Higher order heavy quark Green's functions in Coulomb gauge

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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.