Tri-bimaximal Neutrino Mixing from A(4) and θ_{13} \sim θ_C

Abstract

It is a common believe that, if the Tri-bimaximal mixing (TBM) pattern is explained by vacuum alignment in an A(4) model, only a very small reactor angle, say θ_{13} \sim λ^2_C being λ_C \equiv θ_C the Cabibbo angle, can be accommodated. This statement is based on the assumption that all the flavon fields acquire VEVs at a very similar scale and the departures from exact TBM arise at the same perturbation level. From the experimental point of view, however, a relatively large value θ_{13} \sim λ_C is not yet excluded by present data. In this paper, we propose a Seesaw A(4) model in which the previous assumption can naturally be evaded. The aim is to describe a θ_{13} \sim λ_C without conflicting with the TBM prediction for θ_{12} which is rather close to the observed value (at λ^2_C level). In our model the deviation of the atmospherical angle from maximal is subject to the sum-rule: \sin ^2 θ_{23} \approx 1/2 + \sqrt{2}/2 \sin δ\cos θ_{13} which is a next-to-leading order prediction of our model.