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

Anamaría Font, Fernando Marchesano, Diego Regalado, Gianluca Zoccarato

TL;DR

This work analyzes up-type quark masses in local SU(5) F-theory GUTs by computing $10 imes10 imes5$ Yukawas at an $E_6$ point. A T-brane Higgs background combined with non-perturbative instanton effects generates a rank-3 holomorphic Yukawa matrix with a hierarchical structure that yields a realistic top mass and quark mass ratios after normalizing the wavefunctions. The authors derive holomorphic Yukawas via a residue formula and confirm them with physical Yukawas from overlapping wavefunctions, showing an ${ m O}(1)$ top Yukawa and $(1, ilde{oldsymbol{ ilde{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}}, ilde{oldsymbol{ ilde{oldsymbol{oldsymbol{}}}}^2))$ hierarchies in the up-type sector. They demonstrate how primitive hypercharge fluxes and non-perturbative effects jointly produce the observed up-quark mass pattern, within a bottom-up local framework that connects local data to MSSM phenomenology. The results suggest that SU(5) F-theory GUTs with T-branes are capable of accommodating SM flavor structure, including the large top mass, and point to future work on CKM realizations and global completions.

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.

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

TL;DR

This work analyzes up-type quark masses in local SU(5) F-theory GUTs by computing Yukawas at an point. A T-brane Higgs background combined with non-perturbative instanton effects generates a rank-3 holomorphic Yukawa matrix with a hierarchical structure that yields a realistic top mass and quark mass ratios after normalizing the wavefunctions. The authors derive holomorphic Yukawas via a residue formula and confirm them with physical Yukawas from overlapping wavefunctions, showing an top Yukawa and hierarchies in the up-type sector. They demonstrate how primitive hypercharge fluxes and non-perturbative effects jointly produce the observed up-quark mass pattern, within a bottom-up local framework that connects local data to MSSM phenomenology. The results suggest that SU(5) F-theory GUTs with T-branes are capable of accommodating SM flavor structure, including the large top mass, and point to future work on CKM realizations and global completions.

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.

Paper Structure

This paper contains 23 sections, 203 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Non-perturbative effects in local F-theory models
  3. Local F-theory models and up-type Yukawas
  4. Adding non-perturbative effects
  5. The $E_6$ model
  6. Matter curves near the $E_6$ point
  7. The T-brane background
  8. Primitive worldvolume fluxes
  9. Summary
  10. Holomorphic Yukawas via residues
  11. Non-perturbative Yukawas and residues
  12. Holomorphic Yukawas
  13. Zero mode wavefunctions at the $E_6$ point
  14. Perturbative zero-modes
  15. Non-perturbative corrections
  16. ...and 8 more sections

Figures (1)

  • Figure 1: Sources of corrections to 7-brane Yukawas in the scenario of mm09. The Yukawas on a 7-brane stack wrapping the four-cycle $S_{GUT}$ are modified by the gaugino condensate on 7-branes on a different four-cycle $S_{\rm np}$.