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A simulation study of Z 0 μμγ for photon energy calibration in the CMS experiment OLIVIER BONDU Master’s Thesis TRITA-FYS 2009:47 ISSN 0280-316X ISRN KTH/FYS/–09:47–SE

Transcript of cms-lyon.web.cern.chcms-lyon.web.cern.ch/sites/cms-lyon.web.cern.ch/files/09.09.03-FINAL...cms-lyon.web.cern.ch...

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A simulation study of Z0 → µµγ for photonenergy calibration in the CMS experiment

OLIVIER BONDU

Master’s Thesis

TRITA-FYS 2009:47 ISSN 0280-316X ISRN KTH/FYS/–09:47–SE

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AbstractThe Large Hadron Collider (LHC) at CERN, in Geneva, is expectedto provide experimental evidence either refuting or confirming the exis-tence of the Higgs boson. The decay of this boson into two photons is ofinterest for a possible discovery. Since this particular chanel is relyingon photons, it is of importance to reach the most precise measurementof these as possible.

Due to the centre-of-mass energy and luminosity of the LHC, anaccess to a clean, abundant and fairly isotropic resonant productionof isolated photons will be provided by the Z0 → µµγ channel. Thisphotons will allow a lot of information concerning the performance of theElectromagnetic Calorimeter (ECAL) detector of the Compact MuonSolenoid (CMS) experiment to be extracted.

This work presents the strategies followed to select the Z0 → µµγchannel, as well as preliminary results concerning the use of this channelfor the ECAL photon energy calibration. Even though the work is stillin progress, significant results have been obtained. The obtained purityof the Z0 → µµγ sample is around 95% for a signal efficiency of around20%, which corresponds to an event yield of 3.96 evt/pb. A precision of≈ 120MeV on the photon energy scale with 400 events may be reached,which should be obtainable with 100 pb−1 of data.

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Referat

CERNs Large Hadron Collider (LHC) i Geneve forvantas ge experi-mentella bevis som antingen avfardar eller bekraftar existensen av Hig-gsbosonen. Denna bosons sonderfall till tva fotoner ar av stort intressefor en mojlig upptackt. For denna specifika sonderfallskanal ar det vik-tigt att uppna sa stor presicion i matningarna av dessa fotoner sommojligt.

Till foljd av kollisionsenergin och luminositeten vid LHC, kommerkanalen Z0 → µµγ att ge tillgang till en ren, riklig och tamligen isotropiskresonant produktion av isolerade fotoner. Studier av dessa fotoner gerdetaljerad information om prestanda och upptradande hos den elektro-magnetiska kalorimetern (ECAL) i CMS experimentet (Compact MuonSolenoid).

Denna rapport presenterar strategier for att valja ut Z0 → µµγ-handelser samt preliminara resultat av anvandandet av denna kanalfor fotonenergi-kalibrering av ECAL-kalorimetern. Aven om detta ar-bete fortfarande pagar, har betydelsefulla resultat redan uppnatts. Meden signaleffektivitet av battre an 20 % kan en renhet av Z0 → µµγom nastan 95 % uppnas vilket motsvarar 3.96 handelser/pb. Med 400handelser, motsvarande 100 pb−1, kan en noggrannhet av ≈ 120 MeVav energiskalan for fotoner erhallas.

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Contents

1 Introduction 3

2 The Standard Model, the Higgs boson and the CMS experiment 52.1 The Standard Model: a brief overview . . . . . . . . . . . . . . . . . 52.2 The Large Hadron Collider and the Compact Muon Solenoid exper-

iment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . 62.2.2 The Compact Muon Solenoid experiment . . . . . . . . . . . 8

2.3 The Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Production and decay channels: introduction to H0 → γγ . . 12

2.4 The Z0 → µµγ channel . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Energy corrections . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 The Global Energy scale G and the correction functions F . 192.4.4 Intercalibration coefficients ci . . . . . . . . . . . . . . . . . . 192.4.5 Trigger efficiencies . . . . . . . . . . . . . . . . . . . . . . . . 212.4.6 Interest for the H0 → γγ channel . . . . . . . . . . . . . . . . 22

2.5 Introduction to data analysis . . . . . . . . . . . . . . . . . . . . . . 222.6 Computing tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.6.1 ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6.2 CMSSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6.3 Monte-Carlo Generators . . . . . . . . . . . . . . . . . . . . . 272.6.4 LCG GRID computing . . . . . . . . . . . . . . . . . . . . . . 282.6.5 TotoAnalyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Versions of the Z0 → µµγ event selection 313.1 Technical Design Report & CMS AN 2005/040 . . . . . . . . . . . . 313.2 CMSSW 1.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 CMSSW 1.6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.4 CMSSW 1.6.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5 CMSSW 2.1.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.6 CMSSW 2.2.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

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4 Photon energy scale with Z0 → µµγ events 454.1 Reconstruction of the µµγ system . . . . . . . . . . . . . . . . . . . 454.2 Fit of the µµγ invariant mass in the different bins . . . . . . . . . . 48

4.2.1 Gaussian fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Comments and Outlook 61

6 Conclusion 63Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Bibliography 65

Appendices 67

A Abbreviations 69

B Physics-related definitions and context 71B.1 Natural Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.2 Relativistic kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . 71B.3 Breit-Wigner distribution . . . . . . . . . . . . . . . . . . . . . . . . 72B.4 Crystal-Ball distribution . . . . . . . . . . . . . . . . . . . . . . . . . 73

C Accelerator and detector-related definitions and context 75C.1 Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75C.2 CMS calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76C.3 CMS coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . 76C.4 Azimuthal angle φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76C.5 Pseudo-rapidity η . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76C.6 ∆R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78C.7 Transverse energy and momentum . . . . . . . . . . . . . . . . . . . 78

D Raw results: CMSSW 1.6.12 79

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DisclaimerThe content of the present report DOES NOT represent either official or preliminaryCMS results. All the results presented here are work currently still in progress atpreliminary stages.

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Chapter 1

Introduction

The current document presents the research work I have done at the IPNL1 asa second year Master’s student, under the supervision of Susan Gascon-Shotkin.The subject of this work was A simulation study of Z0 → µµγ for photon energycalibration in the CMS experiment. Specifically, I have been working on extractingthe energy scale for photons detected in the Electromagnetic Calorimeter of theCMS experiment with the physics events Z0 → µµγ .

The global working scheme for this study was:

1. Produce signal and specific background events with Monte-Carlo generators

2. Reconstruct these events within the CMSSW software

3. Discriminate the signal and background events

4. Study the behaviour of the mµµγ invariant mass as a function of the photonproperties

5. Set up a procedure for energy scale extraction for the photons

6. Prepare the validation of the Monte-Carlo production and use the above cal-ibration procedure with real data

This work is too significant to be taken care of within a few months. I howeverhad the chance to work on both items 3 and 4. For the former, I was mainlycross-checking the work of Clement Baty on the subject, since he is a PhD studentworking currently full-time on this topic. For the latter, I was the one leading thetopic under the supervision of my supervisor Suzanne Gascon. Due to lack of time,I could not start the work on item 5. We are waiting for the collisions at the LHCto start before starting the item 6.

All the work presented here is still preliminary and needs improvement. How-ever, we already have some very interesting results. A better energy scale for the

1Institut de Physique Nucleaire de Lyon

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CHAPTER 1. INTRODUCTION

photon could prove to be determinant for discovery of new physics. The idea ofthis work is to have a relatively prompt-feedback (≈ 100 pb−1 of data compulsory)analysis, which is data-driven (in opposition to Monte-Carlo-driven) to adjust theresponse of the electromagnetic calorimeter.

This work on the Z0 → µµγ channel and energy scale of photons is part ofthe preparation for the search of the Higgs boson in the diphoton decay channelH → γγ.

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Chapter 2

The Standard Model, the Higgs bosonand the CMS experiment

2.1 The Standard Model: a brief overviewThe Standard Model[1] of particle physics is the generally accepted model describ-ing fundamental particles and their interactions1. This model is a Quantum FieldTheory, which include naturally both Quantum Mechanics and Einstein’s SpecialRelativity. According to this model, the world is composed of the following funda-mental particles (and their respective antiparticles):

− Six quarks: u (up), d (down), s (strange), c (charm), b (bottom), t (top),

− Six leptons: the electron (e−) and the electron neutrino (νe), the muon (µ−)and the muon neutrino (νµ), the tau (τ−) and the tau neutrino (ντ ).

These particles interact via other particles called gauge bosons. They are thecarriers of the fundamental interactions:

− The photon (γ), carrier of the electromagnetic interaction. It is massless andits behaviour is described by Quantum Electrodynamics (QED),

− The eight gluons (gi), carriers of the strong interaction. They are masslessand their behaviour is described by Quantum Chromodynamics (QCD),

− The W−, W+ and Z0 bosons, carriers of the weak interaction. They aremassive (80.398 GeV for W :s and 91.1876 GeV for Z0 respectively[2]), andtheir behaviour is described by the electroweak theory, which unifies weak andelectromagnetic interactions.

1This means the weak, strong and electromagnetic interactions. The fourth fundamental inter-action, gravitation, is described by Einstein’s general relativity theory, and is not included withinthe Standard Model. Some theories, called GUT (Grand Unified Theories), like string theory, aretrying to solve these incompatibilities.

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CHAPTER 2. THE STANDARD MODEL, THE HIGGS BOSON AND THE CMSEXPERIMENT

A hadron is any particle composed of quarks and gluons, e.g. a proton and aneutron.

This model exists since the 1970’s and has been very powerful for describingand predicting the behaviour of our universe, from the femtoscopic scale up to thegalaxy super-cluster scale. Unfortunately, there are still phenomena that cannot beexplained with this model, e.g. : dark matter, dark energy, origin of electroweaksymmetry breaking, neutrino oscillations, CP violation,etc.

The Higgs boson[3, 4] is an hypothetical particle that may explain the origin ofelectroweak symmetry breaking.

2.2 The Large Hadron Collider and the Compact MuonSolenoid experiment

2.2.1 The Large Hadron Collider

Observing infinitely small particles paradoxically always requires the most complexexperiments, the largest experimental apparati. That is one of the main reasons ofthe creation of CERN2 in Geneva, Switzerland.

The Large Hadron Collider (LHC)[5], has been designed to reach energies neededto create the Higgs boson, and also for studying the new phenomena that are likelyto be produced at these energies. This huge accelerator of 27 km of circumferencehas been constructed in the tunnel previously hosting the LEP3[6]. It will permitthe collision of hadrons (in our case, protons), travelling in opposite directions, upto a centre-of-mass energy (for the proton case) of 14TeV4. Particles are acceleratedin bunches in order to raise luminosity5.

Particles accelerated by the LHC will interact in six points (figure 2.1)6, atwhich four experiments, ATLAS[8], CMS[9], ALICE[10], LHCb[11], TOTEM[12]and LHCf[13] will be observing the produced phenomena. The accelerator will bethe world’s particle collider with the most significant centre-of-mass energy and isplanned to re-start in November 2009, with the first collisions planned for December2009, after last year’s attempt.

The aspects of particle physics to be studied by the six experiments are thefollowing:

− CMS: Compact Muon Solenoid and ATLAS: A Toroidal Lhc ApparatuS, are2Organisation Europeenne pour la Recherche Nucleaire, European Organisation for Nuclear

Research3Large Electron-Positron collider4For comparison,the typical energy obtained in a nuclear fission reaction is around 200 MeV,

i.e. 70 000 times smaller. Each interaction point will see a nominal number of collisions of 31.5 106

collisions per second between bunches. This very high number of collisions is absolutely vital fordiscovery of very rare phenomena, like the Higgs boson.

5Luminosity is the number of events divided by the cross-section. It is expressed usually incm−2s−1. The cross-section represents the probability of interaction (cf. appendix C).

6Pictures in this section are from the CMS brochure[7].

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2.2. THE LARGE HADRON COLLIDER AND THE COMPACT MUON SOLENOIDEXPERIMENT

Figure 2.1. The Large Hadron Collider (LHC) and its four principal experiments.The TOTEM experiment is located near the CMS experiment, and the LHCf exper-iment near the ATLAS experiment[7].

Figure 2.2. The Compact Muon Solenoid (CMS) detector[7].

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CHAPTER 2. THE STANDARD MODEL, THE HIGGS BOSON AND THE CMSEXPERIMENT

each multi-purpose experiments. Each one has made different concept andtechnology choices, aiming mainly both for the search of the Higgs boson andhints on theories beyond the Standard Model (the so-called BSM theories), aswell as precision measurements of Standard Model processes,

− ALICE: A Large Ion Collider Experiment, will specialize in collisions betweenheavy ions and in particular study of the quark-gluon plasma,

− LHCb will study b-mesons in order to measure the asymmetry of fundamentalinteractions, as well as study CP-violating processes,

− TOTEM: TOTal Elastic and diffractive cross-section Measurement will mea-sure the size of the proton and will accurately monitor the LHC’s luminosity,which are not accessible to the general-purposes experiments. This experimentis smaller and is located near the CMS detector,

− LHCf : Large Hadron Collider forward, will use forward particles createdinside the LHC as a source to simulate cosmic rays in laboratory conditions.This experiment is smaller and is located near the ATLAS detector.

2.2.2 The Compact Muon Solenoid experimentThe Compact Muon Solenoid (CMS: figure 2.2) is, together with ATLAS, one of thetwo LHC general detectors, designed to observe a whole range of new phenomena,obtained by head-on collision of two hadron beams. These two experiments wouldbe able to observe the Higgs boson, extra dimensions, supersymmetric particles,etc. , if the particles or phenomena were to be produced.

The detector is called Compact Muon Solenoid because its main characteristicsare :

− Its compactedness: almost 12 500 tons for 21 m length and 15 m of diameter(a lot denser than ATLAS),

− Its muon detectors, allowing for high-quality reconstruction of muons’ mo-menta and trajectories,

− Its superconducting solenoid magnet, producing a 4 T magnetic field.

The CMS detector is cylindrical, closed at its extremities: the central partis called the barrel and the extremities are called the endcaps. The detector iscomposed of 8 layers of subdetectors (cf. figure 2.3):

− The tracker is able to measure the momentum of electrically charged particles,by reconstructing their trajectories within the magnetic field generated bythe super-conducting magnet. This detector is made from silicon. It is alsocapable of locating the decay and interaction vertices7 of the particles with a

7The interaction vertex is roughly the point where the collision happens.

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2.2. THE LARGE HADRON COLLIDER AND THE COMPACT MUON SOLENOIDEXPERIMENT

high precision. This precision is absolutely needed for a correct data analysis,since it helps to identify the starting point of a trajectory. This subdetectorinvolves 106 readout channels,

− The electromagnetic calorimeter (ECAL) is able to measure the energy ofboth photons and electrons. This subdetector is composed of Lead Tungstatecrystals (PbWO4): 61200 crystals in the barrel and 7324 in each endcap. Thecrystals are read by avalanche photo-diodes (APD) in the barrel and vacuumphototriodes (VPT) in the endcaps. This subdetector involves 75 848 readoutchannels,

− The hadronic calorimeter (HCAL) is able to measure the energy of hadrons.It is composed of layers of dense material (steel and brass), with alternativelylayers of scintillating plastic, read by hybrid photo-diodes. This subdetectorinvolves around 10 000 readout channels,

− The super-conducting solenoid, producing a 4T magnetic field, allows differen-tiation of electrically charged particles through their charge and momentum,

− The muon detectors are able to measure the momentum of muons. Thesedetectors are aluminium drift tubes (DT) in the barrel and cathode stripchambers (CSCs) in the endcaps, complemented by resistive plate chambers(RPCs). These detectors have 106 readout channels and represent an activedetection surface of around 25 000 m2.

Figure 2.3. View of the complete detector with labels indicating the different de-tection layers[9].

The overall detection apparatus involves around 75 million readout channels.

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CHAPTER 2. THE STANDARD MODEL, THE HIGGS BOSON AND THE CMSEXPERIMENT

One can note that for the electromagnetic calorimeter, we usually use clusters ofcrystals, grouping together several crystals where the electromagnetic shower tookplace. There are several clustering algorithms, with different goals and performance,as described in the Technical Design Report[9].

The CMS detector is able to detect and differentiate five categories of particlesfrom the Standard Model with very distinctive behaviour (cf. figure 2.4):

muons are the only kind of particles to go through the whole detector while beingdetected, and in particular while being detected in the muon detectors. Theseparticles also leave a track in the tracker,

electrons leave a track in the tracker and lose all their energy by creating electro-magnetic showers in the electromagnetic calorimeter,

charged hadrons leave a track in the tracker, go through the electromagneticcalorimeter, and then lose all their remaining energy by showering mainly inthe hadronic calorimeter,

neutral hadrons don’t leave any track in the tracker and lose all of their energyin the calorimeters,

photons don’t leave any track in the tracker and lose all of their energy in theelectromagnetic calorimeter.

2.3 The Higgs boson

2.3.1 IntroductionThe existence of the Higgs boson has been suggested by Peter Higgs, FrancoisEnglert and Robert Brout in 1964[3, 4]. It is an hypothetical scalar particle (i.e.invariant under Lorentz transformations) predicted by the Standard Model, but ithas never been observed.

It is possible to unify the weak and electromagnetic interactions into a singleinteraction, called the electroweak interaction, when energies of a few hundred GeVare reached. The two interactions then behave the same way. But then a questionarises: why are the weak interaction gauge bosons massive (and thus the range ofthe interaction limited) whereas the photon, the gauge boson of the electromagneticinteraction, is massless (and thus the range of the interaction infinite)? The exis-tence of the Higgs boson solves this “Electroweak Symmetry breaking” problem, bynaturally giving mass to the weak interaction’s gauge bosons by its existence andinteractions. It could also solve the problem of masses of fundamental particles. Allequations in the standard model describe particles as being massless. Mass, in thiscontext, appears by the interaction between the Higgs field and fermions.

In the framework of the Standard Model, all properties of this boson have beentheoretically predicted, like its cross-section, its decay channels, its branching ratios,

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2.3. THE HIGGS BOSON

Figure 2.4. Transverse view of the CMS detector, and behaviour of the differentcategories of particles inside the detectors[7].

etc. , except for its mass. The mass remains unknown, although some limits havebeen set[2]: its mass is above 114.4 GeV[2], with a confidence limit of 95 %, aswe know from direct experimental limit set by the LEP experiments[14]. Fromindirect mass limits from electroweak analyses, we can further say that its mass is129+74−49 GeV[2], also with a confidence limit of 95 %.This boson is a very useful tool in the Standard Model in order to solve the

“Electroweak Symmetry Breaking” problem. However, postulating the existence ofthis particle also raises problems. A quite popular theoretical model among physi-cists, although even more complex, is the so-called SuperSymmetry[15] (SUSY). Inthis model every single particle and antiparticle in the Standard Model would havea supersymmetric partner, and instead of one neutral Higgs boson, we would needfive of them, some electrically charged. Supersymmetric theories could also providecandidates for dark matter.

One should be aware that there exist “Higgsless” models as well, like the tech-nicolor model[16].

This report only considers the Higgs boson predicted by the Standard Model.

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CHAPTER 2. THE STANDARD MODEL, THE HIGGS BOSON AND THE CMSEXPERIMENT

2.3.2 Production and decay channels: introduction to H0 → γγ

The Standard Model Higgs boson can be produced by several processes, shown infigure 2.5. The dominant production channel at LHC energies is gluon fusion (asit can be seen in figure 2.6). The typical cross-section for Higgs boson productionbetween 115 GeV and 150 GeV is around 40 pb (44.2 pb for a mass of 120 GeV).It is not possible with today’s experimental techniques to detect directly the Higgsboson, because its lifetime is too small. We have to detect it through its decayproducts.

Figure 2.5. Feynman diagrams of the main Higgs boson production processes

Figure 2.6. Standard Model Higgs production cross-sections for pp collisions at14 TeV [2].

For the mass range we are interested in, we can see in figure 2.7 that up to

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2.3. THE HIGGS BOSON

' 150 GeV the main decay channel is H0 → bb. However, the LHC is a hadroncollider. Because of the fact that hadrons are not elementary particles (in oppositionto electron-positron colliders for example), we will produce a lot of QCD events aswell as rare events such as the Higgs boson. For this reason, the detection of aninvariant mass resonance from bb events will be extremely difficult, since the hugecross-section for QCD phenomena coming from underlying events will completelyhide this resonance.

Looking more closely at figure 2.7, we will take a particular interest in theH0 → γγ decay channel. This channel will be much easier to study: the twophotons coming from the Higgs decay will be highly energetic because of the largeHiggs mass. QCD events will produce a lot of photons, but much less energetic ones.So even if the branching ratio for this decay is about three orders of magnitudesmaller than for bb, this channel is very clean and much easier to detect, and thisshould compensate for the lower cross-section.

Figure 2.7. Branching ratios for the main decays of the Standard Model Higgsboson[2, 17].

One reason for the lower cross-section of the Higgs decay to two photons is thatthis decay is not direct. Since the Higgs boson is electrically neutral in the StandardModel, it cannot couple directly to photons. As the coupling of the Higgs boson isproportional to fermion mass, the most probable decays are via W boson-loops ort-loops (figure 2.8).

Another reason why we take a particular interest in this decay channel is that itis highly sensitive to BSM theories. Indeed, depending on the model, the H0 → γγdecay channel will either be largely enhanced or largely suppressed due to anomalousgauge coupling effects, as compared to the Standard Model case described above.

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CHAPTER 2. THE STANDARD MODEL, THE HIGGS BOSON AND THE CMSEXPERIMENT

Figure 2.8. Feynman diagrams of some Higgs to two photon decays in the StandardModel.

Studying this decay channel will then provide indirect information about the moregeneral validity of the Standard Model.

2.4 The Z0 → µµγ channel

2.4.1 Introduction

In order to correctly analyze the first data, we need to know as accurately as possiblethe performance of the CMS detector. We need to extract, as soon as possible,quantities such as the reconstruction and identification efficiencies, the energy scaleand the resolution[18]. For now, since the LHC has not yet started, we concentrateon Monte-Carlo-driven methods to obtain these quantities. Alternative data-drivenmethods are needed in order to cross-check the results with real data and to tunethe Monte-Carlo parameters.

From the Tevatron experiments[18], a lot of experience was accumulated inextracting this kind of data for electrons coming from Z0, J/ψ and Υ decays.

At the LHC, because of the higher centre-of-mass energy and luminosity, we willhave access to a clean, abundant and fairly isotropic resonant production of isolatedphotons: a Z0 boson produced at the LHC may decay into two muons (the branchingratio for this particular Z0 decay is 3.366 %). Muons are usually a lot cleaner thanother particles, since they are the only detected particles to go through the wholedetector and they do not shower. One of these muons may then lose energy byBremsstrahlung radiation, i.e. by emitting a photon. The Feynman diagram ofthis process is shown in figure 2.9. Such “signal” events, if reliably separated frombackground processes, will provide us a collection of “certified” photons.

One should note that the notation Z0 → µµγ could be misleading, since it meansZ0 → µµ, with one muon emitting a Bremsstrahlung photon (Final State Radiation,

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FSR, cf. figure 2.9), where it could mean Z0 → γ + µµ (Initial State Radiation,ISR), aslo shown on figure 2.9. We will always refer to the FSR throughout thisreport.

This signal is fully understood and predicted in the framework of the StandardModel, and as such is easily correctly modeled. Our latest estimate for the Z0 →µµγ process cross-section is 26.16 pb for a centre-of-mass energy of 14 TeV, and19.46 pb for a centre-of-mass energy of 10 TeV. These estimates have been donewith the Alpgen[19] matrix element Monte-Carlo generator at Leading Order (LO).

Figure 2.9. Feynman diagrams of the Z0 → µµγ processes allowed in the StandardModel. The diagram on the left represents the Final State Radiation (FSR) process,which is the signal process in our case. This process has a cross-section of 26.16 pbat 14 TeV and 19.46 pb at 10 TeV. The diagram on the right represents the InitialState Radiation (ISR) process. This process will be considered as background in thecase of our study.

We have a large amount of material in front of the Electromagnetic Calorimeter(up to 1.6 radiation lengths), mainly coming from the tracker system. This increasethe probability of interaction of particles with matter and thus has a negative effecton the reconstruction of electrons and photons[18]. Electrons will curve due to themagnetic field and lose energy by Bremsstrahlung. The electromagnetic showers inthe calorimeter will then be wider azimuthally, and some electrons, because of this,will not reach the calorimeter. These two effects lead to a non-linear energy scalefor electrons, that depends on the material distribution in front of the calorimeter,i.e. on pseudo-rapidity and azimuth.

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For photons the problem is not quite the same: if they stay unconverted, thematerial-induced non-linearity is not an issue. However, if the photon converts,its energy is shared by two electrons and the effect described above is doubled.Hence, electron and photon energy scales are different and could be non-linear. Thisexplains the interest in a data-driven way to calibrate photons independently fromthe electrons’ calibration8.

We can already have calibration information concerning the photons using thedecays π0 → γγ and η → γγ as sources of photons[9, 20]. The average energyof such photons is 2.7 GeV for π0’s and 4.7 GeV for η’s9. These sources have amuch larger production cross-section than Z0 → µµγ . We expect to reach 0.5 %intercalibration precision for 95 % of the CMS ECAL barrel as soon as 10 pb−1 ofintegrated luminosity. Concerning the absolute energy scale, we expect a precisionof ≈ 3 − 5 % within days, although with significant systematic errors due to thequantity of background events.

These photon sources will prove to be very useful to determine the absoluteenergy scale at low energies and intercalibrate the ECAL. However, we need theZ0 → µµγ channel in order to calibrate the electromagnetic calorimeter at higherenergies (in particular the absolute energy scale), especially because these energiesare of interest for detecting new physics. In our case, it is of interest for the detectionof a Higgs boson’s decay into photons (H → γγ): as shown in figure 2.10, thediscovery luminosity is directly related to the precision of the calibration we areable to reach with the ECAL.

Furthermore, previous experiments[18], and especially the Fermilab Tevatroncollider, have shown that in the GEANT10[21] description of the detector, theamount of material included in the description of the detector was severely un-derestimated at start-up time, mainly because of the difference between as-builtdetector and as-drafted, because of the complexity of the tracker system, and be-cause of the presence of “services”11 within the detector. In the CDF experiment atTevatron, the magnitude of the disagreement was as large as a factor of two. There-fore, we should expect some disagreement between the Monte-Carlo simulation ofthe CMS detector and the behaviour of the real detector: it is too risky to rely onthe Monte-Carlo simulation data at the time of start-up.

The actual energy correction scheme in the CMSSW12 framework[22] relies solely

8The electron calibration is obtained quite early with the Z0 → e+e− process via the “tag andprobe” method.

9The π0 and η mentioned here are obviously boosted in the laboratory frame, since we havemπ0 = 134.9766 MeV and mη = 547.51 MeV

10GEANT is the principal CERN software to simulate the passage of particles through matterusing Monte-Carlo methods.

11The so-called services are objects that need to be in the detector but that are not at alldetection devices. This includes for example the structure of the detector, electric cables, coolingdevices for superconducting objects... These are poorly accounted for in the description of thedetector, because difficult to model.

12CMSSW stands for CMS SoftWare. It is the basic data simulation, reconstruction and analysisframework for CMS physicists.

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Figure 2.10. Integrated luminosity needed for the discovery of a Standard ModelHiggs boson decaying in a diphoton final state as a function of the calibration precisionof the ECAL[20].

on Monte-Carlo simulation, since we do not have any data yet. It has been designedfor electrons. Studies [22, 23] are currently going on to see the effects of the correc-tion scheme on photons. Due to the above considerations, we need a data-drivensource of correction, since the Monte-Carlo tuning of the correct description of theexperiment is a complex process. The plan for start-up has two aspects:

− Measure the amount of material in situ, using e.g. converted photons, in orderto tune the simulation,

− Extract efficiencies, resolutions and energy scales for electrons and photonsfor different regions of the detector for different identification cuts.

The event selection described in section 3.6 aims to select the FSR radiative Z0

decay events, in order to use the extracted photons as a collection of “Certified”photons, with a very high purity. These photons then may be used for the secondaspect described above. This selection was the first aspect of my work.

From references [18, 24], we expect the invariant mass of the µµγ system, whichis the Z0 reconstructed invariant mass, to be shifted towards larger masses as afunction of the photons’ transverse energy. The fitted values could be shifted by

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almost 0.4GeV, which corresponds to a photon energy scale shift of about 2%. Theseresults are “back-of-the-envelope” calculations, and no study of these affirmationshave been made to date.

Furthermore, these prior studies are not up-to-date with the current descriptionof the detector, and the physics reconstruction chain itself underwent major changes.Studying this parametrization with a more up-to-date framework was the secondaspect of my work.

2.4.2 Energy corrections

The deposited reconstructed energy of particles in the CMS ECAL can be decom-posed into three factors[9]:

Ee,γ = G×F ×∑i

ci ×Ai

where G is a global absolute scale, the function F is a correction function dependingon the type of particle, its position, its momentum and of the clustering algorithmused, the ci factors are the intercalibration coefficients while the Ai are the signalamplitudes, in ADC counts, which are summed over the clustered crystals.

We need to have a correction function in order to compensate the followingeffects:

− The fraction of energy in a fixed array cluster varies as a function of theshower position with respect to the cluster boundary - the highest fractionis contained if the shower is perfectly centred. This can be described as avariation of “local containment”

− There are large losses due to rear leakage for showers close to the barrel inter-module borders.

− The spread of energy due to showering in the tracker material (Bremsstrahlungand photon conversion) and the behaviour of the superclustering algorithmswhich are designed to collect this spread energy.

− The crystals are very similar in size but we have a variation of shower leakageas a function of η (cf. figure 2.11).

In the current working model, F = 1 is chosen for the reference 5 × 5 crystalshower reconstruction (clustering) algorithm, used for converted photons, or forelectrons in the test beam.

It is better to extract information in situ with the running detector for thestudy of more complex physical effects, like conversions and Bremsstrahlung in thetracker material, or for having quickly a more accurate description of the differentcorrection functions. In case of the photon, the channel Z0 → µµγ will be used,and we will also be able to set the global scale G with such a channel.

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Figure 2.11. Illustration of shower leakage in the ECAL.

From the TDR results[9], for an integrated luminosity of 1 fb−1, an average ofnearly 1 photon per crystal with 15 GeV < EγT < 30 GeV will be collected. Astatistical precision better than 0.1 % would be achieved with unconverted photonsfor the intercalibration of 10-crystal-wide rings of crystals (i.e. groups of 3 600crystals) in the barrel.

2.4.3 The Global Energy scale G and the correction functions FFor energy scale measurements, biases have two origins[18, 24]: from instrumentaleffects and from physics effects:

− The instrumental effect comes from the photon energy resolution, which isnot infinitely small. The photon ET spectrum in radiative Z0 decays fallssharply, as shown in figure 2.12. Therefore, a sample of µµγ events with largephoton ET will be enriched by events where the photon energy has been mis-measured: for a given bin in ET , the mismeasurement will “leak” into binswith larger energies, because of the sharpness of the spectrum. Thus, the Z0

peak is shifted towards larger masses, as shown in figure 2.13[24]. The effectof the variation of the energy resolution can be neglected (cf. [24]), as it canbe seen in figure 2.14 for the energy range 15 GeV− 70 GeV.

− The physics effects come from the large natural decay width of the Z0 boson.

We can study as well the dependence of themµµγ reconstructed invariant mass asfunction of the photon physical quantities. We can this way both validate the Monte-Carlo corrections currently applied, and also detect and correct any unforeseendetector or reconstruction bias.

2.4.4 Intercalibration coefficients ciWhen sufficient integrated luminosity will be available, one may also use the Z0 →µµγ channel in order to intercalibrate the ECAL’s crystals. Indeed, the crystalscannot be strictly identical, and their individual responses will differ from one toanother due to different light yields, uniformity, ...

At the time of the start-up, the two channels π0 → γγ and η → γγ will providea sufficient number of photons to intercalibrate the ECAL[9] up to a statisticalprecision of ≈ 5 %.

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Figure 2.12. Photon ET spectrum in radiative Z0 decays[24].

Figure 2.13. Fitted value of the Z0 mass as a function of the photon ET , in GeV.We can note that the mµµγ reconstructed invariant mass tends to shift towards largermasses at large photon ET [18]. The dark points represents generator information,blue points photons smeared using nominal resolution, red points photons with anadditional smearing of 2 %.

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Figure 2.14. Energy resolution of the Electromagnetic Calorimeter[25].

It is expected[9] that for ≈ 1fb−1 of integrated luminosity, one “certified” photonwill be collected per crystal. We will therefore be able to intercalibrate the ECALwith larger energy photons, and the statistical precision could reach 0.1 %.

2.4.5 Trigger efficienciesSince the Z0 → µµγ channel is fully Standard Model physics, we may also use itto measure trigger efficiencies. To do so[26], we consider the superclusters passingthe selection as the test population of size N . Then, we count the quantity Sof these events passing the High Level Trigger (HLT) HLT Photon15 L1R (or anyother trigger, for which we want to measure the efficiency). We define the triggerefficiency ε as the proportion of test events passing the trigger:

ε = S

N

We can obtain the statistical error on this efficiency by using the normal ap-proximation13[26]. We define the total efficiency as:

ε = ε±∆εwhere

∆ε =

√ε(1− ε)N

13In order to justify the use of this approximation, we ask for: N > 30, S > 5 and N − S > 5

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For this particular trigger, the efficiency is[26] ε ≈ 55± 15 %.

2.4.6 Interest for the H0 → γγ channelFor the H0 → γγ discovery channel, it is of very strong interest to have the bestavailable precision on the photon measurement.

It is very desirable to correctly calibrate the ECAL with the Z0 → µµγ channel:

− The photons coming from Z0 → µµγ are much closer to the energy rangeof the photons of H0 → γγ than the previously-used photons coming fromπ0 → γγ and η → γγ.

− The precision on the photon energy measurement will clearly be directly re-lated to the obtainable precision of the Higgs mass if the H0 → γγ is detected,as we have already seen on figure 2.10.

2.5 Introduction to data analysisEvery collision that will happen at the LHC will not produce some brand newphysics. Since protons are composite particles, several partons14 collisions are pos-sible. Among these possibilities, a large part is composed of phenomena that arealready known and studied, for example QCD multi-jets events. These phenomenaare interesting by themselves, but will contribute for a very large part to the back-ground for detecting new physics. The cross-sections of the new phenomena (Higgs,SUSY particles, ...) are very small in comparison (figure 2.15).

At the LHC collisions between protons bunches will happen at 40 MHz. In allthese collisions, there are triggers that will allow a preselection of interesting events.This very first preselection is done online, i.e. while collisions are happening, beforestoring any information. Most data analysis is done offline, i.e. on the stored data,and not during the data acquisition itself. In general there are several levels oftriggers, motivated by both physics reasons (the cross-section of the new phenomenais very small, as shown in figures 2.15 and 2.17) and acquisition system reasons (weneed to decrease the data flux to manageable sizes and rates, as shown in figure2.16). We will only be interested here in data that will pass the so-called HLT(High-Level-Trigger). This is the last trigger level of the online operations. If anevent pass this trigger, it will further be stored. This chain is summarized on figure2.18.

Before considering analysis of real data, it is compulsory to correctly handle thedetector, and to correctly interpret its behaviour. Since the CMS detector is verycomplex, a lot of work is necessary for doing so. Monte-Carlo simulation is a veryuseful tool enabling on one hand to get used to the detector before data-taking startand, on another hand, to study precise theoretical signals and the response of the

14The parton model describes the hadron structure and their collisions at high energies. Quarkand gluons are the two different kinds of partons.

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Figure 2.15. Typical cross-sections as a function of the particle masses, for standardmodel processes and Beyond Standard Model processes.

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Figure 2.16. General architecture of the CMS data acquisition system[9].

Figure 2.17. Illustration of the number of collisions needed to produce new physicsphenomena[7].

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Figure 2.18. Summary of the CMS trigger and data acquisition scheme

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detector to such events. We also need, once data starts to be accumulated, to tunethe Monte-Carlo generators in order to generate data-like signals for further studies.

In order to be able to distinguish new phenomena, we thus first need to simulatethe signal and possible background events, then the response of the detector, andat last to do the reconstruction. The Reconstruction finds out information on thegenerated particles (i.e. the physics events themselves) from the detector response.This way, we reconstruct photons from information from the tracker (no track) andthe ECAL (one supercluster). Finally, in the analysis stage, we attempt to separatethe different responses of the detector, in case of signal and background statistics.Most of the hard work is to reject background while keeping a maximum of signal.

There is a very significant difference in statistics (a factor about 109 betweenQCD and signal is not unusual), and so we need a very good discrimination againstbackground. These studies require a comprehensive approach to the detector andthe analysis itself, in order to observe a signal and not a statistical fluctuation.

In the case of this report, the analyzed signal will be the decay Z0 → µµγ. This signal is Standard Model physics, but we need to extract this signal fordetector performance purposes, as explained above. Some other groups, within theCMS collaboration, are also interested in measuring this process for its own sake,or using the ISR signal for search for anomalous gauge couplings.

2.6 Computing toolsWe present in this section a brief introduction to the different computing tools usedduring this diploma work.

2.6.1 ROOT

The ROOT software[27] written in object-oriented C++ was developed by theCERN, for the numerous particle physics experiments going on there. This softwarehas been designed for statistical applications and data analysis. It contains numer-ous libraries and functionalities, for example for handling histograms or fitting. TheROOT object classes allow a very good flexibility of applications.

The .root file format is used as the basic format throughout the whole recon-struction chain. This format is a tree structure, which is convenient for analysis.

2.6.2 CMSSW

CMSSW[28, 29] stands for CMS SoftWare. It is the principal tool for physicistsof the CMS collaboration. This software can generate events, reconstruct the de-tector’s response, but as well handling calibration and alignment procedures, oranalyze data. It is highly modular, so it can handle very complex tasks.

Every configuration file (the input files of the software) calls other configurationfiles and software packages. We can decide for example to write a configuration fileto generate events (via a Pythia module), then reconstruct it (via the reconstruction

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chain). The software is constantly developed by the physicists themselves, for addingnew abilities every day.

2.6.3 Monte-Carlo GeneratorsWe used during this diploma work several samples, mainly coming from four differ-ent Monte-Carlo generators, one Parton Shower (PS) generator and three MatrixElement (ME) generator.

The parton shower generator is:

Pythia [30] is an event generator for high energy physics. Its main developmentis around production of several particles during the collision of elementaryparticles (like the hadronization process). This include hard interactions incolliders e+e−, pp, ep, pp, ... This software is generating complete events,with as many levels of details as the experimentally-observed events, of coursewithin the current understanding of the underlying physics.

The matrix elements generators are:

Alpgen [19] is dedicated to the study of multiparton hard processes in hadroniccollisions. It performs, at the leading order in QCD and EW interactions,the calculation of the exact matrix elements for a large set of parton-levelprocesses. Parton-level events are generated, providing full information ontheir colour and flavour structure, enabling the evolution of the partons intofully hadronized final states. It needs to be interfaced with Pythia to furtherhadronize the partons.

Madgraph [31] is a software that allows to generate amplitudes and events for anyprocess in any model. Implemented models are the Standard Model, Higgseffective couplings, MSSM, the general Two Higgs doublet model, and severalminor models. This software is generating events with the matrix elementmethod to compute probability amplitudes. It also needs to be interfacedwith Pythia to further hadronize the partons.

Comphep [32] is yet another matrix element Monte-Carlo generator. It also needsto be interfaced with Pythia for further hadronization.

We need both kind of generators. Pythia has serious difficulties to generatecorrectly hard events with a high multicplicity: the results need often strong cor-rections for more than 3 particles in the final state, whereas the matrix elementgenerators are computing exactly the kinematics and cross-section quantities, atleading order (i.e. tree level on Feynman diagrams) up to 8 particles in the finalstate. The parton shower generator, however, has been optimized to handle individ-ual particles, fragmentation and hadronization of quarks (jets), for which the matrixelement method is too much precise for our purposes. The usual way of generatingevents is then to generate the hard process with a matrix element generator, thento interface the result with a parton shower generator.

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2.6.4 LCG GRID computingThe LCG15 computing Grid[33] is the next generation of batch computing. Indeed,the LHC experiments are expected to produce around 27 TB per day of raw data,and around 10 TB of event summary data, which amounts to a total of around10− 15PB of data per year. This kind of data flow would be hardly manageable byonly the CERN computing and storage systems when we need to further calibrateand analyze the data. The LCG has been developed by several national computingcenters, such as the CERN and the CCIN2P3. The Grid is organized as follows:

− The Tier-0 center, i.e. the CERN, handle the raw data flux. It is the centralhub.

− The Tier-1 centers, which comprises 11 computing center sites around theplanet. Every data file stored at CERN will be copied at one T1 center afterinitial processing.

− The Tier-2 centers, which comprises 140 computing centers of smaller capac-ities. These will handle general collaboration wide tasks, like reconstructionand Monte-Carlo generation for local users.

− The Tier-3 and Tier-4 centers will handle other analyses codes and calcula-tions.

As mentioned above in section 2.5, there are several levels of triggers before theoffline storage. There are also different kind of triggers, depending on the underlyingphysics (Does the event contains high energy photons? Does it contains muons or isthere a lot of missing transverse energy?). Depending on the triggers passed, datawill be stored at computing centers.

The interest of the LCG is that whenever we need to launch a job, it willautomatically run at the particular Tier-center whereever on the globe where thedata is. Then, the output result will be sent back to the user, at her or his local Tier-center. This provides a user-transparent way of analyze data, while distributing theload of computing and storage.

During this diploma work, I mostly used the CCIN2P3 batch system and theCERN batch system for my own analysis purposes. I also had the occasion to worka bit on the Grid, which will become the principal tool for these tasks.

2.6.5 TotoAnalyzerTotoAnalyzer is the analysis program of the CMS group at IPNL. It is set upas a package of the CMSSW software developed by Morgan Lethuillier[34] for theanalyses of the group.

Its main feature is to convert the physics objects of the CMSSW global soft-ware into simpler physics objects with the needed information (like the transverse

15LHC Computing Grid

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momentum pT , the pseudo-rapidity η, ...). In case we need for a particular casemore information about the reconstruction itself, this information can be accessedby links within the package.

In the analysis presented here, I used TotoAnalyzer objects such as TRootPhoton,TRootMuon, ... Such objects are high-level reconstructed objects (physics objects),in opposition to lower level reconstructed objects, closer to the detector, such astracks, SuperClusters, ...

It does contain basic features to help with the study of the different researchareas the IPNL group is involved in: H → γγ, t-physics, studies of tracker andECAL performance.

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Chapter 3

Versions of the Z0→ µµγ eventselection

The global philosophy of this selection is to avoid as much as possible biases on thephotons. It is assumed for this selection that the muons are perfectly reconstructed,and in particular that their energy scale has already been measured (which shouldbe possible with 10 pb−1 of integrated lminosity[9]). Hence the Z0 → µµγ willbe a source of “Certified” photons, on which we can further work for other pur-poses (measurements of energy scale, efficiencies of trigger, photon ID and photonisolation, cf. section 2.4).

This section describes and compares several versions of the Z0 → µµγ eventselection and how they evolved. The different versions of the selection correspondto major changes in the software.

For this part, I was working with the PhD student Clement Baty on the 1.6.12and 2.2.9 versions of the selection. My role was mainly to write my own selec-tion code in order to cross-check the results and help with the optimization of theselection.

3.1 Technical Design Report & CMS AN 2005/040A first study has been published in 2004 by the CMS collaboration in its TechnicalDesign Report (volume I)[9] following an internal analysis note[24] by Yuri Gershtein(FSU1).

The sole studied background was the Z0+ jets process, generated with Pythia,and the reconstruction has been done with ORCA (CMSSW’s ancestor). It providesthe following two fake signals:

− Z + jets: two muons produced plus a fake photon coming from producedjets. In such case, the Z0 observed is mostly real and we do not observe anycorrelation between the muons and the photon.

1Florida State University

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− Z(+jets): two muons produced plus a fake photon coming from a muon’spassage through the ECAL. In such case, the Z0 observed is mostly real andthe muon extrapolation to the electromagnetic calorimeter will coincide withthe photon position

The samples are generated for a centre-of-mass energy of 14 TeV.The background samples were generated with Pythia, and with a corresponding

combined integrated luminosity of about 336 pb−1. It was reconstructed usingORCA 8.7.3.

The signal sample has been generated with Comphep interfaced with Pythia(for fragmentation and hadronization), with the following generator cuts2:

− |ηγ | < 2.5 and |ηµ| < 2.5

− ET (µ) > 15 GeV

− ET (γ) > 10 GeV

− 30 GeV < mµµ < 150 GeV

− ∆R(µγ) > 0.01

The last two cuts are to remove singularities in the matrix element and improvegeneration efficiency. One should note that for this study, the center-of-mass energyof the collider was of 14 TeV, as first planned for the start-up.

This sample was not passed through a detector simulation or reconstruction,but instead was only gaussian smeared.

The selection is a very loose one and has been designed in three steps:

− A loose cut on the dimuon mass: 40GeV < Mµµ < 80GeV. Since we do wantto calibrate photons, we need the invariant mass of the dimuon system to belower than the Z0 mass.

− Selection of a photon with pT > 15GeV within a radius of ∆R < 0.8 of eithermuon. We use further only the highest ET photon in the event.

− Cut on the three-body invariant mass 87.2 GeV < Mµµγ < 95.2 GeV

To calculate signal and background yields, events have been counted in the masswindow 87.2GeV to 95.2GeV for the signal and 70GeV to 110GeV for background.For the background, the number of events has been divided by the ratio of the widthof background and signal mass windows (i.e. 5). This is a Poor’s man Poisson”method, in order to evaluate the shape of the background with low statistics.

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3.2. CMSSW 1.3.1

Figure 3.1. Photon spectruminradiative0 decays[24].

The results The main result of this study is the photon ET spectrum (figure3.1):it indicates the event yield. We do not have any precise number on the selectionefficiency. We also lack the production cross-section of the signal.

3.2 CMSSW 1.3.1

This study[35], led by Susan Gascon (IPNL), had two goals: to validate the analysisdone with ORCA by Y. Gershtein within the CMSSW framework, and to studyseveral additional relevant background events that have not been considered so far.This is the first study considering signal and background events fully reconstructedwith the CMSSW software.

The samples used included the ones used for the Y. Gershtein analysis (i.e. thesignal Z0 → µµγ sample and the Z0 + jets sample), but generated with the Alpgengenerator. They are generated for a centre-of-mass energy of 14 TeV. The signalhas been generated with Alpgen, with a cross-section of σ = 26.2pb−1 (at 14 TeV).

The backgrounds events for the CMSSW 1.3.1 study are:

2The definitions of η, φ, ET , mµµ, pT and ∆R can be found in the appendix C.6

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

− the background Z0 + n jets (0 ≤ n ≤ 4) has been produced with the Alpgenevent generator. The cross-section of this process is σ = 2750.3 pb.

− the background γ + light jets (0 GeV < pT < 500 GeV) has been producedwith Pythia. Very few real muons and no real Z0 are observed, but it as ahuge cross-section compared to our signal: σ = 1.706× 108 pb.

− the background inclusive bb (30 GeV < pT < 170 GeV) has been producedwith Pythia. It has a production cross-section of σ = 7.8× 106 pb

− the background tt + n jets (0 ≤ n ≤ 4) has been produced with Alpgen withmatched ME/PS jets. It has a cross-section of σ = 561 pb

The selection is applied as follows (essentially the same as for the CMS AN2005-040):

1. The event must contain at least two global muons3 of opposite charges, andthese must satisfy the Alpgen signal preselection cuts: pT > 10GeV, |η| < 3.0,mµ1µ2 > 20 GeV

2. The event must contain at least one photon, and it must satisfy the Alpgensignal preselection cuts: pT > 10 GeV, |η| < 3.0, ∆R(γ, closest µ of µ1, µ2) >0.05

3. At least one pair of muons must satisfy 40 GeV < mµµ < 80 GeV. This cut isintended to eliminate Drell-Yan background processes, that produce muons.

4. The event must contain a photon-muon pair satisfying ∆R(γ, closest µ of µ1, µ2) <0.8. This cut exploits the correlation γ − µ of the signal. There must be inaddition at least one photon satisfying ET γ > 15 GeV.

5. The event must contain a µµγ triplet satisfying 87.2GeV < mµµγ < 95.2GeV(if the sample studied is signal)

6. The event must contain a µµγ triplet satisfying 70 GeV < mµµγ < 110 GeV(if the sample studied is background). The number of events is then dividedby 5, like in the previous section. This cut is used instead of the cut 6.

The results After the selection, the results presented in table 3.1 are obtained.The obtained purity4 of the final sample is then of 27.6%, for a signal selection

efficiency of 17.7 %, with a final event yield of 4.63 events pb−1. Note that errorshave not been computed on these quantities.

3A standalone muon is a muon defined by a track in the muon detectors. A global muonis defined by having additionnaly a track in the tracker, consistent with the track in the muondetectors.

4The purity is defined as the ratio signal/(signal + background)

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3.3. CMSSW 1.6.7

Sample Initial number of events Number of selected events Selection efficiency(per pb−1) (per pb−1) (in %)

Z0 → µµγ 26.2 4.63 17.7Z0 + jets 2750.3 0.029 10.5× 10−4

γ + jets 1.706× 108 < 0.03 < 1.76× 10−8

bb 7.8× 106 12 1.54× 10−4

tt 561 0.08 1.43× 10−2

Table 3.1. The main selection results for the study of Z0 → µµγ within the CMSSW1.3.1 framework.

3.3 CMSSW 1.6.7Jan Veverka (Caltech5) and Clement Baty (IPNL) have in parallel been conductingthe same study of the selection of the signal. However, the chosen cuts are not quitethe same.

The selection of J. Veverka[36] presented below is then alternative and comple-mentary to ours. It has been restricted to the barrel.

The samples All the samples presented below are generated for a centre-of-massenergy of 14 TeV.

− The signal Z0 → l+l−γ6 has been generated with Pythia. It is the CSA077

inclusive8 sample generated with the following cuts:

– invariant mass of the Z0/γ∗: m(ll) > 40 GeV– |η(l)| < 2.5

Events are considered as signal events when they pass the additional cuts:

– events that are FSR events at generator-level– pT l > 9 GeV– FSR photon: pT γ > 8 GeV– FSR photon: |η(γ)| < 3.0– FSR photon separated from the leptons: min∆R(γ, l) > 0.001

This signal has a production cross-section of σ = 40.97 pb.5California Institute of Technology (USA)6The selection presented here consider electrons as well as muons as leptons coming from the

Z0’s decay.7CSA07 stands for8For a sample considering a decay channel, “inclusive” means that the decay is considered

independently of its production mode.

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

− bb→ llX: 1M (300k) events, with a cross-section: σ = 7.52nb. It is a privateproduction generated with Pythia and fully reconstructed within CMSSW1.6.7, with the following generator cuts:

– pT (l1, l2) > 8 GeV or 13 GeV– |η| < 2.5– ml1,l2 > 35 GeV

− inclusive Z0: 1 M events (both muons and electrons), with a cross-sectionσ = 835pb. It has been generated with Pythia and fully reconstructed withinCMSSW 1.6.7. It is the same sample as for the signal, with a veto ont theMonte-Carlo truth information.

− inclusive tt: 1M events, with a cross-section σ = 850pb. It has been generatedwith Toprex[37], and fully reconstructed within CMSSW 1.3.1

The selection is organized in six steps:

Preselection

− requires two global leptons with opposite charge and a supercluster− pT (l) > 10 GeV and |η(l)| < 2.4− pT (γ) > 10 GeV and |η(γ)| < 1.5− mini=1,2∆R(liγ) > 0.05

Kinematic cuts mainly suppress the Z0 related background

− Leading muon: pT > 15 GeV− mini=1,2∆R(liγ) < 0.9− 45 GeV < ml1l2 < 85 GeV

Jet veto mainly suppresses tt

− second leading central (|η| < 2.4) jet with pT < 15 GeV− llγ candidate event multiplicity < 4 (EB), 3 (EE)

Far lepton isolation mainly suppresses bb without biasing on the photon ID

− Use a solid ∆R < 0.3 cone around the lepton farthest from the photon− Number of tracks with pT > 1.5 GeV be zero and the sum of trackpT < 1 GeV

− ECAL: Sum of island basic cluster deposits < 3 GeV− HCAL: H/E < 0.3 (EB), < 0.35 (EE), where H is the sum of rechits

Number of µµγ candidates mainly suppresses tt-related background events.

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3.4. CMSSW 1.6.12

Sample Initial number of events Number of selected events Selection efficiency(per pb−1) (per pb−1) (in %)

Z0 → µµγ 40.97 5.73 13.99Z0 835 0.21 2.51× 10−2

tt (1.3.1) 850 0.12 1.42× 10−2

bb 7 520 0.14 1.86× 10−3

Table 3.2. The main selection results for the study of Z0 → µµγ within the CMSSW1.6.7 framework.

− the number of µµγ possible triplets passing the previous cuts must beless than 4

mµµγ invariant mass The invariant mass mµµγ must be in the mass windows:85 GeV < mµµγ < 95 GeV.

The results After the selection, the results presented in table 3.2 are obtained.The final purity yielded by the selection is 93 %, for a signal efficiency selection

of 13.99 %, with a final event yield of 5.73 events pb−1. Note that errors have notbeen computed on these quantities.

3.4 CMSSW 1.6.12

The selection of Clement Baty (IPNL)[38] presented thereafter is the continuationof the work started by S. Gascon described above. During this diploma work, Ihave cross-checked the results of this selection, as well as implement a technique toconserve the selected events in a separate root file with all pertinent objects forfurther study.

The main differences with respect to J. Veverka’s selection above are:

− The cut on the ET γ threshold at the generator level (10 GeV for J. Veverka,12 GeV here)

− an additional cut on the highest pT µ. So far the cuts on the muons quanti-ties were only to avoid edge effects from generator-level cuts, this is a newkinematical cut.

The samples All the samples considered are for a centre-of-mass energy of 14TeV.For this study, several different samples9 were used, all have been reconstructed

with CMSSW 1.6.12 and the selection was done within TotoAnalyzer:

9The names indicated in fixed font are the names as specified in DBS

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

− The signal Z0 → µµγ , has been produced by Morgan Lethuillier and is aprivate Monte-Carlo production. It has been generated with Alpgen with thefollowing preselection cuts:

– pT > 10 GeV– |η| < 2.5– ∆R(γ, µnear) > 0.05

The signal has a generated cross-section of σ = 26.16 pb

− The background sample BB2MuMu noMassCut has been generated with Pythia.One should note that despite the name of this sample on DBS10, the contentis not what one would expect: only the production of 1 b-quark is required.It has a cross-section of σ = 3.53 × 106 pb. It has been generated with thefollowing preselection cuts:

– 1 b-quark, 2 muons– |ηµ| < 2.5– pT µi > 2.5 GeV

The next sample (bbNj-alpgen) should be preferentially taken into accountto model the bb-related background events, since it is generated with Alpgen,while the current sample is generated with Pythia (cf. discussion on section2.6.3).

− The background samples bbNj-alpgen contains bb events with N jets (1 <N < 5). The combined cross-section is σ = 377989 pb. It has been generatedwith Alpgen, with the following preselection cuts:

– |ηj | < 5– ∆R(j, j) > 0.7

− The background sample phNj XX YY-alpgen contains one photon with N jets(1 < N < 4) of transverse momentum XX < pT < Y Y . It has a cross-sectionof σ = 136806 pb. It has been generated with Alpgen with the followingpreselection cuts:

– pT j , pT γ > 20 GeV– |ηj | < 5– |ηγ | < 2.5– ∆R(γ, j) > 0.7

10DBS: Data Bookkeeping System: storage organisation of CMS data

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3.4. CMSSW 1.6.12

Sample Initial number of events Number of selected events Selection efficiency(per pb−1) (per pb−1) (in %)

Z0 → µµγ 26.15 5.27 20.13BB2MUMU 3.53× 106 0.39 1.1× 10−7

BBNJETS 3.78× 105 < 7.41× 10−2 1.96× 10−7

PHNJETS-ALL 1.37 × 105 < 3.6× 10−4 3× 10−9

Table 3.3. The main selection results for the study of Z0 → µµγ within the CMSSW1.6.12 framework.

The selection The cuts used for this selection are basically the same as for thestudy of S. Gascon described above, with two additional cuts:

1. The event must contain at least two global muons with opposite charge, andthese must satisfy the Alpgen signal preselection cuts: pT > 10GeV, |η| < 2.5,mµ1µ2 > 20GeV. We additionally require that there exist muons with oppositecharges.

2. The event must contain at least one corrected photon, and it must satisfy theAlpgen signal preselection cuts: pT > 10GeV, |η| < 2.5, ∆R(γ, closest µ of µ1, µ2) >0.05

3. At least one pair of muons must satisfy 40 GeV < mµµ < 80 GeV. This cut isintended to eliminate Drell-Yan background processes, that produce muons.

4. The event must contain a photon-muon pair satisfying ∆R(γ, closest µ of µ1, µ2) <0.8. This cut exploits the correlation γ − µ of the signal. There must be inaddition at least one photon satisfying ET γ > 12 GeV.

5. The event must contain a µµγ triplet satisfying 87.2GeV < mµµγ < 95.2GeV(if the sample studied is signal)

6. The event must contain a µµγ triplet satisfying 70 GeV < mµµγ < 110 GeV(if the sample studied is background). The number of events is then dividedby 5, like in previous sections. This cut is used instead of the cut 6.

7. The farthest muon from the photon must have not deposited more than amaximum quantity of transverse energy in the electromagnetic calorimeter:ISOemET < 1 GeV within a radius ∆R = 0.3 for the selected muon.

8. The muon of the previous cut must have a minimum transverse energy: pT µ >30 GeV

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

The results After the selection, the results presented in table 3.3 are obtained.The obtained purity is 93.09 % for a selection efficiency of 20.13 %, with a

final event yield of 5.27 events pb−1. One should note that this purity and thisselection efficiency represent quite significant improvements with respect to thefirst CMSSW version of the selection, even as more background events have beenextensively produced and studied. Note that errors have not been computed onthese quantities.

3.5 CMSSW 2.1.11This study of Jan Veverka is the natural continuation of his own previous selectionin the version 1.6.7 of CMSSW presented in section 3.3. It is the first study withresults for a centre-of-mass energy of 10 TeV, reflecting the change in the start-upplan for the LHC luminosity and energy. The selection is then improved with respectto the previous iteration, and the study is more first-data-like, due to significantimprovements in the detector simulation and reconstruction algorithms.

The samples All the samples presented here are centrally (collaboration-wide)produced Monte-Carlo samples during the summer 2008 (the so-called Summer08samples).

The samples are the following:

− The signal & background sample Zmumu has been generated with the PythiaMonte-Carlo event generator, with a generator-level cut11: pT > 40GeV. 1.1Mevents have been generated, with a cross-section of σ = 630 pb. The eventsconsidered as signal are here preselected events with a leading superclustermatching to the FSR topology (cf section 3.3).

− The ttbar + jets background has been generated with Madgraph. Thereare 1.2 M events with a cross-section of σ = 317 pb.

− The QCD background has been generated with Pythia with the following gen-erator cuts:

– pT > 20 GeV– pT µ > 15 GeV

There are 6.1 M events with a cross section of 120 nb.

The events have been reconstructed within the versions 2.1.7 and 2.1.8 of CMSSW,and the further analyses and selection have been performed with CMSSW 2.1.11.

11pT is defined as the transverse momentum of the parton. It represents thus a Monte-Carloquantity, which does not have a physical meaning. For example, we usually define this way thetransverse momentum of a single particular quark, while physcially quarks are always bounded.

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3.5. CMSSW 2.1.11

The selection presented here is, as J. Veverka’s previous iteration, restricted tothe barrel.

For technical reasons, the following pre-selection cuts applied:

− At least 2 global muons with pT > 14 GeV and pT > 9 GeV are required.

− At least one (ECAL) supercluster with pT > 9 GeV are required.

The selection is shown below:

Basic Cuts

− At least two global muons are required to have pT > 10 GeV.

− The leading supercluster is required to have pT > 10 GeV.

− The leading supercluster is required to be in the barrel: |eta| < 1.479.

Kinematic Cuts : these cuts focus on suppressing particular background events.

− The leading muon is required to have pT > 15 GeV as in the previousiteration.

− The supercluster and the close muon are required to be separated: 0.05 <∆R < 0.9. This cut unfortunately suppresses a significant part of thesignal.

− A cut on the dimuon invariant mass is required: 45GeV < mµµ < 85GeV.

Muon identification − The two leading muons are required to have oppositecharges. This mainly suppresses the tt and QCD background events.

− The impact parameter of the muon inner track with respect to the pri-mary vertex is required to be < 0.01 cm for both muons, in order tosuppress QCD.

− The number of reconstructed hits of the inner track of both muons isrequired to be > 11. It suppresses mainly muons coming from jets (in-flight decays).

− The muon tracker isolation is required to be < 5GeV for the “far” muon.

The results After the selection, the results presented in table 3.4 are obtained.The obtained purity is 90 % for a selection efficiency of 20.83 %, with a final

event yield of 5.03 events pb−1. Therefore, it appears that this channel will stillbe exploitable, even at the lower centre-of-mass energy of 10 TeV than previouslyplanned (14 TeV). Note that errors have not been computed on these quantities.

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

Sample Initial number of events Number of selected events Selection efficiency(per pb−1) (per pb−1) (in %)Z0 → µµγ 24.15 5.03 20.83

ISR 1.34 0.003 0.22Z+jets 44.54 0.064 0.14ttjets 4.26 0.011 0.26

QCD 4803.89 0.48 0.01

Table 3.4. The main selection results for the study of Z0 → µµγ within the CMSSW2.1.11 framework.

3.6 CMSSW 2.2.9

The selection presented below has been realized by Clement Baty and is the iterationwe are currently working on. The selection has been strictly translated from the1.6.12 version as a first step, and has not yet been further optimized. All thestudied samples are now however produced for a centre-of-mass energy of 10 GeV.One should note that there has been several significant changes within the CMSSWsoftware between the 2.1.X versions and the versions more recent than 2.2.7, inparticular several bugs concerning the digitization step of the reconstruction havebeen corrected. The reconstructed photon objects have as well been subject tosignificant changes.

I have for this version, as for the 1.6.12 version, cross-checked the results obtainedby C. Baty.

The samples We studied in this iteration the same event processes as in theversion 1.6.12, with the important addition of the background sample containingW bosons and jets.

This iteration is, to date, the most extensive, each background process havingbeen produced with more statistics than the previous versions, and already severalinteresting results have been obtained.

The samples used are presented below. Where indicated, two samples are beingused for a given physics process, one as the principal sample, and one as a cross-check sample.

− The signal Z0 → µµγ , generated with Alpgen by J. Tao (IHEP (Beijing) -IPNL (Lyon)). It has a cross-section of σ = 19.46 pb.

− The background sample InclusiveMuPt15 contains inclusive production of atleast one muon with pT > 15 GeV, and has been generated with the Alpgenevent generator, further interfaced with Pythia for parton showering. It hasa cross section of σ = 1.22× 105 pb. This sample is a principal sample.

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3.6. CMSSW 2.2.9

− The background sample InclusivePPmuX contains inclusive production ofmuon from two protons, and has been generated with the Pythia event gen-erator. This sample is used as a cross-check sample for the InclusiveMuPt15principal sample.

− The background sample PhotonJetsXtoY-madgraph contains photon withQCD multi-jets in the energy range X < ET < Y , and has been gener-ated with the Madgraph event generator. The events contain 4 > N > 1 jets.These samples have a combined cross-section of σ = 4.81× 105 pb.

− The background sample TTbar Njet Et30-alpgen contains inclusive produc-tion of tt toN jets, with at least one jet of transverse energy ET > 30, has beengenerated with the Alpgen event generator. These samples have a combinedcross-section of σ = 2.07 × 102 pb. This sample is a principal sample.

− The background sample TTJets-madgraph contains inclusive production of ttquark pairs and its hadronization to jets, and has been generated with theMadgraph event generator. This sample is used as a cross-check sample of theTTbar Njet Et30-alpgen principal sample.

− The background samples W 0jet-alpgen and W Njet PtXtoY-alpgen containinclusive production of one W boson with N jets (1 < N < 5) in the energyrange X < pT < Y , and have been generated with the Alpgen event generator.These samples have a combined cross-section of σ = 3.93× 104 pb.

− The background samples Z 0jet-alpgen and Z Njet PtXtoY-alpgen containinclusive production of one Z boson with N jets (1 < N < 5) in the energyrange X < pT < Y , and have been generated with the Alpgen event generator.They have a combined cross-section of σ = 3.56× 103 pb.

− The background sample ZJets-madgraph contains inclusive production of aZ boson decaying to jets, and has been generated with the Madgraph eventgenerator. This sample was used to cross check the results of the samplesZ 0jet-alpgen and Z Njet PtXtoY-alpgen with another generator.

The selection is exactly the same as the one described in 3.4. It has not yetbeen further optimized, but this very optimization is currently in progress.

The (preliminary) results After the selection, the results presented in table 3.5are obtained.

The obtained purity of the final sample is 94.91%, for a signal efficiency selectionof 20.35%, with a final event yield of 3.96 events pb−1.. One should note that theseresults have not been yet optimized for the lower centre-of-mass energy, but arealready better than in the 1.6.12 version of CMSSW. These results are encouraging,since both the final purity and the selection efficiency have been improved, even as

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CHAPTER 3. VERSIONS OF THE Z0 → µµγ EVENT SELECTION

Sample Initial number of events Number of selected events Selection efficiency(per pb−1) (per pb−1) (in %)

Z0 → µµγ 19.45 3.96 20.35InclusiveMuPt15 1.22× 105 9.64× 10−2 7.90× 10−5

ZJets-alpgen 3.56× 103 1.91× 10−2 5.37 × 10−4

tt-alpgen 2.07 × 102 2.38× 10−2 1.15× 10−2

W + jets - alpgen 3.93× 104 7.24× 10−2 1.85× 10−4

γ + jets - alpgen 4.81× 105 4.24× 10−4 8.81× 10−8

Table 3.5. The main selection results for the study of Z0 → µµγ within the CMSSW2.2.9 framework.

more background events with more significant statistics have been studied. Notethat errors have not been computed on these quantities.

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Chapter 4

Photon energy scale with Z0→ µµγevents

My work presented below has been performed with the version 1.6.12 of CMSSW,and is currently under migration to the version 2.2.9. The idea, as described insection 2.4, is to exploit the fact that the µµγ invariant mass coming from thedecay Z0 → µµγ must compatible with mZ0 = 91.1876 ± 0.0021 GeV [2]. Becauseof the effects described in section 2.4, this is not quite correct. Since the muonkinematic variables are independently and precisely measured, we may assume theyare perfectly known. Then, only the imprecision or bias on the photon energy canexplain the shift in the µµγ mass peak with respect to mZ0 . We expect (from [24]),for 100 pb−1, to have ≈ 1.4 % accuracy of energy scale in each bin of 0.5 unit inpseudo-rapidity η. To have an accuracy of ≈ 0.5%, we expect to need determinationof the Z0 mass to 0.1 GeV, which we expect to have for 400 events per η bin.

4.1 Reconstruction of the µµγ system

We used here as a sample the set of events surviving the selection described in 3.4.There are 2950 events, which corresponds to an integrated luminosity of ≈ 560pb−1

(the cross section of the process is 26.16 pb at 14 TeV) if we take into account theselection efficiency (≈ 20%). This means we would obtain ≈ 520 events for 100pb−1

of data.Our chosen strategy was the following: We first chose to study the evolution of

mµµγ as a function of different kinematic variables: ηγ , pT γ , ET γ and φγ for theentire selected set of events (≈ 560 pb−1). The obtained 2D-histograms are shownin figure 4.1.

We can note that the distribution of the mµµγ points is:

− quite uniform as a function of φγ ,

− denser at the center of the detector as a function of ηγ ,

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γη-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

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Entries 2950Mean x 0.03508Mean y 91.12RMS x 1.838RMS y 1.777

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Figure 4.1. Distribution in the phase space of the mµµγ reconstructed invariantmass, as a function of ηγ , ET γ , pT γ and φγ . The Y -axis range corresponds to themass window of the selection described in 3.4, i.e. 87.2 GeV < mµµγ < 95.2 GeV.

− concentrated on the lowest energies as a function of pT γ and ET γ1

We can further plot profiles (figure 4.2) which resumes the information containedin the figure 4.1 in a more synthetic and readable way. The plot parameters areROOT’s defaults: the position of the point is the arithmetic mean, the error bar isspread/

√N . The particularity of this profile compared to ROOT’s defaults profiles

is that, in this case, the exact same number of events has been put in each bin(namely 100 events for the four upper histograms and 400 for the four lower ones).

We can note on this figure that:

− the mean is never shifted more than 1% from mZ0 ,

1One can note that for the massless photon, we have pT = ET . This was just a check that thetwo quantities are the same after the reconstruction algorithms. We will indifferently use one orthe other further on.

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γη-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

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φ VS 0ZM⁄γµµM

Figure 4.2. Profile in the phase space of the mµµγ reconstructed invariant massdivided by mZ0 . The plot parameters are ROOT’s defaults: the position of the pointis the arithmetic mean, the error bar is spread/

√N . These plots are showing bins

containing 100 points each (except the last bin, the most on the right of each profile,that contains only 50 events) for the 4 upper profiles, and for 400 points each for the4 lower profiles (except for the last bin, that contains only 150 events). So the widthis different for each bin. The zone in η between the green vertical lines represent thezone of the ECAL that is in the endcap but not covered by the preshower (cf. figureC.2). The brown zones represent the “cracks” between the crystal supermodules inη. 47

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CHAPTER 4. PHOTON ENERGY SCALE WITH Z0 → µµγ EVENTS

− the shift from mZ0 is more significant in the endcap (especially EE-),

− we have many more photons in the region 10 GeV < pT γ < 30 GeV,

− the mµµγ is uniform as a function of φ, as expected,

− the error bar has approximately the same size for each bin, so we don’t expecttoo much discrepancy between the spread of the data point for a given bin inη, φ or pT ,

− there is a clear trend towards higher masses as a function of ETWe can see from these results that the reconstruction software is already cor-

rectly handling photons, if the detector simulation perfectly represents the realdetector, which is most probably not the case.

4.2 Fit of the µµγ invariant mass in the different binsThe most correct function to describe the mµµγ distribution would in theory bea Breit-Wigner distribution2 (which represents the natural “physical” spread) con-voluted with a Crystal-Ball distribution3 (which represents the ECAL’s response).However, this convolution is difficult to implement for technical reasons. As a firstapproximation, it is possible to use a Breit-Wigner distribution added with a secondorder polynomial, as in [24].

Once it has been checked that the previous plots are correct, we can further tryto fit in each bin in η, φ, ET the mµµγ distribution with first a Gaussian distribution.Once the work on this Gaussian fitting would be completed, the next step will beto try with the Breit-Wigner distribution added with a second order polynomialfitting, as stated above.

We only presented here the work on the Gaussian distribution, because a fewmore checks about the robustness of the fits on our data have to be done (mostlyconcerning binning issues, as discussed below) before moving to the Breit-Wignerfitting.

In the note [24], a precision of 0.1GeV on mµµγ , corresponding to a precision of0.5% on the photon energy scale, was estimated to be obtained with approximately400 events.

The work presented thereafter will allow us to verify this “back of the envelope”calculation.

4.2.1 Gaussian fittingWe fit the data with the following Gaussian:

f(x) = A· exp (x− (x+ δx))2

2 (σ + δσ)2

2More information on the Breit-Wigner distribution are available in the appendix B.3.3More information on the Crystal-Ball distribution are available in the appendix B.4.

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4.2. FIT OF THE µµγ INVARIANT MASS IN THE DIFFERENT BINS

where:

− x (mean) is the value of the mean of the Gaussian fitting of the reconstructedinvariant mass mµµγ

− δx (error) is the error of the fit on the Gaussian fitting of the reconstructedinvariant mass mµµγ

− σ (sigma) is the standard deviation of the Gaussian fitting of the reconstructedinvariant mass mµµγ

− δσ (deltaSigma) is the error on the standard deviation of the Gaussian fittingof the reconstructed invariant mass mµµγ

In addition, we define the following:

− x−mZ0 (shift) is the energy shift between the mean of the fitted Gaussian ofthe reconstructed invariant mass and the expected invariant mass mZ0

− χ2/ndf (chi2) is the fit adequation with the Gaussian hypothesis of the datapeak

− σ/x is a pseudo-normalization of the standard deviation which is commonlyused. It was not used for the results presented here.

We can see in figure 4.3 the histogram containing all 2 950 events. When we fitthis mass spectrum, we can see that the Gaussian is not centered on mZ0 but isshifted of x −mZ0 = −86.56 MeV. The mean of the fit has been determined witha precision δx = 43.35 MeV, so the shift is physically meaningful, since it is greaterthan the precision on the mean4.

We made bins of equal statistics in order to evaluate what is the minimal inte-grated luminosity compulsory to obtain the claimed precision on the Z0 mass peak.A typical fit result is shown in figure 4.4, for a test bin in each three variables (η,ET , φ) containing 100 events, with 50 bins for the mass spectrum for the upperhistograms and 20 bins for the lower ones. The “random” population represents arandom set of events, like in figure 4.3. The typical histograms for 400 events arealso available in figure 4.5.

We made this fit automatically on every bin of n events (we present here theresults for the cases n = 100, 400 events, for 50 and 20 bins in mass window for thefitting. The raw averaged results of the cases n = 50, 500, 560 events are availablein the appendix D, for 10 to 50 bins in the mass window).

We present thereafter the values of x (figure 4.6), x−mZ0 (figure 4.7), δx (figure4.8), χ2/ndf (figure 4.11), σ (figure 4.9) and δσ (figure 4.10) averaged for all the

4To start working on quantitative physics results, however, it is conventionnaly asked for| x−mZ0

δx| > 3

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88 89 90 91 92 93 94 95

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/ ndf 2χ 81.45 / 47Prob 0.001352Constant 2.46± 96.32 Mean 0.0± 91.1 Sigma 0.04± 1.99

mumugammaInvMass

Figure 4.3. Gaussian fit of the reconstructed mass mµµγ for all the 2950 events.The mean of the fit is x = 91.10 GeV and the standard deviation is σ = 1.99 GeV.We then have a shift from mZ0 of x −mZ0 = −86.56 MeV, where the error on thedetermination of the mean is δx = 43.35MeV. The shift is then something noticeableand not some artifact due to the lack of precision of the shift, since |x−mZ0 | > δx.

possible bins containing n = 100 events in black and n = 400 events in red5, fora fitting in the mass window containing 50 bin for the upper histograms, and 20for the lower ones. Note that we do not fit the last bin if it contains less than therequired n events.

The fitted value is correctly dispersed around the central value of mZ0 . We cannote the improvement by going from n = 100 events (in black) to n = 400 events(in red).

As shown in figure 4.8, we can see that the error on the determination of the meanof the Gaussian distribution x largely improved by going from n = 100 events (inblack) to n = 400 events (in red). We gain around 200MeV in precision whatever thevariable. There is also noticeable changes for n = 100 when fitting in a 20 bins masswindow instead of 50. However, we aim to obtain a precision of 0.1GeV = 100MeV.One can note on this figure that the precision we obtain is looser that the expected100 MeV, and is of the order of 120 MeV as shown in tables 4.1 for a Gaussian and50 bins for the mass spectrum (see discussion below) and 4.2 for 20 bins. n = 400events is then not enough to claim the expected precision.

As shown in figure 4.9, the natural width of the fitted invariant reconstructedmass mµµγ stands around 2.8 GeV for n = 100 events (in black) and around 2 GeV

5For a total of 2950 events, we have E(2950/100) = 29 possible bins containing 100 events, andE(2950/400) = 7 possible bins containing 400 events.

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for 100 random events (bin 2)γµµM

Figure 4.4. Typical fits for 100 events per bin in η, ET , φ and random distributions.There are 50 bins in the energy range 87.2GeV < mµµγ < 95.2GeV for the four upperhistograms, and 20 bins in the energy range for the four lower ones.

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Figure 4.5. Typical fits for 400 events per bin in η, ET , φ and random distributions.There are 50 bins in the energy range 87.2GeV < mµµγ < 95.2GeV for the four upperhistograms, and 20 bins in the energy range for the four lower ones.

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Figure 4.6. Distribution of the Gaussian fitted mean x for bins containing 100events (in black) or 400 events (in red), for 50 bins for the mass spectrum for theupper histogram and 20 bins for the lower one. The X-axis is in GeV, and thehistograms have been normalized to 1.

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Entries 29Mean 3.186RMS 266.6

η for sorted bins in 0Z - mxFitSummary :

fitSummaryHist[1][0][1]

Entries 7Mean -89.56RMS 132.7

fitSummaryHist[1][0][1]

Entries 7Mean -89.56RMS 132.7

fitSummaryHist[1][1][0]

Entries 29Mean -75.92RMS 332.8

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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fitSummaryHist[1][1][0]

Entries 29Mean -75.92RMS 332.8

T for sorted bins in E0Z - mxFitSummary :

fitSummaryHist[1][1][1]

Entries 7Mean -99.48RMS 71.32

fitSummaryHist[1][1][1]

Entries 7Mean -99.48RMS 71.32

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Entries 29Mean 32.75RMS 294.9

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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Entries 29Mean 32.75RMS 294.9

φ for sorted bins in 0Z - mxFitSummary :

fitSummaryHist[1][2][1]

Entries 7Mean -71.18RMS 123.6

fitSummaryHist[1][2][1]

Entries 7Mean -71.18RMS 123.6

fitSummaryHist[1][3][0]

Entries 29Mean -33.42RMS 267.4

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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Entries 29Mean -33.42RMS 267.4

for random bins0Z - mxFitSummary :

fitSummaryHist[1][3][1]

Entries 7Mean -116RMS 95.35

fitSummaryHist[1][3][1]

Entries 7Mean -116RMS 95.35

fitSummaryHist[1][0][0]

Entries 29Mean -4.033RMS 278.7

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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fitSummaryHist[1][0][0]

Entries 29Mean -4.033RMS 278.7

η for sorted bins in 0Z - mxFitSummary :

fitSummaryHist[1][0][1]

Entries 7Mean -63.23RMS 89.55

fitSummaryHist[1][0][1]

Entries 7Mean -63.23RMS 89.55

fitSummaryHist[1][1][0]

Entries 29Mean -63.49RMS 257.3

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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Entries 29Mean -63.49RMS 257.3

T for sorted bins in E0Z - mxFitSummary :

fitSummaryHist[1][1][1]

Entries 7Mean -122RMS 98.66

fitSummaryHist[1][1][1]

Entries 7Mean -122RMS 98.66

fitSummaryHist[1][2][0]

Entries 29Mean -5.853RMS 291.1

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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Entries 29Mean -5.853RMS 291.1

φ for sorted bins in 0Z - mxFitSummary :

fitSummaryHist[1][2][1]

Entries 7Mean -70.53RMS 96.15

fitSummaryHist[1][2][1]

Entries 7Mean -70.53RMS 96.15

fitSummaryHist[1][3][0]

Entries 29Mean -96.31RMS 355.1

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

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Entries 29Mean -96.31RMS 355.1

for random bins0Z - mxFitSummary :

fitSummaryHist[1][3][1]

Entries 7Mean -79.15RMS 87.33

fitSummaryHist[1][3][1]

Entries 7Mean -79.15RMS 87.33

Figure 4.7. Distribution of the Gaussian fitted shift with mZ0 mµµγ − mZ0 forbins containing 100 events (in black) or 400 events (in red), for 50 bins for the massspectrum for the upper histogram and 20 bins for the lower one. The X-axis is inMeV, and the histograms have been normalized to 1.

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Entries 29Mean 378.8RMS 52.05

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Entries 29Mean 378.8RMS 52.05

η for sorted bins in xδFitSummary :

fitSummaryHist[2][0][1]

Entries 7Mean 123RMS 17.2

fitSummaryHist[2][0][1]

Entries 7Mean 123RMS 17.2

fitSummaryHist[2][1][0]

Entries 29Mean 408.6RMS 61.68

0 50 100 150 200 250 300 350 400 450 5000

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fitSummaryHist[2][1][0]

Entries 29Mean 408.6RMS 61.68

T for sorted bins in ExδFitSummary :

fitSummaryHist[2][1][1]

Entries 7Mean 117.3RMS 12.66

fitSummaryHist[2][1][1]

Entries 7Mean 117.3RMS 12.66

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Entries 29Mean 412.4RMS 56.84

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Entries 29Mean 412.4RMS 56.84

φ for sorted bins in xδFitSummary :

fitSummaryHist[2][2][1]

Entries 7Mean 116.9RMS 6.688

fitSummaryHist[2][2][1]

Entries 7Mean 116.9RMS 6.688

fitSummaryHist[2][3][0]

Entries 29Mean 389.8RMS 56.51

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Entries 29Mean 389.8RMS 56.51

for random binsxδFitSummary :

fitSummaryHist[2][3][1]

Entries 7Mean 121.9RMS 14.97

fitSummaryHist[2][3][1]

Entries 7Mean 121.9RMS 14.97

fitSummaryHist[2][0][0]

Entries 29Mean 255.5RMS 47.59

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Entries 29Mean 255.5RMS 47.59

η for sorted bins in xδFitSummary :

fitSummaryHist[2][0][1]

Entries 7Mean 120.6RMS 12.93

fitSummaryHist[2][0][1]

Entries 7Mean 120.6RMS 12.93

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Entries 29Mean 249.2RMS 55.43

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Entries 29Mean 249.2RMS 55.43

T for sorted bins in ExδFitSummary :

fitSummaryHist[2][1][1]

Entries 7Mean 119.8RMS 11.94

fitSummaryHist[2][1][1]

Entries 7Mean 119.8RMS 11.94

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Entries 29Mean 262RMS 54.09

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Entries 7Mean 119.6RMS 6.205

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Entries 7Mean 119.6RMS 6.205

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Entries 29Mean 254.4RMS 76.5

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Entries 29Mean 254.4RMS 76.5

for random binsxδFitSummary :

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Entries 7Mean 118.9RMS 16.61

fitSummaryHist[2][3][1]

Entries 7Mean 118.9RMS 16.61

Figure 4.8. Distribution of the Gaussian fitted error on the mean δx for binscontaining 100 events (in black) or 400 events (in red), for 50 bins for the massspectrum. The X-axis is in MeV, and the histograms have been normalized to 1.

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Entries 29Mean 2.948RMS 0.5675

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Entries 29Mean 2.948RMS 0.5675

η for sorted bins in σFitSummary :

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Entries 7Mean 1.939RMS 0.1797

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Entries 7Mean 1.939RMS 0.1797

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Entries 29Mean 2.831RMS 0.8849

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Entries 29Mean 2.831RMS 0.8849

T for sorted bins in EσFitSummary :

fitSummaryHist[4][1][1]

Entries 7Mean 1.896RMS 0.1342

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Entries 7Mean 1.896RMS 0.1342

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Entries 29Mean 2.796RMS 0.5156

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RMS 0.07695

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Mean 1.897

RMS 0.07695

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Entries 29Mean 2.716RMS 0.4772

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Entries 29Mean 2.716RMS 0.4772

for random binsσFitSummary :

fitSummaryHist[4][3][1]

Entries 7Mean 1.912RMS 0.1303

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Entries 7Mean 1.912RMS 0.1303

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Entries 29Mean 1.975RMS 0.2901

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Entries 29Mean 1.975RMS 0.2901

η for sorted bins in σFitSummary :

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Entries 7Mean 1.982RMS 0.1435

fitSummaryHist[4][0][1]

Entries 7Mean 1.982RMS 0.1435

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Entries 29Mean 1.978RMS 0.3973

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Entries 29Mean 1.978RMS 0.3973

T for sorted bins in EσFitSummary :

fitSummaryHist[4][1][1]

Entries 7Mean 1.96RMS 0.1164

fitSummaryHist[4][1][1]

Entries 7Mean 1.96RMS 0.1164

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Entries 29Mean 1.952RMS 0.2085

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Entries 29Mean 1.952RMS 0.2085

φ for sorted bins in σFitSummary :

fitSummaryHist[4][2][1]

Entries 7Mean 1.969RMS 0.1055

fitSummaryHist[4][2][1]

Entries 7Mean 1.969RMS 0.1055

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Entries 29Mean 1.917RMS 0.4038

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Entries 29Mean 1.917RMS 0.4038

for random binsσFitSummary :

fitSummaryHist[4][3][1]

Entries 7Mean 1.98RMS 0.1712

fitSummaryHist[4][3][1]

Entries 7Mean 1.98RMS 0.1712

Figure 4.9. Distribution of the Gaussian fitted standard deviation σ for bins con-taining 100 events (in black) or 400 events (in red), for 50 bins for the mass spectrumfor the upper histogram and 20 bins for the lower one. The X-axis is in GeV, and thehistograms have been normalized to 1.

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Entries 29Mean 665.8RMS 199.1

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Entries 29Mean 665.8RMS 199.1

η for sorted bins in σδFitSummary :

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Entries 7Mean 130RMS 28.63

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Entries 7Mean 130RMS 28.63

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Entries 29Mean 639.2RMS 153.6

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Entries 29Mean 639.2RMS 153.6

T for sorted bins in EσδFitSummary :

fitSummaryHist[5][1][1]

Entries 7Mean 119.6RMS 12.53

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Entries 7Mean 119.6RMS 12.53

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Entries 29Mean 645.1RMS 142.5

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Entries 29Mean 645.1RMS 142.5

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Entries 7Mean 119.6RMS 12.76

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Entries 7Mean 119.6RMS 12.76

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Entries 29Mean 657.5RMS 172.7

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Entries 29Mean 657.5RMS 172.7

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Entries 7Mean 124.2RMS 17.1

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Entries 29Mean 322.5RMS 129.6

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Entries 29Mean 322.5RMS 129.6

η for sorted bins in σδFitSummary :

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Entries 7Mean 123.9RMS 22.78

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Entries 29Mean 326.2RMS 146.5

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Entries 29Mean 326.2RMS 146.5

T for sorted bins in EσδFitSummary :

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Entries 7Mean 122.4RMS 8.582

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Entries 29Mean 304.8RMS 97.88

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Entries 29Mean 304.8RMS 97.88

φ for sorted bins in σδFitSummary :

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Entries 7Mean 124.1RMS 16.77

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Entries 7Mean 124.9RMS 20.44

fitSummaryHist[5][3][1]

Entries 7Mean 124.9RMS 20.44

Figure 4.10. Distribution of the Gaussian fitted error on the standard deviation σfor bins containing 100 events (in black) or 400 events (in red), for 50 bins fot themass spectrum for the upper histogram and 20 bins for the lower one. The X-axis isin MeV, and the histograms have been normalized to 1.

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for n = 400 events (in red). The natural width of the Z0 boson is[2] 2.4952 GeV.The improvement from n = 100 events (in black) to n = 400 events (in red) is herenot so straightforward. The expected natural width is too large for n = 100 events,but this was expected due to the lack of statistics. The fact that the natural widthis not large enough for n = 400 events is due to the limitation of the fitting functionitself, as discussed thereafter, since it does remain stable for a lower number of binsin the mass window (20 instead of 50). The fitted error on the natural width (figure4.10) behaves as expected: it improves with more statistics, and improves for alower number of bins for low statistics.

We can see in figure 4.11 that the goodness of the fit improves with the numberof statistics. However, even for n = 400 events, the distribution of the χ2 is notcentered exactly on 1. This is due to the fact that the Gaussian distribution doesnot describe accurately our data, as discussed earlier.

To resume these results, we can see that we have statistical fluctuation even witha choice of an event quantity to work with (n = 100), and significant differencesbetween two event quantities (n = 100, 400), or two different binnings (20, 50).Recall that our goal for the moment is to obtain a precision of 0.1 GeV on themµµγ reconstructed invariant mass. In table 4.1 are presented the averages of thefit parameters for a bin of n = 100, 400 events for 50 bins.

This gives a raw idea of the results we can obtain and of the dependence ofthe precision of the fit as a function of the number of events considered. However,we put aside that the typical fits shown in figure 4.4 are not very good. Indeedsuch plots have 50 bins for the mass spectrum. The problem is now to find theoptimum situation, for the number of bins, so that the fit becomes stable and givebinning-independent results. This will give more reliable and stable results aboutthe correction to apply to the photon objects. This step does matter, since we needto have stable results with the Gaussian fitting before trying out the Breit-Wignerfitting, in order to compare comparable and robust results.

The average results for 20 bins in the mass spectrum are presented in table 4.2,while the plots have already been shown.

We can see that the binning of the mass spectrum can strongly influence thefitting at low statistics: we can reach a precision of ≈ 270 MeV with 20 bins forn = 100 events. The results do not change much however for n = 400 events. As ourgoal is to obtain the best precision with the minimum of statistics, the binning is anissue. We are currently trying to find the best binning to have binning-independentfits, i.e. robust and stable fits. This step is some achievement desired before aimingto fit the data with more complex functions.

The work presented here could not unfortunately be completed. However, I willcontinue working on this very topic as part of my PhD thesis, that I will start in thesame laboratory this autumn. We have already obtained a precision of 120 MeV onthe Z0 peak with 400 events, and it seems ≈ 560 events would be needed in orderto reach the claimed precision (cf. aditional results in the appendix D).

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0.8

0.9

1

fitSummaryHist[3][2][0]

Entries 29

Mean 0.6726

RMS 0.09719

φ^2 / ndf for sorted bins in χFitSummary :

fitSummaryHist[3][2][1]

Entries 7Mean 1.14RMS 0.213

fitSummaryHist[3][2][1]

Entries 7Mean 1.14RMS 0.213

fitSummaryHist[3][3][0]

Entries 29Mean 0.6437RMS 0.1003

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fitSummaryHist[3][3][0]

Entries 29Mean 0.6437RMS 0.1003

^2 / ndf for random binsχFitSummary :

fitSummaryHist[3][3][1]

Entries 7Mean 1.181RMS 0.205

fitSummaryHist[3][3][1]

Entries 7Mean 1.181RMS 0.205

Figure 4.11. Distribution of the χ2/ndf of the fits for bins containing 100 events (inblack) or 400 events (in red), for 50 bins fot the mass spectrum for the upper histogramand 20 bins for the lower one. If close to 1, this means the data is Gaussian-likedistributed. The histograms have been normalized to 1.

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CHAPTER 4. PHOTON ENERGY SCALE WITH Z0 → µµγ EVENTS

50 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.1 −86.56 43.35 1.733 1.99 44.81 0.02184100 evtsηγ 91.23 44.31 608.4 0.6542 2.948 968.3 0.0323pT γ 91.11 −75.92 576.5 0.6579 2.831 957.1 0.03106φγ 91.18 −6.606 538 0.6726 2.796 854.1 0.03067

random 90.55 −633.6 1406 0.6437 3.37 1442 0.0389400 evtsηγ 91.1 −89.56 123 1.099 1.939 130 0.02129pT γ 91.09 −99.48 117.3 1.182 1.896 119.6 0.02082φγ 91.12 −71.18 116.9 1.14 1.897 119.6 0.02082

random 91.07 −116 121.9 1.181 1.912 124.2 0.02099

Table 4.1. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 50 bins.

20 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.12 −68.49 43.83 2.584 2.023 46.2 0.0222100 evtsηγ 91.14 −46.45 271.2 0.9594 1.975 322.5 0.02168pT γ 91.12 −63.49 270.4 1.042 1.978 326.2 0.02171φγ 91.18 −5.853 262 1.186 1.952 304.8 0.02141

random 91.14 −49.44 270.3 1.051 1.917 330.6 0.02103400 evtsηγ 91.12 −63.23 120.6 1.172 1.982 123.9 0.02175pT γ 91.07 −122 119.8 1.471 1.96 122.4 0.02152φγ 91.12 −70.53 119.6 1.471 1.969 124.1 0.02161

random 91.11 −79.15 118.9 1.382 1.98 124.9 0.02173

Table 4.2. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 20 bins.

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Chapter 5

Comments and Outlook

Several improvements and further studies are needed for both the selection of theZ0 → µµγ events and the energy scale correction, as presented in the previoussections.

Concerning the selection, we need to migrate to the CMSSW 3.X.Y versions,currently in development. The Monte-Carlo productions are in progress and shouldbe available for the autumn. An active collaboration with Caltech is planned forthis new iteration, in order to benefit from improvements done to the selectionsfrom both sides.

An integration of the selection within CMSSW (as a package) is also a goal sincethe selection of Z0 → µµγ events starts to be stable enough to be used.

Concerning the energy scale, the following improvements and studies are manda-tory:

− We need to do a systematic study of the number of events per bin on theresults.

− We need to do a systematic study of the influence of the binning within a binin η, φ, pT , random, in order to make the fit binning-independent.

− We need to determine the optimum number of events yiedling which will allowus to justify the energy scale corrections on real data.

− We should plot the figure 4.2 but with the Gaussian fit parameters or theBreit-Wigner fit parameters instead of ROOT’s default, in order to visualizethe evolution of the mµµγ invariant mass.

− Continue the study of energy scale corrections in full 2.2.9 framework (a mi-gration is in progress).

− We need to correlate this work with the Monte-Carlo photon correction schemeactually under study, since we may have to implement yet another correction.

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CHAPTER 5. COMMENTS AND OUTLOOK

− We need to aim for integrating this selection and this energy scale correctionwithin the CMSSW framework, and also within the PAT (Physics AnalysisToolkit) package syntax.

− We assumed the muons were perfectly reconstructed. Only ≈ 10 pb−1 of datais needed to calibrate them, so it should not be that bad of an approximation,but this should be checked anyway.

− We need to verify the kinematic propgation of the precision on the µµγ peakposition to the precision on the photon enery, and likewise, that of the shiftin µµγpeak position to that of photon energy.

− As a final step, we should of course correct the photons’ energy scale, andincorporate this machinery into the photon correction class.

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Chapter 6

Conclusion

The work that has been presented here is still in progress, but significant results havealready been obtained: We have a selection of Z0 → µµγ events with a selectionefficiency of 20% which leads to a purity better than 90%, with a final event yield ofaround 4 events pb−1 for a centre-of-mass energy of 10TeV. Concerning the energyscale correction on the photons, we now know that a precision of around 120 MeVon the Z0 mass peak may be reached with 400 events, which should be obtainedwith less than 100 pb−1 of data.

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Bibliography

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[2] C. Amsler et al. Review of particle physics. Phys. Lett., B667:1, 2008.

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[9] CMS Collaboration. CMS physics technical design report volume I : Detectorperformance and software. Technical report, CERN/LHCC 2006-001 CMSTDR 8.1, 2006.

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BIBLIOGRAPHY

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[15] Stephen P. Martin. A Supersymmetry Primer. 1997.

[16] Kenneth D. Lane. Technicolor 2000. 2000.

[17] Marcela S. Carena and Howard E. Haber. Higgs boson theory and phenomenol-ogy. ((V)). Prog. Part. Nucl. Phys., 50:63–152, 2003.

[18] Salavat Abdullin et al. Tevatron-for-LHC Report: Preparations for Discoveries.2006.

[19] Michelangelo L. Mangano, Mauro Moretti, Fulvio Piccinini, Roberto Pittau,and Antonio D. Polosa. ALPGEN, a generator for hard multiparton processesin hadronic collisions. JHEP, 07:001, 2003.

[20] Riccardo Paramatti et al. Ecal energy scale/calibration, 2009. Electron andphoton commissioning workshop, 16.06.2009.

[21] S. Agostinelli et al. GEANT4: A simulation toolkit. Nucl. Instrum. Meth.,A506:250–303, 2003.

[22] Yurii Maravin et al. ECAL supercluster energy corrections/scale and errorparametrization: derivation from data. CMS, Egamma group: Electron andphoton commissioning workshop, 2009.

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[28] The CMS offline workbook. https://twiki.cern.ch/twiki/bin/view/CMS/WorkBook.

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Appendix A

Abbreviations

BSM Beyond the Standard Model: theories aiming to be more general or differentthan the Standard Model.

CERN Organisation Europeenne pour la Recherche Nucleaire: the world’s largestorganisation for scientific research.

CMS Compact Muon Solenoid: one the two general-purpose experiments at theLHC.

CMSSW CMS SoftWare: the main simulation, reconstruction and analysis com-puting framework used to handle and analyze the data generated by the CMSexperiment.

DBS Data Bookkeeping System[39]: a database that indexes event-data for theCMS collaboration. The primary functionality is to provide cataloging byproduction and analysis operations. It also lists collaboration-wide Monte-Carlo productions.

GEANT GEometry ANd Tracking: the principal software used in particle physicsto simulate the passage of particles through matter using Monte-Carlo meth-ods.

GUT Grand Unified Theory: theory aiming to unify both the Standard Model andEinstein’s General relativity theory.

LHC Large Hadron Collider: hadron particle accelerator and collider, planned tostart during autumn 2009.

QCD Quantum Chromodynamics: the quantum theory describing the strong in-teraction.

QED Quantum Electrodynamics: the quantum theory describing the electromag-netic interactions.

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APPENDIX A. ABBREVIATIONS

ROOT Object oriented C++ package developed at CERN providing a set of statis-tical tools to analyze experimental data from high-energy physics experiments.

SUSY SUperSYmmetry: theory in which any particle of the Standard Model wouldhave a ”Supersymmetric” partner, with identical quantum numbers except forspin (all fermions will be transformed to bosons and vice-versa).

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Appendix B

Physics-related definitions and context

B.1 Natural Units

We commonly and conventionally use in particle physics the so-called natural unitsand not the usual international unit system.

The three basic physical quantities in the international units system are thelength, measured in m, the mass, measured in kg and the time, measured in s. Allother quantities and units can be derived from these three.

In natural units, the set of units is the electron-Volt eV, the Planck constant~ = 1.054× 10−34 Js and the speed of light in vacuum c = 299 792 458ms−1. Hence,since ~ and c are now units and not quantities anymore, we do not write them inequations anymore.

This is equivalent to setting ~ = c = 1 as often read in textbooks, which is in apurely mathematical sense true, but conceptually and physically incorrect.

For example, the Z0 mass[2] is expressed in eV instead of eV.c−2: mZ0 =91.1876 GeV

B.2 Relativistic kinematics

Minkowski metric and four momentum For describing particles in the frame-work of special relativity, we have two equivalent descriptions: either space-timecoordinates (t, x, y, z) or energy-momentum coordinates (E, px, py, pz). Since weare considering particles also as quantum objects, the latter description make moresense.

We consider the so-called Minkowski metric:1 0 0 00 −1 0 00 0 −1 00 0 0 −1

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APPENDIX B. PHYSICS-RELATED DEFINITIONS AND CONTEXT

and, along with this metric, we consider the four-momentum of a particle Pµ =(E, ~p).

Lorentz invariance The norm of this four-momentum is then || (Pµ) || =√E2 − ~p2.

We define a quantity as Lorentz-invariant, if its norm is the same whatever theGalilean frame of reference.

One can determine the mass of a particle A by knowing the energy E and the3-momentum ~p of its decay products b1 and b2:

m2A =

(Pµb1 + Pµb2

)2

This is obtained because, in the centre-of-mass frame (where the particle isobviously at rest ~p = 0), we have for a particle of mass m: (Pµ)2 = E2 = m2

(which corresponds to the famous Einstein equation E = m). Because we assumedconservation of both energy and momentum, the four-momentum is also a Lorentz-invariant quantity and we have the energy-momentum relation E2 = ~p2 +m2.

Invariant mass For this reason, by using this formula, we can reconstruct themass of a particle too short-lived to be directly detected. By knowing the four-momentum of each decay product (i.e. energy, which is technically known with thecalorimeters, and momentum, which is proportional to the curvature of the particlein the magnetic field), we are able to compute the so-called invariant mass.

B.3 Breit-Wigner distributionThe relativistic Breit-Wigner distribution (figure B.1) describes the mass peak inthe relativistic case. Indeed, because most particles are unstable, they have a non-zero decay width Γ, i.e. there is a natural uncertainty on the mass of the particle.This can be viewed as a consequence of Heisenberg’s uncertainty principle:

∆E· ∆t >~2

.The general Breit-Wigner formula is the following:

ρ(E) ∼ 1(E2 −M2)2 +M2Γ2

We will observe a Breit-Wigner distribution, e.g. in the case studied here, whenplotting the reconstructed invariant mass of the Z0 in the process Z0 → µµγ withthe information on the muons and photon.

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B.4. CRYSTAL-BALL DISTRIBUTION

Figure B.1. Breit-Wigner distribution

B.4 Crystal-Ball distributionThe Crystal-Ball distribution typically describes the response of a scintillating crys-tal detector (as is in our case the ECAL). Its name comes from the Crystal-Balldetector, which was on the SPEAR particle accelerator, as a part of the StanfordLinear Accelerator Center.

The Crystal-Ball function is given by:

f(x, α, n, x, σ) = N ·

e−(x−x)2

2σ2 , forx−xσ > −αA·

(B − x−x

σ

)−n, forx−xσ 6 −α

where: A =(n|α|

)n· e−

|α|22

B = n|α| − |α|

with N as a normalization factor, and α, n, x, σ are parameters fitted with thedata.

This function describes a line shape composed of a central Gaussian, with apower law tail to low energy joined to the Gaussian. The distribution is shown infigure B.2

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APPENDIX B. PHYSICS-RELATED DEFINITIONS AND CONTEXT

Figure B.2. Typical shape of a Crystal-Ball distribution. The red distributioncorresponds to α = 10, the green one to α = 1 and the blue one to α = 0.1.

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Appendix C

Accelerator and detector-relateddefinitions and context

C.1 AcceleratorIn the beam, protons are grouped in 2 808 bunches. The organisation of the beamin bunches is a convenient way to raise the luminosity.

The cross-section of a process represents the probability of its production.Is has the dimension of a surface and is usually expressed in subunits of barn:1 b = 10−28 m2

The instantaneous luminosity is defined by:

L = fn2

S

where f = 40 MHz is the bunch crossing frequency, n = 1.1 × 1011 is the averagenumber of protons per bunch and S = 16 µm2 is the beam RMS section. Thenominal (ultimate) luminosity of the LHC is then:

L = 1034 cm−2s−1 ≡ 10−2 pb−1s−1

but for the start up the luminosity will only be:

L = 1033 cm−2s−1

For comparison, the Tevatron, which is to this day the most powerful acceleratorrunning, has a luminosity of L = 3.2× 1032 cm−2s−1.

The integrated luminosity is defined in a straight-forward way as the integralof luminosity over time:

L =∫Ldt

It represents the amount of accumulated data. For example, during a week(≈ 600 000 s) at nominal luminosity, the LHC will accumulate around 6 fb−1 ofdata, which is what the Tevatron has accumulated in 5 years of running.

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APPENDIX C. ACCELERATOR AND DETECTOR-RELATED DEFINITIONS ANDCONTEXT

For the process Z0 → µµγ which has a cross-section of 26.16 pb at 14 TeV, wewould have with a selection efficiency of 20 %, 100 events after ≈ 19110 s for aninstantaneous luminosity of L = 1033 cm−2s−1.

C.2 CMS calorimetersThe calorimeters are named as follows:

H stands for the Hadronic calorimeter

E stands for the Electromagnetic calorimeter

as well as

B stands for the Barrel

E stands for the Endcap

This way, EE means Endcap part of the Electromagnetic calorimeter.We may add + and − notations for the endcaps: EE+ means Endcap part with

the z > 0 of the Electromagnetic calorimeter.

C.3 CMS coordinate systemIn order to locate the particles, we use a coordinate system (x, y, z). The origin ofthe frame is at the nominal collision point at the centre of the detector. The y-axispoints vertically towards the upward direction, the x-axis points radially towardsthe centre of the accelerator. The z-axis complete the basis in a direct way.

C.4 Azimuthal angle φThe azimuthal angle φ is measured in the direct way from the x-axis in the planx− y. The polar angle θ is measured from the z-axis.

C.5 Pseudo-rapidity ηPseudo-rapidity η (figure C.1) is defined by:

η = − ln[tan

2

)]Pseudo-rapidity is a relevant variable easier to use for some theoretical consider-

ations. Particles have trajectories fully included within the detector up to η = 2.4.The electromagnetic calorimeter goes up to η = 3.0 (cf. figure C.2).

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C.5. PSEUDO-RAPIDITY η

Figure C.1. Longitudinal view of the detector and the different values of η corre-sponding to the principal zones of the detector (η = 0 in the x− y plan, and η →∞on the z-axis)[9].

Figure C.2. View of the electromagnetic calorimeter (ECAL) and the correspondingvalues in terms of pseudo-rapidity η [9].

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APPENDIX C. ACCELERATOR AND DETECTOR-RELATED DEFINITIONS ANDCONTEXT

C.6 ∆RThe ∆R of two particles is defined as:

∆R =√

(∆η)2 + (∆φ)2

where {∆η = η1 − η2∆φ = φ1 − φ2

C.7 Transverse energy and momentumThe transverse energy ET and the transverse momentum pT are computed in thex− y plan. The full energy is defined as:

E = ET + Ez

The full (three-)momentum is defined as:

~p = ~pT + ~pz

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Appendix D

Raw results: CMSSW 1.6.12

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APPENDIX D. RAW RESULTS: CMSSW 1.6.12

10 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.12 −70.42 44.24 4.113 2.041 46 0.022450 evtsηγ 91.16 −22.72 410.2 0.9444 2.018 501.7 0.02214pT γ 91.09 −96.55 520 0.9796 2.193 657.2 0.02409φγ 91.15 −41.15 506.6 0.9446 2.066 898.1 0.02268

random 91.22 31.61 2046 0.9563 2.17 829.7 0.02375100 evtsηγ 91.16 −24.57 248.9 1.053 1.981 273 0.02173pT γ 91.1 −84 256.4 1.046 2.003 268.7 0.02199φγ 91.16 −28.14 236.8 1.069 1.916 241 0.02102

random 91.1 −87.38 271.2 1.217 2.005 297.3 0.022400 evtsηγ 91.13 −53.78 122.9 1.531 2.035 127.8 0.02233pT γ 91.07 −119.7 120 1.506 2.001 121.2 0.02197φγ 91.11 −79.59 120.5 1.614 2.016 125.9 0.02212

random 91.1 −86.84 122.8 1.873 2.04 129.3 0.0224500 evtsηγ 91.13 −55.07 108 1.465 2.025 110.8 0.02222pT γ 91.07 −120.9 107.4 1.639 2.007 108.7 0.02204φγ 91.1 −91.9 108 1.736 2.026 111.5 0.02224

random 91.11 −76.57 108.1 2.331 2.033 114.7 0.02232560 evtsηγ 91.12 −69.38 103.9 1.708 2.048 108.6 0.02248pT γ 91.08 −111.5 102.5 1.559 2.028 105 0.02226φγ 91.12 −69.81 100.7 1.815 2.014 104.5 0.02211

random 91.1 −87.87 102.6 1.947 2.037 107.3 0.02236

Table D.1. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 10 bins.

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20 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.12 −68.49 43.83 2.584 2.023 46.2 0.022250 evtsηγ 90.36 −826 1403 0.7875 2.809 1226 0.03427pT γ 92.12 931.5 1776 0.7637 3.005 1442 0.03119φγ 91.08 −111.8 1587 0.7874 2.87 1626 0.03165

random 90.49 −695.9 2495 0.7613 3.219 1471 0.03721100 evtsηγ 91.14 −46.45 271.2 0.9594 1.975 322.5 0.02168pT γ 91.12 −63.49 270.4 1.042 1.978 326.2 0.02171φγ 91.18 −5.853 262 1.186 1.952 304.8 0.02141

random 91.14 −49.44 270.3 1.051 1.917 330.6 0.02103400 evtsηγ 91.12 −63.23 120.6 1.172 1.982 123.9 0.02175pT γ 91.07 −122 119.8 1.471 1.96 122.4 0.02152φγ 91.12 −70.53 119.6 1.471 1.969 124.1 0.02161

random 91.11 −79.15 118.9 1.382 1.98 124.9 0.02173500 evtsηγ 91.14 −46.71 105.6 1.162 1.983 109.3 0.02176pT γ 91.07 −119.2 106 1.394 1.963 108.3 0.02156φγ 91.1 −88.89 108.2 1.461 2.007 111.8 0.02203

random 91.11 −80.91 105.3 1.561 1.987 111.5 0.02181560 evtsηγ 91.11 −76.05 101.8 1.301 2.006 105.6 0.02202pT γ 91.06 −127.1 101.1 1.404 1.985 104 0.0218φγ 91.14 −47.83 100.3 1.554 1.99 105.2 0.02183

random 91.11 −73.76 99.15 1.227 1.984 101.7 0.02178

Table D.2. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 20 bins.

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APPENDIX D. RAW RESULTS: CMSSW 1.6.12

30 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.1 −85.61 43.38 2.242 1.996 44.87 0.0219150 evtsηγ 91.99 801.9 1469 0.5765 3.386 1846 0.036pT γ 91.34 150.4 1723 0.5643 3.332 1952 0.03623φγ 91.21 24.71 2027 0.5657 3.502 2376 0.03837

random 90.87 −314.1 2131 0.5593 3.576 2004 0.04011100 evtsηγ 91.17 −21.22 334.6 0.8711 2.19 437.3 0.02403pT γ 91.17 −21.19 332.4 0.8775 2.185 433.8 0.02397φγ 91.16 −28.97 346.3 1.012 2.177 453.9 0.02389

random 91.25 63.2 366.5 0.8962 2.205 562 0.02417400 evtsηγ 91.1 −83.13 116.5 1.305 1.883 113.6 0.02067pT γ 91.04 −144.6 116.4 1.154 1.9 114.3 0.02087φγ 91.12 −71.04 118.9 1.243 1.963 124.9 0.02155

random 91.1 −82.83 115.2 1.374 1.901 114.7 0.02086500 evtsηγ 91.16 −28.34 102.4 1.461 1.896 102.5 0.0208pT γ 91.06 −131.8 104 1.251 1.91 102.2 0.02098φγ 91.08 −106.9 108.3 1.465 1.97 109.5 0.02163

random 91.11 −80.53 102.7 1.457 1.927 104.6 0.02115560 evtsηγ 91.1 −82.61 99.59 1.305 1.955 101 0.02146pT γ 91.05 −134.4 99.24 1.243 1.943 99.72 0.02134φγ 91.09 −92.72 99.91 1.424 1.953 101.3 0.02144

random 91.09 −93.54 97.43 1.242 1.933 96.35 0.02122

Table D.3. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 30 bins.

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40 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.12 −67.54 43.5 1.643 2.007 45.77 0.0220350 evtsηγ 91.38 190.5 2669 0.4307 3.876 2883 0.0423pT γ 91.35 162.9 3410 0.4344 4.341 3141 0.04764φγ 90.83 −355 3370 0.4324 4.565 3054 0.05164

random 90.88 −309.3 3869 0.42 4.63 3152 0.0514100 evtsηγ 91.14 −52.41 446.8 0.7706 2.55 657.6 0.02798pT γ 91.13 −57.18 438.8 0.7572 2.527 628.6 0.02774φγ 91.16 −24.58 421.6 0.8371 2.485 601.3 0.02726

random 91.02 −169.8 1255 0.7276 3.022 1260 0.03352400 evtsηγ 91.1 −86.56 116.4 1.046 1.9 117.1 0.02085pT γ 91.08 −107.7 117.4 1.156 1.914 120.8 0.02102φγ 91.13 −53.41 114 1.272 1.875 114.3 0.02057

random 91.06 −125 116.1 1.32 1.863 116.8 0.02046500 evtsηγ 91.12 −67.76 102.7 1.04 1.913 104 0.02099pT γ 91.08 −109.6 104.5 1.166 1.911 103.8 0.02098φγ 91.09 −100.9 105.7 1.265 1.93 105 0.02118

random 91.1 −86.87 101.8 1.289 1.904 105.8 0.0209560 evtsηγ 91.1 −86.2 98.51 1.135 1.935 99.53 0.02124pT γ 91.05 −134.2 98.98 1.182 1.931 100 0.02121φγ 91.14 −45.55 97.81 1.368 1.926 101.9 0.02114

random 91.13 −56.02 96.01 1.093 1.912 95.57 0.02099

Table D.4. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 40 bins.

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APPENDIX D. RAW RESULTS: CMSSW 1.6.12

50 bins < x > < x−mZ0 > < δx > < χ2/ndf > < σ > < δσ > < σ/x >GeV MeV MeV GeV MeV

2950 evts 91.1 −86.56 43.35 1.733 1.99 44.81 0.0218450 evtsηγ 91.36 172.4 3740 0.3454 4.695 4351 0.05114pT γ 90.85 −341 3431 0.3396 4.767 3714 0.05367φγ 90.79 −401 5061 0.3446 5.033 4164 0.05708

random 90.48 −708.4 2565 0.3556 4.428 3681 0.0513100 evtsηγ 91.23 44.31 608.4 0.6542 2.948 968.3 0.0323pT γ 91.11 −75.92 576.5 0.6579 2.831 957.1 0.03106φγ 91.18 −6.606 538 0.6726 2.796 854.1 0.03067

random 90.55 −633.6 1406 0.6437 3.37 1442 0.0389400 evtsηγ 91.1 −89.56 123 1.099 1.939 130 0.02129pT γ 91.09 −99.48 117.3 1.182 1.896 119.6 0.02082φγ 91.12 −71.18 116.9 1.14 1.897 119.6 0.02082

random 91.07 −116 121.9 1.181 1.912 124.2 0.02099500 evtsηγ 91.08 −104.6 103.6 1.138 1.878 102 0.02062pT γ 91.08 −110.2 103.9 1.087 1.884 102.3 0.02069φγ 91.11 −75.33 105.3 1.218 1.911 104.3 0.02097

random 91.1 −86.74 105.9 1.25 1.929 111.9 0.02117560 evtsηγ 91.07 −113.1 99.7 1.105 1.92 100 0.02108pT γ 91.06 −129.2 97.61 1.216 1.89 97.05 0.02076φγ 91.1 −84.54 98.67 1.319 1.901 99.02 0.02086

random 91.1 −86.1 98.94 1.107 1.918 99.82 0.02106

Table D.5. Results for N events per bin in η, pT and φ. The mµµγ bin contains Nevents fitted with 50 bins.

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