Yukawa couplings in heterotic standard models

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 QHu, Qd, LHν and Le 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. © SISSA 2006.