Equivalence between Zwanziger's horizon function and Gribov's no-pole ghost form factor

TL;DR

This paper demonstrates that Zwanziger's horizon function and the ghost form factor in Gribov's no-pole condition are equivalent by explicitly calculating the ghost form factor up to third order and showing it matches the horizon function.

Contribution

The work explicitly shows the equivalence between Zwanziger's horizon function and the ghost form factor in Gribov's approach, clarifying their relationship.

Findings

Ghost form factor matches Zwanziger's horizon function up to third order.

Explicit calculation confirms the theoretical equivalence.

Supports the consistency of Gribov-Zwanziger confinement framework.

Abstract

The ghost form factor entering the Gribov no-pole condition is evaluated till the third order in the gauge fields. The resulting expression turns out to coincide with Zwanziger's horizon function implementing the restriction to the Gribov region in the functional integral.