  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.

High Energy Physics - Phenomenology;High Energy Physics - Theory