  The parity-violating nucleon-nucleon (NN) potential is considered up to
next-to-next-to leading order in heavy-baryon chiral perturbation theory. We
include one-pion exchange at leading order and the two-pion exchange and
two-nucleon contact terms at next-to-next-to-leading order. The effects of
intermediate (two-pion exchange) and short-range (two-nucleon contact) terms
are probed by calculating the photon asymmetry $A_\gamma$ in $\vec{n} p \to d
\gamma$ employing Siegert's theorem and an accurate phenomenological potential
for the parity-conserving NN interaction. We explore in detail the
uncertainties due to the parameters that control the contribution of the
short-range interaction. We obtain about 20% uncertainty in the value of
$A_\gamma$ up to the next-to-next-to leading order. We discuss the implication
of this uncertainty for the determination of the weak pion-nucleon coupling
constant and how the uncertainty can be reduced.
