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

Understand

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.