$SU(5)$ GUTs with $A_4$ modular symmetry

TL;DR

This paper integrates $SU(5)$ GUTs with $A_4$ modular symmetry, analyzing quark and lepton mass matrices across various models, and predicts observable neutrino parameters to guide future experiments.

Contribution

It systematically classifies and analyzes seven types of $SU(5)$ models with $A_4$ modular symmetry, providing 53 benchmark models with minimal free parameters and detailed predictions.

Findings

Identified seven model types with specific matter field assignments.

Provided 53 optimized benchmark models fitting current data.

Predicted neutrino parameters that can be tested in future experiments.

Abstract

We combine $SU(5)$ 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. Classifying the models according to the representation assignments of the matter fields under $A_4$, we find that there are seven types of $SU(5)$ models with $A_4$ modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models.