Color confinement and screening in the $\theta$ -vacuum

Abstract

QCD perturbation theory ignores the compact nature of $SU(3)$ gauge group that gives rise to the periodic $\theta$-vacuum of the theory. We propose to modify the gluon propagator to reconcile perturbation theory with the anomalous Ward identities for the topological current in the $\theta$-vacuum. As a result, the gluon couples to the Veneziano ghost describing the tunneling transitions between different Chern-Simons sectors of the vacuum; we call the emerging gluon dressed by ghost loops a "glost". We evaluate the glost propagator and find that it has the form $G(p)=(p^2+{\chi }_{top}/p^2{)}^{-1}$ where ${\chi }_{top}$ is the Yang-Mills topological susceptibility related to the ${\eta }^{\prime }$ mass by Witten-Veneziano relation; this propagator describes confinement of gluons at distances $\sim {\chi }_{top}^{-1/4}\simeq 1$ fm. The same functional form of the propagator was originally proposed by Gribov as a solution to the gauge copies problem that plagues perturbation theory. The resulting running coupling coincides with the perturbative one at $p^2\gg \sqrt{{\chi }_{top}}$, but in the infrared region either freezes (in pure Yang-Mills theory) or vanishes (in full QCD with light quarks), in accord with experimental evidence. Our scenario makes explicit the connection between confinement and topology of the QCD vacuum; we discuss the implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.

arXiv comment7 pages, 4 figures; slightly extended version

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• Accessing the topological susceptibility via the Gribov horizon
• $\theta$-dependence of the lightest meson resonances in QCD
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• Thermal radiation and inclusive production in the CGC/saturation approach at high energies
• Non-linear chiral magnetic waves
• Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• Shear and bulk viscosity of quark-gluon plasma with Gribov gluons and quasiparticle quarks
• Superfluid helium II as the QCD vacuum
• Heavy quark dynamics via Gribov-Zwanziger approach
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• The Veneziano ghost, glost and gauge copies in QCD
• Electromagnetic Debye mass within Gribov-Zwanziger action
• High energy evolution for Gribov-Zwanziger confinement: solution to the equation
• Color confinement, dark matter and the missing of anti-matter
• Roundtable: What can we learn about confinement and anomalous effects in QCD using analog systems?
• Anisotropy effects on heavy quark dynamics in Gribov modified gluon plasma