Yukawa Couplings in Heterotic Standard Models

TL;DR

This paper develops a formalism to compute Yukawa couplings in heterotic string models, applying it to a minimal model that reproduces the MSSM and reveals a natural hierarchy among fermion families.

Contribution

Introduces a new formalism for calculating Yukawa couplings in heterotic models, explicitly applied to a minimal model with realistic fermion mass textures.

Findings

Explicit Yukawa couplings computed for the minimal heterotic model

Yukawa textures suggest a natural hierarchy among fermion families

Selection rules restrict possible interactions based on Calabi-Yau geometry

Abstract

In this paper, we present a formalism for computing the Yukawa couplings in heterotic standard models. This is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q*H*u, Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These interactions are subject to two very restrictive selection rules arising from the geometry of the Calabi-Yau manifold. We apply our formalism to the "minimal" heterotic standard model whose observable sector matter spectrum is exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly computed in this context. These interactions exhibit a texture rendering one out of the three quark/lepton families naturally light.