  In this paper we discuss the incorporation of gauge links in hadronic matrix
elements that describe the soft hadronic physics in high energy scattering
processes. In this description the matrix elements appear in soft correlators
and they contain non-local combinations of quark and gluon fields. In our
description we go beyond the collinear approach in which case also the
dependence on transverse momenta of partons is taken into consideration. The
non-locality in the transverse direction leads to a complex gauge link
structure for the full process, in which color is entangled, even at
tree-level. We show that at tree-level in a 1-parton unintegrated (1PU)
situation, in which only the transverse momentum of one of the initial state
hadrons is relevant, one can get a factorized expression involving transverse
momentum dependent (TMD) distribution functions. We point out problems at the
level of two initial state hadrons, even for relatively simple processes such
as Drell-Yan scattering.
