A prediction of neutrino mixing matrix with CP violating phase

Abstract

The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $\delta_{\rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^\circ$ within $1\sigma (3\sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.