  We study the one-loop correction in Transverse-Momentum-Dependent(TMD)
factorization for Drell-Yan processes at small transverse momentum of the
lepton pair. We adopt the so-called subtractive approach, in which one can
systematically construct contributions for subtracting long-distance effects
represented by diagrams. The perturbative parts are obtained after the
subtraction. We find that the perturbative coefficients of all structure
functions in TMD factorization at leading twist are the same. The perturbative
parts can also be studied with scattering of partons instead of hadrons. In
this way, the factorization of many structure functions can only be examined by
studying the scattering of multi-parton states, where there are many diagrams.
These diagrams have no similarities to those treated in the subtractive
approach. As an example, we use existing results of one structure function
responsible for Single-Spin-Asymmetry, to show that these diagrams in the
scattering of multi-parton states are equivalent to those treated in the
subtractive approach after using Ward identity.
