Flavour in $SU(5)$ Finite Grand Unified Models

TL;DR

This paper investigates finite $SU(5)$ supersymmetric models with specific flavor symmetries, analyzing their mass matrices, parameter constraints, and potential to reproduce observed quark masses and mixings, with some models achieving all-loop finiteness.

Contribution

It introduces new finite $SU(5)$ models with flavor symmetries, explores their mass textures, and determines the minimal phases and parameter restrictions, advancing the understanding of Yukawa couplings in these theories.

Findings

Some models are phenomenologically promising with realistic mass textures.

Parametric solutions restrict Yukawa couplings at the GUT scale.

An all-loop finite model reproduces quark masses and mixing patterns.

Abstract

Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings.