Higher-point correlations from the JIMWLK evolution

TL;DR

This paper introduces a new approximation method to derive higher-point correlation functions from the JIMWLK evolution, simplifying complex calculations by relating them to the 2-point function, applicable in both strong and weak scattering regimes.

Contribution

The paper presents a novel approximation scheme that expresses arbitrary n-point functions in terms of the 2-point function within the JIMWLK framework, valid at large number of colors.

Findings

Derived functional relations for n-point functions in terms of the 2-point function.

Validated the approximation for quadrupole and sextupole configurations.

Showed consistency with known models and numerical solutions.

Abstract

We develop a new approximation scheme aiming at extracting higher-point correlation functions from the JIMWLK evolution, in the limit where the number of colors is large. Namely, we show that by exploiting the structure of the 'virtual' terms in the Balitsky-JIMWLK equations, one can derive functional relations expressing arbitrary n-point functions of the Wilson lines in terms of the 2-point function (the scattering amplitude for a color dipole). These approximations are correct not only in the regime of strong scattering, where the evolution is indeed controlled by the 'virtual' terms, but also in the regime of weak scattering, where they reduce to the corresponding BFKL solutions. This last feature follows from the fact that the JIMWLK Hamiltonian is a linear combination of the pieces responsible for the 'real' and 'virtual' terms, respectively. We apply this scheme to two examples: the 'color quadrupole' (the 4-point function of the Wilson lines which enters the cross-section for the production of a pair of jets at forward rapidities) and the 'color sextupole' (the 6-point function). For particular configurations of the quadrupole, our general formula reduces to relatively simple expressions that have been previously proposed on the basis of the McLerran-Venugopalan model and which were recently shown to agree quite well with exact, numerical, solutions to the JIMWLK equation.