Summing large Pomeron loops in the saturation region: amplitude and multiplicity distributions for dipole-dipole scattering

TL;DR

This paper derives parton densities at high energies by reconciling solutions to the BK equation with Pomeron diagram summations, and analyzes their implications for dipole-dipole scattering, gluon multiplicity, and entropy in the saturation regime.

Contribution

It introduces a novel approach to combine the BK equation solutions with Pomeron loop contributions, providing new insights into high-energy scattering amplitudes and gluon multiplicity distributions.

Findings

Scattering matrix exhibits suppression consistent with Iancu and Mueller's predictions.

Gluon multiplicity follows the KNO law in the saturation region.

Entropy relates to the gluon distribution as S_E = ln(x G(x,Q^2)).

Abstract

In this paper we found the parton densities at high energies. Their expressions stems from our attempts to reconcile the exact solution to the Balitsky-Kovchegov (BK) equation, which describes the rare fluctuation in the dipole-target scattering, with the fact that this equation sums the 'fan' Pomeron diagrams. Using these densities we can calculate the contributions of large Pomeron loops to dipole-dipole scattering at high energies. We detected that the scattering matrix for this process has the same suppression as was predicted by Iancu and Mueller from their estimates of the 'rare' fluctuation in QCD. 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 $S_E = \ln(x G(x,Q^2))$. $xG$ has to be in the saturation region at high energies.