Texture-zero patterns of lepton mass matrices from modular symmetry

TL;DR

This paper systematically analyzes texture-zero patterns in lepton mass matrices within the $ ext{T'}$ modular symmetry framework, identifying viable models that fit experimental data and predicting lepton mixing parameters.

Contribution

It introduces a comprehensive classification of texture-zero patterns in lepton mass matrices derived from $ ext{T'}$ modular symmetry, including phenomenologically viable models and detailed benchmark analyses.

Findings

Minimal viable model depends on 7 parameters including $ au$

Identifies texture-zero patterns compatible with experimental data

Provides predictions for lepton mixing angles and CP phases

Abstract

Texture zeros in fermion mass matrices have been widely considered in tackling the Standard Model flavour puzzle. In this work, we perform a systematic analysis of texture zeros in lepton mass matrices in the framework of $\Gamma_{3}'\cong T'$ modular symmetry. Assuming that the lepton fields transform as irreducible representations of $T'$, we obtain all possible texture-zero patterns for both charged-lepton and neutrino mass matrices which can be achieved from $T'$ modular symmetry. We provide representative models for the phenomenologically-viable textures which can accommodate the experimental data. The predictions for lepton mixing angles, CP-violating phases, light neutrino masses and effective neutrino mass relevant for neutrinoless doble beta decay, are discussed. We find that the minimal viable lepton model depends on only $7$ real free parameters including the modulus $\tau$ (the corresponding charged-lepton mass matrix contains $4$ vanishing entries, and the neutrino mass matrix has $1$ texture zero). Finally, we study in detail three benchmark models, one for each neutrino mass generation mechanism considered (Dirac, Majorana via Weinberg operator and Majorana via minimal type-I seesaw mechanism).