Accessing the topological susceptibility via the Gribov horizon

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 Padé 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.

17 pages, 4 figures. v2: corrected typos, new figures, improved style of presentation

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Cited by in corpus (12)

• High Precision Statistical Landau Gauge Lattice Gluon Propagator Computation vs. the Gribov-Zwanziger approach
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• Estimation of the diffusion coefficient of Heavy Quarks in light of Gribov-Zwanziger action
• QCD mesonic screening masses using Gribov quantization
• Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
• Shear and bulk viscosity of quark-gluon plasma with Gribov gluons and quasiparticle quarks
• Heavy quark dynamics via Gribov-Zwanziger approach
• Electromagnetic Debye mass within Gribov-Zwanziger action
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges
• High energy evolution for Gribov-Zwanziger confinement: solution to the equation
• High Precision Statistical Landau Gauge Lattice Gluon Propagator Computation