QCD corrections to inclusive $\Delta S=1,2$ transitions at the next-to-leading order

Abstract

The 2--point functions for $\Delta S=1$ current-current and QCD-penguin operators, as well as for the $\text{ds}$ operator, are calculated at the next-to-leading order. The calculation is performed in two different renormalization schemes for ${\gamma }_5$, and the compatibility of the results obtained in the two schemes is verified. The scale- and scheme-invariant combinations of spectral 2--point functions and corresponding Wilson-coefficients are constructed and analyzed. For $\Delta S=1$, the QCD corrections to the CP-conserving part, dominated by current-current operators, are 40\%--120\% at $q^2={\left(1-3\text{mbox}\mathrm{GeV}\right)}^2$, whereas the correction to the imaginary part, mainly coming from the penguin operator $Q_6$, are 100\%--240\%. The large size of the gluonic corrections to current-current operators provides a qualitative understanding of the observed enhancement of $\Delta I=1/2$ transitions. In the $\Delta S=2$ sector the QCD corrections are quite moderate ($\approx -20\%$).

Comments: 28 pages, CERN-TH.7151/94, FTUV/94-6, IFIC/94-3, 3 figures and 4 macros included as uuencoded tar-file