High energy evolution for Gribov-Zwanziger confinement: solution to the equation

TL;DR

This paper solves a new high energy scattering evolution equation derived from the Gribov-Zwanziger confinement approach, showing it aligns with QCD BFKL evolution and addresses issues at large impact parameters.

Contribution

It provides an exact solution to the Gribov-Zwanziger based evolution equation, revealing its similarity to QCD BFKL evolution and its implications for confinement and large impact parameter behavior.

Findings

Energy dependence matches QCD BFKL evolution

Eigenfunctions coincide with QCD BFKL at high transverse momenta

Eigenfunctions exhibit exponential suppression at long distances

Abstract

In this paper we solved the new evolution equation for high energy scattering amplitudethat stems from the Gribov-Zwanziger approach to the confinement of quarks and gluons. We found that (1) the energy dependence of the scattering amplitude turns out to be the same as for QCD BFKL evolution; (2) the spectrum of the new equation does not depend on the details of the Gribov-Zwanzinger approach and (3) all eigenfunctions coincide with the eigenfunctions of the QCD BFKL equation at large transverse momenta $\kappa\,\geq\,1$. The numerical calculations show that there exist no new eigenvalues with the eigenfunctions which decrease faster than solutions of the QCD BFKL equation at large transverse momenta. The structure of the gluon propagator in Gribov-Zwanziger approach, that stems from the lattice QCD and from the theoretical evaluation, results in the exponential suppression of the eigenfunctions at long distances and in the resolution of the difficulties, which the Colour Glass Condensate (CGC) and some other approaches, based on perturbative QCD, face at large impact parameters. We can conclude that the confinement of quark and gluons, at least in the form of Gribov-Zwanziger approach, does not influence on the scattering amplitude except solving the long standing theoretical problem of its behaviour at large impact parameters.