Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation

TL;DR

This paper introduces a new non-linear equation in the CGC/saturation framework that models the impact parameter dependence of scattering amplitudes, leading to an exponential decay at large impact parameters and satisfying the Froissart bound.

Contribution

A novel non-linear equation incorporating impact parameter diffusion in the CGC/saturation approach, addressing the long-standing issue of power-like fall off in scattering amplitudes.

Findings

The new equation aligns with previous impact parameter diffusion models.

It predicts exponential decay of scattering amplitudes at large impact parameters.

Restores Froissart bound in high-energy scattering models.

Abstract

In this paper we propose a solution to the long standing problem in the CGC/saturation approach: the power-like fall off of the scattering amplitudes at large $b$. We propose a new non-linear equation, which takes into account random walks both in transverse momenta of the produced gluons and in their impact parameters. We demonstrate, that this equation is in accord with previous attempts to include the diffusion in impact parameters in the BFKL evolution equation. We show in the paper, that the solution to a new equation results in the exponential decrease of the scattering amplitude at large impact parameter, and in the restoration of the Froissart theorem.