Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6'

TL;DR

This paper computes Yukawa couplings and mass terms for non-chiral states in a string theory Standard Model setup with D6-branes on T6/Z6', revealing detailed flavor structures and mass generation mechanisms.

Contribution

It provides explicit calculations of perturbative Yukawa couplings and mass terms for non-chiral matter in a D-brane Standard Model, including flavor patterns and supersymmetry breaking interactions.

Findings

Lepton Yukawa couplings are flavor diagonal at leading order.

Quark sector exhibits complex mixing patterns.

Mass hierarchies arise from D6-brane displacements and singlet vevs.

Abstract

The perturbative leading order open string three-point couplings for the Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kaehler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While N=2 supersymmetric sectors acquire masses via only two D6-brane displacements - which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation -, the remaining vector-like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along flat directions. Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.