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Measurement of Violation in the Decay → ∓ with Data Measurement of 혾홋 violation in the decay 혽0→→혿∗∗±±혿∓ with data from the LHCb experiment Dissertation zur Erlangung des akademischen Grades Dr. rer. nat. vorgelegt von Margarete Schellenberg geboren in Dortmund Lehrstuhl für Experimentelle Physik V Fakultät Physik Technische Universität Dortmund Dortmund, 23. Oktober 2019 Der Fakultät Physik der Technischen Universität Dortmund zur Erlangung des akade- mischen Grades eines Dr. rer. nat. vorgelegte Dissertation. 1. Gutachter: Prof. Dr. Bernhard Spaan 2. Gutachter: Prof. Dr. Kevin Kröninger Datum des Einreichens der Arbeit: 23.10.2019 Datum der mündlichen Prüfung: 28.11.2019 Abstract This thesis presents the first LHCb measurement of 퐶푃 violation in 퐵0 → 퐷∗±퐷∓ decays. Due to the 푏 → 푐푐푑 transition, 퐵0 → 퐷∗±퐷∓ decays give access to higher-order Stan- dard Model contributions. The decay-time-dependent measurement is performed on a dataset corresponding to an integrated luminosity of 9 fb−1 recorded by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The 퐶푃 observables are measured with an unbinned maximum likelihood fit as 푆퐷∗퐷 = −0.861 ± 0.077 (stat) ± 0.019 (syst) , Δ푆퐷∗퐷 = 0.019 ± 0.075 (stat) ± 0.012 (syst) , 퐶퐷∗퐷 = −0.059 ± 0.092 (stat) ± 0.020 (syst) , Δ퐶퐷∗퐷 = −0.031 ± 0.092 (stat) ± 0.016 (syst) , 퐴퐷∗퐷 = 0.008 ± 0.014 (stat) ± 0.006 (syst) . To date, the analysis is the most precise single measurement of 퐶푃 violation in this decay channel. All parameters are consistent with their current world average values. Kurzfassung In dieser Arbeit wird die erste LHCb-Messung von 퐶푃-Verletzung in Zerfällen von 퐵0 → 퐷∗±퐷∓ vorgestellt. Aufgrund des 푏 → 푐푐푑-Übergangs, besteht Zugang zu Stan- dardmodellbeiträgen höherer Ordnung. Die zerfallszeitabhängige Messung wird auf einem Datensatz durchgeführt, der einer integrierten Luminosität von 9 fb−1 entspricht, und der vom LHCb-Detektor bei Proton-Proton-Kollisionen mit Schwerpunktsener- gien von 7, 8 und 13 TeV aufgenommen wurde. Die 퐶푃-Observablen werden in einem ungebinnten Maximum-Likelihood-Fit bestimmt zu 푆퐷∗퐷 = −0,861 ± 0,077 (stat) ± 0,019 (syst) , Δ푆퐷∗퐷 = 0,019 ± 0,075 (stat) ± 0,012 (syst) , 퐶퐷∗퐷 = −0,059 ± 0,092 (stat) ± 0,020 (syst) , Δ퐶퐷∗퐷 = −0,031 ± 0,092 (stat) ± 0,016 (syst) , 퐴퐷∗퐷 = 0,008 ± 0,014 (stat) ± 0,006 (syst) . Die Analyse stellt die bisher präziseste Einzelmessung von 퐶푃-Verletzung in diesem Zerfallskanal dar. Alle Parameter sind konsistent mit ihren aktuellen Weltmittelwerten. Contents 1 Introduction 1 2 Fundamentals of Flavour Physics 5 2.1 The Standard Model of particle physics . 5 2.1.1 Elementary particles . 6 2.1.2 Fundamental interactions . 7 2.2 Origin of 퐶푃 violation in the Standard Model . 7 2.3 Neutral meson system . 11 2.4 Classes of 퐶푃 violation . 15 2.4.1 Direct 퐶푃 violation . 15 2.4.2 Indirect 퐶푃 violation . 16 2.4.3 퐶푃 violation in the interference of decay and decay after mixing 16 2.5 퐶푃 violation in the decay 퐵0 → 퐷∗±퐷∓ ................... 18 2.5.1 퐵0–퐵0 mixing phenomenology . 18 2.5.2 Decay amplitudes in 퐵0 → 퐷∗±퐷∓ ................. 20 3 The LHCb Experiment at the LHC 27 3.1 The LHC . 27 3.2 The LHCb detector . 29 3.2.1 Track reconstruction system . 31 3.2.2 Particle identification system . 33 3.2.3 Trigger . 35 3.3 LHCb Software . 37 3.3.1 Event reconstruction . 37 3.3.2 Stripping . 39 3.3.3 Simulation . 39 3.4 Prospects of data processing at LHCb . 40 4 Data Analysis Techniques 43 4.1 Maximum likelihood method . 43 iii Contents 4.2 sPlot technique . 44 4.3 Boosted decision tree . 45 4.4 Bootstrapping method . 47 4.5 Decay-chain fitting . 47 4.6 Flavour tagging . 47 4.6.1 Same-side flavour tagging . 49 4.6.2 Opposite-side flavour tagging . 50 5 Datasets and Selection 51 5.1 Reconstruction . 51 5.2 Stripping selection . 52 5.3 Preselection . 55 5.4 Types of backgrounds . 56 5.5 Vetoes of physical background . 57 5.6 Multivariate selection . 61 5.6.1 Training of the boosted decision tree . 61 5.6.2 Classifier cut optimisation . 64 5.7 Final selection . 67 6 Modelling of the invariant Mass Distribution in the Signal Region 69 6.1 Extraction of parameterisations from simulated events . 69 6.1.1 Signal candidates . 70 6.1.2 Mis-identified background . 72 6.1.3 Partially reconstructed background . 72 6.2 Extended maximum likelihood fit to LHCb data . 75 7 Measurement of 혾홋 Violation in 혽ퟬ → 혿∗±혿∓ Decays 79 7.1 Decay-time parameterisation . 79 7.2 Flavour tagging calibration . 81 7.2.1 Strategy . 81 7.2.2 Single tagger calibration . 82 7.2.3 Tagger combination calibration . 83 7.3 Decay-time resolution . 88 7.4 Decay-time-dependent efficiency . 90 7.5 Instrumental asymmetries . 92 7.5.1 Strategy . 92 7.5.2 Measurement of the detection asymmetry . 94 iv Contents 7.6 Determination of 퐶푃 parameters . 97 8 Fit Validation and Studies of systematic Effects 103 8.1 Model for fit validation and estimation of systematic uncertainties . 103 8.2 Cross-checks . 104 8.2.1 Fit validation using pseudo-experiments . 105 8.2.2 Fit validation using simulated signal events . 105 8.2.3 Cross-checks on subsets of the data . 106 8.2.4 Estimation of statistical uncertainties . 107 8.3 Estimation of systematic uncertainties . 107 8.3.1 Mass model . 107 8.3.2 Decay-time-dependent efficiency . 109 8.3.3 Decay-time resolution . 110 8.3.4 External inputs to the decay-time fit . 110 8.3.5 Flavour tagging calibration . 111 8.3.6 Systematic uncertainty on the determination of the detection asymmetry . 111 8.4 Total systematic uncertainties . 114 9 Conclusion and Outlook 117 Bibliography 121 Acknowledgements 133 v 1 Introduction Over the last decades, the Standard Model of particle physics (SM) has been intensively evaluated through experiments and is established as an accurate description of the constituents of nature and their fundamental interactions. Although the SM is an extraordinary successful theory, especially in the interplay between theoretical predic- tions and experimental verifications, there are still weaknesses and unsolved questions: For example, the neutrinos are assumed to be massless in the SM, while experimental observations of neutrino oscillations revealed that mass differences between neutrino generations exist [1, 2]. Moreover, cosmological observations indicate that the SM describes only about 5% of the energy in today’s universe [3]. Additional 26% consist of so-called dark matter, while the remaining 69% comprise so-called dark energy. Dark matter becomes evident through gravitational interactions, as it is needed to explain the rotational speed of stars, gases and dust clouds in galaxies [4, 5]. The dark energy on the other hand is postulated to explain the observed accelerated expansion of the universe. Both, the dark matter and the dark energy, are not described by the SM. In addition, gravity, best known from our daily lives, is not explained by the SM, since the integration of gravity into this theory has turned out to be a complicated challenge. Then, there is the biggest question that the SM cannot answer: What happened to the antimatter that was created after the Big Bang? The Big Bang took place about 13.8 billion years ago [3] and led to an equal production of matter and antimatter in the early universe. However, inspecting our universe today, from the smallest scales on Earth to the huge stellar formations, reveals an almost exclusive composition of matter. Hence, it is a major challenge in physics to discover what happened to the antimatter resulting in the baryonic asymmetry observed today. The most common theory to explain the baryonic asymmetry is baryogenesis, which implies the fulfilment of three conditions that were proposed by Andrei Sakharov in 1967 [6]: Firstly, there must have been a deviation from the thermal equilibrium at the early time of the universe. Secondly, the baryon number and thirdly, the charge symmetry (퐶) as well as the combination of charge and parity symmetry (퐶푃) must be violated. More than 50 years ago, 퐶 violation and shortly afterwards also 퐶푃 violation 1 1 Introduction were discovered in particle decays and successfully incorporated in the SM [7]. To date, measurements show that the size of the 퐶푃 violation is compatible with the SM predictions, however, it is an order of magnitude too small to account for the observed matter-antimatter asymmetry [8]. In the SM, 퐶푃 violation is manifested in the Cabibbo- Kobayashi-Maskawa (CKM) matrix, which is unitary and describes the probabilities of quark-flavour transitions. The unitarity leads to conditions that can partly be illustrated as triangles in the complex plane, of which the most common one is called the CKM triangle. In order to probe the SM, high precision measurements of the side lengths and angles of the CKM triangle are performed. These measurements are then combined to reveal, if the CKM triangle is a closed triangle in nature and, hence, if the CKM matrix is indeed a unitary matrix. One angle of the CKM triangle is represented by the parameter 훽. It can be extracted from the quantity sin 2훽, which can be measured with high precision in so-called golden 0 0 plated modes like 퐵 → 퐽/휓퐾S . Such decays allow for a very clean prediction from the theoretical and for an excellent signature in the detector from an experimental point 0 0 0 ∗± ∓ of view. In contrast to 퐵 → 퐽/휓퐾S decays, the decay 퐵 → 퐷 퐷 allows to measure the quantity sin 2훽eff, as further hadronic contributions and phases exist.
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