On discrete flavour symmetries, neutrino mass and mixing

Abstract

Neutrino mixing is a thriving area of particle physics research, with the recent discovery of non-zero ?13 inspiring a large amount of research into the field. This thesis presents two models which aim to explain the observed neutrino mixing patterns in the context of Grand Unified Theories, which also output quark masses and mixings.

A model predicting Tri-Bimaximal mixing is presented which combines a previously published SU(5) model with an A4 family symmetry. Extra adjoint fermionic matter is present as prescribed by the original Unified model, and this provides 2 seesaw particles; however they are constrained to give the same contribution to neutrino mixing once the flavour symmetry is imposed. This motivates the addition of an extra field in order to obtain two non-zero neutrino masses. This model has the desirable property of having a diagonal Majorana sector, something which is normally assumed in such models.

In order to explain the discovery of non-zero ?13, a second model is presented which produces Tri-Maximal mixing, a perturbed version of Tri-Bimaximal mixing which retains the solar prediction whilst changing the atmospheric and reactor predictions. This is also performed in a unified context and therefore charged lepton corrections to mixing are related to the Cabibbo angle in a new way via a sum rule.

Finally the impact of flavour symmetries on leptogenesis is discussed; it is mentioned that models which predict neutrino mixing can very often lead to 0 leptogenesis and therefore no baryon asymmetry in the Universe. However this conclusion is drawn without considering the difference in scales between flavour symmetry breaking and leptogenesis. When this is taken into account it is shown in the context of two simple models that successful leptogenesis can be achieved.

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