Modelling the quark propagator

We are interested in developing covariant, confining, and asymptotically free models of hadrons. With this goal in mind we have carried out a study of dynamical chiral symmetry breaking without imposing the frequently used approximation αs[-(p-k)2]congruent αs(-p2>), where p2>≡max(p2,k2) for the running coupling constant in the quark Schwinger--Dyson equation. We present numerical results in Landau gauge and compare these with earlier results obtained when using this approximation. We see in this context that a gluon propagator which has the form 1/q4 in the infrared is too singular and must be regulated. We derive a suitably generalized expression for the pion decay constant fπ. With essentially one free parameter we are able to reproduce reasonable results for various physical quantities of interest including fπ, left-angle bar qq right-angle, and ΛQCD. copyright 1991 Academic Press, Inc