Layout of Wilson lines and light-cone peculiarities of transverse-momentum dependent PDFs

TL;DR

This paper examines the gauge invariance and path-dependence issues in transverse-momentum dependent PDFs, analyzing Wilson line configurations and divergences to ensure consistency with collinear PDFs.

Contribution

It provides a comparative analysis of Wilson line layouts on- and off-light-cone, addressing divergences and gauge invariance in TMDs, clarifying their operator structure.

Findings

Wilson line configurations impact gauge invariance of TMDs

Comparison shows consistency with collinear PDFs across formulations

Discussion of UV/rapidity divergence treatment

Abstract

We consider the problems of gauge invariance, path-dependence and treatment of overlapping UV/rapidity divergences peculiar to the transverse-momentum dependent parton distribution functions (TMDs). For different formulations of the TMDs available in the literature, we check the consistency of the TMD matrix elements with the collinear parton distribution functions possessing the well-known operator structure. Comparative on- and off-light-cone layout of the Wilson lines which secure the gauge-invariance of the TMDs is presented and briefly discussed.