Froissart bound and gluon number fluctuations

TL;DR

This paper investigates how gluon number fluctuations influence the impact parameter dependence of scattering amplitudes, showing they lead to saturation of the Froissart bound and produce a Gaussian impact parameter profile.

Contribution

It demonstrates that gluon fluctuations cause the scattering amplitude to saturate the Froissart bound and results in a Gaussian impact parameter dependence.

Findings

Gluon fluctuations saturate the Froissart bound.

Impact parameter dependence becomes Gaussian due to fluctuations.

Growth of the black disk radius is enhanced by fluctuations.

Abstract

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.