Universality of soft and collinear factors in hard-scattering factorization
John C. Collins, Andreas Metz
TL;DR
The paper addresses the apparent process-dependence of transverse-momentum-dependent (TMD) non-perturbative functions in QCD factorization caused by Wilson-line directions. By a careful analysis of contour deformations out of the Glauber region and a subtractive factorization framework, it shows that with appropriately chosen Wilson lines, the fragmentation function and soft factor are universal across e+e− annihilation, SIDIS, and Drell–Yan, while parton densities are universal up to a sign for T‑odd functions under time reversal. Rapidity-divergence regulators using light-like Wilson lines do not spoil universality when counterterms are space-like or when Ji–Ma–Yuan prescriptions are employed consistently. These results extend the Collins–Soper–Sterman formalism, clarifying the conditions for universality and informing phenomenology in hadron-hadron collisions, though full proofs for all hadron-hadron processes remain challenging.
Abstract
Universality in QCD factorization of parton densities, fragmentation functions, and soft factors is endangered by the process dependence of the directions of Wilson lines in their definitions. We find a choice of directions that is consistent with factorization and that gives universality between e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the Drell-Yan process. Universality is only modified by a time-reversal transformation of the soft function and parton densities between Drell-Yan and the other processes, whose only effect is the known reversal of sign for T-odd parton densities like the Sivers function. The modifications of the definitions needed to remove rapidity divergences with light-like Wilson lines do not affect the results.