Unequal rapidity correlators in the dilute limit of JIMWLK

TL;DR

This paper investigates unequal rapidity correlators within the JIMWLK framework, revealing linear evolution equations at large rapidity separations and connecting the Langevin formalism to BFKL dynamics in the dilute limit.

Contribution

It introduces a method to study two-particle correlations at different rapidities using the Langevin approach, and demonstrates the linear evolution of these correlators even in nonlinear regimes.

Findings

Evolution between rapidities is linear, even in nonlinear limit.

Langevin formalism reduces to BFKL in dilute limit.

Provides a stochastic interpretation of BFKL evolution.

Abstract

We study unequal rapidity correlators in the stochastic Langevin picture of Jalilian-Marian - Iancu - McLerran - Weigert - Leonidov - Kovner (JIMWLK) evolution in the Color Glass Condensate effective field theory. By separately evolving the Wilson lines in the direct and complex conjugate amplitudes, we use the formalism to study two-particle production at large rapidity separations. We show that the evolution between the rapidities of the two produced particles can be expressed as a linear equation, even in the full nonlinear limit. We also show how the Langevin formalism for two-particle correlations reduces to a BFKL picture in the dilute limit and in momentum space, providing an interpretation of BFKL evolution as a stochastic process for color charges.