Flavor Symmetries in an SU(5) Model of Grand Unification

TL;DR

This paper explores how imposing various flavor symmetries on a minimal non-supersymmetric SU(5) grand unified theory can reduce free parameters and enhance predictability, identifying 25 viable symmetry cases.

Contribution

It systematically classifies all possible flavor symmetries in the Yukawa sector of the minimal SU(5) GUT without extra fields, revealing 25 realistic symmetry scenarios.

Findings

Identified 25 distinct flavor symmetry cases including $bZ_2$, $bZ_3$, $bZ_4$, and U(1) symmetries.

Found no non-Abelian flavor symmetry cases compatible with the model.

Reduced the number of free parameters in the model through symmetry constraints.

Abstract

We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric $\mathrm{SU}(5)$ grand unified theory, without introducing additional flavor-related fields. Such symmetries reduce the number of free parameters in the model and therefore lead to more predictive models. We consider the Yukawa sector of the Lagrangian, and search for all possible flavor symmetries. As a result, we find 25 distinct realistic flavor symmetry cases, with $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$, and $\mathrm{U}(1)$ symmetries, and no non-Abelian cases.