Exponential parameterization of the neutrino mixing matrix: comparative analysis with different data sets and CP violation

The exponential parameterization of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is used for a comparative analysis of different neutrino mixing data. The UPMNS matrix is considered as the element of the SU(3) group and the second-order matrix polynomial is constructed for it. The inverse problem of constructing the logarithm of the mixing matrix is addressed. In this way the standard parameterization is exactly related to the exponential parameterization. The exponential form allows easy factorization and separate analysis of the rotation and the CP violation. With the most recent experimental data on neutrino mixing (May 2016), we calculate the values of the exponential parameterization matrix for neutrinos with account for the CP violation. The complementarity hypothesis for quarks and neutrinos is demonstrated to hold, despite a significant change in the neutrino mixing data. The values of the entries of the exponential mixing matrix are evaluated with account for the actual degree of the CP violation in neutrino mixing and without it. Various factorizations of the CP-violating term are investigated in the framework of the exponential parameterization.