Froissart bound and gluon number fluctuations

We study the effect of gluon number fluctuations (Pomeron loops) on the impact parameter behavior of the scattering amplitude in the fixed coupling case. We demonstrate that the dipole-hadron cross section computed from gluon number fluctuations saturates the Froissart bound and the growth of the radius of the black disk with rapidity is enhanced by an additional term as compared to the single event case. We find that the physical amplitude has a Gaussian impact parameter dependence once the gluon number fluctuations are included. This indicates that the fluctuations may be the microscopic origin for the Gaussian impact parameter dependence of the scattering amplitude.