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 ${\gamma }_5$ 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.

8 pages, Latex A complete postscript file is available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /ttp93-26/ttp93-26.ps, Local preprint# TTP93-26

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• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• Mass Corrections to the Tau Decay Rate

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