Quark Propagator and Meson Correlators in the QCD Vacuum

Abstract

Equal time, point to point correlation functions for spatially separated meson currents are calculated with respect to a variational construct for the ground state of QCD. Given such an ansatz we make no further approximations in the evaluation of the correlators. Our calculations for the vector, axial vector and scalar channels show qualitative agreement with the phenomenological predictions, whereas the pseudoscalar channel does not. However, the pseudoscalar correlator, when approximated by saturating with intermediate one pion states agrees with results obtained from spectral density functions parameterised by pion decay constant and $<-\bar ψψ>$ value obtained from chiral perturbation theory. We discuss this departure in the pseudoscalar channel, in context of the quark propagation in the vacuum.