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

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 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 Koba, Nielsen, and Olesen law that leads to the entropy <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>S</a:mi></a:mrow><a:mrow><a:mi>E</a:mi></a:mrow></a:msub><a:mo>=</a:mo><a:mi>ln</a:mi><a:mo stretchy="false">(</a:mo><a:mi>x</a:mi><a:mi>G</a:mi><a:mo stretchy="false">(</a:mo><a:mi>x</a:mi><a:mo>,</a:mo><a:msup><a:mrow><a:mi>Q</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msup><a:mo stretchy="false">)</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:math>. <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>x</g:mi><g:mi>G</g:mi></g:mrow></g:math> has to be in the saturation region at high energies. Published by the American Physical Society 2024