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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.

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