Final state interactions and gauge invariant parton distributions

TL;DR

Final state interactions in DIS contribute to gauge-invariant transverse momentum-dependent parton distributions (TMD PDFs). The authors show these effects originate from a transverse gauge link at light-cone infinity, necessary for gauge invariance in the light-cone gauge, and they demonstrate how boundary conditions can shift FSIs between initial and final states without altering integrated collinear PDFs. Through scalar QED models and the dipole picture, they connect the transverse link to Sivers-type phases and clarify implications for DIS vs Drell-Yan universality at the unintegrated level. These results deepen the understanding of gauge structures in parton distributions and their phenomenological consequences for spin and small-x physics.

Abstract

Parton distributions contain factorizable final state interaction effects originating from the fast-moving struck quark interacting with the target spectators in deeply inelastic scattering. We show that these interactions give rise to gauge invariance of the transverse momentum-dependent parton distributions. As compared to previous analyses, our study demonstrates the existence of extra scaling contributions from transverse components of the gauge potential at the light-cone infinity. They form a transverse gauge link which is indispensable for restoration of the gauge invariance of parton distributions in the light-cone gauge where the gauge potential does not vanish asymptotically. Our finding helps to explain a number of features observed in a model calculation of structure functions in the light-cone gauge.