Unitarization of the BFKL Pomeron on a Nucleus

TL;DR

This paper develops an exact solution to the evolution equation for multiple pomeron exchanges, demonstrating how it unitarizes the scattering cross section and structure functions at high energies in hadronic and nuclear interactions.

Contribution

It introduces a perturbation series solution for the evolution equation of multiple pomeron exchanges, extending understanding of unitarization in high-energy QCD processes.

Findings

The solution unitarizes the total deep inelastic scattering cross section at high energies.

The F2 structure function becomes proportional to ln s, indicating unitarization.

The approach can be applied to diffraction phenomena.

Abstract

We analyze the evolution equation describing all multiple hard pomeron exchanges in a hadronic or nuclear structure functions that was proposed earlier. We construct a perturbation series providing us with an exact solution to the equation outside of the saturation region. The series demonstrates how at moderately high energies the corrections to the single BFKL pomeron exchange contribution which are due to the multiple pomeron exchanges start unitarizing total deep inelastic scattering cross section. We show that as energy increases the scattering cross section of the quark-antiquark pair of a fixed transverse separation on a hadron or nucleus given by the solution of our equation inside of the saturation region unitarizes and becomes independent of energy. The corresponding F_2 structure function also unitarizes and becomes linearly proportional to ln s. We also discuss possible applications of the developed technique to diffraction.