Yukawa couplings and fermion mass structure in F-theory GUTs

TL;DR

This work analyzes Yukawa couplings in F-theory GUTs with family symmetries from $SU(5)_{\bot}$ within $E_8$, showing how heavy messenger states generate light-generation masses via non-renormalisable operators. The authors develop a local overlap calculus for zero modes and extend it to massive KK/messenger modes, enabling a semi-realistic $SU(5)\times U(1)^3$ model that yields near tri-bi-maximal neutrino mixing and realistic quark masses. A key result is that determinant and subdeterminant cancellations in the mass matrices significantly shape hierarchies and mixing, complicating naïve texture zero assumptions but offering routes to fit data through radiative corrections or flux-induced textures. The paper also demonstrates multiple mechanisms—Higgs doublet-triplet splitting via flux or Wilson lines, and differential quark-lepton textures via flux—to address residual GUT relations, with potential implications for proton stability and Lepton-Quark mass splittings in a globally consistent framework.

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.

Figures (6)

• Figure 1: Tree level graphs for the top and bottom Yukawa couplings $\lambda^{t,b}_{33}$.
• Figure 2: The two graphs generating the $\lambda^{d}_{23}$ down quark Yukawa coupling.
• Figure 3: Graphs generating the $\lambda^{d}_{12}$ down Yukawa coupling. Mass insertions in KK-mode lines are not shown to avoid clutter.
• Figure 4: Graphs generating the $\lambda^{u}_{22}$ up Yukawa coupling.
• Figure 5: Graphs generating the $\lambda^{u}_{12}$ up Yukawa coupling. Mass insertions in KK-mode lines are not shown to avoid clutter.