Tribimaximal mixing from small groups

Abstract

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 $\ensuremath{\le}6$. We find that 44 groups can accommodate models that are consistent with experiment at $3\ensuremath{\sigma}$, and 38 groups can have models that are tribimaximal. For ${A}_{4}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{3}$, ${T}_{7}$, and ${T}_{13}$ we look at correlations between the mixing angles and make a prediction for ${\ensuremath{\theta}}_{13}$ that will be testable in the near future. We present the details of a model with ${\ensuremath{\theta}}_{12}=33.9\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\theta}}_{23}=40.9\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\theta}}_{13}=5.1\ifmmode^\circ\else\textdegree\fi{}$ to show that the recent tentative hints of a nonzero ${\ensuremath{\theta}}_{13}$ can easily be accommodated. The smallest group for which we find tribimaximal mixing is ${T}_{7}$. We argue that ${T}_{7}$ and ${T}_{13}$ are as suited to produce tribimaximal mixing as ${A}_{4}$ 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.