  We study the scattering of a single parton state with a multi-parton state to
derive the complete results of perturbative coefficient functions at leading
order, which appear in the collinear factorization for Single transverse-Spin
Asymmetry(SSA) in Drell-Yan processes with a transversely polarized hadron in
the initial state. We find that the factorization formula of SSA contains
hard-pole-, soft-quark-pole- and soft-gluon-pole contributions. It is
interesting to note that the leading order perturbative coefficient functions
of soft-quark-pole- and soft-gluon-pole contributions are extracted from parton
scattering amplitudes at one-loop, while the functions of hard-pole
contributions are extracted from the tree level amplitudes at tree-level. Our
method to derive the factorization of SSA is different than the existing one in
literature. A comparison of our results with those obtained by other method is
made.
