# Accessing the topological susceptibility via the Gribov horizon

## TL;DR

This paper investigates the topological susceptibility in SU(3) and SU(2) Yang-Mills theories using a BRST invariant approach that incorporates Gribov copies and a non-perturbative gluon propagator, clarifying its role in confinement and the $U(1)_A$ problem.

## Contribution

It introduces a BRST invariant method to analyze topological susceptibility considering Gribov copies and non-perturbative effects, improving understanding of confinement and the $U(1)_A$ problem.

## Key findings

- Topological susceptibility calculated with a non-perturbative gluon propagator.
- Incorporation of Gribov copies within a BRST invariant framework.
- Results support a connection between topological susceptibility and confinement mechanisms.

## Abstract

The topological susceptibility, $\chi^4$, following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the $\eta^{\prime}$ mass, the so-called $U(1)_{A}$ problem. A nonzero $\chi^4$ is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current. In a recent paper (Phys.Rev.Lett.114 (2015) 24, 242001), an explicit relationship between this Veneziano ghost and color confinement was proposed, by connecting the dynamics of the Veneziano ghost, and thus the topological susceptibility, with Gribov copies. However, the analysis is incompatible with BRST symmetry (Phys.Rev.D 93 (2016) no.8, 085010). In this paper, we investigate the topological susceptibility, $\chi^4$, in SU(3) and SU(2) Euclidean Yang-Mills theory using an appropriate Pad\'e approximation tool and a non-perturbative gluon propagator, within a BRST invariant framework and by taking into account Gribov copies in a general linear covariant gauge.