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TFH Mixing Patterns, Large $θ_{13}$ and $Δ(96)$ Flavor Symmetry

We perform a comprehensive analysis of the Toorop-Feruglio-Hagedorn (TFH) mixing patterns within the family symmetry $Δ(96)$. The general neutrino mass matrix for the TFH mixing and its symmetry properties are investigated. The possible realizations of the TFH mixing in $Δ(96)$ 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 $Δ(96)\times Z_3\times Z_3$ and $Δ(96)\times Z_5 \times Z_2$ respectively. The next to leading order terms introduce corrections of order $λ^2_c$ 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.