Unequal rapidity correlators in the dilute limit of the JIMWLK evolution

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 Balitsky-Fadin-Kuraev-Lipatov (BFKL) picture in the dilute limit and in momentum space, providing an interpretation of BFKL evolution as a stochastic process for color charges.