# Neutrino mass matrices with one texture equality and one vanishing neutrino mass

## TL;DR

This paper systematically investigates Majorana neutrino mass matrices with one texture equality and one zero mass, identifying viable patterns consistent with recent experimental data and exploring their implications for neutrino mixing and CP violation.

## Contribution

It identifies five and ten viable mass matrix patterns for normal and inverted hierarchies, respectively, with detailed phenomenological analysis and a theoretical realization example.

## Key findings

- Five patterns compatible with normal hierarchy at 3σ
- Ten patterns compatible with inverted hierarchy at 3σ
- Strong correlations between oscillation parameters and CP violation

## Abstract

In the light of latest data of neutrino oscillation experiments, we carry out a systematic investigation on the texture structures of Majorana neutrino mass matrix $M_{\nu}$, which contain one vanishing neutrino mass and an equality between two matrix elements. Among 15 logically possible patterns, it is found that for norm order ($m_{3}>m_{2}>m_{1}=0$) of neutrino masses only five of them are compatible with recent experimental data at the $3\sigma$ level, while for inverted order ($m_{2}>m_{1}>m_{3}=0$) ten patterns is phenomenologically allowed. In the numerical analysis, we perform a scan over the parameter space of all viable patterns to get a large sample of scattering points. We present the implications of each allowed pattern for three mixing angles $(\theta_{12},\theta_{2},\theta_{3})$, leptonic CP violation and neutrinoless double-beta decay, predicting strong correlations between oscillation parameters. The theoretical realization of a concrete example is discussed in the framework of Froggatt-Nielsen mechanism.