A partial $\mu$-$\tau$ symmetry and its prediction for leptonic CP violation

Abstract

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.

arXiv commentLaTex 11 pages, 3 figues, more dicussions added, references updated, matches the published version

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