Analysis of the CP violation and complementarity of mixing for quarks and neutrinos in the exponential and cobimaximal parameterizations of the mixing matrix

The latest (November 2018) experimental data on neutrino mixing is analyzed in the framework of standard, cobimaximal and exponential parameterizations. The logarithm of the mixing matrix is found and the matrix elements values for the exponential and cobimaximal mixing matrix forms are determined. The exponential form allows factorization of the matrices responsible for the rotations in the real space and the CP violation in the form of the rotation in imaginary space. Exponential form also allows easy verification of complementarity of quark and neutrino mixing. In the exponential mixing parameterization the angle between the rotation axis for quarks neutrinos is studied and the complementarity of quark and neutrino mixing is investigated. Entries for the cobimaximal matrix are identified to comply with experimental data and provide exact quark-neutrino mixing complementarity. Jarlskog invariant is employed to study the degree of CP violation for various parameters of mixing matrices in the standard, cobimaximal and exponential parameterizations. The mixing matrix is studied as the group SU(3) element with the help of the exponential parameterization. SU(3) group parameters φ и are written for the mixing matrix; their dependence of the degree of the CP violation is explored.