Fitting fermion masses and mixings in F-theory GUTs

TL;DR

This paper investigates Yukawa couplings in local F-theory SU(5) GUT models with E7 symmetry, demonstrating a unique hierarchical flavor structure that yields realistic fermion masses and mixings, applicable to E8 models as well.

Contribution

It identifies a unique E7-based model with hierarchical fermion masses and computes Yukawa couplings over a broad parameter space, advancing understanding of flavor structure in F-theory GUTs.

Findings

Hierarchical fermion masses and mixings are achievable in the model.

The model's Yukawa couplings are consistent with observed fermion data.

Results extend to E8 enhancement, indicating a universal flavor structure.

Abstract

We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the $E_7$ symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique $E_7$ model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework.