Residual symmetries for neutrino mixing with a large θ13 and nearly maximal δD.

The residual Z(2)(s)(k) and Z(2)(s)(k) symmetries induce a direct and unique phenomenological relation with θx (≡ θ13) expressed in terms of the other two mixing angles θs(≡ θ12) and θa(≡ θ23) and the Dirac CP phase δD. Z(2)(s)(k) predicts a θx probability distribution centered around 3°-6° with an uncertainty of 2°-4°, while those from Z(2)(s)(k) are approximately a factor of 2 larger. Either result fits the T2K, MINOS, and Double Chooz measurements. Alternately, a prediction for the Dirac CP phase δD results in a peak at ± 74° (± 106°) for Z(2)(s)(k) or ± 123° (± 57°) for Z(2)(s)(k) which is consistent with the latest global fit. We also give a distribution for the leptonic Jarlskog invariant Jν which can provide further tests from measurements at T2K and NOνA.