Flavour-tagged Measurement of CP Observables in B0 D K Decays s s∓ ± with the! LHCb Experiment Dissertation zur Erlangung des akademischen Grades Dr. rer. nat. vorgelegt von Ulrich Paul Eitschberger geboren in Dorsten Fakultät Physik Technische Universität Dortmund Dortmund, im März 2018 Der Fakultät Physik der Technischen Universität Dortmund zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften vorgelegte Dissertation. 1. Gutachter: Prof. Dr. Bernhard Spaan 2. Gutachter: Prof. Dr. Kevin Kröninger Datum des Einreichens der Arbeit: 27.03.2018 Datum der mündlichen Prüfung: 28.05.2018 Abstract 0 In this thesis, the LHCb measurement of CP violation in Bs Ds∓K± decays is dis- 0 ! cussed. In Bs Ds∓K± decays, CP violation arises in the interference between decay ! 0 0 and decay after Bs –Bs mixing. A decay-time-dependent measurement of the involved CP parameters is enabled by the flavour tagging, which infers the production flavour 0 of the Bs mesons. The analysed data has been recorded by the LHCb experiment in proton-proton 0 collisions at centre-of-mass energies of 7 and 8 TeV. The CP parameters in Bs Ds∓K± are determined to be ! C = 0.73 0.14 (stat) 0.05 (syst) , ∆Γ ± ± Af = 0.39 0.28 (stat) 0.15 (syst) , ∆Γ ± ± Af¯ = 0.31 0.28 (stat) 0.15 (syst) , ± ± Sf = 0.52 0.20 (stat) 0.07 (syst) , − ± ± Sf¯ = 0.49 0.20 (stat) 0.07 (syst) . − ± ± 0 Due to the interference between b csu¯ and b u¯cs transitions in Bs Ds∓K± de- cays, the CP parameters are sensitive! to the CKM! angle γ. It is measured! to be +17 0 γ = 128 22 ◦, representing the most precise γ measurement using Bs decays to date. − Kurzfassung 0 In dieser Dissertation wird die Messung von CP-Verletzung in Bs Ds∓K±-Zerfällen 0 ! mit Daten des LHCb-Experiments diskutiert. In Zerfällen von Bs Ds∓K± tritt CP-Ver- 0 !0 letzung in der Interferenz zwischen Zerfall und Zerfall nach Bs –Bs Mischung auf. Eine zerfallszeitabhängige Messung der beteiligten CP-Parameter wird durch das Flavour 0 Tagging ermöglicht, welches die Produktionszustände der Bs -Mesonen bestimmt. Die analysierten Daten wurden vom LHCb-Experiment in Proton-Proton-Kollisionen bei Schwerpunktsenergien von 7 und 8 TeV aufgezeichnet und entsprechen einer in- 1 0 tegrierten Luminosität von 3 fb− . Die CP-Parameter im Zerfallskanal Bs Ds∓K± werden gemessen zu ! C = 0,73 0,14 (stat) 0,05 (syst) , ∆Γ ± ± Af = 0,39 0,28 (stat) 0,15 (syst) , ∆Γ ± ± Af¯ = 0,31 0,28 (stat) 0,15 (syst) , ± ± Sf = 0,52 0,20 (stat) 0,07 (syst) , − ± ± Sf¯ = 0,49 0,20 (stat) 0,07 (syst) . − ± ± 0 Die CP-Parameter sind sensitiv auf den CKM-Winkel γ, da im Zerfallskanal Bs Ds∓K± Übergänge von b csu¯ und b u¯cs interferieren. Der CKM-Winkel wird bestimmt! +17 ! ! 0 zu γ = 128 22 ◦. Es handelt sich um die bisher präziseste γ-Messung mit Bs -Zerfällen. − iii Contents 1 Introduction 1 2 The Standard Model of Particle Physics 3 2.1 Fundamental particles and interactions . 3 2.2 Symmetries and symmetry violations . 5 2.3 Limitations of the Standard Model . 7 3 CP Violation 9 3.1 The CKM mechanism . 9 3.2 Unitarity triangles . 12 3.3 Mixing and decay of neutral B mesons . 13 3.4 Manifestations of CP violation . 17 3.4.1 Direct CP violation . 18 3.4.2 Indirect CP violation . 18 3.4.3 CP violation in interference . 19 0 3.5 CP violation in Bs Ds∓K± decays . 20 ! 0 3.6 Determination of the CKM angle γ from Bs Ds∓K± decays . 23 ! 4 The LHC and the LHCb Experiment 25 4.1 The LHC and the CERN accelerator complex . 25 4.2 The LHCb detector . 27 4.2.1 Tracking system . 28 4.2.2 Particle identification system . 30 4.3 The LHCb trigger system . 32 4.3.1 Hardware trigger . 32 4.3.2 Software trigger . 33 4.4 Offline data processing with the LHCb software . 34 4.4.1 Event reconstruction . 34 4.4.2 Global preselection . 35 4.5 Simulated data . 36 4.5.1 Fully simulated Monte Carlo . 36 4.5.2 Pseudo-experiments and toy studies . 37 4.6 Run conditions . 37 5 Analysis Tools 39 5.1 Maximum likelihood method . 39 5.2 The sPlot technique . 40 v Contents 5.3 Decision trees and boosting . 41 6 Flavour Tagging 43 6.1 Same-side tagging . 44 6.2 Opposite-side tagging . 45 6.3 Output and performance of tagging algorithms . 46 6.4 Combination of tagging algorithms . 47 6.5 Calibration of flavour-tagging algorithms . 48 0 0 6.6 Flavour-tagging calibrations with B J= K∗ decays . 50 6.6.1 Calibration of the OS tagger combination! . 56 6.6.2 Calibration of the SS pion tagger for the LHCb Run 1 sin(2β) measurement . 58 6.6.3 Calibration of the new OS charm tagger . 62 7 Data Preparation 65 7.1 Reconstruction and preselection . 65 0 0 + 7.2 Cut-based selection of Bs Ds∓K± and Bs Ds−π . 67 0 ! + ! 7.3 Cut-based selection of B D−π ....................... 71 7.4 Multivariate selection . .! . 72 7.4.1 Training of the BDT . 72 7.4.2 BDT classifier cut optimisation . 76 7.5 Simulated data samples . 78 8 Fit to invariant mass and PID distributions 81 0 + 8.1 Control mode B D−π ............................ 81 8.2 Components . .! . 84 8.2.1 Signal candidates . 84 8.2.2 Fully reconstructed backgrounds . 85 8.2.3 Partially reconstructed backgrounds . 86 8.2.4 Combinatorial background . 87 8.3 Results . 88 8.4 Validation . 93 0 9 Measurement of CP Violation in Bs Ds∓K ± Decays 95 9.1 Decay-time PDF without detector effects! . 95 9.2 Asymmetries in production and detection . 96 9.3 Decay-time resolution . 97 9.4 Decay-time acceptance . 101 9.5 Flavour tagging . 105 0 9.6 Bs Ds∓K± decay-time fit . 109 9.7 Systematic! uncertainties . 111 9.7.1 Validation of the fit procedure . 112 9.7.2 Closure tests with fully simulated events . 113 9.7.3 Influence of fixed parameters . 115 vi Contents 9.7.4 Decay-time resolution . 116 9.7.5 Correlations among the MD fit observables . 117 9.7.6 Decay-time acceptance . 117 9.7.7 Negligible effects and total systematic uncertainties . 118 9.8 Determination of the CKM angle γ . 119 10 Discussion and Outlook 123 10.1 Compatibility of the γ measurement . 123 0 10.2 Perspective of decay-time-dependent γ measurements with Bs Ds∓K± decays . .! . 124 0 + 10.3 Measurement of ∆ms with Bs Ds−π decays . 125 10.4 Per-event decay-time acceptance! . 125 11 Conclusion 127 Bibliography 129 Acknowledgements 141 vii 1 Introduction Particle physics aims to understand the nature of the smallest constituents of matter and the interactions among them. The most successful theory in this field is the Stan- dard Model of particle physics (SM). Its current formulation was finalised during the mid-1970s after the existence of quarks had been experimentally confirmed [1,2]. All particles that were postulated by the SM, like the top quark or the tau neutrino, have been discovered by various experiments in the last decades. The last particle to be ex- perimentally established was the Higgs boson [3–5]. While experiments have proven the reliability of the SM predictions up to high precision, there are still many motiva- tions to keep on searching for physics beyond the SM. One of the most striking short- comings of the SM is its inability to explain the matter-antimatter asymmetry that is observed in today’s universe. According to big bang theories, matter and antimatter have been produced in equal amounts at the beginning of the universe. However, today we are surrounded by clusters of matter, while the antimatter seems to have almost completely vanished. This leads to the concept of baryogenesis, which implies that the matter excess was created after the big bang. In 1967, Andrei Sakharov pro- posed three conditions that are prerequisites for any baryogenesis [6]. Firstly, a pro- cess must exist that violates the conservation of the baryon number. Secondly, there need to be interactions outside of the thermal equilibrium. Lastly, both the C and the CP symmetries need to be violated, which expressed in simple terms states that matter and antimatter behave differently. Currently, there is no evidence for violation of the baryon number conservation as the lifetime of the proton is measured to be 34 above 1.6 10 years [7]. There are several scenarios for the emergence of thermal non-equilibrium× in the immediate aftermath of the big bang [8]. Furthermore, pro- cesses that violate the C and CP symmetries were already found in 1964 [9]. The SM does include CP violation, but the allowed amount is magnitudes too small to explain the size of the observed matter-antimatter asymmetry [10]. This is a clear hint for the existence of physics beyond the SM and makes studying CP violation even fifty years after its discovery a promising field of research. The only source of CP violation in the SM is a single complex phase in the Cabbibo- Kobayashi-Maskawa (CKM) quark-mixing matrix [11]. A fundamental requirement of the SM is that the CKM matrix is unitary. Confirming or falsifying the unitarity represents a strong test of the SM itself. This test is illustrated by means of the so- called CKM triangle, which represents the unitarity of the CKM matrix as a triangle in the complex plane.