Flavor Symmetry, Leptogenesis and Grand Unification Theories

Abstract

Many neutrino experiments in the last few years have shown concrete evidence for neutrino mass and leptonic mixing; an indication of new physics beyond the standard model. In this thesis, we systematically study the flavor symmetry indicated by the low scale neutrino experiment data with the assumption that the seesaw mechanism is the reason for the light neutrino masses. In the flavor basis, the testable exchange symmetry between muon neutrino and tau neutrino (\mu-\tau$) is introduced to explain the near maximal atmospheric mixing angle and vanishing reactor mixing angle. This symmetry can reduce the seesaw parameters naturally and make it possible to connect the baryon asymmetry of our universe to the low scale neutrino data if leptogenesis causes the baryon asymmetry. We also show this leptonic symmetry can be extended to the quark sector and present a realistic supersymmetry $SU(5)$ grand unification model. Motivated by solar mixing angle $\sin^2\theta_{\rm solar}\simeq1/3$, we embed the $\mu-\tau$ symmetry in an $S3$ permutation symmetry and obtain a so-called tri-bimaximal mixing pattern. We study the stability of the texture under radiative corrections. This $S3$ model is so constrained that the CP-violating phases of the low scale mixing are those generating the baryon asymmetry within leptongesis. Attempting to unify three families of fermions within the grand unification theories, we treat three families of fermions as the three dimensional irreducible representation of $S4$ and build a realistic model based on $SO(10)$ gauge group. This model predicts degenerate a right-handed neutrino mass spectrum. In this thesis, we also address the issue of the natural realization of the seesaw mechanism in the supersymmetric minimal $SO(10)$ model. We realize the type II seesaw dominance by invoking a warped extra dimension, while keeping predictivity of the model.