Infrared behaviour of propagators and vertices

Abstract We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P (k 2 ):=1/[1+Π(k 2 )] , where Π ( k 2 ) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P (k 2 =0)=0 and max ( P (k 2 ))∼10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P (k 2 ) via numerical simulations.