Texture-zero patterns of lepton mass matrices from modular symmetry
Gui-Jun Ding, F. R. Joaquim, Jun-Nan Lu
Abstract
A bstract 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 $$ {\Gamma}_3^{\prime}\cong {T}^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mn>3</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo>≅</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> 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 double beta decay, are discussed. We find that the minimal viable lepton model depends on only 7 real free parameters including the modulus τ (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).