Mixed quark-gluon condensate from instantons

We calculate the vacuum expectation value of the dimension-5 “mixed” quark-gluon operator, Oσ = Ψ12λaσμνΨFμνa, in the instanton vacuum. Within the 1Nc-expansion the QCD operator is replaced by an effective many-fermion operator, which is averaged over the effetive theory of massive quarks derived from instantons. We find m02 ≡ 〈Oσ〉/〈ΨΨ〉 ≈ 4ϱ– = 1.4 GeV2, somewhat larger than the estimate from QCD sum rules for the nucleon.