A partial μ–τ symmetry and its prediction for leptonic CP violation

We find that the lepton flavor mixing matrix U should possess a partial μ–τ   permutation symmetry |Uμ1|=|Uτ1||Uμ1|=|Uτ1|, and the latter predicts a novel correlation between the Dirac CP-violating phase δ   and three flavor mixing angles θ12θ12, θ13θ13 and θ23θ23 in the standard parametrization. Inputting the best-fit values of these angles reported by Capozzi et al., we obtain the prediction δ≃255°δ≃255° in the normal neutrino mass ordering, which is in good agreement with the best-fit result δ≃250°δ≃250°. In this connection the inverted neutrino mass ordering is slightly disfavored. If this partial μ–τ   symmetry is specified to be |Uμ1|=|Uτ1|=1/6, one can reproduce the phenomenologically-favored relation sin2⁡θ12=(1−2tan2⁡θ13)/3sin2⁡θ12=(1−2tan2⁡θ13)/3 and a viable two-parameter description of U   which were first uncovered in 2006. Moreover, we point out that the octant of θ23θ23 and the quadrant of δ   can be resolved due to the slight violation of |Uμ2|=|Uτ2||Uμ2|=|Uτ2| and |Uμ3|=|Uτ3||Uμ3|=|Uτ3| either at the tree level or from radiative corrections.