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

Abstract

We find that the lepton flavor mixing matrix $U$ should possess a partial $μ$-$τ$ permutation symmetry $|U^{}_{μ1}| = |U^{}_{τ1}|$, and the latter predicts a novel correlation between the Dirac CP-violating phase $δ$ and three flavor mixing angles $θ^{}_{12}$, $θ^{}_{13}$ and $θ^{}_{23}$ in the standard parametrization. Inputting the best-fit values of these angles reported by Capozzi {\it et al}, we obtain the prediction $δ\simeq 255^\circ$ in the normal neutrino mass ordering, which is in good agreement with the best-fit result $δ\simeq 250^\circ$. In this connection the inverted neutrino mass ordering is slightly disfavored. If this partial $μ$-$τ$ symmetry is specified to be $|U^{}_{μ1}| = |U^{}_{τ1}| =1/\sqrt{6}~$, one can reproduce the phenomenologically-favored relation $\sin^2θ^{}_{12} = \left(1 - 2\tan^2θ^{}_{13}\right)/3$ and a viable two-parameter description of $U$ which were first uncovered in 2006. Moreover, we point out that the octant of $θ^{}_{23}$ and the quadrant of $δ$ can be resolved thanks to the slight violation of $|U^{}_{μ2}| = |U^{}_{τ2}|$ and $|U^{}_{μ3}| = |U^{}_{τ3}|$ either at the tree level or from radiative corrections.