Tribimaximal mixing from small groups

Current experimental data on the neutrino parameters are in good agreement with tribimaximal mixing and may indicate the presence of an underlying family symmetry. For 76 flavor groups, we perform a systematic scan for models: The particle content is that of the standard model plus up to three flavon fields, and the effective Lagrangian contains all terms of mass dimension ≤6. We find that 44 groups can accommodate models that are consistent with experiment at 3σ, and 38 groups can have models that are tribimaximal. For A ₄×Z₃, T₇, and T₁₃ we look at correlations between the mixing angles and make a prediction for θ₁₃ that will be testable in the near future. We present the details of a model with θ₁₂=33.9°, θ₂₃=40. 9°, θ₁₃=5.1° to show that the recent tentative hints of a nonzero θ₁₃ can easily be accommodated. The smallest group for which we find tribimaximal mixing is T₇. We argue that T ₇ and T₁₃ are as suited to produce tribimaximal mixing as A₄ and should therefore be considered on equal footing. In the appendixes, we present some new mathematical methods and results that may prove useful for future model building efforts.