Quark sector of Coulomb gauge Quantum Chromodynamics

TL;DR

This paper investigates the quark sector of Coulomb gauge QCD using functional integrals, deriving equations for bound states, and establishing a connection between gluon propagators and confinement, with exact solutions for heavy quark systems.

Contribution

It provides a nonperturbative analytic solution for quark bound states and confining potentials within Coulomb gauge QCD, demonstrating the exactness of the rainbow-ladder approximation in this context.

Findings

Derived quark contributions to Dyson-Schwinger equations.

Presented analytic solutions for meson and baryon bound states.

Connected gluon propagator properties to confinement and string tension.

Abstract

The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented. The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion. By 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. Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented. The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found. It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed. Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived. It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.