Color effects for transverse momentum dependent parton distribution functions in hadronic processes

In the Drell-Yan process (DY) a quark and an antiquark, coming from two different protons, produce a colorless virtual photon. In the proton description, we include transverse momentum dependent parton distribution functions (TMD PDFs), which go beyond the ordinary collinear PDFs. As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when one looks at azimuthal asymmetries. Matrix elements used in the description of hadronic processes, such as DY, require the inclusion of gauge links, coming from gluon contributions in the process, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state the color flow between different parts of the process causes entanglement. We show that in the process of color disentangling each gauge link remains sensitive to this color flow. After disentanglement, we find that particular combinations of TMDs require a different numerical color factor than one might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as the DY process.