Perturbative QCD with Quark and Gluon Condensates

Abstract

QCD perturbation theory using quark and gluon propagators that have an extra term at zero four-momentum is equivalent to standard PQCD in the presence of massless quark and gluon pairs in the perturbative vacuum. We verify at low orders in perturbation theory that $<\bar\psi\psi> \neq 0$ and that quarks acquire a constituent mass. Thus chiral symmetry is spontaneously broken, and the conservation of the axial vector current ensures a massless pion. The gluon pairs generate an $<F_{\mu\nu}F^{\mu\nu}>$ expectation value and a tachyonic gluon mass. Lorentz and gauge symmetry is preserved, and the short-distance structure of PQCD is unaffected. The modified perturbative expansion thus contains relevant elements of QCD at both short and long distances.