Constituent gluons and the static quark potential

TL;DR

This paper proposes a hybrid lattice-QCD inspired approach using dressed propagators to approximate Hamiltonian matrix elements in Coulomb gauge, applied to the static quark potential, highlighting the role of constituent gluons in confinement.

Contribution

It introduces a lattice-improved tree diagram method for approximating Hamiltonian matrix elements in Coulomb gauge, incorporating constituent gluons into the static quark potential analysis.

Findings

The Coulomb string tension is about four times the asymptotic string tension.

A single constituent gluon can significantly reduce the overshoot in the potential.

The static potential remains linear up to 2.4 fm with a modified string tension.

Abstract

We suggest that Hamiltonian matrix elements between physical states in QCD might be approximated, in Coulomb gauge, by "lattice-improved" tree diagrams; i.e. tree diagram contributions with dressed ghost, transverse gluon, and Coulomb propagators obtained from lattice simulations. Such matrix elements can be applied to a truncated-basis treatment of hadronic states which include constituent gluons. As an illustration, we apply this hybrid approach to the heavy quark potential, for quark-antiquark separations up to 2.4 fm. The Coulomb string tension in SU(3) gauge theory is about a factor of four times greater than the asymptotic string tension. In our approach we show that a single constituent gluon is in principle sufficient, up to 2.4 fm, to reduce this overshoot by the factor required. The static potential remains linear, although the precise value of the string tension depends on details of the Couloumb gauge ghost and gluon propagators in the infrared regime. In this connection we present new lattice results for the transverse gluon propagator in position space.