# Two simple textures of the magic neutrino mass matrix

## TL;DR

This paper introduces two simple modifications to the tri-bimaximal neutrino mixing matrix by breaking its mu-tau symmetry with a complex magic matrix, exploring their phenomenological consequences.

## Contribution

It proposes two new textures of the neutrino mass matrix that incorporate a complex magic matrix to break mu-tau symmetry in TBM mixing.

## Key findings

- Two viable neutrino mass matrix textures identified
- Predictions for neutrino mixing angles and CP violation
- Implications for neutrino mass hierarchy

## Abstract

The Tri-Bimaximal (TBM) mixing predicts a vanishing $\theta_{13}$. This can be attributed to the inherited $\mu-\tau$ symmetry of TBM mixing. We break its $\mu-\tau$ symmetry by adding a complex magic matrix with one variable to TBM neutrino mass matrix with one vanishing eigenvalue. We present two such textures and study their phenomenological implications.