Coulomb confinement in the Hamiltonian limit

TL;DR

This paper investigates the Coulomb string tension in SU(2) lattice gauge theory, finding it to be approximately twice the Wilson string tension, which clarifies previous overestimations and has implications for understanding confinement.

Contribution

The study provides a refined lattice determination of the Coulomb string tension, correcting previous inflated values and offering a more accurate estimate relevant for confinement models.

Findings

Coulomb string tension is about twice the Wilson string tension.

Previous literature overestimated the Coulomb string tension.

Refined lattice calculations yield a more accurate value for $\sigma_C/\sigma_F$.

Abstract

The Gribov--Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang--Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, $\sigma_{C}$, to be about three times larger than the Wilson loop string tension, $\sigma_F$. It is far above the Zwanziger variational bound, $\sigma_C \geq \sigma_F$. We argue that the value established in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension's enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as $\sigma_C/\sigma_F = 2.0 \pm 0.4$ and discuss its phenomenological implications.