Physics beyond the standard model: moduli stabilisation and neutrino physics

Abstract

We look at models of neutrino mass and mixing which represent an important aspect of physics beyond the Standard Model (SM). We derive approximate analytic formulae for the neutrino mixing angles in general SD involving NLO and NNLO corrections. These expressions, which are given in terms of input see-saw parameters, provide a useful guide for unified model building. We then evaluate these formulae in the cases of CSD and PCSD for two numerical GUT inspired models in order to measure the effect of NLO and NNLO corrections. In addition to this, we analyse the effects of charged lepton corrections and Renormalisation Group (RG) running on neutrino mixing angles and various sum rules, in models where tri-bimaximal mixing is exactly achieved at high energy scale. We find the RG corrections to neutrino sum rules to be typically small for the case of hierarchical neutrinos.

Another aspect of physics beyond the Standard Model concerns the search for viable four dimensional string models. We look at moduli stabilisation in the framework of four dimensional models arising from heterotic and type IIA string theories. The superpotentials in these models involve flux and non-perturbative terms. We consider a set of conditions which lead to moduli solutions for Minkowski minima of the scalar potential. Following this procedure, we correct models presented in the literature and uplift the at directions. We also study inflation in the framework of these models. We find that it is successfully achieved along the axionic directions of the moduli fields for values of the initial conditions within substantial regions of parameter space. A very interesting structure of the potential is obtained when considering the evolution of two axionic directions in one of the models in the presence of a gaugino condensate term. This structure, which involves the existence of multiple local minima surrounding the global one, represents a perfect background for realising inflation.

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