  Two factorization approaches have been proposed for single transverse spin
asymmetries. One is the collinear factorization, another is the
transverse-momentum-dependent factorization. They have been previously derived
in a formal way by using diagram expansion at hadron level. If the two
factorizations hold or can be proven, they should also hold when we replace
hadrons with parton states. We examine these two factorizations at parton level
with massless partons. It is nontrivial to generate these asymmetries at parton
level with massless partons because the asymmetries require helicity-flip and
nonzero absorptive parts in scattering amplitudes. By constructing suitable
parton states with massless partons we derive the two factorizations for the
asymmetry in Drell-Yan processes. It is found from our results that the
collinear factorization derived at parton level is not the same as that derived
at hadron level. Our results with massless partons confirm those derived with
single massive parton state in our previous works.
