Hybrid Seesaw Neutrino Masses with A_4 Family Symmetry

Abstract

We consider the scenario in which neutrino data are explained by the interplay of type I and II seesaw terms in the Majorana neutrino mass matrix ${\cal M}_ν= {\cal M}_L - {\cal M}_D {\cal M}_R^{-1} {\cal M}_D^T$. We construct a predictive model with ${\cal M}_L$ proportional to the unit matrix, 3 diagonal texture zeros in ${\cal M}_R$, and ${\cal M}_D$ diagonal. We show how this pattern can be maintained by the non-Abelian discrete symmetry $A_4$, and discuss its phenomenological consequences. It turns out that the two types of seesaw give contributions of the same order to ${\cal M}_ν$. In the CP conserving case, we find $\sinθ_{13}\approx 2/(\tan 2θ_{23} \tan 2θ_{12})$ and we predict inverted (normal) ordering of the mass spectrum for $\tan^2θ_{12} < 0.5 ~(>0.5)$.