Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis

TL;DR

This paper investigates the renormalization-group properties of gauge-invariant TMD parton distribution functions in QCD, focusing on anomalous dimensions and the role of gauge contours and soft counter terms.

Contribution

It introduces a detailed analysis of the anomalous dimensions of TMD PDFs, emphasizing the impact of cusp-like junctions in gauge contours and proposing a soft counter term to ensure gauge invariance.

Findings

Cusp-like junctions induce anomalous dimensions in gauge contours.

A soft counter term along the cusped contour compensates for renormalization effects.

Differences between Mandelstam formalism and direct gauge contours are clarified.

Abstract

The renormalization-group properties of gauge-invariant transverse-momentum dependent (TMD) parton distribution functions (PDF) in QCD are addressed. We perform an analysis of their leading-order anomalous dimensions, which are local quantities, making use of the renormalization properties of contour-dependent composite operators in QCD. We argue that attaching individual gauge links with transverse segments to quark fields in the light-cone gauge, the associated gauge contours are joined at light-cone infinity through a cusp-like junction point. We find that the renormalization effect on the junction point creates an anomalous dimension which has to be compensated in order to recover the results in a covariant gauge. To this end, we include in the definition of the TMD PDF an additional soft counter term (gauge link) along that cusped contour. We show that the eikonal factors entering this counter term are peculiar to the Mandelstam field formalism and are absent when one uses a direct gauge contour.