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Inclusive Low-Mass Drell-Yan Cross-Section at Lhcb at S = 8Tev

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Inclusive Low-Mass Drell-Yan Cross-Section at Lhcb at S = 8Tev Inclusive Low-Mass Drell-Yan Cross-Section at LHCb at ps = 8 TeV Dissertation zur Erlangung der naturwissenschaftlichen Doktorw¨urde (Dr. sc. nat.) vorgelegt der Mathematisch-naturwissenschaftlichen Fakult¨at der Universit¨atZ¨urich von Andreas Robert Weiden aus Deutschland CERN-THESIS-2020-279 29/01/2020 Promotionskommission Prof. Dr. Ulrich Straumann (Vorsitz, Leitung der Dissertation) Dr. Katharina M¨uller Prof. Dr. Nicola Serra Z¨urich, 2020 Die vorliegende Arbeit wurde von der Mathematisch-naturwissenschaftlichen Fakult¨atder Universit¨atZ¨urich im Herbst-Semester 2020 als Dissertation angenommen. Promotionskommission: Prof. Dr. Ulrich Straumann (Vorsitz und Leitung der Dissertation) Dr. Katharina M¨uller Prof. Dr. Nicola Serra ABSTRACT The LHCb experiment, one of the four main experiments at the LHC, is optimized for decays of particles containing a b- or c-quark. The LHCb detector is a single-arm forward spectrometer with an acceptance from approximately 30 to 250 mrad, with respect to the incoming proton beams. In addition to its main goal, its unique geometry makes it also a very interesting detector to probe general physics in the forward region. This includes electroweak boson production, which can provide important insights into the parton distribution functions (PDFs) of the proton. As part of this electroweak program, a measurement of the differential and double-differential inclusive Drell-Yan cross-sections with subsequent decay to muon-pairs dσ(pp Z/γ∗ µ+µ−) d2σ(pp Z/γ∗ µ+µ−) ! ! and ! ! dMµµ dy dMµµ 2 is performed in the range 10:5 < Mµµ < 110 GeV=c and 2 < y < 4:5. The cross-section measurement benefits from the high-precision calibration of the absolute luminosity at LHCb. For this measurement, data corresponding to 2.0 fb−1 collected with the LHCb detector at a centre-of-mass energy of ps = 8 TeV are analysed. The cross-sections are compared to theoretical next-to-next-to leading order perturbative QCD predictions using four different PDF sets, none of which included measurements from this hitherto unexplored region in phase space. The differential cross-section as a function of invariant mass of the dilepton pair is found to be in general agreement with the different predictions, however some systematic discrepancies are found when studying the double-differential cross-section as a function of rapidity of the dilepton pair. Overall the measurement presented here is systematically limited in the region which would be of most interest as input for future PDF sets, the low mass region. Nevertheless, it is hoped that the data presented here will help place new constraints on the quark and anti-quark content of the proton PDFs down to very low values of the momentum fraction of the partons, x. i ii ACKNOWLEDGEMENTS Writing a thesis is like a journey. You can choose the way you set out on, but you don't always know where it leads or how long it will take to get there. I would like to thank all people who have accompanied me along the way. Vaney, for helping me stay the course by giving me a goal. Luan, for being that goal. Mama und Papa, for always telling me I can do this if I want to. Thorsten, for moral support from afar. Prof. Ueli Straumann and Dr. Katharina M¨ullerfor their advice and their insights. The Zurich LHCb group, for making the journey enjoyable. iii iv F¨urOmi und P¨unktchen v vi CONTENTS Abstract i Acknowledgements iii Contents vii 1 Introduction1 2 Theoretical Introduction3 2.1 The Standard Model of Particle Physics...................3 2.1.1 Composite particles...........................6 2.1.2 Experimental confirmation.......................7 2.2 Electro-weak symmetry breaking.......................7 2.3 Quantum-Chromo-Dynamics.......................... 11 2.3.1 Asymptotic freedom and confinement................. 12 2.3.2 Parton Density Functions....................... 14 2.4 The Drell-Yan process............................. 18 2.4.1 The general 2 2 process....................... 18 2.4.2 The differential! Drell-Yan cross-section................ 22 2.4.3 The FEWZ tool............................. 26 3 The LHCb experiment at the LHC 27 3.1 Particle accelerators.............................. 27 3.2 The Large Hadron Collider........................... 29 3.3 The LHCb experiment............................. 31 3.3.1 Tracking system............................. 36 3.3.2 Calorimeter system........................... 40 3.3.3 Muon system.............................. 41 3.3.4 Particle identification using RICH detectors............. 44 3.3.5 Trigger and event reconstruction.................... 45 3.3.6 Production of simulated events.................... 48 3.4 Luminosity determination at LHCb...................... 50 3.4.1 Relative luminosity determination................... 52 vii 3.4.2 The Van-der-Meer method....................... 54 3.4.3 The Beam-Gas-Imaging method.................... 56 3.4.4 Absolute luminosity calibration at 8 TeV............... 58 3.4.5 Determining the luminosity of leading bunches............ 58 4 Measurement of the Drell-Yan cross-section 63 4.1 Previous measurements............................. 64 4.2 Trigger and data selection........................... 66 4.2.1 Signal samples.............................. 66 4.2.2 Background samples.......................... 68 4.2.3 Overview over samples......................... 71 4.3 Fit templates.................................. 71 4.3.1 The isolation variable.......................... 72 4.3.2 Signal template............................. 77 4.3.3 Background templates......................... 78 4.4 Determining the signal yields......................... 79 4.4.1 Initial fit................................. 81 4.4.2 Residual signal removal......................... 82 4.4.3 Fixed background fraction....................... 89 4.4.4 Toy studies............................... 92 4.5 Bin migration.................................. 95 4.5.1 Bin migration as a function of mass.................. 96 4.5.2 Bin migration as a function of mass and rapidity.......... 100 4.6 Efficiencies.................................... 102 4.6.1 Trigger efficiency............................ 102 4.6.2 Tracking efficiency........................... 108 4.6.3 Muon ID efficiency........................... 110 4.6.4 Combined reconstruction and trigger efficiency............ 112 4.6.5 Global event cut efficiency....................... 114 4.6.6 Vertex χ2 cut efficiency......................... 117 5 Systematic uncertainties 125 5.1 Fitting...................................... 125 5.1.1 Signal template............................. 126 5.1.2 Heavy-flavour template......................... 130 5.1.3 Toy studies and bin migration..................... 133 5.2 Efficiencies.................................... 134 5.3 Luminosity................................... 134 5.4 Cross-checks................................... 135 5.4.1 Number of bins............................. 135 5.4.2 Magnetic polarity............................ 135 5.5 Total systematic uncertainty.......................... 137 5.5.1 As a function of mass.......................... 137 5.5.2 As a function of mass and rapidity.................. 137 6 Results 141 6.1 Total cross-section at the Z-peak....................... 142 6.2 Differential cross-section as a function of mass................ 143 viii 6.3 Double-differential cross-section as a function of mass and rapidity..... 146 7 Conclusions & Outlook 149 A Theoretical predictions of the Drell-Yan cross-section 151 B Measured values of the Drell-Yan cross-section 155 C Individual fit results 157 C.1 As a function of invariant mass........................ 158 C.2 As a function of invariant mass and rapidity................. 160 D Using a feed forward neural network to identify Drell-Yan events at the LHCb experiment 165 E Uncertainties of differences and ratios for correlated variables 169 F Individual contributions to the systematic uncertainty 171 G Correlation with Z-measurement 173 Bibliography 175 ix x CHAPTER 1 INTRODUCTION He was determined to discover the underlying logic behind the universe. Which was going to be hard, because there wasn't one. Terry Pratchett - Mort While there might be no underlying logic behind the universe, trying to find such a logic has nevertheless been a very fruitful endeavour for humanity. By discovering patterns in nature, one can make predictions about future behaviour. This has opened the gateway to technology. In recent times one frontier of human knowledge has been particle physics. The Standard Model of Particle Physics has been developed as a quantum field theory in order to describe the fundamental building blocks of nature. It is the most fundamental logic we have discovered so far and is briefly introduced in Chapter2. One part of the Standard Model is Quantum-Chromo-Dynamics, the quantum theory that describes the strong interaction, which is responsible for the proton being held together and which is introduced in Section 2.3. Contrary to the other fundamental forces, the strong interaction does not diminish with distance, but increases in strength. Using perturbation theory to describe QCD processes is not possible in general because of this. However, for processes which can be separated into a high-energy (small distances) part and a low-energy (large distances) part, the latter can be described by process independent parton density functions determined using data as inputs, which are introduced in Section 2.3.2. The parton density functions allow perturbative calculations of the high-energy process by encapsulating the low-energy
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