JIMWLK evolution in the Gaussian approximation

TL;DR

This paper introduces a Gaussian mean field approximation for the JIMWLK evolution equations in high-energy QCD, valid across different scattering regimes, simplifying the calculation of multi-point Wilson line correlators.

Contribution

It provides a controlled Gaussian approximation scheme for JIMWLK equations, relating higher n-point functions to the dipole S-matrix and revealing a new symmetry property of the evolution.

Findings

The approximation reproduces BFKL dynamics at weak scattering.

It accurately describes evolution towards saturation and black disk limits.

Higher n-point functions can be computed from the dipole S-matrix using simplified equations.

Abstract

We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors Nc. This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite Nc. Any higher n-point function with n greater than or equal to 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.