Study of neutrino mass matrices with vanishing trace and one vanishing minor

TL;DR

This paper systematically studies neutrino mass matrices with a vanishing minor and trace, constraining CP phases and analyzing implications for neutrinoless double beta decay and flavor symmetries.

Contribution

It introduces a comprehensive analysis of neutrino mass textures with specific constraints, linking phenomenological viability to flavor symmetry realizations.

Findings

Identifies viable neutrino mass textures consistent with current data.

Constrains CP phases using mass ratio and mixing angle measurements.

Predicts neutrinoless double beta decay rates for viable textures.

Abstract

In this work we carry out a systematic texture study of the neutrino mass matrix with the ansatzes - (i) one vanishing minor and (ii) the zero sum of the mass eigenvalues with the CP phases (henceforth vanishing trace). There are six possible textures of a neutrino mass matrix with one vanishing minor. The viability of each texture is checked with $3\sigma$ values of current neutrino data by drawing scatter plots. In our analysis we are motivated to use the ratio of solar to atmospheric mass-squared differences $R_{\nu}$ for its precise measurement (and also the atmospheric mixing angle $\theta_{23}$) to constrain phenomenologically first the Dirac CP phase $\delta$ in the range of $0^{\degree}-360^{\degree}$ for a given texture with the solutions of the constraint equations. Subsequently we employ this constrained $\delta$ to determine the range of completely unknown Majorana CP Phases ($\alpha$ and $\beta$) for all the viable textures. We also check the neutrinoless double beta decay rate, $|m_{ee}|$ and the Jarlskog invariant, $J_{cp}$ for the textures. Finally the symmetry realization of all the viable textures under the flavor symmetry group $Z_5$ via seesaw mechanism is implemented along with the FN mechanism to determine mass hierarchy structure.