Yukawa couplings and fermion mass structure in F-theory GUTs

TL;DR

This paper develops a method to calculate Yukawa couplings in F-theory GUTs, applying it to fermion mass matrices, and explores implications for quark and neutrino masses, mixing, and Higgs sector splitting.

Contribution

It introduces a novel calculation approach for Yukawa couplings in F-theory GUTs, including massive states, and analyzes resulting fermion mass structures and mixings.

Findings

Realistic quark mass matrices achieved

Tri-bi-maximal neutrino mixing accommodated

New features in fermion mass structure compared to Abelian models

Abstract

The calculation of Yukawa couplings in F-theory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion masses based on family symmetries coming from the SU(5)_\perp factor in the underlying E(8) theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen non-renormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU(5) model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tri-bi-maximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector.