Three-quark confinement potential from the Faddeev equation

TL;DR

This paper derives a nonperturbative three-quark confinement potential from the Faddeev equation within Coulomb gauge QCD, linking the potential to the temporal gluon propagator and confirming only color singlet baryons are physical.

Contribution

It provides an analytic solution to the three-quark Faddeev equation in Coulomb gauge QCD, connecting confinement potential to gluon propagator and clarifying baryon color singlet constraints.

Findings

Confinement potential is directly related to the temporal gluon propagator.

Only color singlet three-quark states are physically permissible.

Analytic nonperturbative solution obtained for equal quark separations.

Abstract

In the heavy quark limit of Coulomb gauge QCD and by truncating the Yang-Mills sector to include only dressed two-point functions, an analytic nonperturbative solution to the Faddeev equation for three-quark bound states in the case of equal quark separations is presented. A direct connection between the temporal gluon propagator and the three-quark confinement potential is provided and it is shown that only color singlet qqq (baryon) states are physically allowed.