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