Renormalization of 4-quark operators and QCD sum rules

Abstract

We compute the renormalization mismatch displayed in 1-loop approximation by classically equivalent 4-quark operators and coming from different possible definitions of the γ 5 matrix in dimensional regularization. The result is then employed to study the effect of the various treatments of γ 5 upon the size of radiative corrections to 4-quark condensates in the QCD sum rules for ρ and A 1 mesons. We find that a fully anticommuting γ 5 which automatically respects non-anomalous chiral Ward-Slavnov identities leads to considerably smaller corrections and reduces theoretical uncertainty in the QCD prediction for the τ hadronic decay rate.