Lepton Mixing and Flavor Symmetries

Abstract

The masses in the quark sectors are set in strong hierarchy while the hierarchy is smaller in the lepton sector. The mixing in the lepton sector is large (one mixing angle is close to maximal, one is large and the _third is small), while the mixing in the quark sector is smalL The horizontal or flavor symmetry was proposed to give answers to all above mentioned observations. In this thesis we study the lepton mixing and how to infer the flavor symmetry from it. First we study the widely proposed mixing which is called tri-bimaximal (TBM) and try to answer the question "Is TBM an accidental symmetry". The TBM mixing is not accidental if structures of the corresponding leptonic mass matrices follow immediately from a certain (residual or broken) flavor symmetry. We study the effect of the deviation of the mixing parameters (angles and phase) from their TBM values on the TBM symmetry which is the symmetry manifesting in the mass matrix. We show that possible deviations from the TBM mixing can lead to strong modifications of the mass matrix and strong violation of the TBM mass relations. As a result, the mass matrix may have an "anarchical" structure with random values of elements or it may have some symmetry which differs from the TBM symmetry. Interesting examples include matrices with texture zeros, matrices with certain "flavor alignment" as well as hierarchical matrices with a two-component structure, where the dominant and sub-dominant contributions have different symmetries. This opens up new approaches to understand lepton mixing. We study two methods to deal with flavor symmetry. The first is the conventional way called (top- down) in which one can consider the invariance of the Lagrangian under a certain group and finally try to obtain the desired mixing and masses to check whether this group can be considered as the flavor symmetry group or not. Following this method we study a model based on the discrete group .6.(27) t>< 52 account for the recent neutrino oscillation data that deviate from TBM. Breaking of the .6.(27) group with a certain vacuum