Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D

Abstract

The residual Z^s_2(k) and bar Z^s_2(k) symmetries induce a direct and unique phenomenological relation with theta_x (= theta_13) expressed in terms of the other two mixing angles, theta_s (= theta_12) and theta_a (= theta_23), and the Dirac CP phase delta_D. Z^s_2(k) predicts a theta_x probability distribution centered around 3^o ~ 6^o with an uncertainty of 2^o to 4^o while those from bar Z^s_2(k) are approximately a factor of two larger. Either result fits the T2K, MINOS and Double CHOOZ measurements. Alternately a prediction for the Dirac CP phase delta_D results in a peak at +-74^o (+-106^o) for Z^s_2(k) or +-123^o (+-57^o) for bar Z^s_2(k) which is consistent with the latest global fit. We also give a distribution for the leptonic Jarslkog invariant J_v which can provide further tests from measurements at T2K and NOvA.