THE CONVERGENCE RADIUS OF THE CHIRAL EXPANSION IN THE DYSON-SCHWINGER APPROACH

We determine an upper bound on the convergence radius m(conv) for the expansion in the current quark mass using the Dyson-Schwinger (DS) equation of QCD in the rainbow approximation. Using a gluon propagator, which has the form D-mu nu(p) similar to delta(mu nu)X(2)e(-p2/Delta) at small p(2) and the standard logarithmic form in the UV region we find that m(conv) increases with decreasing width Delta and increasing strength X(2). For those values of X(2) and Delta, which have been shown to provide a good description of low energy hadronic phenomena, m(conv) lies around 400MeV, which is clearly larger than the mass of the strange quark. Our analysis also explains the rather low value of m(conv) approximate to 50...80 MeV in the Nambu-Jona-Lasinio model, which as itself can be regarded as a special case of the rainbow DS models, where the gluon propagator is a constant in momentum space.