Neutrino Mass Matrix Subject to $\mu-\tau$ Symmetry and Invariant under a Cyclic Permutation

TL;DR

This paper investigates neutrino mass matrices constrained by $$ symmetry and cyclic permutation invariance, finding that initial models are incompatible with data, but modifications yield viable inverted hierarchy masses.

Contribution

It introduces a modified neutrino mass matrix with a zero sum rule to achieve realistic inverted hierarchy neutrino masses.

Findings

Initial $$ symmetric model incompatible with experimental data.

Modified mass matrix with zero sum rule produces viable inverted hierarchy masses.

Neutrino mass hierarchy consistent with experimental observations after modification.

Abstract

Neutrino masses arise via a seesaw mechanism and its mass hierarchy, with assumption that heavy Majorana neutrino mass matrix subject to $\mu-\tau$ symmetry and invariant under a cyclic permutation, are evaluated. Within this scenario, the neutrino masses: $\left|m_{1}\right|=\left|m_{2}\right|<\left|m_{3}\right|$ are obtained, which are incompatible with the experimental data. By modifying neutrino mass matrix with the zero sum rule condition, the neutrino masses in inverted hierarchy: $\left|m_{3}\right|<\left|m_{1}\right|<\left|m_{2}\right|$ are obtained.