Tri-linear couplings in an heterotic minimal supersymmetric Standard Model

We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [V. Bouchard, R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783-791, hep-th/0512149]. This recently constructed model is based on a compactification of the E8×E8 heterotic string theory on a Calabi-Yau threefold with Z2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. In the observable sector the massless particle content is that of the three-family supersymmetric Standard Model with n=0,1,2 massless Higgs pairs, depending on the location in the vector bundle moduli space, and no exotic particles. We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms. In particular, the proton is stable. Another interesting feature is the existence of tri-linear couplings, on the loci with massless Higgs pairs, generating μ-mass parameters for the Higgs pairs and neutrino mass terms, with specific vector bundle moduli playing the role of right-handed neutrinos.