Heavy quarks, gluons and the confinement potential in Coulomb gauge

TL;DR

This paper analyzes heavy quark interactions in Coulomb gauge QCD, revealing that the rainbow-ladder approximation is exact and linking the gluon propagator to the confinement potential, with only color singlet bound states being physical.

Contribution

It demonstrates the nonperturbative exactness of the rainbow-ladder approximation and establishes a direct connection between the gluon propagator and the confinement potential in Coulomb gauge QCD.

Findings

Rainbow-ladder approximation is nonperturbatively exact.

Direct link established between gluon propagator and confinement potential.

Only color singlet states are physically allowed.

Abstract

We consider the heavy quark limit of Coulomb gauge QCD, with the truncation of the Yang-Mills sector to include only (dressed) two-point functions. We find that the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is nonperturbatively exact and moreover, we provide a direct connection between the temporal gluon propagator and the quark confinement potential. Further, we show that only bound states of color singlet quark-antiquark (meson) and quark-quark (SU(2) baryon) pairs are physically allowed.