Relations between quark and gluon condensates from one-loop effective actions in constant background fields

Abstract

The quark condensate is obtained in terms of vacuum expectation values of gluonic gauge-invariants from the one-loop QCD effective action for chromomagnetic and self-dual constant background fields in presence of massive quarks. Heavy quark expansion results—as used in QCD sum rules—are recuperated for heavy quarks and a zero chiral limit is attained for 〈 ψψ〉 unless a parity-violation condensate 〈F a μ v F ̃ a μ v 〉 = O(m) exists.