The exponential parameterization of the neutrino mixing matrix as an SU(3) group element and an account for new experimental data

Resumo

The exponential form of the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix for neutrinos is considered in the context of the fundamental representation of the SU(3) group. The logarithm of the mixing matrix is obtained. Based on the most recent experimental data on neutrino mixing, the exact values of the entries of the exponential matrix are calculated. The exact values for its real and imaginary parts are determined, respectively, in charge of the mixing without CP violation and of the pure CP violation effect. The hypothesis of complementarity for quarks and neutrinos is confirmed. The factorization of the exponential mixing matrix, which allows the separation of the mixing and of the CP violation itself in the form of the product of rotations around the real and imaginary axes, is demonstrated.