Probing $\delta_{CP}$ phase and charged lepton flavour violation with $A_4$ flavor symmetry and deviations to tri-bi-maximal mixing via $z_2 \times z_2$ invariant perturbation in the neutrino sector

Abstract

In this work, a flavour theory of a neutrino mass model based on $A_{4}$ symmetry is considered to explain the phenomenology of CP violation phase and charged lepton flavour violation. The spontaneous symmetry breaking of $A_{4}$ symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. $\mathrm{A} z_{2} × z_{2}$ invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of $\theta_{13}$ and $\mathbf{C P}$ violation. We consider an effective theory with an $A_{4} × z_{2} × z_{2}$ symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the $A_{4}$ symmetry.