Exponential parameterization of neutrino mixing matrix with account for CP-violation data

TL;DR

This paper introduces an exponential parameterization of the neutrino mixing matrix that facilitates analysis of CP-violation effects, based on recent experimental data, and explores its implications for neutrino and quark complementarity.

Contribution

It presents a novel exponential form of the neutrino mixing matrix that separates CP-violating and Majorana terms, and demonstrates its consistency with experimental data and quark-neutrino complementarity.

Findings

Determined the exponential matrix entries for neutrino mixing without CP-violation.

Estimated the CP-violating parameter based on current experimental data.

Confirmed the unitarity of the exponential parameterization and CP-violation transformation.

Abstract

The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is discussed. The exponential form allows easy factorization and separate analysis of the CP-violating and Majorana terms. Based upon the recent experimental data on the neutrino mixing, the values for the exponential parameterization matrix for neutrinos are determined. The matrix entries for the pure rotational part in charge of the mixing without CP-violation are derived. The complementarity hypothesis for quarks and neutrinos is demonstrated. The comparison of the results, based on most recent and on old data is held. The CP-violating parameter value is estimated, based on the so far imprecise experimental indications, regarding CP-violation for neutrinos. The unitarity of the exponential parameterisation and the CP-violating term transform is confirmed. The transform of the neutrino mass state vector by the exponential matrix with account for CP-violation is shown.