Up-type quark masses in SU(5) F-theory models

TL;DR

This paper investigates how F-theory SU(5) models can naturally generate large top quark masses through local singularity structures and instanton effects, aligning with observed quark mass hierarchies.

Contribution

It explicitly computes Yukawa couplings near E6 singularities in F-theory models, demonstrating how instantons induce hierarchical up-type quark masses.

Findings

Non-zero Yukawa couplings for all U-quark families due to instantons.

Hierarchical structure of quark masses derived from wavefunction profiles.

Model successfully reproduces the measured top quark mass and mass ratios.

Abstract

F-theory SU(5) unification has been proposed as a scenario where the mass of the top quark is naturally large, as opposed to type II SU(5) models. We analyze this claim from the viewpoint of local SU(5) F-theory models, by explicitly computing the 10 x 10 x 5 Yukawa couplings that are developed in the vicinity of an E6 singularity. Realizing this singularity via T-branes allows for a non-trivial mass for the top quark, while lighter generations of up-type quarks still have vanishing Yukawa couplings. Nevertheless, we show that by taking instanton effects into account non-vanishing Yukawas are induced for all U-quark families, together with a hierarchical structure at the level of the superpotential. Finally, by solving for internal wavefunction profiles we compute physical U-quark Yukawa couplings and show that this F-theory scenario allows to describe the measured top quark mass, as well as the observed quotients of U-quark masses.