Renormalization-group anatomy of transverse-momentum dependent parton distribution functions in QCD

TL;DR

This paper investigates the divergences in transverse-momentum dependent parton distribution functions in QCD, revealing how different gauge prescriptions affect the presence of cusp-like anomalous dimensions and the role of the soft factor.

Contribution

It demonstrates that the choice of pole prescription in light-cone gauge influences divergence structures, and clarifies how the soft factor cancels or reduces these divergences.

Findings

Extra divergences appear with certain pole prescriptions in light-cone gauge.

The Mandelstam-Leibbrandt prescription avoids cusp-like anomalous dimensions.

The soft factor cancels divergences or reduces them to unity depending on the prescription.

Abstract

The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.