An Algebraic Analysis of Neutrino Masses and Mixings and its Implications on $\mu$-$\tau$ Symmetric Mass Matrix

TL;DR

This paper provides an algebraic framework for analyzing Majorana neutrino masses and mixings, deriving relations between mass matrix elements and mixing parameters, and exploring implications of $$-$ au$ symmetry and its deviations.

Contribution

It introduces an analytical approach to relate neutrino mass matrix elements with mixing angles and CP phase, especially under $$-$ au$ symmetry assumptions.

Findings

Relations between mass matrix elements and mixing parameters derived.

Deviation of $ heta_{23}$ from maximal mixing linked to other mixing angles.

Analysis supports $$-$ au$ symmetry implications on neutrino mixing.

Abstract

We diagonalize Majorana neutrino mass matrix with the help of PMNS matrix and obtain analytical relations between the mass matrix elements and mixing parameters, viz., three mixing angles- $\theta_{12}, \theta_{23}, \theta_{13}$ and Dirac CP phase \delta. We analyse our results in a special $\mu$-$\tau$ symmetric mass matrix which corresponds to maximal atmospheric mixing ($\theta_{23}=\pi/4$) and maximal CP violation ($\delta=-\pi/2$). The analysis shows that a deviation of $\theta_{23}$ from its maximal value can be correlated with the prediction of other two mixing angles.