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MASTER THESIS Linking the B-Physics Anomalies and Muon G MSc PHYSICS AND ASTRONOMY GRAVITATION, ASTRO-, AND PARTICLE PHYSICS MASTER THESIS Linking the B-physics Anomalies and Muon g − 2 A Phenomenological Study Beyond the Standard Model By Anders Rehult 12623881 February - October 2020 60 EC Supervisor/Examiner: Second Examiner: prof. dr. Robert Fleischer prof. dr. Piet Mulders i Abstract The search for physics beyond the Standard Model is guided by anomalies: discrepancies between the theoretical predictions and experimental measurements of physical quantities. Hints of new physics are found in the recently observed B-physics anomalies and the long-standing anomalous magnetic dipole moment of the muon, muon g − 2. The former include a group of anomalous measurements related to the quark-level transition b ! s. We investigate what features are required of a theory to explain these b ! s anomalies simultaneously with muon g − 2. We then consider three kinds of models that might explain the anomalies: models with leptoquarks, hypothetical particles that couple leptons to quarks; Z0 models, which contain an additional fundamental force and a corresponding force carrier; and supersymmetric scenarios that postulate a symmetry that gives rise to a partner for each SM particle. We identify a leptoquark model that carries the necessary features to explain both kinds of anomalies. Within this model, we study the behaviour of 0 muon g − 2 and the anomalous branching ratio of Bs mesons, bound states of b and s quarks, into muons. 0 ¯0 0 ¯0 The Bs meson can spontaneously oscillate into its antiparticle Bs , a phenomenon known as Bs −Bs mixing. We calculate the effects of this mixing on the anomalous branching ratio. We then identify parameter space 0 ¯0 that explains the anomalous branching ratio and muon g − 2 within Bs − Bs constraints. Furthermore, we study the potential for CP violation, the breaking of a discrete symmetry of our universe, subject to the same constraints and find that sizeable mixing-induced CP violation is possible within the model. Acknowledgements First of all, I would like to thank Prof. Dr. Robert Fleischer, whose corrections and nudges have repeatedly pulled me out of the mud and refocused my aim. Your guidance and expertise have been invaluable in sharpening my understanding of particle physics phenomenology and all that comes with it, and I greatly look forward to continuing to learn from your mentorship during the years ahead. I would like to thank all the people at Nikhef and elsewhere who have been generous with their time and help. Thank you to Dr. Melissa van Beekveld, Dr. Anastasiia Filimonova, Eleftheria Malami, and Ruben Jaarsma for your guidance and technical support. Thank you to Dr. Darren Scott for never turning down an opportunity for discussion. It is funny how you can learn more from thirty minutes spent in front of a blackboard than from three hours behind a computer screen. I would like to thank Prof. Dr. Bob van Eijk, who ignited my interest in particle physics and inspired me to take the leap from engineering into physics. Without you, I would not be anywhere near Nikhef, I would not have gone to CERN, and I would not be studying particle physics. Thank you for all these things. The past half year has been a peculiar time, not least for carrying out a research project. I cannot help but think how difficult working remotely would have been thirty years ago, and I suppose I should thank the staff of Zoom for providing the means to do so. I could not have written this thesis without the support of the people around me. I would like to thank my family for keeping me sane back home during the first three months after COVID-19 hit. Without you, I would have been climbing my walls within weeks. Finally, I would like to thank Jonathan Ågren. Our frequent conversations routinely remind me of why I study physics. Particularly during the final stretch of this work, your drive has fuelled my drive. When a candle falters, another candle burning bright is all that is needed to light its flame again. ii Contents 1 Introduction 1 1.1 Conventions . 3 2 Quantum field theory and the Standard Model 5 2.1 Quantum electrodynamics . 5 2.2 Electroweak theory . 7 2.3 Quantum chromodynamics . 8 2.4 Generating masses—the Higgs mechanism . 9 2.5 Field content of the Standard Model . 13 3 Flavour physics 15 3.1 The CKM matrix . 15 3.2 CP violation . 18 3.3 B physics . 20 4 Effective field theory 21 4.1 Operator product expansion . 21 4.2 Calculating Wilson coefficients . 22 4.3 Probing new physics through effective field theory . 23 0 ¯0 5 Bs − Bs mixing 25 5.1 Mixing amplitude and phase . 25 5.2 Theoretical vs. time-integrated branching ratios . 26 6 The B-physics anomalies 29 iii iv CONTENTS 6.1 Lepton flavour universality violation . 29 + − 6.2 The rare decay Bs ! µ µ ..................................... 31 6.3 CP asymmetries . 34 7 Muon g − 2 35 7.1 Classical to quantum . 35 7.2 Radiative corrections . 37 8 Model-dependent analysis 39 8.1 Leptoquarks . 39 8.2 The scalar leptoquark S1 ...................................... 40 8.3 Calculation of Wilson coefficients . 41 + − 8.4 Calculation of the theoretical branching ratio of Bs ! µ µ and muon g − 2 ......... 42 8.5 Calculation of Aµµ and the CP asymmetries S and C ................... 44 ∆Γs µµ µµ 0 ¯0 8.6 Bs − Bs mixing constraints . 44 8.7 Results for Aµµ and S ...................................... 46 ∆Γs µµ + − 8.8 Results for the time-integrated branching ratio of Bs ! µ µ .................. 47 8.9 Z0 models............................................... 51 8.10 Supersymmetry . 53 9 Conclusions 55 Appendices 57 A Standard Model Lagrangian 59 B SARAH and SPheno 61 C SARAH model file for the S1 scalar leptoquark model 67 References . 69 1 | Introduction One does not need to go far back in time to find an understanding of fundamental physics radically different from ours. When Dalton hypothesized and subsequently discovered the building blocks of molecules in the early 1800s [1], he named them atoms, reintroducing a term meaning indivisible and coined by the Greek philosopher Democritus some two thousand years beforehand. After the discoveries of electrons, protons, and neutrons by Thomson1 [2], Rutherford [3], and Chadwick2 [4] respectively, it was clear that Dalton had jumped the gun by assigning this name to his newly-discovered particles. Following the discovery of quarks at SLAC3 [5], we know that a rich phenomenology is contained even within protons and neutrons. The contemporary understanding of the fundamental constituents of matter is as excitations of quantum fields, structures that permeate space and time. Our current knowledge of these fields, and of particles that arise from them, is encapsulated in the Standard Model (SM) of particle physics. With the 2012 discovery of the last missing piece of the SM, the Higgs boson4, by the ATLAS [6] and CMS collaborations [7], all particles of the SM are verified to exist. The SM describes many phenomena with remarkable accuracy. However, it does not offer a complete description of experimentally observed phenomena. It does not explain dark matter, the substance that outweighs the “normal” matter described by the SM five times to one, making up 27% of the energy content of the observable universe as opposed to the 5% that normal matter accounts for [8]. Nor does it explain dark energy, the source of the acceleration of our universe’s expansion that makes up the remaining 68% [9]. It does not account for the observation of massive neutrinos [10], electrically neutral particles that interact very weakly with normal matter and are modelled as massless in the SM. In the SM, matter can only be created and annihilated in equal amounts with corresponding antimatter that carries opposite charges—e.g. electric charge—to its matter counterpart. Because of this, the SM does not explain the remarkable absence of antimatter in our observed universe [11]. Finally, the SM does not include a description of gravity, which becomes important for particle physics at very high energy scales, nor is it consistent with general relativity, the theoretical framework currently used to describe gravity at such scales [12]. Physics aimed at explaining these phenomena by extension of the SM is referred to as beyond the SM (BSM) physics, and any physics that is not part of the SM is called new physics (NP). As the precisions of our theoretical predictions and experimental measurements have increased over the years, a new avenue of particle physics research has opened. In addition to trying to produce NP particles directly in experiments at the high-energy frontier, we can probe the potential effects of NP indirectly by studying low-energy processes with very high precision. In such processes, evanescent NP particles may pop in and out of existence as virtual particles, quantum fluctuations that cause small but measurable effects. This high-precision frontier poses a challenge for theorists and experimentalists alike, and its exploration is the motivation behind experimental endeavours such as the upcoming high-luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN planned for this decade [13]. To search for NP at the high-precision frontier, physicists look for where the experimental values of measurable quantities, observables, differ from 1Nobel prize 1906: Thomson 2Nobel prize 1935: Chadwick 3Nobel prize 1980: Friedman, Kendall, Taylor 4Nobel prize 2013: Englert, Higgs 1 2 CHAPTER 1. INTRODUCTION the values predicted by the SM. Such inconsistencies are known as anomalies and are smoking-gun signals of NP. A promising field of study at the high-precision frontier is that of B physics. This field concerns the study of particles called B mesons, bound states of two quarks whereof one is a bottom quark.
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