A predictive A4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum Rule

We propose a novel A4 model in which the Tri-Bimaximal (TB) neutrino mixing and the charged lepton mass hierarchy are reproduced simultaneously. At leading order, the residual symmetry of the neutrino sector is Z2 x Z2 which guarantees the TB mixing without adjusting ad hoc free parameters. In the charged lepton sector, one of the previous Z2 is maximally broken and the resulting mass matrix is nearly diagonal and hierarchical. A natural mechanism for the required vacuum alignment is given with the help of the supersymmetry and an abelian symmetry factor. In our model, subleading effects which could lead to appreciable deviations from TB mixing are very restrictive giving rise to possible next-to-leading predictions. From an explicit example, we show that our ``constrained'' A4 model is a natural framework, based on symmetry principle, to incorporate the TB sum rule: sin^2(\theta_{12})=1/3+2\sqrt{2}(cos(\delta) sin(\theta_{13})/3).