Resumming subleading Sudakov logarithms in saturation regime

TL;DR

This paper analyzes the scale dependence of gluon TMDs in the saturation regime, demonstrating that the same RG equations govern their evolution as at larger x, enabling resummation of leading logarithms.

Contribution

It introduces a method to resum both double and single leading logarithms of gluon TMDs in the saturation regime using combined RG and Collins-Soper equations.

Findings

Scale dependence governed by the same RG equation as at larger x

Resummation of double and single leading logarithms achieved

Unified treatment of TMD evolution in saturation regime

Abstract

We investigate the scale dependence of transverse momentum dependent(TMD) gluon distribution in saturation regime. We found that in the Collins-2011 scheme, the scale dependence of small x gluon TMD is governed by the same renormalization group(RG) equation that holds at moderate or large $x$. Following the standard procedure, one then can resum both double leading logarithm and single leading logarithm in saturation regime by jointly solving the Collins-Soper equation and the RG equation.