Tri-linear couplings in an heterotic minimal supersymmetric Standard Model

Abstract

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 E 8 × E 8 heterotic string theory on a Calabi–Yau threefold with Z 2 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.