Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy

TL;DR

This paper investigates the spatial correlations of the saturation scale in high-energy QCD models, revealing strong correlations that imply limited gluon density fluctuations over certain domain sizes.

Contribution

It provides analytical expressions for impact-parameter space correlations in a hierarchical saturation model, suggesting similar behavior in full QCD.

Findings

Saturation scale correlations are strong across impact-parameter space.

Domains of size exp[const*ln^2(1/α_s^2)]/Q_s are nearly uniform.

Gluon density fluctuations are limited within these domains.

Abstract

In order to get an estimate of the homogeneity of the distribution of matter in a fast hadron or nucleus, we compute the correlations of the saturation scales Q_s between different points in impact-parameter space, in some specific saturation models. We find that these correlations are quite strong: The saturation scale is nearly uniform in domains whose sizes scale like exp[const*ln^2(1/\alpha_s^2)]/Q_s, which means that the density of gluons should not fluctuate significantly over regions of that typical size. We expect these conclusions as well as the explicit analytical expressions we obtain for the correlations to be true also for full QCD in appropriate limits.