One-loop renormalization of quark TMD in the light-cone gauge: CSS evolution

TL;DR

This paper computes one-loop corrections to quark TMDs in the light-cone gauge, demonstrating how CSS evolution equations emerge from renormalization and identifying the origin of double logarithms in the resummation.

Contribution

It provides a detailed calculation of the one-loop renormalization of quark TMDs using the ML prescription, clarifying the origin of CSS evolution and double logs.

Findings

CSS evolution equations derived from one-loop renormalization.

Double log contributions originate from ghost-like zero-modes.

Use of the ML prescription clarifies singularity handling in light-cone gauge.

Abstract

We calculate the one-loop corrections to the quark TMD in the light-cone gauge using the background field formalism, with the Mandelstam-Leibbrandt (ML) prescription for the extra singularity present in the light-cone gauge propagator. We use the pure rapidity regulator for rapidity divergences. The Collins-Soper-Sterman (CSS) evolution equations are indeed obtained from the one loop renormalization of the quark TMD. In this setup, the double log contribution to the CSS resummation is found to come from the ghost-like zero-mode from the ML prescription, in the diagrams with a gluon propagator ending on the transverse part of the gauge link at infinity.