Correlations in impact-parameter space in saturation models

TL;DR

This paper investigates the correlation of saturation scales across impact parameters in saturation models, revealing strong correlations and near-uniformity in matter distribution, supported by analytical formulas and numerical simulations.

Contribution

It provides analytical expressions for impact-parameter correlations in saturation models, supported by numerical validation, and argues their applicability to full QCD in asymptotic limits.

Findings

Saturation scales are highly correlated across impact parameters.

The saturation scale is nearly uniform in a wide impact-parameter domain.

Analytical formulas are supported by numerical simulations and expected to hold in full QCD.

Abstract

In order to get an estimate of the homogeneity of the distribution of matter in a fast hadron, we compute the correlation of the saturation scales between different impact parameters. We find that these correlations are quite strong: The saturation scale is nearly uniform in a wide domain around each point in impact-parameter space. We provide analytical expressions for the correlations, which are supported by numerical simulations. Although the numerical calculations are done for specific saturation models which are obtained from QCD after drastic simplifications, we expect our analytical formulas to be correct for full QCD in asymptotic limits, since their derivation requires only a few general assumptions.