Infrared behavior of the ghost propagator in the Landau gauge Yang-Mills theory

TL;DR

This paper proves that in Landau gauge Yang-Mills theory, the ghost propagator behaves like a free particle in the infrared, challenging the original Gribov prediction and implications for color confinement.

Contribution

It demonstrates the finite, non-zero behavior of the ghost dressing function in the infrared within the Gribov-Zwanziger framework for any D>2, revising the understanding of confinement criteria.

Findings

Ghost dressing function is finite and non-zero at zero momentum.

Ghost propagator behaves like a free particle in the infrared.

Original Gribov prediction on confinement needs reconsideration.

Abstract

We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge should be reconsidered in connection with color confinement.