Dipole-dipole scattering: summing large Pomeron loops in non-linear evolution with leading twist kernel

TL;DR

This paper demonstrates that dipole density equations in QCD naturally include 'fan' diagrams, and calculates the impact of large Pomeron loops on high-energy dipole-dipole scattering, aligning with known entropy predictions.

Contribution

It introduces a solution to dipole density equations incorporating large Pomeron loops using a simplified leading twist kernel, extending the understanding of high-energy scattering processes.

Findings

Dipole densities match the analytic solution of the BK equation.

Large Pomeron loops contribute significantly to dipole-dipole scattering.

Produced gluons follow the KNO law, consistent with entropy predictions.

Abstract

It is shown in this paper that the QCD equations for dipole density have the natural solution: the 'fan' diagrams of the Pomeron calculus. We found the dipole densities comparing the analytic solution to the Balitsky-Kovchegov (BK) equation for the simplified leading twist kernel with the $t$ channel unitarity. Using these densities we calculate the contributions of large Pomeron loops to dipole-dipole scattering at high energies. Applying the Abramovsky,Gribov and Kancheli cutting rules we found that the produced gluons are distributed accordingly the KNO (Koba, Nielsen and Olesen) law which leads to the entropy $S_E = \ln(x G(x,Q^2))$ in an agreement with Kharzeev - Levin predictions.