On the IR behaviour of the Landau-gauge ghost propagator

TL;DR

This paper analytically investigates the infrared behavior of the Landau-gauge ghost propagator, demonstrating the existence of a finite solution supported by identities and lattice data, challenging the conventional divergent view.

Contribution

It proves the existence of a finite ghost dressing function solution in the IR regime and shows it is favored by Slavnov-Taylor identities and lattice simulations.

Findings

Finite ghost dressing function at zero momentum is a valid solution.

Slavnov-Taylor identities support the finite solution.

Lattice simulations are consistent with the finite solution.

Abstract

We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.