Geometry of gauge links in operator definitions of transverse-momentum dependent PDFs: A comparative view

TL;DR

This paper reviews and compares various gauge-invariant operator definitions of transverse-momentum dependent parton densities, focusing on the geometry of gauge links and their compatibility with collinear PDFs.

Contribution

It provides a comparative analysis of different approaches to defining gauge-invariant TMDs, emphasizing the geometry of Wilson lines and their relation to soft factors.

Findings

Analyzes the geometry of gauge links in TMDs and soft factors.

Discusses compatibility of different operator definitions with collinear PDFs.

Explores potential connections between various TMD operator frameworks.

Abstract

Different approaches to the problem of a gauge-invariant operator definition of transverse-momentum dependent parton densities (TMDs) are reviewed and compared from the point of view of their compatibility with the operator definition of collinear (integrated) parton distribution functions. In particular, geometry of the longitudinal and transverse gauge links (Wilson lines) both in unsubtracted quark TMDs and in the associate soft factors is addressed. A possible connection between different operator definitions is also discussed.