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

TL;DR

This paper introduces an exponential parameterization of the neutrino mixing matrix, enabling a clearer analysis of CP violation and comparison across different data sets, with implications for understanding neutrino and quark mixing.

Contribution

It develops a novel exponential parameterization approach for the neutrino mixing matrix, relating it to standard forms and analyzing CP violation effects in detail.

Findings

The exponential parameterization aligns with standard matrix forms.

CP violation effects are explicitly incorporated in the matrix entries.

The complementarity hypothesis between quark and neutrino mixing is supported.

Abstract

The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is used for 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 related to the exponential parameterization exactly. The exponential form allows easy factorization and separate analysis of the rotation and the CP violation. With the most recent experimental data on the 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 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.