Time-reversal-odd phenomena in QCD
  Single-spin asymmetries were long thought to vanish in high-energy scattering processes because of their specific time-reversal behavior. Time-reversal-odd phenomena, however, appear naturally when one includes effects of intrinsic transverse momenta of partons. The partons, quarks and gluons, enter the description of high-energy scattering processes in correlators which contain quark and gluon fields. The correlators, parameterized in terms of distribution and fragmentation functions, constitute matrix elements of non-local field configurations. For transverse momentum dependent (TMD) correlators the non-locality is along a light-front, in contrast to the non-locality along the light-cone for collinear correlators, integrated over transverse momenta. The TMD correlators require a careful treatment to assure color gauge invariance, leading to nontrivial gauge links connecting the parton fields. These give rise to time-reversal-odd phenomena, showing up as single spin and azimuthal asymmetries. The gauge links, arising from multi-gluon initial and final state interactions, depend on the color flow in the process, which has consequences for issues like universality and factorization. 
P.J. Mulders