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

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.