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

TL;DR

This paper investigates specific textures of the charged lepton mass matrix with zeros that, when combined with a diagonal neutrino mass matrix, produce lepton mixing consistent with observed data, including a non-zero θ13.

Contribution

It identifies and analyzes the maximum-zero textures of the charged lepton mass matrix compatible with experimental data, providing explicit textures and relations among their entries.

Findings

Ten three-zero textures are compatible with data.

Derived relations among matrix entries relate to charged lepton masses.

Presented Yukawa textures with relative sizes of non-zero entries.

Abstract

Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix $U_l$.