A scan for models of neutrino mixing from non-abelian discrete symmetries

The structure of the neutrino mixing matrix is indicative of an underlying family symmetry that interrelates the three generations of fermions in the Standard Model. We systematically scan the parameter space of 76 discrete non-Abelian family symmetries and construct all models with the Standard Model particle content and up to three flavon fields where we include nonrenormalizable interactions of mass dimension five and six. We find that of the 76 groups that we considered, 44 groups can accommodate models that are consistent with experiment at 3σ, and 38 groups can have models that are tribimaximal. One immediate consequence is that A₄ is not "special", but should be considered on equal footing with other groups such as T₇ that is the smallest group for which we find tribimaximal mixing, and T₁₃ that has the largest fraction of TBM models. We present the details of a model with θ₁₂ = 33.9°,θ₂₃ = 49.1°,θ₁₃ = 5.1° to show that a non-zero θ₁₃ can easily be accommodated.