One-loop renormalization of the quark TMD in projectile light-cone gauge

Abstract

We use the background field formalism to calculate next-to-leading-order corrections to a quark transverse momentum dependent parton distribution function (TMD) in the projectile light-cone gauge, i.e. $A^{+}=0$ for a left-moving target. We calculate the full result using the Mandelstam-Leibbrandt prescription for handling the light-cone singularity. From the one-loop renormalization of the quark TMD, we obtain the Collins-Soper-Sterman (CSS) evolution equations. The projectile light-cone gauge is widely used in calculations within the gluon saturation regime. Our work therefore opens a way to understanding the connections between the TMD and Colour Glass Condensate (CGC) approaches within the same framework.

7 pages, 1 figure. Talk by MT at the DIS 2026 conference