Correlations in impact-parameter space in saturation models

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.