Coulomb gauge confinement in the heavy quark limit

TL;DR

This paper derives an exact nonperturbative solution linking the confinement potential to the gluon propagator in Coulomb gauge, revealing that only color-singlet bound states exist in the heavy quark limit.

Contribution

It provides an analytic solution connecting the string tension to the gluon propagator and confirms the confinement of mesons and baryons in the heavy quark limit.

Findings

Exact rainbow-ladder approximation in heavy quark limit

Direct link between string tension and gluon propagator

Only color-singlet bound states are confined

Abstract

The relationship between the nonperturbative Green's functions of Yang-Mills theory and the confinement potential is investigated. By rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion in Coulomb gauge, restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact in this case and an analytic, nonperturbative solution is presented. It is found that there is a direct connection between the string tension and the temporal gluon propagator. Further, it is shown that for the 4-point quark correlation functions, only confined bound states of color-singlet quark-antiquark (meson) and quark-quark (baryon) pairs exist.