  We consider the direct photon production in two hadron collision with one of
the hadrons being transversely polarized. By using the contour gauge for gluon
fields, we find that there are new twist-$3$ terms present in the hadron tensor
of the considering process in addition to the standard twist-$3$ terms. In this
work, we demonstrate that the significance of these new terms are two-fold:
first, they are crucial to both the QED and QCD gauge invariance and, second,
their contributions to the hadron tensor are at least the same as those from
the standard ones. We also study the resuting effects which are responsible for
the universality breaking of the corresponding twist-$3$ parton distributions.
