R(ll) < 2.0 has very low background resulting in seemingly low p-value in the three rightmost bins in Fig 7.5(d). Considering that this is likely to be an effect of the low statistics the more conservative cut 0.3 < R(ll) <.5 is chosen for the signal region. 7.2.3 Validation and Final Selection of Cuts he cuts selected in the previous section are summarized in ab. 7.2. o validate the cut values chosen the sensitivity to signal models is studied for each cut separately. After all cuts in ab. 7.2 are applied, one cut at a time is removed and the p-value for different cut values on the removed cut is calculated. In Fig. 7.6 this is shown for all variables reviewed in the previous section. he sensitivity to the two signal points with gaugino mass difference of 50 GeV and 00 GeV is low for all investigated cuts and the discussion is therefore focused on models with higher mass difference. Figure 7.6(a) shows p-values for different cuts on E miss,rel after all other cuts are applied. he behavior of the sensitivity varies with the mass difference between the gauginos in the signal models. For medium mass difference the sensitivity displays a clear improvement for cuts around E miss,rel > 70 GeV. For high mass differences however, the sensitivity continues to increase as the cut is tightened. herefore the benefits on the two types of events must be weighed against each other; a loose cut benefits the first type and a tight cut benefits the latter. As a compromise E miss,rel > 80 GeV is suitable and is chosen
7.2 Method 6 Variable Value Variable Value N C20 2 p l > 35 GeV N B20 + N F30 = 0 p l2 > 20 GeV p jet > 45 GeV m Z m ll < 0 GeV p jet2 > 45 GeV p ll > 80 GeV m j j [50,00] GeV R(ll) [0.3,.5] E miss,rel > 80 GeV able 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 jet,2 > 45 GeV are applied. he figure shows that beyond [40, 40] GeV this cut does not greatly affect the sensitivity and therefore the cut p jet,2 > 45 GeV, which is preferred for the background calculation, can be used. As seen in Fig. 7.6(c) the cut 50 < m j j < 00 GeV is a natural choice for the invariant mass of the jets. Figure 7.6(d) shows no effect on the sensitivity for different cuts on p ll below 00 GeV. However, a cut on p ll > 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 ll > 80 GeV. In Fig. 7.6(e) it is seen that 0.3 < R(ll) <.5 gives the lowest p-value and this cut is therefore selected.
62 Choice of Signal Region Events / 20 GeV 4 0 3 0 2 0 0 Base, E miss, rel >80 GeV L dt = 20.3 fb Z ee,µµ ZW, ZZ WW Z τ τ top Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 χ ±=350 GeV, m 0=50 GeV χ Events / 20 GeV 4 0 3 0 2 0 0 Base, E miss, rel >80 GeV L dt = 20.3 fb Z ee,µµ ZW, ZZ WW Z τ τ top Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 χ ±=350 GeV, m 0=50 GeV χ 0 0 0 50 0050200250300350400450500 (a) jet p [GeV] 0 50 0050200250300350400450500 (b) jet2 p [GeV] p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ 2 m 0 χ,χ 2 m 0 χ,χ 2 ±=250 GeV, m =00 GeV 0 χ ±=300 GeV, =00 GeV 0 mχ ±=350 GeV, =50 GeV 0 mχ 0 [20,20] [30,30] [35,25] [35,35] [40,35] [40,40] [45,40] [45,45] [50,45] [50,50] Cut value [p (c) jet,p jet2 ] [GeV] Figure 7.3: Distribution of the transverse momentum of the leading (a) and second leading (b) jets, after the base cuts and E miss,rel > 80 GeV are applied. he stacked histograms show the different components of the background and the overlaid dashed lines show the distribution for three different signal points. he error band represents the quadratic sum of the error on Monte Carlo statistics and a flat systematic error of 20%. (c) Sensitivity to different signal points, measured with the p-value described in section 7.2., after different combinations of cuts on the p of the two leading jets. Lower p-value means higher sensitivity. he error on p is determined by shifting the background estimate by its total uncertainty. [45,45] GeV is selected for the signal region.
7.2 Method 63 Events / 50 GeV 3 0 2 0 0 Base, E miss, rel L dt = 20.3 fb >80 GeV, p j,2 >45 GeV Z ee,µµ ZW, ZZ WW Z τ τ top Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 χ ±=350 GeV, m 0=50 GeV χ p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 0 2 m 0 χ,χ 2 m 0 χ,χ 2 m 0 χ,χ 2 ±=250 GeV, m =00 GeV 0 χ ±=300 GeV, =00 GeV 0 mχ ±=350 GeV, =50 GeV 0 mχ 0 0 00 200 300 400 500 600 700 800 900 (a) M jj [GeV] [0,00] [0,50] [0,200] [50,00] [50,50] [50,200] Cut value M jj [GeV] (b) Figure 7.4: (a) Distribution of the invariant mass of the two leading jets after the base cuts, E miss,rel > 80 GeV and p jet,2 > 45 GeV are applied. he stacked histograms show the different components of the background and the overlaid dashed lines show the distribution for three different signal points. he error band represents the error on Monte Carlo statistics and a flat systematic error of 20%. (b) Sensitivity to different signal points, measured with the p-value described in section 7.2., after different cuts on m j j. Lower p-value means higher sensitivity. he error on p is determined by shifting the background estimate by its total uncertainty. he cut 50 < m j j < 00 GeV is selected for the signal region.
64 Choice of Signal Region Events / 20 GeV 2 0 0 Base, E miss, rel L dt = 20.3 fb >80 GeV, M =[50,00] GeV, p jj Z ee,µµ ZW, ZZ WW Z τ τ top j,2 >45 GeV Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 χ ±=350 GeV, m 0=50 GeV χ Events / bin 2 0 0 Base, E miss, rel L dt = 20.3 fb >80 GeV, M =[50,00] GeV, p jj Z ee,µµ ZW, ZZ WW Z τ τ top j,2 >45 GeV Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ 2 m 0 χ, χ 2 χ ±=350 GeV, m 0=50 GeV χ 0 0 50 0050200250300350400450500 (a) pll [GeV] 0 0 2 3 4 5 6 (b) R(ll) p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ 2 m 0 χ,χ 2 m 0 χ,χ 2 ±=250 GeV, m =00 GeV 0 χ ±=300 GeV, =00 GeV 0 mχ ±=350 GeV, =50 GeV 0 mχ p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ 2 m 0 χ,χ 2 m 0 χ,χ 2 ±=250 GeV, m =00 GeV 0 χ ±=300 GeV, =00 GeV 0 mχ ±=350 GeV, =50 GeV 0 mχ 0 0 2 0 2 0 >60 >70 >80 >90 >00 >20 >40 >60 >80 >200 (c) ll Cut value p [GeV] [0.3,0.9] [0.3,.][0.3,.3] [0.3,.5][0.3,.7] [0.3,.9][0.3,2.] (d) Cut value R(ll) Figure 7.5: Distribution of the transverse momentum of the dilepton system (a) and the angle between the leptons (b) after the base cuts, E miss,rel > 80 GeV, p jet,2 > 45 GeV and 50 < m j j < 00 GeV are applied. he stacked histograms show the different components of the background and the overlaid dashed lines show the distribution for three different signal points. he error band represents the error on Monte Carlo statistics and a flat systematic error of 20%. (c) and (d) Sensitivity to different signal points, measured with the p-value described in section 7.2., after different cuts on p ll and R(ll) respectively. Lower p-value means higher sensitivity. he error on p is determined by shifting the background estimate by its total uncertainty. he cuts p ll > 80 GeV and 0.3 < R(ll) <.5 are selected for the signal region.
7.2 Method 65 p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =00 GeV 0 χ 2 m 0 χ,χ ±=300 GeV, =00 GeV 0 mχ 2 m 0 χ,χ ±=350 GeV, =50 GeV 0 mχ 2 p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =00 GeV 0 χ 2 m 0 χ,χ ±=300 GeV, =00 GeV 0 mχ 2 m 0 χ,χ ±=350 GeV, =50 GeV 0 mχ 2 0 0 2 0 >50 >60 >70 >80 >90 >00 >0 >20 >30 >40 miss, rel Cut value E [GeV] (a) 2 0 [20,20] [30,30] [35,25] [35,35] [40,35] [40,40] [45,40] [45,45] [50,45] [50,50] Cut value [p (b) jet,p jet2 ] [GeV] p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =00 GeV 0 χ 2 m 0 χ,χ ±=300 GeV, =00 GeV 0 mχ 2 m 0 χ,χ ±=350 GeV, =50 GeV 0 mχ 2 p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =00 GeV 0 χ 2 m 0 χ,χ ±=300 GeV, =00 GeV 0 mχ 2 m 0 χ,χ ±=350 GeV, =50 GeV 0 mχ 2 0 0 2 0 2 0 [0,00] [0,50] [0,200] [50,00] [50,50] [50,200] (c) [GeV] Cut value M jj >60 >70 >80 >90 >00 >20 >40 >60 >80 >200 (d) Cut value p ll [GeV] p 0 m 0 χ,χ ±=200 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =50 GeV 0 χ 2 m 0 χ,χ ±=250 GeV, m =00 GeV 0 χ 2 m 0 χ,χ ±=300 GeV, =00 GeV 0 mχ 2 m 0 χ,χ ±=350 GeV, =50 GeV 0 mχ 2 0 2 0 [0.3,0.9] [0.3,.][0.3,.3] [0.3,.5][0.3,.7] [0.3,.9][0.3,2.] Cut value R(ll) (e) Figure 7.6: After all cuts are in place one cut at a time is removed and the sensitivity for different cuts on each variable is studied. he figure of merit is the p-value defined in section 7.2.. he variables shown are (a) E miss,rel, (b) p jet,2, (c) m j j, (d) p ll and (e) R(ll).
66 Choice of Signal Region 7.3 Results he signal region is now fixed to the selections of ab. 7.2. able 7.3 shows the number of Monte Carlo events in the signal region for each background source. Also the expected number of events for three signal points are shown. After all cuts have been applied the expected sensitivity is calculated for supersymmetric models with pp χ 2 0 + χ ± W ± χ 0 + Z χ. 0 In Fig. 7.7 the p-value (see Sec. 7.2.) for each signal point is plotted as color scale in the m χ 0 2, χ ±,m χ 0 plane. A flat systematic error of 20% on the expected number of background events is used. p < 0.05 means that the probability of the signal plus background fluctuating to the expected b is less than 5%. If no excess over the expected Standard Model background is observed in the signal region that signal model can be excluded with 95% confidence level. Source ee µµ ee + µµ ZW, ZZ 0.59±0.5 0.39±0. 0.99±0.7 WW 0.00±0.00 0.04±0.03 0.04±0.03 op 0.02±0.0 0.0±0.0 0.03±0.0 Higgs 0.00±0.00 0.00±0.00 0.00±0.00 Z ττ 0.00±0.00 0.00±0.00 0.00±0.00 Z+jets 0.00±0.00 0.00±0.00 0.00±0.00 otal MC background 0.62±0.5 0.45±0..07±0.7 m χ 0 2, χ ± = 250 GeV, m χ 0 = 00 GeV.20±0.20.46±0.2 2.66±0.29 m χ 0 2, χ ± = 300 GeV, m χ 0 = 00 GeV.70±0.6.79±0.6 3.50±0.23 m χ 0 2, χ ± = 350 GeV, m χ 0 = 50 GeV.94±0.2.77±0. 3.7±0.6 able 7.3: Background composition of the signal region based on Monte Carlo simulation. he given errors are purely statistical. he contour in Fig. 7.7 indicates the area where p < 0.05 and shows the expected exclusion 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 exclusion reach is improved. Chargino and neutralino masses up to m χ 0 2, χ ± = 40 GeV are within reach for a massless χ. 0 he actual observed limit from measurements on collision data can be expected to change with respect to the limit in Fig. 7.7. he systematic uncertainties in this chapter are taken to be 20%, a number estimated from previous studies. he exact size of the systematic uncertainties is dependent on signal region definition and not fully known until the analysis is complete. At later stages of the analysis the systematic error on the signal region 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] 0 m χ 450 400 350 300 250 200 50 00 50 L dt = 20.3 fb s = 8 ev ee + µµ ± 2 χ m 0,χ 0 < m χ 0 χ m 0 00 50 200 250 300 350 400 450 500 ± [GeV] 2 0 m χ = m Z m χ 0,χ 2 0.3 p 0.25 0.2 0.5 0. 0.05 0 Figure 7.7: Expected sensitivity for different gaugino masses in the m χ 0 2, χ ±,m χ 0 plane. he figure of merit on the color z-axis is the probability p defined in section 7.2.. A flat systematic error of 20% on the expected number of background events is used in the sensitivity calculation. he contour indicates the limit where p < 0.05 which is the expected exclusion 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 in chapter 7. he processes are grouped in several categories described below. In this chapter the techniques used to derive these backgrounds are briefly described for each group and more details are given in Paper III. he measurement of the Z + jets background is the focus of chapter 9 of this thesis. 8. Diboson production, ZW and ZZ Events contributing to this background come from the processes ZZ llνν and ZW lllν where one lepton fails to be reconstructed. he jets come essentially from ISR. riboson processes are added to this category. As seen in ab. 7.3, this is the largest expected background. It is difficult to find a control region similar to the signal region and sufficiently pure in ZZ and ZW. herefore the background is estimated from Monte Carlo simulated data. Special control samples with three and four reconstructed leptons, enriched in ZZ llll and ZW lllν respectively, are used to validate the shape and scale of the simulated data. An additional uncertainty is assigned to the estimated background to account for discrepancies between simulated and collision data. 8.2 op he t t and Wt backgrounds have very similar E miss,rel shapes and are therefore estimated together. For this background a data driven method is used. A control region is identified with events with two leptons outside the Z-window and with one b-tagged jet. he number of events at high E miss,rel is extracted and compared to the simulation. he ratio between data 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 electrons from photon conversions. hese 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 misidentified as a lepton, processes with one or no real lepton can appear to have two leptons, thus contributing to the background in the signal region. Processes contributing to this or fake lepton background are s- and t-channel single top, t t where at least one W decays hadronically, W + jets, b b, and multijet QCD production. All background processes with fake leptons are estimated collectively using a data driven method known as the matrix method. his method uses the real efficiency, i.e. the probability of a real lepton passing the selections criteria, and the fake rate, i.e. the probability of a fake lepton passing the same criteria, to statistically predict the number of fake leptons in the signal region. he real efficiency and fake rate are measured in data. A similar 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 normalized 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 ll)+jets background, two methods were developed for Paper III. he E miss,rel in this background is fake E miss,rel, mainly due to the jet resolution rather than the presence of high p invisible particles. It is desirable to use a data driven technique, since Monte Carlo simulations run out of statistics and it is nearly impossible simulate the statistics necessary. Another reason to rely on data is that the Z +jets process has a large cross section, thus a low rate of events with high calorimeter noise could lead to a significant number of Z + jets events migrating towards the signal region. wo methods have been developed in support of Paper III, the method relying on photon control regions developed by the author described in chapter 9, and the jet smearing method described below which is used for the final numbers in Paper III. he jet smearing method uses a sample enriched in Z +jets events with well measured jets to define seed events. his is implemented by requiring E miss / E sum <.5 GeV /2. Each seed event is smeared multiple times by multiplying the four-momentum of each jet with a random number from a jet response function. he jet response function is obtained from simulation and adjusted to data in a control sample. he smearing is repeated 0,000 times for each seed event. hus pseudo-data with jet resolution following the adjusted jet response is obtained. he pseudo-data is normalized to data in the low E miss,rel region and the number of Z + jets events is evaluated in the high E miss,rel region.
9 Data Driven Z +jets Background Estimation his chapter presents one of two methods developed for the estimation of the Z +jets background in the search for supersymmetry described in Paper III. In a previously unexplored signal region it is important to cross check results with different methods, and at the end of the chapter the two methods are compared and the strong and weak points of each are discussed. 9. Motivation Although simulations indicate that the number of Z +jets events in the high E miss,rel is low, it is important to confirm this point using a data driven method. he E miss,rel schematically be seen as coming from two sources: real E miss,rel and fake E miss,rel. region can Real E miss,rel arises when neutrinos or other weakly interacting neutral particles such as hypothetical neutralinos pass through the detector, carrying away momentum that cannot be detected. Fake E miss,rel is due to instrumental effects, such as the resolution of leptons and jets. he fake E miss,rel is difficult to model in simulations. (Z/γ ll) + jets where both leptons have been identified do not have true E miss,rel, since no particles invisible to the detector are present. he missing energy in these events arises mainly from the limited resolution of the jet energy. In ALAS the jet energy resolution is approximately 7 GeV for a jet with p = 45 GeV [68], while the uncertainty for leptons with p around 30 GeV is close to 2% or 0.6 GeV per lepton [69, 42]. Figure 9. shows the distribution of E miss,rel in the signal region for different background processes and signal models. he sharp drop of the Z ll + jets background at E miss,rel = 70 GeV is the result of too low Monte Carlo statistics. he low number of predicted events causes large statistical errors and it is not time efficient to produce the number of simulated events required for an accurate background estimate. herefore a data driven background estimate is preferred. Using a data driven technique should capture detector effects that could lead to a low rate of events with high mismeasured E miss,rel contributing to the signal region.
72 Data Driven Z + jets Background Estimation Events / 0 GeV 5 0 4 0 3 0 2 0 0 Signal Region, ee +µµ L dt = 20.3 fb Z ee,µµ ZW, ZZ WW Z τ τ top Higgs m 0 ±=250 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=300 GeV, m 0=00 GeV χ, χ χ 2 m 0 ±=350 GeV, m 0=50 GeV χ, χ 2 χ 0 0 50 00 50 200 250 300 350 400 miss, rel E [GeV] Figure 9.: Distribution of the relative missing transverse momentum within the signal region without the cut on E miss,rel > 80 GeV. he band on the total background is the error from Monte Carlo statistics and a flat systematic error of 20%. he dashed lines show the E miss,rel distribution from three benchmark signal models. his chapter presents a data driven estimate of the Z + jets background using control regions selected with one or two photons plus jets. he Z + jets background events surviving to the signal region must be characterized by a high p Z-boson recoiling against a jet system that sets the missing energy; the single photon and diphoton regions are characterized by a high p photon or diphoton system recoiling against a jet system, as depicted in Fig. 9.2. Jet Z l Jet γ Jet γ Jet l Jet Jet γ (a) (b) (c) Figure 9.2: Sketch of the event topology for (a) a Z + jets event, (b) a single photon plus jets event, and (c) a diphoton plus jets event
9.2 Missing ransverse Momentum in Photon Control Regions 73 9.2 Missing ransverse 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 be defined. If the shape of the E miss,rel distribution in the control region is close enough to that in the signal region, the number of background events can be extracted from collision data in the control region and transferred to the signal region. In the present case photon control regions are chosen. Since photon energy resolution is similar to that of electrons the missing energy in such regions is dominated by jet effects and presents the same jet resolution effects. his chapter investigates two different photon control regions and the advantages and disadvantages for each are discussed. 9.2. Diphoton Control Region Photons and electrons are measured via electromagnetic showers in the EM calorimeter and contribute in the same way to the E miss resolution. Also the muons have a comparable resolution. In all three cases the E miss,rel spectrum will be dominated by the jet energy resolution. he distribution of fake E miss is therefore expected to be similar in the signal region and in a control region with cuts mimicking the signal region but with the two leptons replaced by two photons. Since the two photons exactly match the number of leptons, the total number of objects present in the detector is the same in the control and signal regions, and the E miss,rel (defined in Eq. 6.5.3) distribution is also expected to be similar in the two regions. Figure 9.3(a) shows the E miss,rel 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. he error band represents the error on Monte Carlo statistics and systematic uncertainties combined. As seen in Fig. 9.3(a), the core of the E miss,rel distribution in the diphoton control region agrees well within errors with the distributions from the signal region. However it is again clear that the simulation runs out of statistics with increasing E miss,rel. herefore it is important to check the shapes also in collision data. In Sec. 9.7 the shape of the diphoton E miss,rel template from data is compared to the shape of the E miss,rel in the signal region. he agreement is good in data and it is concluded that the E miss,rel distribution in control region can be used to estimate the number of Z + jets events with high E miss,rel in the signal region. he choice of a diphoton region however has the disadvantage of low statistics. No simulated events survive the hard cuts of the signal region. o circumvent this problem it is investigated whether some cuts can be relaxed to increase the number of events, as described in further detail later in this chapter. he shape of the E miss,rel distribution is unaffected by changes to the cuts on m γγ, R(γγ), m j j, and p jet2. herefore slightly relaxed cuts in the control region can be used. he selections defining the diphoton control
74 Data Driven Z + jets Background Estimation Arbitrary units 0 2 0 Diphoton Control Region (p γγ >80 GeV) γγ ee µµ Arbitrary units 0 2 0 Single Photon Control Region (p >80 GeV) γ γ 80 ee µµ 3 0 3 0 4 0 4 0 ll/γγ 5 0 3 2 0 0 50 00 50 200 250 300 350 400 miss, rel E [GeV] (a) ll/γ 80 5 0 3 2 0 0 50 00 50 200 250 300 350 400 miss, rel E [GeV] (b) Figure 9.3: he E miss,rel distribution from simulation in (a) the diphoton control region (γγ) and (b) the single photon control region (γ80), see ab. 9.. he E miss,rel distribution in the control regions is marked by black circles, and that of the electron and muon channels of the signal region are marked by red triangles and green squares respectively. he error band represents the error on Monte Carlo statistics, theoretical uncertainties and systematic uncertainties combined. For the distribution in (b) the correction discussed in Sec. 9.2.2 is applied. region are given in ab. 9.. he looser control region cuts are used in Fig. 9.3(a). Even after the looser cuts of the control region are applied few events remain, causing a large statistical error. 9.2.2 Single Photon Control Region A different approach for a control region is to use γ + jets events. Photons and Z-bosons are both vector bosons and are produced via similar processes. If the photon in a γ + jets event has high p, the jet activity balancing the event is expected to be similar to that in a Z +jets event. Since the E miss,rel mostly arises from jet activity, the E miss,rel spectrum should be similar in high-p γ + jets events and in Z + jets events. he cuts in the single photon control region closely mimic those in the signal region except the lepton selections. he signal region cut on the dilepton momentum p ll is translated into a cut on the p of the single photon, and the cut on p of the second leading jet is relaxed in order to gain statistics. he selections of the control and signal regions are defined in ab. 9..
9.3 Control Region Denitions 75 Correction for E miss,rel he single photon control region exhibits a slightly harder E miss,rel spectrum than the signal region. he explanation for this lies in the definition of E miss,rel given in Eq. 6.5.3 ). If the angle φ γ, j between a reconstructed object and the direction of the E miss is small ( φ γ, j < π/2), only the component of E miss perpendicular to the object is considered, defining the variable E miss,rel. If the number of reconstructed objects in the detector is larger, the probability that φ γ, j < π/2 increases giving a smaller E miss,rel. In the single photon control region only one photon is required instead of two as in the diphoton control region. Also in the signal region two particles (e/µ) are present. herefore the number of objects potentially close to the direction of the E miss the single photon control region, which translates into a harder E miss,rel is lower in spectrum. Since the background estimate requires close agreement between the E miss,rel distributions in the control and signal regions, the E miss,rel in the single photon control region must 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, or photons in the detector. his direction defines a so called pseudo photon. When calculating the E miss,rel the direction of this pseudo photon is considered along with the other objects, giving the same number of objects in the control and signal regions. Figure 9.3(b) shows the E miss,rel distribution after the correction is applied. he agreement between the control and signal regions is within errors in the core of the distribution. he low Monte Carlo statistics in the signal region prevents a comparison in the high E miss,rel region. In Sec. 9.7 the single photon E miss,rel template from data is compared to the shape of the E miss,rel in dilepton data and the agreement is good. Compared to the diphoton control region the single photon control region benefits from higher statistics, which is reflected in smaller statistical errors. 9.3 Control Region Denitions he cuts of the control regions are chosen to correspond to those of the signal region. However some modifications are necessary to increase statistics. he signal region cuts on variables related to leptons are translated into corresponding cuts on photon variables. For the diphoton control region the cuts on m j j, R(ll), and m Z m ll are removed and the cut on the p of the second leading jet is lowered from 45 GeV to 20 GeV in order to increase statistics. he diphoton control region uses a diphoton trigger where both photons are required to pass a p > 20 GeV threshold. For the single photon control region all cuts involving the second leading lepton are ignored, since only one photon is present. he cut on m j j has been relaxed to m j j < 600 GeV, which increases statistics while still reducing the amount of QCD con- ) For photon events the term φ l, j in Eq. 6.5.3 is substituted by φ γ, j.
76 Data Driven Z + jets Background Estimation tamination in the region. For the single photon control region a combination of three photon triggers are used, requiring photon p larger than 40, 80, and 20 GeV respectively. he cuts defining the control regions are detailed in ab. 9.. Signal region γ80 γγ N C20 2 2 2 N B20 + N F30 = 0 = 0 = 0 p jet > 45 GeV > 45 GeV > 45 GeV p jet2 > 45 GeV > 20 GeV > 20 GeV m j j [50,00] GeV < 600 GeV N l = 2 = 0 = 0 N γ = = 2 p γ/l > 35 GeV > 80 GeV > 35 GeV p γ2/l2 > 20 GeV > 20 GeV p γγ/ll > 80 GeV > 80 GeV R(γγ/ll) [0.3,.5] m Z m ll < 0 GeV able 9.: Definition of the single photon and diphoton control regions, with the signal region definition as comparison. N l denotes the number of tight electrons or muons, and N γ denotes the number of tight photons whose definition are outlined in chapter 4. p γ/l, p γ2/l2, and p γγ/ll denote the p of the photons in the control regions and the p of the leptons in the signal region. R(γγ/ll) denotes the distance between the photons or leptons in the control and signal regions respectively. 9.4 he ABCD Method If the shape of the E miss,rel spectrum in the control region is approximately the same as in the signal region, a template E miss,rel spectrum from the control region can be used to obtain the number of events with E miss,rel > 80 GeV in the signal region. However, the E miss,rel templates from single photon, diphoton, and dilepton data can be contaminated by processes with true E miss,rel which contribute to a high tail of E miss,rel. he events with true E miss,rel must be subtracted from the photon templates before the templates can be used as a model for the fake E miss,rel in the signal region. he number of such events is obtained from simulation and is the focus of section 9.5.
9.4 he ABCD Method 77 he number of Z + jets events in the high E miss,rel region is predicted following these steps:. Extract the shape of a E miss,rel template in the photon control region in collision data. 2. Validate the normalization of real E miss,rel processes by comparing Monte Carlo simulations to data in the photon control regions. 3. Subtract (using Monte Carlo simulation) processes with real E miss,rel obtain a fake E miss,rel template. from data to 4. Use dilepton events with E miss,rel < 40 GeV, which are dominated by Z + jets, to normalize the fake E miss,rel template. 5. Finally use the normalized fake E miss,rel template to predict the number of Z + jets events with E miss,rel > 80 GeV in the signal region. ll NR A Signal Region B γγ /γ NR C Control Region D 0 0 20 40 60 80 00 20 40 60 80 200 [GeV] miss, rel E Figure 9.4: Schematic picture showing the signal region, control region and normalization regions (NR) used to estimate the Z + jets background. A schematic picture of the control region, signal region and normalization regions is shown in Fig. 9.4. Agreement between the shape of the E miss,rel distribution in the control and signal regions translates into the relation B/A = D/C, were A, B, C, and D are the number of Z + jets events in the regions defined in Fig. 9.4. he number of fake
78 Data Driven Z + jets Background Estimation E miss,rel events is obtained by subtracting the number of real E miss,rel events, denoted by subscript MC, from the number of events from data, denoted by subscript data, in each region: B data B MC A data A MC = D data D MC C data C MC (9.) he sought number of Z +jets events, N(Z +jets), in the signal region is B data B MC. From Eq. 9. this number is obtained from [ ] Adata A MC N(Z + jets) = (D data D MC ) (9.2) C data C MC An important aspect to determining the number of Z + jets events is the ability to predict the number of events with real E miss,rel in the photon control regions, as detailed in Sec. 9.5. 9.5 Sample Composition From Eq. 9.2 it appears crucial to be able to subtract the processes with real E miss,rel from the control regions to get an accurate estimate of the number of Z + jets events. he goal of this section is to determine which processes should be included in the real E miss,rel template for the two control regions. he Monte Carlo samples used to simulate the processes are described and the theoretical uncertainties on the cross sections are stated. hese uncertainties are later propagated to the final fake E miss,rel template. 9.5. γ + jets In the single photon control region the goal is to extract the E miss,rel template for the process γ + jets from data. herefore it is not included in the real E miss,rel contribution which is subtracted from data. In the diphoton control region γ + jets events can enter if a fake prompt photon arises. he E miss,rel in these events is fake and the process is therefore not included in the real E miss,rel template. Monte Carlo samples generated with Pythia8 [70, 7] are used to validate the agreement between simulation and collision data in the control regions but do not enter in any of the terms in Eq. 9.2. 9.5.2 γγ + jets his group of processes dominates the low E miss,rel region in the diphoton control region. Events of this process group that pass into the diphoton control region do not have any real E miss,rel and are therefore not included in the real E miss,rel template.
9.5 Sample Composition 79 If one photon fails reconstruction the process will contribute significantly to the single photon control region. However, in this case the non-reconstructed photon will contribute to the E miss,rel. his contribution is much larger than the E miss,rel from resolution effects and has no corresponding contribution in the signal region. herefore the process group is subtracted from the fake E miss,rel template. he diphoton Monte Carlo sample is generated with Pythia8 and contains processes of two types: processes with two prompt photons produced by hard scattering and processes with one prompt photon and one photon from initial state radiation. he events with two prompt photons are weighted with a k-factor of 8 to normalize the cross section to NLO. he cross section on both types of processes are assigned an uncertainty of 30%. he k-factor and the uncertainty thereupon are estimated using DIPHOX [72]. 9.5.3 W/Z + 0γ his class of processes contains the processes (Z ll) + jets, (Z νν) + jets, and (W lν) + jets. Any observed photons are misidentified electrons or jets. (Z νν) + jets and (W lν) events always have real E miss,rel due to the neutrinos and are subtracted from the fake E miss,rel template for both single photon and diphoton control regions. In the control regions a veto on electrons and muons is applied which means no leptons have been reconstructed. Z ll events do not normally have real E miss,rel. However, in order for a Z ll event to pass into the single photon control region where electron and muon vetoes are applied, one lepton must be misidentified as a photon and the other lepton must fail reconstruction entirely. he lepton that is not reconstructed will contribute its entire transverse momentum to the E miss,rel, causing a much higher E miss,rel than expected from resolution effects. here is no equivalent contribution in the signal region and therefore the process is subtracted from the fake E miss,rel 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 electrons misidentified as photons. In such an event no objects have completely failed reconstruction. he energy resolution and energy scale are very similar for electrons and photons and the E miss,rel is not affected by the misidentification of the electrons. herefore the process is not included in the E miss,rel 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 a jet. In order for the event to pass the control region criteria, the muons must entirely fail reconstruction. If the photons are radiated from the muons and carry a large part of the momentum the muons would be lost and the p of the muon would be replaced by the p of the photon in Eq. 4.2. It is however very unlikely that a radiated photon would carry all of the muon momentum. Instead the muons are not reconstructed for other reasons, for instance by falling out of the muon system acceptance. No such contribution is present in the signal region since two leptons are required. herefore the process is subtracted from
80 Data Driven Z + jets Background Estimation the fake E miss,rel template for both single photon and diphoton control regions. In the signal region the Z ττ background has been estimated with Monte Carlo. In order not to double count this background the process is included in the real E miss,rel processes to be subtracted from the photon control regions. It is however a very small contribution. he samples are generated with Alpgen [73] and the parton showering is modeled with Pythia. he cross sections are calculated with FEWZ [74] at NNLO and have a theoretical uncertainty of 5%. 9.5.4 W/Z + γ his group contains the processes (W lν) + γ + jets, (Z ll) + γ + jets, and (Z νν)+γ + jets. he (W lν) + γ and (Z νν)+γ events always have real E miss,rel due to the neutrinos and are subtracted from the fake E miss,rel template for both single photon and diphoton control regions. In order for the (Z ll) + γ events to pass to one of the control regions at least one lepton must fail to be reconstructed. his gives real E miss,rel and the process must be subtracted from the fake E miss,rel template since no corresponding contribution is present in the signal region which requires two leptons. he W + γ events are generated with Alpgen and the parton showering is performed by HERWIG/JIMMY [75, 76]. he cross sections are calculated at NLO with MCFM [77]. A k-factor of k =.4 is applied and a theoretical uncertainty of 50% is used [78]. he Z + γ events are modeled with Sherpa [79]. he cross sections are calculated at NLO with MCFM. he theoretical uncertainty is 5% [78]. 9.5.5 W/Z + 2γ he group comprises the processes (W lν) + γγ, (Z ll) + γγ, and (Z νν) + γγ. he latter has real E miss,rel due to the neutrinos and is therefore included in the real E miss,rel processes to be subtracted from the photon control regions. In order for the other processes to pass the control region criteria one or more lepton must completely fail reconstruction and the process group is therefore subtracted from the fake E miss,rel template. he Z samples are generated with Sherpa, and the W samples are generated with Alpgen with hadronic showering provided by HERWIG/JIMMY. he cross sections are calculated at leading order and a NLO k-factor is applied. he uncertainty on the k-factor is 5% for the Sherpa samples [80] and 00% for the Alpgen samples [8]. 9.5.6 op + X his group contains all processes that include top quarks. Leptonic top quark decays are associated with real E miss,rel these processes are included in the real E miss,rel processes to be subtracted from the photon control regions. Hadronic top quark decays entering the signal region are estimated by the matrix method and are therefore subtracted from
9.5 Sample Composition 8 the photon control regions in order to avoid double counting. he samples used for the op + X processes are described below. op Pair Production he top quark pair production sample is generated with MC@NLO [82] and the hadronic showering is modeled with Jimmy. he cross section is calculated to approximately NNLO with a theoretical uncertainty of 6% [83]. Single op hree different subprocesses contribute to the production of single top quarks at the LHC: the t-channel, the s-channel, and the Wt-channel. he t-channel processes are generated using AcerMC [84] with the hadronic showering modeled by Pythia. he s- and Wtchannels are generated using MC@NLO with hadronic showering modeled by Jimmy. he cross sections are calculated at approximately NNLO [85, 86, 87]. he theoretical uncertainty on the cross sections is of the order 3 4% for the t- and s-channels and 7% for the Wt-channel. op Pair + Bosons he production of top quark pairs in association with electroweak bosons is modeled at leading order with MadGraph [88] with parton showering by Pythia. A k-factor is applied to normalize the events to NLO. he uncertainty of the k-factor is 30% for t t +W and 50% for t t + Z and t t +WW [89, 90]. op Pair + γ he production of top quark pairs with an associated photon is generated using MadGraph and the parton showering is modeled by Pythia. he cross section has been measured in ALAS and was in good agreement with the Standard Model expectation [9]. he uncertainty of the measurement was 25% and this uncertainty is assumed for the cross section of the process. 9.5.7 Diboson his 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. Due to neutrinos or undetected leptons all processes in this group have real E miss,rel and are therefore subtracted from the fake E miss,rel template. he diboson processes are generated using a combination of the Monte Carlo generators Sherpa, gg2ww [92], and gg2zz [93], where the latter two provide corrections for gluon induced QCD loop processes producing pairs of W and Z bosons respectively. he parton showering for the processes generated with gg2ww and gg2zz is performed
82 Data Driven Z + jets Background Estimation by HERWIG/JIMMY. he cross sections are calculated with MCFM to NLO with a theoretical uncertainty of 5 7%. he gluon induced QCD corrections have larger theoretical uncertainties but contribute only about 5% of the diboson background. he triboson samples are generated with MadGraph interfaced with Pythia for hadronic showering. he cross sections are calculated at leading order and a k-factor is applied to normalize the samples to NLO. However the k-factor varies over the phase space and therefore a conservative theoretical uncertainty of 00% is applied [94]. 9.5.8 Multijet QCD his process group contains pure multijet QCD processes. No real E miss,rel is present so the processes are not subtracted from the fake E miss,rel template; the Monte Carlo samples generated with Pythia8 are only used to evaluate the agreement between simulation and collision data in the following sections. Since the processes are not subtracted from the fake E miss,rel template, they do not enter any term of Eq. 9.2 and the theoretical uncertainty on the cross section does not affect the final uncertainty on the number of Z + jets events in the signal region. herefore no theoretical uncertainty is applied. 9.5.9 Summary of Processes with Real E miss,rel A summary of which process groups are subtracted from the photon control regions is found in ab. 9.2. All the processes contributing to real E miss,rel are subtracted from the data in the single photon and diphoton control regions. he uncertainties from the theoretical cross sections are propagated as well as the detector systematic uncertainties on the fake E miss,rel template. miss rel 9.6 Validation of Normalization of real E Processes For the subtraction of real E miss,rel processes it is important to verify that the simulated samples and theoretical cross sections provide an accurate model. For this purpose collision data and simulated data in the control regions are compared. Figure 9.5 shows the E miss (a) and E miss,rel (b) spectra in the diphoton control region, (c) and (d) show the E miss and E miss,rel spectra in the single photon control region. he lower part of the figure shows the ratio between collision data and the prediction. he error band incorporates the error from Monte Carlo statistics, theoretical uncertainties from real E miss,rel processes, luminosity uncertainty and systematic uncertainties. he statistics in the diphoton control region is low in the high E miss,rel region. herefore a single wide bin is used in the region where E miss,rel > 80 GeV. In both control regions the simulated and collision data agree well within errors, which indicates that the real E miss,rel estimate is at the right level. Figure 9.6 shows a comparison between collision and simulated data for (a) the p of
9.7 Photon emplate Comparison with Dilepton Data 83 Diphoton Control Region Single Photon Control region γ + jets Not subtracted Not subtracted γγ Not subtracted Subtracted W + 0γ Subtracted Subtracted (Z ee) + 0γ Not subtracted Subtracted (Z µ µ) + 0γ Subtracted Subtracted (Z νν) + 0γ Subtracted Subtracted W/Z + γ Subtracted Subtracted W/Z + 2γ Subtracted Subtracted op + X Subtracted Subtracted Diboson Subtracted Subtracted QCD Not subtracted Not subtracted able 9.2: Summary of process groups are subtracted from the photon control regions to obtain the fake E miss,rel template. the diphoton system in the control region, and (b) the p of the photon in the single photon control region. he error band incorporates the error on Monte Carlo statistics, theoretical uncertainties from real E miss,rel processes, luminosity uncertainty and systematic uncertainties. Also in these variables excellent agreement is observed. 9.7 Photon emplate Comparison with Dilepton Data As discussed in previous sections, it is important for the ABCD method that the shape of the E miss,rel spectra of the signal and control regions are the same. he real E miss,rel contribution can now be subtracted from the data, enabling a comparison between the fake E miss,rel in ee/µµ and photon data. Some caution is necessary at this point to avoid unblinding the signal region, thus contaminating the shape with signal. wo different approaches are possible. he first approach consists in comparing the fake E miss,rel template from the photon control regions to a subset of dilepton data. Although this check involves the signal region itself, unblinding is avoided by limiting the data set size. Previous studies have shown that for 5 fb there is no sensitivity to pp χ 2 0 χ± Z χ W 0 χ 0 in the signal region. Figure 9.7 shows photon fake E miss,rel templates from data, with real E miss,rel processes subtracted, normalized to unit area in (a) the diphoton region and (b) the single photon region. he photon templates are marked by black circles and the electron and muon channels of the signal region are marked by red triangles and green squares respectively. In this figure 5 fb of data is used for the dilepton distributions. he core of the distribution is shown in logarithmic scale and the high E miss,rel region, which becomes
84 Data Driven Z + jets Background Estimation Events / 20 GeV 7 0 6 0 5 0 4 0 3 0 Diphoton Control Region (p L dt = 20.3 fb γγ >80 GeV) + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) Events / bin 7 0 6 0 5 0 4 0 3 0 Diphoton Control Region (p L dt = 20.3 fb γγ >80 GeV) + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) 2 0 2 0 0 0 0 0 data / pred. 2 0 0 50 00 50 200 250 300 350 400 miss E [GeV] data / pred. 2 0 0 50 00 50 200 250 300 350 400 miss, rel E [GeV] (a) (b) Events / 20 GeV 8 0 7 0 6 0 5 0 4 0 3 0 2 0 0 0 Single Photon Control Region (p >80 GeV) L dt = 20.3 fb γ + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) Events / 20 GeV 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 0 0 Single Photon Control Region (p >80 GeV) L dt = 20.3 fb γ + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) data / pred. 2 0 0 50 00 50 200 250 300 350 400 miss E [GeV] data / pred. 2 0 0 50 00 50 200 250 300 350 400 miss, rel E [GeV] (c) (d) Figure 9.5: Comparison between simulated and collision data in the control regions. (a) shows E miss and (b) shows E miss,rel in the diphoton control region, (c) shows E miss and (d) shows E miss,rel in the single photon control region. he lower panel of the figure shows the ratio between collision data and the prediction. he error band incorporates the error on Monte Carlo statistics, theoretical uncertainties on the real E miss,rel processes, luminosity uncertainty and systematic uncertainties. slightly negative after the subtraction of real E miss,rel, is inset in linear scale. he other approach utilizes a relaxed dilepton signal region where the signal is so di-
9.7 Photon emplate Comparison with Dilepton Data 85 Events / 40 GeV 7 0 6 0 5 0 4 0 3 0 2 0 0 0 Diphoton Control Region (p L dt = 20.3 fb γγ >80 GeV) + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) Events / 40 GeV 8 0 7 0 6 0 5 0 4 0 3 0 2 0 0 0 Single Photon Control Region (p >80 GeV) L dt = 20.3 fb γ + jet γγ Z νν W/Z 0 γ W/Z + γ W/Z + 2 γ top + X Diboson QCD Monte Carlo Data ( s =8 ev) data / pred. 2 0 0 00 200 300 400 500 600 700 800 γ γ 900 000 2 [GeV] P data / pred. 2 0 0 00 200 300 400 500 600 700 800 900 000 [GeV] γ p (a) (b) Figure 9.6: Comparison between simulated and collision data. (a) shows the p of the diphoton system in the diphoton control region, and (b) the p of the photon in the single photon control region. he lower panel of the figure shows the ratio between collision data and the prediction. he error band incorporates the error on Monte Carlo statistics, theoretical uncertainties on the real E miss,rel processes, luminosity uncertainty and systematic uncertainties. luted that the effect of the signal on the E miss,rel shape becomes negligible. his method requires that the relaxation of cuts itself does not affect the E miss,rel shape. Removing the cuts on m j j and R(ll) dilutes the signal sufficiently to effectively eliminate all sensitivity to the signal. Figure 9.8 shows photon fake E miss,rel templates from data, with real E miss,rel processes subtracted, normalized to unit area in (a) the diphoton region and (b) the single photon region. he relaxed and diluted signal region is used for the dilepton distributions. In the case of the relaxed signal region, Fig. 9.8, the shape of the two lepton E miss,rel distributions are very similar. Both single photon and diphoton control regions exhibit E miss,rel shapes within errors of the dilepton shapes for most of the E miss,rel range. In the case where the full signal region selection is used for the comparison, Fig. 9.7, the E miss,rel shape in the control regions closely follow that in the electron channel. In the muon channel a small deviation is noted around E miss,rel = 50 GeV. In spite of these deviations between the E miss,rel shape in the control regions and that in the muon channel it is concluded that agreement is sufficient. he deviation is largest in the region E miss,rel = 40 80 GeV, which is not used in the ABCD-method. In the normalization region (E miss,rel < 40 GeV) and the high E miss,rel region (E miss,rel > 80 GeV)
86 Data Driven Z + jets Background Estimation Arbitrary units 0 Diphoton template (p >80 GeV) 0.05 γγ 0.0 0.005 γγ ee, 5 fb µµ, 5 fb Arbitrary units 0 Single photon template (p >80 GeV) γ 0.0 0.005 γ 0.05 80 ee, 5 fb µµ, 5 fb 2 0 0 0.005 0 50 00 50 200 250 300 350 2 0 0 0.005 0 50 00 50 200 250 300 350 3 0 3 0 4 0 0 50 00 50 200 250 300 350 400 (a) miss, rel E [GeV] 4 0 0 50 00 50 200 250 300 350 400 (b) miss, rel E [GeV] Figure 9.7: Photon fake E miss,rel templates from data, with real E miss,rel processes subtracted, normalized to unit area in (a) the diphoton (γγ) control region and (b) the single photon (γ80) control region. he photon templates are marked by black circles, and the electron and muon channels of the signal region are marked by red triangles and green squares respectively. For the dilepton distributions only 5 fb of data is used for blinding purposes. he error band incorporates the statistical, theoretical, and systematic uncertainties from the real E miss,rel processes. the agreement is within errors. he deviation could be taken into account as a systematic uncertainty. his uncertainty would however be negligible compared to the much larger uncertainties on Monte Carlo statistics and jet energy resolution, which are discussed in the following sections. 9.8 Systematic Uncertainties Following Eq. 9.2, the number of Z + jets events in the signal region is estimated using a photon template constructed by subtracting Monte Carlo simulated real E miss,rel processes from collision data in the one or two photon control regions. he simulated processes that model the real E miss,rel are affected by a number of systematic uncertainties which must be propagated into a final uncertainty on the number of Z + jets events. he missing transverse momentum is the negative sum of the energy of all jets, leptons, photons, and unidentified energy deposits. herefore uncertainties on any of these quantities will be propagated into a total uncertainty on the E miss,rel he impact on the E miss,rel. shape is investigated separately for the various sources of
9.8 Systematic Uncertainties 87 Arbitrary units 0 Diphoton template (p >80 GeV) 0.05 γγ 0.0 0.005 γγ ee, relaxed SR µµ, relaxed SR Arbitrary units 0 Single photon template (p >80 GeV) 0.05 γ 80 0.0 0.005 γ ee, relaxed SR µµ, relaxed SR 2 0 0 0.005 0 50 00 50 200 250 300 350 2 0 0 0.005 0 50 00 50 200 250 300 350 3 0 3 0 4 0 0 50 00 50 200 250 300 350 400 (a) miss, rel E [GeV] 4 0 0 50 00 50 200 250 300 350 400 (b) miss, rel E [GeV] Figure 9.8: Photon fake E miss,rel templates from data, with real E miss,rel processes subtracted, normalized to unit area in (a) the diphoton (γγ) control region and (b) the single photon (γ80) control region. he photon templates are marked by black circles, and the electron and muon channels of the signal region are marked by red triangles and green squares respectively. For the dilepton distributions a relaxed version of the signal region is used. he error band incorporates the statistical, theoretical, and systematic uncertainties from the real E miss,rel processes. uncertainty. he E miss,rel shape is determined using nominal values for all parameters. his is the nominal distribution marked by circles in the sketch in Fig. 9.9. he shape of the E miss,rel is reevaluated separately for each source of systematic uncertainty. A single source of systematic uncertainty is applied, entering as a shift of one standard deviation, ±σ, in a parameter. hus two additional E miss,rel shapes are produced, marked in the sketch by for the +σ and for the σ. For each bin, the deviation between the nominal and shifted distributions is determined. hus the impact of that specific source of uncertainty is obtained. his procedure is repeated for all sources of systematic uncertainties. he impacts of all sources of systematic uncertainties are added in quadrature in each bin to give the total systematic uncertainty of the E miss,rel shape. When the real E miss,rel processes are subtracted from data, the systematic uncertainties are added to the statistical error from data, thereby giving the total uncertainty on the template to be used to model Z + jets. E miss,rel he sources of systematic uncertainties are described in the following sections.
88 Data Driven Z + jets Background Estimation Arbitrary units 00 80 Nominal Syst +σ Syst -σ 60 40 20 0 0 50 00 50 200 250 300 350 400 miss,rel E shapes where a param- Figure 9.9: Sketch showing a nominal E miss,rel eter has been shifted by ±σ. shape, and E miss,rel 9.8. heoretical Uncertainty on Cross Sections Each process contributing to the real E miss,rel is normalized with its theoretical cross section before it is subtracted from the measured E miss,rel template in the control regions. he cross section of each process is varied independently. he uncertainties on the theoretical cross sections are stated in Sec. 9.5. 9.8.2 Jets he jet energies in simulation must be scaled to match the energy scale in data. he amount by which the jets must be scaled is called the jet energy scale, JES. he JES has an uncertainty due to pile-up and near-by jets and varies with jet p and η. he jet energy resolution (JER) in simulation would be slightly better than in data if it was not smeared. he amount of smearing is not perfectly known. he uncertainties on the jet energy scale and resolution have been determined using both test beam and collision data [95]. o determine the impact of the uncertainty on the jet energy resolution, the p of jets is smeared according to a Gaussian with unit mean and width from a p dependent resolution function. he uncertainty on jet measurement is the largest source of systematic uncertainties for both diphoton and single photon control regions.
9.8 Systematic Uncertainties 89 9.8.3 Unidentied Energy Deposits Unidentified energy deposits are significant energy deposits in the calorimeter that are not included in any of the identified particles. he energy scale and energy resolution for these energy deposits are not perfectly known but do affect the E miss,rel [96]. he impact of the unidentified energy scale and resolution uncertainties on the shape of the E miss,rel distribution is determined by varying an unidentified jet energy scale and resolution. It is one of the largest sources of systematic uncertainties in both diphoton and single photon control regions. 9.8.4 Leptons In the control regions a lepton veto is applied, and changes in lepton momentum or energy affects the number of events passing the control region selection and may also affect the shape of the E miss,rel distribution. Changes in the electron energy may also affect the overlap removal between jets and electrons. he sources of uncertainty on electron energy considered are the electron energy scale, the electron energy resolution, the electron trigger efficiency, and the electron reconstruction efficiency. Previous ALAS analyses have shown that the systematic uncertainty from muons is similar in size as that from electrons. herefore the muon contribution is set to equal the electron contribution in this analysis. 9.8.5 Photons In order to compensate for discrepancies in photon shower shape variables between simulation and collision data, so called fudge factors are applied on the simulation. As the fudge factors are applied to variables used for photon identification, this gives an uncertainty on the photon identification efficiency. he 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 E < 40 GeV,.5% for E > 40 GeV and η <.8, and 2.5% for E > 40 GeV and η >.8. For converted photons the uncertainty is 2.5% for E < 40 GeV and.5% for E > 40 GeV [97]. Also uncertainties on photon identification efficiency, photon resolution, and photon scale make slight contributions to the total systematic uncertainty. 9.8.6 Pile-up he 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 average µ is calculated for each lumi-block 2) of that run. Monte Carlo simulations on the 2) A lumi-block is an approximately two-minute interval of a run.
90 Data Driven Z + jets Background Estimation other hand, are often prepared before the actual data runs. he Monte Carlo samples are generated using an anticipated distribution of µ, necessarily different from the actual distribution. he Monte Carlo events are reweighted at the analysis level to correct for discrepancies between the simulated µ distribution and that measured in data. he correction factor by which the Monte Carlo pile-up is reweighted is associated with an uncertainty 2.8%. In order to quantify the effect of this uncertainty on the E miss,rel shape, the correction factor is shifted up and down by one standard deviation and the resulting E miss,rel distributions are compared to the nominal distribution. 9.8.7 Luminosity he simulation entering the real E miss,rel processes is normalized to the integrated luminosity of the collision data. he integrated luminosity has an uncertainty, which is added to the other systematic uncertainties. he uncertainty on the integrated luminosity is 2.8%. It is derived, following the same methodology as that detailed in Ref. [66], from a preliminary calibration of the luminosity scale derived from beam-separation scans performed in November 202. 9.9 Results he method described in section 9.4 is used to estimate the number of Z + jets events in the signal region. A E miss,rel template is extracted from collision data in the control regions. Real E miss,rel processes are subtracted from the template as described in section 9.5. his fake E miss,rel template is normalized to the dilepton sample in the E miss,rel < 40 GeV region. Integrating the normalized template above E miss,rel = 80 GeV gives N(Z +jets) as seen in Eq. 9.2. he systematic errors on the real E miss,rel template described in the previous section are added in quadrature to the statistical errors from Monte Carlo and data control region statistics. his gives an uncertainty on the expected N(Z + jets). able 9.3 lists the expected N(Z + jets) as predicted with the diphoton and single photon control regions with total systematic and statistical uncertainties. he lower part of the table shows a breakdown of the uncertainties. Due to the subtraction of the real E miss,rel processes the predicted N(Z + jets) is negative but consistent with zero. he E miss,rel in Z + jets events is fake, arising from instrumentation effects. he dominating source of E miss,rel is the jet energy resolution. his is reflected in a large systematic uncertainty due to the jets. he single photon control region globally gives the more precise estimate. his is due to the much higher statistics in the control region, reflected in the significantly lower statistical errors compared to the diphoton control region.
9.0 Statistical Combination of the Control Regions 9 γγ γ80 e + e µ + µ e + e µ + µ Prediction.75 2.03 0.02 0.03 otal uncertainty ±.75 ±2.04 ±0.88 ±.02 Data statistics ±0.53 ±0.6 ±0.04 ±0.05 MC statistics ±.2 ±.30 ±0.08 ±0.09 heory ±0.20 ±0.23 ±0.03 ±0.04 Jets ±.5 ±.34 ±0.86 ±.00 Unidentified energy ±0.35 ±0.4 ±0.08 ±0.09 Leptons ±0.04 ±0.06 ±0.7 ±0.20 Photons ±0.06 ±0.07 ±0.0 ±0.0 Pile-up ±0.06 ±0.07 ±0.0 ±0.0 Luminosity ±0.05 ±0.05 ±0.0 ±0.0 able 9.3: Predicted number of Z + jets event in the signal region with breakdown of systematic errors. 9.0 Statistical Combination of the Control Regions As the single photon and diphoton control regions are orthogonal it is natural to statistically combine the results from the two regions. his allows for a more precise estimate with a smaller impact of systematic errors. One of the most commonly used approaches for statistical combination of results is the Best Linear Unbiased Estimate method, known as the BLUE method [98]. 9.0. he BLUE Method Assuming a measurement of a parameter with true value y true has been performed n times with the result y,...,n, and each measurement is associated with a weight w,...,n, the combined estimate y is a linear combination of the available measurements: y = n i= w i y i (9.3) If the individual estimates are unbiased, the combined estimate is unbiased as well. herefore the expectation value of the combination and the individual measurements are equal, y = y i = y true, which constrains the linear coefficients to: n i=0 w i =. (9.4)
92 Data Driven Z + jets Background Estimation he set of coefficients which minimizes the combined variance is chosen. he coefficients are given by the following equation, where E is the covariance matrix: w i = j E i j i j E i j (9.5) his reduces to the usual w i = /σi 2 / /σ 2 j for uncorrelated errors. If a high positive correlation of uncertainties is present the linear coefficients can assume negative values, see discussion in Ref. [99, 00]. In the case of the combination of the diphoton and single photon control regions, the uncertainties are highly positively correlated because of the jet uncertainty. herefore some negative BLUE coefficients are expected. 9.0.2 Result of the Statistical Combination In order to construct a covariance matrix for the two control regions, it is necessary to distinguish between correlated and uncorrelated uncertainties. he systematic uncertainties due to detector effects are treated as correlated, while the uncertainties on data and Monte Carlo statistics are uncorrelated. he uncertainties on theoretical cross sections are partially correlated, but since the two control regions are dominated by different processes and thus different theoretical uncertainties, this contribution is considered uncorrelated. Applying the BLUE method to the estimates from the single photon and diphoton control regions gives the weights w γγ = 0.37 and w γ+jets =.37 for the dielectron channel, and w γγ = 0.39 and w γ+jets =.39 for the dimuon channel. As expected some of the weights become negative. As an effect of the negative weights, the combined estimate becomes positive, N(Z +jets) = 0.22±0.87 in the ee channel and N(Z +jets) = 0.25 ±.0 in the µµ channel. A breakdown of the combined systematic errors is found in ab. 9.4. he uncorrelated uncertainties appear twice as they enter separately for the two control regions. 9. Discussion In this chapter a new approach for a data driven estimate of the number of Z +jets events in a dilepton signal region using photon data is presented. It utilizes the similarities between single photons and diphoton systems recoiling against jets and Z-bosons recoiling against jets. wo control regions are defined, based on single photon and diphoton data. Both control regions are shown to be useful, as they within errors reproduce the spectrum of the signal region. he predicted number of Z + jets events in the signal region is consistent with zero for both control regions. For the diphoton control region the low statistics is a concern as the statistical uncertainty on the predicted number of events is very large. he statistical uncertainties are larger than the systematic uncertainties. he single photon region does better in this as- E miss,rel
9. Discussion 93 e + e µ + µ Prediction 0.22 0.25 otal uncertainty ±0.87 ±.0 Data statistics γγ ±0.073 ±0.085 Data statistics γ + jets ±0.045 ±0.057 MC statistics γγ ±0.53 ±0.8 MC statistics γ + jets ±0.09 ±0.03 heory γγ ±0.027 ±0.032 heory γ + jets ±0.034 ±0.046 Jets ±0.820 ±0.953 Unidentified energy ±0.043 ±0.045 Leptons ±0.88 ±0.29 Photons ±0.003 ±0.002 Pile-up ±0.003 ±0.002 Luminosity ±0.005 ±0.004 able 9.4: Predicted number of Z + jets event in the signal region with breakdown of systematic errors, determined using a BLUE combination of the single photon and diphoton control regions. pect. he dominating systematic uncertainty for both control regions is that due to jet energy scale and resolution. he two control regions are completely orthogonal and can therefore be statistically combined. he combination is performed using the BLUE method. he high positive correlation of the systematic uncertainties gives negative weights, and the resulting combined estimate is compatible with zero. 9.. Comparison to the Jet Smearing Method he jet smearing method uses seed events which are smeared to obtain pseudo-data with a E miss,rel spectrum similar to that of the signal region. his way an arbitrarily large sample can be produced and the statistical uncertainties are small. However, this method arguably loses part of the benefit of a data driven method since only the well known resolution effects are taken into account in the smearing. It is possible that a low rate unknown detector problem causing mismeasurement of jets could produce events entering into the signal region. hese events would not be reproduced by the jet smearing method. he background estimate using photon control regions on the other hand is sensitive to this type of mismeasurement. he E miss,rel template is derived in events with similar topology to that of the signal region and therefore any unknown detector problems
94 Data Driven Z + jets Background Estimation would affect the control region to the same extent. he photon control regions, especially the diphoton control region, instead suffer from large statistical uncertainties, which is reflected in a larger overall uncertainty compared to the jet smearing method. Both methods of background estimation produce compatible results. he jet smearing estimate is 0.3 ± 0.2 and the photon control region estimate is 0.47 ±.87 for the combined ee and µ µ channels.
0 Exclusion Limits In this chapter results from unblinded data in the signal region is compared to the expected sum of Standard Model backgrounds. he backgrounds are determined with the methods described in the previous chapters. Since no excess over background is observed, upper limits on the gaugino masses are derived. 0. he CL S Method In order to exclude signal models, a signal plus background hypothesis is assumed. Considering an expected background b and a signal model with expectation s, a p-value for measuring N data under the hypothesis s + b is calculated, p s+b = P(N data s + b). If the resulting p-value is smaller than a predefined α, p s+b < α, the model is excluded with confidence level α. For instance, if p s+b < 0.05, the model is excluded with 95% confidence level. In high energy physics, when dealing with models with very low cross sections to which the experiment has low sensitivity, this method can encounter problems. A downward fluctuation of the observed number of events in data (i.e. when fewer events are observed than the expected background b) will produce a low p-value and a signal model can be excluded despite the lack of sensitivity of the experiment. o circumvent this problem, the CL S method assigns a weight to the p-value. his weight is constructed so that it decreases with decreasing sensitivity: CL S = p s+b p b (0.) where p b is the probability of observing N data under a background only hypothesis: p b = P(N data b). In the case of low sensitivity the numerator and denominator both decrease, thus preventing the condition CL S < α from being fulfilled. Since the denominator by construction is always less than or equal to unity, the CL S method will produce limits that are more conservative than the nominal α confidence level [0, 02]. he systematic uncertainties are modeled with nuisance parameters which are random variables added to the nominal background estimates. Each independent source of systematic uncertainty is model-led by its own nuisance parameter. he p-value p b is evaluated for the set of nuisance parameters that best best fits the data in the background only hypothesis. his is referred to as a background only fit.
96 Exclusion Limits he CL S method is commonly used for setting exclusion limits in high energy physics experiments and it is the method used to set limits in this analysis. 0.2 Results able 0. summarizes the predicted Standard Model backgrounds and the measured number of events in data for the ee and µµ channels. he third column shows the sum of the two channels. ee µµ ee + µµ ZW, ZZ 0.56 ± 0.36 0.4 ± 0.30 0.98 ± 0.62 WW 0.00 ± 0.00 0.07 0.07 +0.09 0.07 0.07 +0.09 op 0.02 ± 0.02 0.0 ± 0.0 0.03 ± 0.02 Z + jets 0.22 ± 0.87 0.25 ±.0 0.47 ±.87 Other 0.00 0.00 +0.2 0.00 0.00 +0.09 0.00 0.00 +0.5 otal SM 0.8 ± 0.8 0.75 ± 0.95.56 ±.68 Data 0 able 0.: Composition of the signal region using expected background yields obtained with the techniques described in chapter 8 and after a background only fit to the data. Exclusion limits determined with the CL S method are shown in Fig. 0.(a). Figure 0.(b) shows exclusion limits obtained by combining the dilepton limit from Paper III with the three-lepton search [62]. In both (a) and (b) the dashed black line marks the expected limit and the solid red line represents the observed limit. he yellow band around the expected limit indicates the ±σ limit where all experimental uncertainties, statistical and systematic, are considered. he dashed red lines around the observed limit represent the ±σ contours which are obtained by shifting the cross section of the signal models by ±σ. he limits are shown in the m χ 0 2, χ ±,m χ 0 plane. he limits stated in the text correspond to the observed limit where the signal cross sections have been reduced by σ. Using the background estimate from ab. 0. degenerate χ 2 0 and χ ± masses between 70 GeV and 330 GeV are excluded at 95% confidence level for models with a massless χ. 0 his limit is slightly lower than the expected sensitivity estimated in Sec. 7.3. Several factors 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 proper systematic uncertainty which is higher. Second, the sensitivity quoted in Sec. 7.3 was estimated by the p-value of the signal plus background, p s+b, while Fig. 0.(a) uses the CL S method. he CL S method gives a more conservative limit. he exclusion limits obtained in the analysis of Paper III have been combined with results from the ALAS search for weakly produced supersymmetry in the three-lepton
0.2 Results 97 [GeV] m χ 350 300 0 250 200 50 - L dt = 20.3 fb s = 8 ev ee + µµ m 0 ± χ,χ 2 0 < m χ 0 m χ 2 0 - m χ = m Z SUSY Obs limit (± σ theory ) Exp limit (± σ exp ) m 0 χ 2 = 2m 0 χ 00 50 0 00 50 200 250 300 350 400 450 500 ± [GeV] (a) m χ 0,χ 2 (b) Figure 0.: (a) Observed and expected 95% confidence level limit contours for chargino and neutralino production in the simplified model scenario with decay via gauge bosons and two leptons in the final state; and (b) exclusion limits obtained by combining the dilepton limit from Paper III with the three-lepton search [62]. channel, see chapter 6. he fit is performed on the combined likelihood function using all signal regions. For models with a massless χ 0 degenerate χ 2 0 and χ ± masses between 00 GeV and 45 GeV are excluded with 95% confidence level. he combination shows a significant improvement compared to the results obtained from either of the two searches. he dotted lines in Fig. 0.(a) and (b) indicate relations in the mass hierarchy that have implications on the preferred decay channels of the supersymmetric particles. Onshell Z bosons are allowed below the line marked m χ 0 m 2 χ 0 = m Z. Models close to the diagonal are called compressed spectra models, for which special signal regions are required due to the much lower p of the particles produced in the gaugino decays.