Mixed quark-gluon condensate from instantons

Abstract

We calculate the vacuum expectation value of the dimension-5 "mixed" quark-gluon operator, $O_{\sigma }=\bar{\psi }({\lambda }^a/2){\sigma }_{\mu \nu }\psi F_{\mu \nu }^a$, in the instanton vacuum. Within the $1/N_c$--expansion the QCD operator is replaced by an effective many-fermion operator, which is averaged over the effective theory of massive quarks derived from instantons. We find $m_0^2\equiv ⟨O_{\sigma }⟩/⟨\bar{\psi }\psi ⟩\approx 4{\bar{\rho }}^{-2}=1.4Ge{V}^2$, somewhat larger than the estimate from QCD sum rules for the nucleon.

Comments: 10 p, LaTeX, 1 figure included using epsf