Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions

TL;DR

This paper analyzes transverse-momentum dependent parton distribution functions using their renormalization properties, identifying the role of cusped Wilson lines and introducing a soft counter term to account for cusp anomalous dimensions, thus clarifying their gauge structure.

Contribution

It introduces a new understanding of the Wilson line structure in TMD PDFs, incorporating a soft counter term to handle cusp anomalous dimensions in light-cone gauge.

Findings

Cusped Wilson lines are essential in TMD PDFs.

A soft counter term cancels cusp anomalous dimensions.

The soft factor represents an intrinsic gauge phase.

Abstract

We perform an analysis of transverse-momentum dependent parton distribution functions, making use of their renormalization properties in terms of their leading-order anomalous dimensions. We show that the appropriate Wilson line in the light-cone gauge, associated with such quantities, is a cusped one. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transverse-momentum dependent parton distribution functions an additional soft counter term (gauge link) along that contour. We demonstrate that this is tantamount to an ``intrinsic (Coulomb) phase'', which accumulates the full gauge history of the color-charged particle.