Nonperturbative study of the four-point heavy quark Green's functions in Coulomb gauge

TL;DR

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

Contribution

It introduces a leading-order heavy quark mass expansion and truncates the Yang-Mills sector to derive exact solutions for the Green's functions.

Findings

Exact solutions for four-point quark Green's functions

Identification of poles related to bound state energies

Separation of physical and unphysical poles

Abstract

The heavy quark sector of Coulomb gauge QCD is investigated, by making a heavy quark mass expansion of the QCD action and restricting to the leading order. With the truncation of the Yang-Mills sector to include only dressed two-point functions, we study the Dyson-Schwinger equations for the four-point quark Green's functions (proper and amputated). In this limit, we provide an exact solution for the four-point quark Green's functions and show that the corresponding poles relate to the bound state energy of the heavy quark system. Moreover, a natural separation between the physical and unphysical poles in the Green's functions emerges.