We study a model Dyson-Schwinger equation for the quark propagator closed using an Ansatz for the gluon propagator of the form D(q)∼${\mathit{q}}^2$/[(${\mathit{q}}^2$${)}^2$+${\mathit{b}}^4$] and two Ansa$uml—tze for the quark-gluon vertex: the minimal Ball-Chiu form 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=${\mathit{b}}_{\mathit{c}}$ such that the model does not support dynamical chiral symmetry breaking for b>${\mathit{b}}_{\mathit{c}}$. We discuss and apply a confinement test which suggests that, for all values of b, the quark propagator in the model 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 behavior of QCD.

• Received 13 September 1993

DOI:https://doi.org/10.1103/PhysRevD.49.4683