Tri-Bi-Maximal flavor pattern deviation using equivalent class

Abstract

We assume that the neutrino mass matrix Mν, in the model-independent context, is diagonalized by the Tri-Bi-Maximal (TBM) pattern. In the following, we explore the TBM mixing pattern deviation by considering different textures for the charged lepton matrix, which are classified into equivalence classes that allow us to reproduce the experimental data on neutrino oscillation. Our target is on the charged lepton matrix with the minimum number of free parameters, i.e., the maximum number of zeros of the texture that allows us to correctly reproduce the value of the reactor mixing angle θ13. We show a deviation from the TBM pattern in terms of the charged leptonic masses, which provides a prediction value for the phase factors in the charged lepton mass matrices. These are related to the “Dirac-like” CP and “Majorana-like” phase factors. For the last type of phase, we show its phenomenological implications through effective Majorana mass in the neutrinoless double-beta decay.