Flavor Hierarchy From F-theory

TL;DR

This paper demonstrates that F-theory models with background fluxes naturally produce hierarchical Yukawa matrices and CKM matrices, aligning well with observed quark and lepton mass hierarchies.

Contribution

It shows that flux-induced corrections in F-theory lead to realistic fermion mass hierarchies and mixing angles, providing a geometric origin for flavor structure.

Findings

Hierarchical Yukawa matrices arise from flux corrections.

CKM matrix elements match observed hierarchies.

Flux variations generate small U(1) violations leading to flavor hierarchies.

Abstract

It has recently been shown that F-theory based constructions provide a potentially promising avenue for engineering GUT models which descend to the MSSM. In this note we show that in the presence of background fluxes, these models automatically achieve hierarchical Yukawa matrices in the quark and lepton sectors. At leading order, the existence of a U(1) symmetry which is related to phase rotations of the internal holomorphic coordinates at the brane intersection point leads to rank one Yukawa matrices. Subleading corrections to the internal wave functions from variations in the background fluxes generate small violations of this U(1), leading to hierarchical Yukawa structures reminiscent of the Froggatt-Nielsen mechanism. The expansion parameter for this perturbation is in terms of alpha_(GUT)^(1/2). Moreover, we naturally obtain a hierarchical CKM matrix with V_(12) ~ V_(21) ~ epsilon, V_(23) ~ V_(32) ~ epsilon^(2), V_(13) ~ V_(31) ~ epsilon^(3), where epsilon ~ alpha_(GUT)^(1/2), in excellent agreement with observation.