Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude

TL;DR

This paper derives a high energy evolution equation within the Gribov-Zwanziger framework, showing it predicts an exponential decrease of the scattering amplitude at large impact parameters, addressing key issues in high energy QCD theories.

Contribution

It introduces a new evolution equation based on the Gribov-Zwanziger approach that resolves the large impact parameter behavior in high energy scattering.

Findings

Predicts exponential decrease of scattering amplitude at large impact parameter

Shows the evolution leads to a Froissart disc with radius proportional to rapidity

Demonstrates the equation resolves difficulties in the CGC effective theory

Abstract

In this paper we derive the high energy evolution equation in the Gribov-Zwanziger approach, for the confinement of quarks and gluons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter, and resolves the main difficulties of CGC (Colour Glass Condensate) high energy effective theory. Such behaviour occurs if the gluon propagator in Gribov-Zwanziger approach, does not vanish at small momenta. Solving the non-linear equation for deep inelastic scattering, we show that the suggested equation leads to a Froissart disc with radius ($R_F$), which increases as $ R_F \,\propto Y = \ln (1/x)$, and with a finite width for the distribution over $| b - R_F|$.