Parametrization of lepton mixing matrix in terms of deviations from bi-maximal and tri-bimaximl mixing

TL;DR

This paper introduces a parametrization of the lepton mixing matrix based on deviations from bi-maximal and tri-bimaximal mixing, revealing similarities to the quark CKM matrix.

Contribution

It provides a new parametrization framework for the PMNS matrix and explores the structure of charged lepton mixing matrices deviating from known patterns.

Findings

Charged lepton mixing matrices are close to the CKM matrix.

The parametrization captures deviations from ideal mixing schemes.

Similar structures are found in matrices deviating from bi-maximal and tri-bimaximal mixing.

Abstract

We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine corresponding charged lepton mixing matrix in terms of those three parameters which can deviate bi-maximal or tri-bimaximal mixing. We find that the charged lepton mixing matrices which can deviate bi-maximal mixing matrix and tri-bimaximal mixing matrix exhibit similar structures. Numerical analysis shows that these charged lepton mixing matrices are close to CKM matrix of quark sector.