Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing

Abstract

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 $|\delta_e| \simeq 3\pi/4 \sim \pi/2$ 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.