Renormalization of 4-Quark Operators and QCD-Sum Rules

We compute the renormalization mismatch displayed in 1–loop approximation by classically equivalent 4-quark operators and coming from different possible definitions of the ${\gamma }_5$ matrix in dimensional regularization. The result is then employed to study the effect of the various treatments of ${\gamma }_5$ upon the size of radiative corrections to 4-quark condensates in the QCD sum rules for $\rho$ and $A_1$ mesons. We find that a fully anticommuting ${\gamma }_5$ which automatically respects non-anomalous chiral Ward-Slavnov identities leads to considerably smaller corrections and reduces theoretical uncertainty in the QCD prediction for the $\tau$ hadronic decay rate.