A Modular $SU(5)$ Littlest Seesaw

TL;DR

This paper develops a Grand Unified $SU(5)$ model incorporating modular $S_4$ symmetries to explain fermion masses and mixings, extending the littlest modular seesaw framework with novel symmetry protections and hierarchical structures.

Contribution

It introduces a modular $SU(5)$ GUT model with three $S_4$ symmetries, utilizing symmetry protected zeroes to control deviations and generate fermion hierarchies without hierarchical Yukawa couplings.

Findings

Model successfully suppresses deviations in leptonic and down quark sectors.

Hierarchical fermion masses arise from symmetry content, not Yukawa hierarchy.

Provides a unified framework for quark and lepton mass and mixing patterns.

Abstract

We extend the littlest modular seesaw to a Grand Unified scenario based on $SU(5)$ endowed with three modular $S_4$ symmetries. We leverage symmetry protected zeroes in the leptonic and down quark sectors to suppress deviations to the littlest modular seesaw predictions, but not contributions to the quark mixing. The model is supplemented by two weighton fields, such that the hierarchical nature of the charged-lepton masses, as well as the quark masses and mixing, stem from the content and symmetries of the model, rather than a hierarchical nature of the Yukawa coefficients.