$SO(10)$ models with $A_4$ modular symmetry

TL;DR

This paper integrates $A_4$ modular symmetry into $SO(10)$ GUTs to analyze fermion mass matrices, providing detailed numerical fits and predictions for neutrino properties and CP phases.

Contribution

It presents the first comprehensive analysis of $SO(10)$ GUTs with $A_4$ modular symmetry, including minimal and non-minimal models with detailed numerical fits.

Findings

Successful models match experimental fermion masses and mixings.

Predictions for leptonic CP phases and neutrinoless double beta decay.

Graphical correlations between model parameters and observables.

Abstract

We combine $SO(10)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of $\Gamma_3\simeq A_4$, with a Higgs sector comprising a single Higgs multiplet $H$ in the ${\mathbf{10}}$ fundamental representation and one Higgs field $\overline{\Delta}$ in the ${\mathbf{\overline{126}}}$ for the minimal models, plus and one Higgs field $\Sigma$ in the ${\mathbf{120}}$ for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models.