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The Event-Mixing Technique for Modeling the T¯T Background in a Search for Supersymmetry in the Di-Lepton Channel

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The Event-Mixing Technique for Modeling the T¯T Background in a Search for Supersymmetry in the Di-Lepton Channel The Event-Mixing Technique for Modeling the t¯t Background in a Search for Supersymmetry in the Di-Lepton Channel Dissertation zur Erlangung des Doktorgrades des Department Physik der Universit¨atHamburg vorgelegt von Hannes Schettler aus T¨ubingen Hamburg 2013 Gutachter der Dissertation: Dr. Isabell Melzer-Pellmann Prof. Dr. Peter Schleper Gutachter der Disputation: Dr. Isabell Melzer-Pellmann Jun.-Prof. Dr. Christian Sander Datum der Disputation: 20.08.2013 Vorsitzender des Pr¨ufungsausschusses: PD Dr. Michael Martins Vorsitzender des Promotionsausschusses: Prof. Dr. Peter Hauschildt Leiterin des Fachbereichs Physik: Prof. Dr. Daniela Pfannkuche Dekan der Fakult¨atf¨urMathematik, Informatik und Naturwissenschaften: Prof. Dr. Heinrich Graener Abstract In this thesis a search for Supersymmetry in the opposite-sign same-flavor di-lepton channel is presented. Data recorded by the CMS detector at the LHC accelerator corresponding to an integrated luminosity of 12:2 fb−1 at a center-of-mass energy of 8 TeV is analyzed. Events with at least two muons or two electrons with opposite charge, a significant transverse momentum imbalance, and at least one or at least two jets are selected. Supersymmetric particle decays are expected to form an edge-like structure in the di-lepton mass spectrum. The main background from Standard-Model processes is t¯t pair production. This background is estimated in a data- driven way using the event-mixing technique. Since event mixing is novel to estimate t¯t events, the method is validated in detail. In the analyzed data no significant excess w. r. t. the event-mixing prediction is observed. In a counting experiment as well as in a fit of the shape of the distribution the data is in agreement with the expectations from the Standard Model. Hence, exclusion limits are calculated in terms of number of events forming an edge in the di-lepton mass spectrum. Additionally, the results are interpreted within a simplified model spectrum, assuming direct gaugino production and a decay chain likeχ ~0 `~±`∓ χ~0`+`−. Limits are set on the masses of the supersymmetric 2 ! ! 1 particles. Kurzfassung In dieser Arbeit wird eine Suche nach Supersymmetrie im Zwei-Leptonen-Kanal mit gegens¨atz- lichen Vorzeichen und gleichem Flavor vorgestellt. Daten, aufgezeichnet vom CMS-Detektor am LHC-Beschleuniger, entspechend einer integrierten Luminosit¨at von 12:2 fb−1 bei einer Schwer- punktsenergie von 8 TeV, werden analysiert. Ereignisse mit mindestens zwei Myonen oder zwei Elektronen gegens¨atzlicher Ladung, einer signifikanten Imbalance des transversalen Impulses und mindestens ein oder mindestens zwei Jets werden selektiert. Von supersymmetrischen Teil- chenzerf¨allen wird erwartet, dass sie eine kantenf¨ormige Struktur im zwei-Leptonen-Massen- spektrum bilden. Der Hauptuntergrund an Standard-Modell-Prozessen ist t¯t-Paarproduktion. Dieser Untergrund wird Daten getrieben abgesch¨atzt mithilfe der Event-Mixing-Technik. Da Event-Mixing erstmalig zur Absch¨atzung von t¯t-Ereignissen benutzt wird, wird die Methode detailiert validiert. In den analysierten Daten wird keine signifikante Abweichung zur Event-Mixing-Vorhersage beobachtet. Sowohl in einem Z¨ahlexperiment als auch in einem Fit der Form der Verteilung sind die Daten in Ubereinstimmung¨ mit den Erwartungen des Standard-Modells. Daher werden Ausschlussgrenzen auf die Anzahl der Ereignisse errechnet, die eine Kante im Zwei-Leptonen- Massenspektrum bilden. Zus¨atzlich werden die Ergebnisse innerhalb eines simplified model " spectrum\ interpretiert, das von direkter Gaugino-Produktion und einer Zerfallskette wieχ ~0 2 ! `~±`∓ χ~0`+`− ausgeht. Die Ausschlussgrenzen werden auf die Massen der supersymmetrischen ! 1 Teilchen gesetzt. iii Contents 1. Introduction 1 2. Concepts and Recent Observations in Particle Physics3 2.1. The Standard Model of Particle Physics......................3 2.1.1. Particle Content of the Standard Model..................3 2.1.2. Gauge Interactions..............................6 2.1.3. Higgs Mechanisms.............................. 12 2.2. The Supersymmetric Extension of the Standard Model.............. 16 2.2.1. Problems of the Standard Model and Possible Solutions......... 18 2.2.2. Particle Content of Supersymmetric Models................ 22 2.2.3. Breaking Mechanism of Supersymmetry.................. 23 2.2.4. Searches for Supersymmetry......................... 24 3. The LHC and the CMS Experiment 29 3.1. The Large Hadron Collider............................. 29 3.1.1. The LHC Cavities and Magnets....................... 30 3.1.2. The Pre-Acceleration Chain......................... 31 3.1.3. The Experiments at LHC.......................... 32 3.2. The CMS Experiment................................ 33 3.2.1. The Tracking System............................ 34 3.2.2. Calorimetry.................................. 36 3.2.3. The Solenoid................................. 40 3.2.4. The Muon system.............................. 40 3.2.5. Triggering and Data Acquisition...................... 41 3.2.6. Data Quality Monitoring.......................... 42 3.2.7. The Scientific Program and Results Achieved so far........... 42 4. Object Reconstruction and Event Selection 47 4.1. Particle Flow..................................... 47 4.2. Physics Objects.................................... 49 4.2.1. Muons..................................... 49 4.2.2. Electrons................................... 51 4.2.3. Jets...................................... 52 4.2.4. Missing Transverse Energy......................... 58 4.2.5. Vertices and Pile-up............................. 61 4.3. Event and Object Selection............................. 62 4.3.1. Lepton Definition............................... 62 4.3.2. Jets and Hadronic Energy.......................... 64 4.3.3. Event Selection................................ 65 4.4. Event Numbers and Basic Distributions...................... 66 v Contents 5. The Event-Mixing Method 71 5.1. Kinematic Endpoints in Supersymmetric Decay Cascades............ 71 5.2. Concept of the Event-Mixing Method....................... 73 5.2.1. History of Event-Mixing Techniques.................... 73 5.2.2. t¯t Background Prediction based on Event Mixing............. 75 5.3. Method Validation with Simulated Events..................... 75 5.3.1. Event Kinematics in the Simulated t¯t Background............ 75 5.3.2. t¯t Spin Correlation.............................. 88 5.3.3. Contamination from Other Background Processes............ 91 5.3.4. Signal Contamination and Prediction Correlation............. 94 5.3.5. Effects of Event Selection Cuts....................... 95 5.3.6. Other MC Generators............................ 99 5.4. Digression: Angle-Momenta Mixing......................... 100 6. Search Results 107 6.1. Application of the Event-Mixing Method...................... 107 6.1.1. Prediction in Data vs. Prediction in MC.................. 110 6.2. Systematic Uncertainties............................... 111 6.2.1. Lepton Energy Scale............................. 112 6.2.2. Lepton-Lepton Spacial Separation..................... 113 6.2.3. Selection Cut Variation........................... 114 6.2.4. Different Monte-Carlo Samples....................... 114 6.2.5. Uncertainties in MadGraph t¯t Simulation................ 115 6.2.6. Uncertainty on Top Quark Mass...................... 116 6.2.7. Arbitrariness of Parton Density Functions................. 116 6.2.8. Drell-Yan and Di-Boson Contamination.................. 117 6.2.9. Summary: Corrections from Monte Carlo................. 119 6.3. A Counting Experiment............................... 119 7. Interpretation 125 7.1. Background Hypothesis Tests............................ 125 7.2. Signal Hypotheses Tests............................... 126 7.2.1. Generic Mass Edge Scan........................... 128 7.2.2. Exclusion Limits in an SMS Parameter Space............... 137 8. Conclusions 143 8.1. Outlook........................................ 144 A. Lorentz-Vector Components of Leptons in Data and MC 147 B. Mass Edges 149 B.1. Three-Body Decay.................................. 149 B.2. Two Subsequent Two-Body Decays......................... 149 C. Additional Material: Kinematic Correlation 151 C.1. Quantification of the φ1 vs. φ2 Correlation.................... 151 C.2. Correlation Coefficients in Bins of t¯t Boost and Di-Top Mass.......... 153 C.3. t¯t Boost vs. Di-Top Mass Correlation....................... 157 vi Contents D. Background Contamination Effects in 1-Jet Selection 159 E. Cut Threshold Variations 161 E.1. Jet Multiplicity.................................... 161 E.2. Simultaneous Variations............................... 162 miss E.2.1. Lepton pT vs. ET ............................. 162 E.2.2. Lepton pT vs. Lepton η ........................... 163 E.2.3. Lepton pT vs. # Jets............................ 164 miss E.2.4. ET vs. Lepton η .............................. 165 miss E.2.5. ET vs. # Jets............................... 166 E.2.6. Lepton η vs. # Jets............................. 167 E.3. Angle-Momenta Correlation............................. 168 vii 1. Introduction Symmetry considerations have always been a fruitful source of inspiration grasping the princi- ples of nature and its constituents. Ancient natural philosophers assumed the most symmetric polyhedrons { the Platonic solids { to be the basic entity of matter. Plato associated each ele- ment (fire, air, water, and earth) with one regular solid. Even though todays understanding of nature is less idealistic, the concept of symmetry is still
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