  We calculate, at the classical level, the superpotential tri-linear couplings
of the only known globally consistent heterotic minimal supersymmetric Standard
Model [ hep-th/0512149 ]. This recently constructed model is based on a
compactification of the E_8 x 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 \mu-mass
parameters for the Higgs pairs and neutrino mass terms, with specific vector
bundle moduli playing the role of right-handed neutrinos.
