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The measurement of the reactor angle by the Daya Bay and RENO experiments in2012 has ruled out the tri-bimaximal paradigm. Adopting an S4 family symmetry,we propose direct models of the trimaximal type TM1 in which the tri-bimaximalKlein symmetry of the neutrino sector is broken to a residual Z2 symmetry. Insuch a scenario, the solar mixing angle is decreased compared to itstri-bimaximal value by about one degree, thus bringing it in excellentagreement with experimental observation. The atmospheric mixing angle, on theother hand, depends on the CP violating Dirac phase delta. Imposing CPconservation in the family symmetry limit, we show how to break the CP symmetryvia flavon VEVs with well-defined complex phases, so that sizable deviations ofthe atmospheric angle from maximal mixing, consistent with the latest globalfits, are produced.

Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation