Derivation of the Gauge Link in Light Cone Gauge

TL;DR

This paper derives the gauge link at light cone infinity in light cone gauge using a more regular and general method, clarifying its origin and differences in scattering processes.

Contribution

It introduces a novel, more general derivation of the gauge link at light cone infinity, accounting for different boundary conditions and process-specific differences.

Findings

Gauge link arises from pinched poles in propagators.

Derived a general gauge link beyond transverse direction.

Clarified differences between scattering processes.

Abstract

In light cone gauge, a gauge link at light cone infinity is necessary for transverse momentum-dependent parton distribution to restore the gauge invariance in some specific boundary conditions. We derive such transverse gauge link in a more regular and general method. We find the gauge link at light cone infinity naturally arises from the contribution of the pinched poles: one is from the quark propagator and the other is hidden in the gauge vector field in light cone gauge. Actually, in the amplitude level, we have obtained a more general gauge link over the hypersurface at light cone infinity which is beyond the transverse direction. The difference of such gauge link between semi-inclusive deep inelastic scattering and Drell-Yan processes can also be obtained directly and clearly in our derivation.