Testing the Gaussian Approximation to the JIMWLK Equation

TL;DR

This paper confirms that the JIMWLK equation's solutions for small-x parton correlators can be effectively approximated by a Gaussian wavefunction, validated through numerical methods and applicable to fixed and running coupling scenarios.

Contribution

It provides an independent numerical validation that the Gaussian approximation accurately describes the JIMWLK evolution, including for open color correlators and near unitarity limits.

Findings

Gaussian approximation closely matches JIMWLK solutions

Numerical confirmation of the Levin-Tuchin formula

Applicability to both fixed and running coupling evolution

Abstract

In processes involving small-x partons, like in deep inelastic scattering and in hadronic collisions at high energy, the final state can be expressed in terms of correlators of Wilson lines. We study such high-point correlators evolving according to the JIMWLK equation and we confirm the results of previous numerical and analytic work, by using an independent method, that the solution to the JIMWLK equation can be very well approximated by an appropriate Gaussian wavefunction. We explore both fixed and running coupling evolution, where in the latter the scale is set according to various prescriptions. As a byproduct, we also numerically confirm to high accuracy the validity of the law governing the behavior of the S-matrix close to the unitarity limit, the Levin-Tuchin formula. We furthermore outline how to calculate correlators with open color indices.