Higher order heavy quark Green's functions in Coulomb gauge

TL;DR

This paper derives an exact solution for heavy quark 4-point Green's functions in Coulomb gauge, revealing their pole structure and connection to bound state energies in heavy quark systems.

Contribution

It provides an exact analytical solution for heavy quark Green's functions under specific approximations, linking poles to bound states.

Findings

Poles correspond to bound state energies.

A separation between physical and unphysical poles is identified.

Solution is valid in the heavy quark mass limit.

Abstract

The Dyson-Schwinger equation for the 4-point quark Green's functions is studied. In the limit of the heavy quark mass and with the truncation to include only the dressed two point functions for the Yang-Mills sector, we provide an exact solution for the 4-point quark Green's functions, in both quark-antiquark and diquark channels, and show that the corresponding poles relate to the bound state energy of the heavy quark systems. Moreover, a natural separation between physical and unphysical poles in the Green's functions emerges.