TFH Mixing Patterns, Large $\theta_{13}$ and $\Delta(96)$ Flavor Symmetry

We perform a comprehensive analysis of the Toorop-Feruglio-Hagedorn (TFH) mixing patterns within the family symmetry $\Delta(96)$. The general neutrino mass matrix for the TFH mixing and its symmetry properties are investigated. The possible realizations of the TFH mixing in $\Delta(96)$ are analyzed in the minimalist approach. We propose two dynamical models which produce the TFH mixing patterns at leading order. The full flavor symmetries are $\Delta(96)\times Z_3\times Z_3$ and $\Delta(96)\times Z_5 \times Z_2$ respectively. The next to leading order terms introduce corrections of order $\lambda^2_c$ to the three mixing angles in both models. The allowed mixing patterns are studied under the condition that the Klein four subgroups and the cyclic $Z_N$ subgroups with $N\geq3$ are preserved in the neutrino and the charged lepton sector respectively. We suggest that the deformed tri-bimaximal mixing is a good leading order approximation to understanding a largish reactor angle.