Non-diagonal charged lepton mass matrix, the TBM and non-zero $\theta_{13}$

TL;DR

This paper investigates specific charged lepton mass matrix textures with maximum zeros that, when combined with a TBM neutrino matrix, produce lepton mixing consistent with experimental data, including non-zero θ13.

Contribution

It identifies and analyzes charged lepton mass matrix textures with three or four zeros that yield realistic lepton mixing angles, providing explicit textures and relations among their entries.

Findings

Identified textures with three and four zeros compatible with data

Derived relations among matrix entries based on charged lepton masses

Provided explicit Yukawa textures consistent with observed mixing angles

Abstract

Assuming that the neutrino mass matrix is diagonalized by the TBM, we looked for the charged lepton mass matrix textures which render a lepton mixing matrix consistent with data. We were interested in the textures with the maximum number of zeros, so, we explored the cases of real matrices with three (and also four zeros) and found which of them provide solutions in agreement with data. We present the successful Yukawa textures and obtained the relative sizes of their non-zero entries. We found some interesting relations among the entries of these textures in terms of the charged lepton masses.