Renormalization-group approach to transverse-momentum dependent parton distribution functions in QCD

TL;DR

This paper investigates the renormalization of transverse-momentum dependent parton distribution functions in QCD, identifying UV divergences related to gauge contours and proposing a soft counter term to ensure proper renormalization.

Contribution

It introduces a soft counter term involving a cusped contour to eliminate anomalous dimensions in TMD PDFs, advancing their gauge-invariant renormalization.

Findings

UV divergences linked to cusp-like junctions in gauge contours.

A proposed soft counter term removes anomalous dimensions.

Enhanced understanding of TMD PDF renormalization in QCD.

Abstract

We discuss the renormalization of gauge-invariant transverse-momentum dependent (TMD), i.e., unintegrated, parton distribution functions (PDFs) and carry out the calculation of their anomalous dimension at one loop. We show that in the light-cone gauge, TMD PDFs contain UV divergences that may be attributed to the renormalization effect on a cusp-like junction point of the gauge contours at infinity. In order to eliminate the anomalous dimension ensuing from this cusp, we propose to use in the definition of the TMD PDFs, a soft counter term in terms of a path-ordered phase factor along a particular cusped contour extending to transverse light-cone infinity and comprising light-like and transverse segments. We argue that this additional factor is analogous to the "intrinsic" Coulomb phase factor found before in QED.