We study a model Dyson-Schwinger equation for the quark propagator closed using an { \it Ansatz} for the gluon propagator of the form \mbox{ $D(q) \sim q^2/[(q^2)^2 + b^4]$} and two { \it Ans\"{ a}tze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the model { \bf is not} confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behaviour of QCD.
Categories: hep-ph nucl-th