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 $\ds$ 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 $q^2=\left(1-3\,\mbox{\rm GeV}\right)^2$, 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 ($\approx -20\%$).

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

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Cited by in corpus (28)

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• Chiral Perturbation Theory
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• Strong Enhancement of ${\epsilon }^{\prime }/\epsilon$ Through Final State Interactions
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• The Standard Model Prediction for epsilon'/epsilon
• Implications of TeV Flavor Physics for the ΔI =1/2 Rule and the B-meson Semileptonic Branching Ratio
• Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions
• Weak $K$--Amplitudes in the Chiral and $1/N_c$--Expansions
• Next-to-leading Order Radiative Corrections to the Decay $b\to ccs$
• Isospin Breaking in K -> Pi Pi Decays
• Standard Model Confronting New Results for epsilon'/epsilon
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion
• Final State Interactions in Kaon Decays
• The Impact of Flavour Changing Neutral Gauge Bosons on B->X_s gamma
• The $\Delta I=1/2$ Selection Rule
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Theoretical Review of B-Physics
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
• Updating the Unitarity Triangle: Top Quark Mass Versus Nonperturbative Uncertainties
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• The heavy quark expansion for lifetimes: Towards the QCD corrections to power suppressed terms
• Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
• Updated Standard Model Prediction for ${\epsilon }^{\prime }/\epsilon$
• Theoretical overview of kaon decays
• Theoretical status of epsilon'/epsilon
• Chiral loop corrections and isospin violation effects in epsilon'/epsilon