Collinearly improved JIMWLK evolution in Langevin form

TL;DR

This paper introduces a method to resum large collinear logarithmic corrections in the JIMWLK evolution equation using a Langevin formulation, incorporating transverse scale dependence and running coupling effects.

Contribution

It develops a collinearly-improved Langevin equation for Wilson line evolution, including transverse size dependence and resummation of running coupling corrections.

Findings

Resums collinear logarithms to all orders in JIMWLK evolution.

Incorporates transverse size dependence into Wilson line operators.

Allows resummation of one-loop running coupling corrections.

Abstract

The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections.