School of Physics - Theses
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ItemResonant Leptogenesis and Quark-Lepton Unification with Low-Scale Seesaws( 2020)The seesaw mechanism, where a hierarchy exists between the moduli of different entries of a mass mixing matrix, is a simple and theoretically attractive explanation for the observed large hierarchy between the neutral- and charged-fermion masses of the Standard Model. The simplest neutrino mass seesaw predicts that, upon diagonalisation, the physical mass states will either all be Majorana or all form pseudo-Dirac pairs. Non-minimal variants of this seesaw often generate a hybrid scenario with the physical mass states being a combination of both Majorana and pseudo-Dirac pairs. Such models often predict unique phenomenology and also allow for much lower mass scales of new physics. This thesis explores the implications such non-minimal variants can have beyond the simple generation of neutrino mass, particularly the possible role they may have in explaining the observed matter-antimatter asymmetry as well as implications for particular models of quark-lepton unification. Chapter 1 reviews the current experimental evidence for neutrino mass and discusses some possible tree-level origins. The matter-antimatter asymmetry is introduced and the conditions necessary for the dynamical generation of this observed asymmetry are reviewed. The idea of thermal leptogenesis is outlined as a simple mechanism for generating an asymmetry dynamically at an epoch between the the period of reheating and the electroweak phase transition of the early universe. Finally, the idea that quarks and leptons are related by hidden symmetries are discussed with a particular emphasis on the quark-lepton unifying Pati-Salam gauge group. In Chapter 2 we consider the leptogenesis implications for the Standard Model extended by two gauge-singlet fermions for each generation of charged lepton. We focus on the possibility of resonant scenarios without the need for inter-generational mass degeneracies and therefore do not require a possible flavour symmetry origin. The possible connection between neutrino parameters measureable in low-energy experiments and the generation of a matter-antimatter asymmetry is explored. In Chapter 3 we extend the analysis of the previous chapter and highlight how a flavour symmetry can allow for leptogenesis in a much wider region of parameter space for the extended seesaw used in \Cref{Chapter2}. The benefits of this extended seesaw, compared to the minimal seesaw scenario, when the proposed flavour symmetry is included are discussed and implications for low-energy flavour-violation experiments are explored. In Chapter 4 different possible Pati-Salam models are discussed with an emphasis on the connection between the scale of Pati-Salam breaking and the scale of heavy neutrino masses. Models allowing for the breaking scale to occur close to the electroweak scale are introduced. The dominant experimental probe of Pati-Salam is discussed and the current limits on the scale of breaking are calculated. Simple extensions of this model are proposed which both break an undesired mass degeneracy in the theory and allow for a significant reduction in the experimental limits on Pati-Salam breaking. A thorough analysis of the possible allowed parameter space in which both of these effects occur is explored and any possible connection to the symmetries of the theory is made. Chapter 5 briefly concludes.
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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.
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ItemLearning invariant representations with applications to high-energy physics( 2020)In searches for new physics in high-energy physics, experimental analyses are primarily concerned with physical processes which are rare or hitherto unobserved. To claim a statistically significant discovery or exclusion of new physics when studying such decays, it is necessary to maintain an appropriate signal to noise ratio. This makes systems capable of efficient discrimination of signal from datasets overwhelmingly dominated by background events an important component of modern experimental analyses. However, na\"ive application of these methods is liable to raise poorly understood systematic effects which may ultimately degrade the significance of the final measurement. To understand the origin of these systematic effects, we note that there are certain protected variables in experimental analyses which should remain unbiased by the analysis procedure. Variables that the input parameters of models of new physics are strongly dependent upon and variables used to model background contributions to the total measured event yield fall into this category. Systems responsible for separating signal from background events achieve this by sampling events with signal-like characteristics from all candidate events. If this procedure introduces sampling bias into the distribution of protected variables, this introduces systematic effects into the analysis which are difficult to characterize. Thus it is desirable for these systems to distinguish between signal and background events without using information about certain protected variables. Beyond high-energy physics, building systems that make decisions independent of certain protected or sensitive information is an important theme in the real-world application of machine learning and statistics. We address this task as an optimization problem of finding a representation of the observed data that is invariant to the given protected quantities. This representation should satisfy two competing criteria. Firstly, it should contain all relevant information about the data so that it may be used as a proxy for arbitrary downstream tasks, such as inference of unobserved quantities or prediction of target variables. Secondly, it should not be informative of the given protected quantities, so that downstream tasks are not influenced by these variables. If the protected quantities to be censored from the intermediate representation contain information that can improve the performance of the downstream task, it is likely that removing this information will adversely affect this task. The challenge lies in balancing both objectives without significantly compromising either requirement. The contribution of this thesis is a new set of methods for addressing this problem. This thesis is divided into two parts, which are largely independent of one another. The first part of this thesis is about constraining the optimization procedure by which the representation is learnt to reduce the informativeness of the representation of the given protected quantities, such that the representation is invariant to changes in these quantities. The second part of this thesis approaches the problem from a latent variable model perspective, in which additional unobserved (latent) variables are introduced which explain the interaction between different attributes of the observed data. These latent variables can be interpreted as a more fundamental, compact lower-dimensional representation of the original high-dimensional unstructured data. By constraining the structure of this latent space, we demonstrate we can isolate the influence of the protected variables into a latent subspace. This allows downstream tasks to only access a relevant subset of the learned representation without being influenced by protected attributes of the original data. The feasibility of our proposed methods is demonstrated through application to a challenging experimental analysis in precision flavor physics at the Belle II experiment - the study of the $b \rightarrow s \gamma$ transition, a sensitive probe of potential new physics.