  In the field theoretical description of hadronic scattering processes, single
transverse-spin asymmetries arise due to gluon initial and final state
interactions. These interactions lead to process dependent Wilson lines in the
operator definitions of transverse momentum dependent parton distribution
functions. In particular for hadron-hadron scattering processes with hadronic
final states this has important ramifications for possible factorization
formulas in terms of (non)universal TMD parton distribution functions. In this
paper we will systematically separate the universality-breaking parts of the
TMD parton correlators from the universal T-even and T-odd parts. This might
play an important role in future factorization studies for these processes. We
also show that such factorization theorems will (amongst others) involve the
gluonic pole cross sections, which have previously been shown to describe the
hard partonic scattering in weighted spin asymmetries.
