School of Physics - Theses
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ItemA Taste of Flavour and Neutrino Physics with Scalar Leptoquarks( 2022)Flavour physics is the branch of particle physics that examines the structure of the flavour sector of the Standard Model. This sector, describing fermion masses and their mixing, involves a large number of free parameters which are determined via experimental input. Thus, understanding the nature of the flavour sector provides a key motivation for many theories beyond the Standard Model. The accidental lepton-flavour symmetry of the Standard Model need not be preserved in extended models. Although neutrinos are massless particles in the Standard Model, and thus their flavour is conserved, strong experimental evidence of neutrino flavour oscillations requires that neutrinos are actually massive. Since those masses, though nonzero, are constrained to be tiny, it is well motivated that they are generated in some exotic way. This observation highlights the need for new physics to explain lepton-flavour violation in the neutrino sector. In this thesis, we explore not only neutrinos and their flavour violation, but also how this violation could manifest in the charged-lepton sector. Extensions to the Standard Model discussed in this thesis centre around hypothetical particles called leptoquarks, which directly couple quarks and leptons. Their interactions naturally lead to violation of lepton flavour symmetries, and imbue a sense of linkage between these two classes of Standard Model fermions. Moreover, the simple nature of scalar leptoquark extensions motivate us to consider where these could fall within the larger framework of unified models of nature. In particular, these could explain the structure of the (presently semi-empirical) flavour sector. Chapter 1 provides background on the Standard Model of particle physics, and outlines the relevant conventions adopted in this thesis. Chapter 2 reviews the present landscape of the flavour and neutrino sectors, including an overview of experimental results to guide the ensuing work. Chapter 3 centres on understanding divergences in the Standard Model, and how one can extend this theory of nature within a framework of effective field theory. Chapters 4, 5 and 6 present a series of original studies that highlight the potential impact of scalar leptoquarks on the structure of the flavour and neutrino sectors. Chapter 4 explores the viability of scalar leptoquarks to generate large corrections to charged-lepton dipole moments. We identify the mixed-chiral scalar leptoquarks (S1 and R2) capable of generating chirally-enhanced and sign-dependent contributions to lepton magnetic moments (as favoured by present measurements). We find that TeV scale particles are capable of addressing present anomalies in the magnetic dipole moments of the electron and the muon. Moreover, signals of these models in the muon electric dipole moment are found to be within reach of future experimental programs. Chapter 5 presents a next-to-minimal scalar leptoquark model capable of reconciling recent experimental B-anomalies, and of radiatively generating neutrino masses. Building upon a single leptoquark model for addressing these B-anomalies, we combine two existing neutrino-mass models (containing the leptoquarks S1 and S3, and a vector-like quark) and find that this hybrid model is able to ameliorate the anomalies in b to s transitions, charged-current b decays, and the muon magnetic moment. Furthermore, it is capable of generating radiative neutrino masses consistent with experimental values. Chapter 6 involves the study of a discrete flavour-group model built around a scalar S1 leptoquark extension. Beginning with a GF = D17 x Z17 flavour group, we outline how this model is capable of generating the textures of charged-fermion masses and mixings, as well as the leptoquark couplings required to address anomalies in charged-current b decays and the muon magnetic moment.
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ItemModels of radiative neutrino mass and lepton flavour non-universality( 2020)This thesis presents a series of original studies exploring the space of neutrino-mass models, and the connection that a class of these models might have with the recently purported violations of lepton flavour universality measured in $B$-meson decays. We begin by describing and implementing an algorithm that systematises the process of building models of Majorana neutrino mass starting from effective operators that violate lepton number by two units. We use the algorithm to generate computational representations of all of the tree-level completions of the operators up to and including mass-dimension eleven, almost all of which correspond to models of radiative neutrino mass. Our study includes lepton-number-violating operators involving derivatives, updated estimates for the bounds on the new-physics scale associated with each operator, an analysis of various features of the models, and a look at some examples. Accompanying this work we also make available a searchable database containing the catalogue of neutrino-mass models, as well as the code used to find the completions. The anomalies in $B$-meson decays have known explanations through exotic scalar leptoquark fields. We add to this work by presenting a detailed phenomenological analysis of a particular scalar leptoquark model: that containing $S_{1} \sim (\mathbf{3}, \mathbf{1}, -\tfrac{1}{3})$. We find that the leptoquark can accommodate the persistent tension in the ratios $R_{D^{(*)}}$ as long as its mass is lower than approximately $\SI{10}{\TeV}$, and show that a sizeable Yukawa coupling to the right-chiral tau lepton is necessary for an acceptable explanation. Agreement with the measured $R_{D^{(*)}}$ values is mildly compromised for parameter choices addressing the tensions in the $b \to s$ transition. The leptoquark can also reconcile the predicted and measured value of the anomalous magnetic moment of the muon, and appears naturally in models of radiative neutrino mass. As a representative example, we incorporate the field into a two-loop neutrino mass model from our database. In this specific case, the structure of the neutrino-mass matrix provides enough freedom to explain the small masses of the neutrinos in the region of parameter space dictated by agreement with the anomalies in $R_{D^{(*)}}$, but not in the $b \to s$ transition. In order to address the shortcomings of the $S_{1}$ scenario, we construct a non-minimal model containing the scalar leptoquarks $S_{1}$ and $S_{3} \sim (\mathbf{3}, \mathbf{3}, -\tfrac{1}{3})$ along with a vector-like quark, necessary for lepton-number violation. We find that this new model permits a simultaneous explanation of all of the flavour anomalies in a region of parameter space that also reproduces the measured pattern of neutrino masses and mixing. A characteristic prediction of our model is a rate of muon--electron conversion in nuclei fixed by the $b \to s$ anomalies and the neutrino mass. The next generation of muon--electron conversion experiments will thus potentially discover or falsify our scenario. We also present a general overview from our model database of those minimal radiative neutrino-mass models that contain leptoquarks that are known to explain the anomalies in $R_{D^{(*)}}$ and the $b \to s$ transition. We hope that our model database can facilitate systematic analyses similar to this, perhaps on both the phenomenological and experimental fronts. We conclude by presenting a study of the diphoton decay of a scalar $\mathrm{SU}(N)$ bound state, motivated by the 2016 \SI{750}{\GeV} diphoton excess.