Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation

TL;DR

This paper investigates finite volume effects in the initial conditions for the JIMWLK equation derived from the McLerran-Venugopalan model, proposing a regularization method to minimize these effects for accurate numerical solutions.

Contribution

It identifies large finite volume effects in the initial condition construction and introduces a regularization procedure to reduce these effects in numerical simulations.

Findings

Finite volume effects are significant in the initial condition setup.

Infrared regularization can mitigate finite volume effects.

The proposed method improves the accuracy of JIMWLK evolution simulations.

Abstract

We revisit the numerical construction of the initial condition for the dipole amplitude from the McLerran-Venugopalan model in the context of the JIMWLK evolution equation. We observe large finite volume effects induced by the Poisson equation formulated on a torus. We show that the situation can be partially cured by introducing an infrared regularization. We propose a procedure that has negligible finite volume corrections. The control of the finite volume and finite lattice spacings effects is crucial when considering the numerical solutions of the JIMWLK evolution equation with the collinear improvement.