Simple renormalizable flavor symmetry for neutrino oscillations

The recent measurement of a non-zero neutrino mixing angle $\theta_{13}$ requires a modification of the tri-bimaximal mixing pattern that predicts a zero value for it. We propose a new neutrino mixing pattern based on a spontaneously-broken $A_{4}$ flavor symmetry and a type-I seesaw mechanism. Our model allows for approximate tri-bimaximal mixing and non-zero $\theta_{13}$, and contains a natural way to implement low and high energy CP violation in neutrino oscillations, and leptogenesis with a renormalizable Lagrangian. Both normal and inverted mass hierarchies are permitted within $3\sigma$ experimental bounds, with the prediction of small (large) deviations from maximality in the atmospheric mixing angle for the normal (inverted) case. Interestingly, we show that the inverted case is excluded by the global analysis in $1\sigma$ experimental bounds, while the most recent MINOS data seem to favor the inverted case. Our model make predictions for the Dirac CP phase in the normal and inverted hierarchies, which can be tested in near-future neutrino oscillation experiments. Our model also predicts the effective mass $|m_{ee}|$ measurable in neutrinoless double beta decay to be in the range $0.04\lesssim |m_{ee}| \lesssim 0.15$ eV for the normal hierarchy and $0.06\lesssim |m_{ee}| \lesssim 0.11$ eV for the inverted hierarchy, both of which are within the sensitivity of the next generation experiments.