Analysis of the CP Violation and Complementarity of Mixing for Quarks and Neutrinos in the Exponential and Cobimaximal Parametrizations of the Mixing Matrix

Abstract

The latest (November 2018) experimental data on neutrino mixing is analyzed in the framework of standard, cobimaximal and exponential parametrizations. The logarithm of the mixing matrix is found and the matrix element values for the exponential and cobimaximal mixing matrix forms are determined. The exponential form allows factorization of the matrices that are responsible for the rotations in real space and the CP violation in the form of the rotation in imaginary space. The exponential form also allows easy verification of the complementarity of quark and neutrino mixing. In the exponential mixing parametrization 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. The Jarlskog invariant is employed to study the degree of CP violation for various parameters of mixing matrices in the standard, cobimaximal and exponential parametrizations. The mixing matrix is studied as the group SU(3) element with the exponential parametrization. SU(3) group parameters φ and θ are written for the mixing matrix; their dependence of the degree of the CP violation is explored.