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

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.