Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing

We investigate a general structure of lepton mixing matrix resulting from the SU${}_F$(3) gauge family model with an appropriate vacuum structure of SU${}_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase ${\delta }_e$ and the leptonic Wolfenstein parameters ${\lambda }_e$, $A_e$, ${\rho }_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the leptonic Wolfenstein parameters. It is found that the phase ${\delta }_e$ is strongly constrained and only a large or nearly maximal leptonic CP-violating phase $\mathrm{\mid }{\delta }_e\mathrm{\mid }\simeq 3\pi \mathrm{/}4\sim \pi \mathrm{/}2$ is favorable when ${\lambda }_e>0.15$. In particular, when taking ${\lambda }_e$ to be the Cabbibo angle $\gl_e\simeq \lambda \simeq 0.225$, a sensible result for leptonic Wolfenstein parameters and CP violation is obtained with $A_e=1.40$, ${\rho }_e=0.20$, $\delta_{e}\sim 101.76;^o$, which is compatible with the one in quark sector. An interesting correlation between leptons and quarks is observed, which indicates a possible common origin of masses and mixing for the charged-leptons and quarks.