Statistical fluctuations of correlators in the Color Glass Condensate

TL;DR

This paper analyzes the statistical errors in Monte Carlo sampling of Wilson line correlators within the Color Glass Condensate framework, focusing on how averaging techniques influence error magnitude and momentum dependence.

Contribution

It introduces a detailed study of statistical errors in Monte Carlo sampling of Wilson line correlators, highlighting the impact of averaging over the barycenter coordinate on error reduction.

Findings

Averaging over the barycenter coordinate significantly reduces statistical error.

Different approximants for the dipole amplitude vary in finite-sample error behavior.

Momentum dependence of the statistical error is altered by averaging techniques.

Abstract

In the McLerran-Venugopalan model, correlators of Wilson lines are given by an average over a Gaussian ensemble of random color sources. In numerical implementations, these averages are approximated by a Monte-Carlo sampling. In this paper, we study the statistical error made with such a sampling, with emphasis on the momentum dependence of this error. Using the example of the dipole amplitude, we consider various approximants that are all equivalent in the limit of infinite statistics but differ with finite statistics and compare their statistical errors. For correlation functions that are translation invariant, we show that averaging over the barycenter coordinate drastically reduces the statistical error and more importantly modifies its momentum dependence.