Single Transverse Spin Asymmetries at Parton Level

Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other 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 patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton 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.