Dipole-dipole scattering amplitude in CGC approach

TL;DR

This paper develops recurrence relations for dipole densities in QCD, solves them within the diffusion approximation, and finds that the resulting scattering amplitude decreases at large rapidity, highlighting artifacts of the approximation.

Contribution

It introduces recurrence relations for dipole densities and analyzes their solutions to understand high-energy scattering amplitudes in the CGC framework.

Findings

Sum of large Pomeron loops leads to decreasing scattering amplitude at high rapidity

Diffusion approximation causes unitarization without saturation effects

High-energy dipole-dipole scattering behavior is affected by approximation artifacts

Abstract

In this paper we propose recurrence relations for the dipole densities in QCD, which allows us to find these densities from the solution to the BFKL equation. We resolve these relations in the diffusion approximation for the BFKL kernel. Based on this solution, we found the sum of large Pomeron loops. This sum generates the scattering amplitude that decreases at large values of rapidity $Y$. It turns out that such behaviour of the scattering amplitudes is an artifact of diffusion approximation. This approximation leads to the unitarization without saturation both in deep inelastic scattering and in dipole-dipole interaction at high energies.