Remarks on High Energy Evolution

TL;DR

The work analyzes high-energy QCD evolution beyond the mean-field Kovchegov limit by deriving a generalized B-JIMWLK^2 equation for an arbitrary projectile and by extracting a tractable dipole-model limit at large N_c. It presents an algebraic, operator-based derivation of the evolution, including finite-density corrections, and connects the full JIMWLK framework to a classical dipole dynamics via a stochastic ensemble of initial conditions. This leads to a practical numerical strategy: solve the classical dipole equation for s(Y) and then average over initial distributions to obtain observables, while quantifying 1/N_c corrections that require higher-color correlations. The paper also proposes explicit models for target fluctuations (e.g., MV-inspired distributions) and discusses the role of impact-parameter dependence, setting up a framework to study fluctuations and correlations beyond the mean-field evolution.

Abstract

We make several remarks on the B-JIMWLK hierarchy. First, we present a simple and instructive derivation of this equation by considering an arbitrary projectile wave function with small number of valence gluons. We also generalize the equation by including corrections which incorporate effects of high density in the projectile wave function. Second, we systematically derive the dipole model approximation to the hierarchy. We show that in the dipole approximation the hierarchy has a simplifying property that allows its solution by solving the classical equation followed by averaging over the ensemble of initial conditions.