  In this paper, we present a formalism for computing the non-vanishing Higgs
mu-terms in a heterotic standard model. This is accomplished by calculating the
cubic product of the cohomology groups associated with the vector bundle moduli
(phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms
proportional to phi H Hbar in the low energy superpotential which, for non-zero
moduli expectation values, generate moduli dependent mu-terms of the form <phi>
H Hbar. It is found that these interactions are subject to two very restrictive
selection rules, each arising from a Leray spectral sequence, which greatly
reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We
apply our formalism to a specific heterotic standard model vacuum. The
non-vanishing cubic interactions phi H Hbar are explicitly computed in this
context and shown to contain only four of the nineteen vector bundle moduli.
