Relating different approaches to nonlinear QCD evolution at finite gluon density

TL;DR

The paper analyzes how different nonlinear low-x evolution equations in QCD relate in the finite gluon density regime. It shows that the BK equation is obtained from the JKLW equation in the limit of small induced field, linking the projectile-based and target-based formalisms. It argues that higher nonlinearities in JKLW correspond to the breakdown of the eikonal approximation when target fields become large, and discusses gauge-related subtleties and the iε issues in translating results between the two pictures. This work clarifies the connections among BK, JKLW, and related Wilson-line formalisms, highlighting the regime of validity and the need to account for non-eikonal corrections to predict final-state observables in dense gluon systems.

Abstract

We analyze the relation between evolution equations at low x that have been derived in different approaches in the last several years. We show that the equation derived by Balitsky and Kovchegov is obtained from the Jalilian-Marian-Kovner-Leonidov-Weigert (JKLW) equation in the limit of small induced charge density. We argue that the higher nonlinearities resummed by the JKLW equation correspond, in physical terms, to the breakdown of the eikonal approximation when the gluon fields in the target are large.