Deviation to the Tri-Bi-Maximal flavor pattern and equivalent classes

TL;DR

This paper investigates deviations from the Tri-Bi-Maximal neutrino mixing pattern by analyzing specific charged lepton mass matrices with texture zeros, exploring their impact on mixing angles and neutrinoless double-beta decay.

Contribution

It introduces a classification of charged lepton mass matrices with minimal free parameters that can reproduce observed neutrino mixing angles, extending the TBM framework.

Findings

Identifies specific texture zero configurations compatible with experimental data.

Provides parameter space analysis for mixing angles based on charged lepton mass matrices.

Discusses implications for neutrinoless double-beta decay phases.

Abstract

In the model-independent context, where the neutrino mass matrix is assumed to be diagonalized by means of a unitary matrix that possess the Tri-Bi-Maximal (TBM) flavor mixing pattern. We present an analysis where the TBM deviation is explored by considering different forms, with texture zeros, for the charged lepton mass matrix. These last mass matrices are classified into equivalent classes. We are interested in the charged lepton mass matrices with the minimum free parameter number, $i.e.$ the maximum number of texture zeros, that allows us to correctly reproduce the reactor mixing angle value. We show a deviation from the TBM pattern in terms of the charged lepton masses as well as the theoretical expressions and their parameter space for the mixing angles. Finally, we present the phenomenological implications of numerical values of the "Majorana-like" phase factors on the neutrinoless double-beta decay.