TFH mixing patterns, large θ13 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)×Z3×Z3 and Δ(96)×Z5×Z2 respectively. The next to leading order terms introduce corrections of order λc2 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 ZN subgroups with N⩾3 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.