# Unequal rapidity correlators in the dilute limit of JIMWLK

## TL;DR

This paper analyzes unequal rapidity correlators within the JIMWLK framework, revealing linear evolution equations and connecting the Langevin formalism to BFKL dynamics in the dilute limit, advancing understanding of two-particle production at high energies.

## Contribution

It introduces a diagrammatic interpretation of long-range correlators and demonstrates how the Langevin formalism simplifies to BFKL evolution in the dilute limit.

## Key findings

- Evolution between rapidities is linear even in the nonlinear regime.
- Langevin formalism reduces to BFKL in the dilute limit.
- Provides a stochastic process 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. We discuss a diagrammatic interpretation of the long-range correlators. 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.