Abstract
We find that the lepton flavor mixing matrix U should possess a partial μ–τ permutation symmetry |Uμ1|=|Uτ1|, and the latter predicts a novel correlation between the Dirac CP-violating phase δ and three flavor mixing angles θ12, θ13 and θ23 in the standard parametrization. Inputting the best-fit values of these angles reported by Capozzi et al., we obtain the prediction δ≃255° in the normal neutrino mass ordering, which is in good agreement with the best-fit result 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 sin2θ12=(1−2tan2θ13)/3 and a viable two-parameter description of U which were first uncovered in 2006. Moreover, we point out that the octant of θ23 and the quadrant of δ can be resolved due to the slight violation of |Uμ2|=|Uτ2| and |Uμ3|=|Uτ3| either at the tree level or from radiative corrections.
Highlights
We find that the lepton flavor mixing matrix U should possess a partial μ-τ permutation symmetry |Uμ1| = |Uτ1|, and the latter predicts a novel correlation between the Dirac CP-violating phase δ and three flavor mixing angles θ12, θ13 and θ23 in the standard parametrization
The μ-τ symmetry is powerful in the sense that it can constrain the neutrino mass texture and predict θ23 = 45◦ together with θ13 = 0◦ or δ = 90◦, but its validity has been being challenged since a relatively large value of θ13 was uncovered by the Daya Bay experiment [5] in 2012
In this Letter we stress that even a partial μ-τ symmetry, defined as |Uμi| = |Uτi|, is powerful enough for us to establish some testable relations among the three neutrino mixing angles and the Dirac CP-violating phase
Summary
We come to an important conclusion from looking at the global fit of the present neutrino oscillation data: behind the observed pattern of lepton flavor mixing should be the partial μ-τ symmetry |Uμ1| = |Uτ1|, and leptonic CP violation must be quite significant. [7] slightly favor the second octant of θ23, the best-fit value of δ is closer to the prediction based on the partial μ-τ symmetry |Uμ2| = |Uτ2| in the normal neutrino mass ordering.
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