A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing

We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of ${\theta }_{13}$ is within the sensitivity of the experiments which will take data in the near future. The light neutrino spectrum, typical of $A_4$ see-saw models, with its phenomenological implications, also including leptoproduction, is studied in detail.