Model for fermion masses and lepton mixing in SO(10)×A4

Abstract

The discrete flavor symmetry ${A}_{4}$ explains very well neutrino data at low energy, but it seems difficult to extend it to grand unified models since, in general, left-handed and right-handed fields belong to different ${A}_{4}$ representations. Recently a model has been proposed where all the fermions equally transform under ${A}_{4}$. We study here a concrete $SO(10)$ realization of such a model providing small neutrino masses through the see-saw mechanism. We fit the charged fermion masses run up to the unification scale. Some fermion masses properties come from the $SO(10)$ symmetry while lepton mixing angles are a consequence of the ${A}_{4}$ properties. Moreover, our model predicts the absolute value of the neutrino masses; these are in the range ${m}_{\ensuremath{\nu}}\ensuremath{\simeq}0.005--0.052\text{ }\text{ }\mathrm{eV}$.