QCD corrections to inclusive ΔS = 1, 2 transitions at the next-to-leading order

Abstract

The two-point functions for ΔS = 1 current-current and QCD-penguin operators, as well as for the ΔS = 2 operator, are calculated at the next-to-leading order. The calculation is performed in two different renormalization schemes for γ5, and the compatibility of the results obtained in the two schemes is verified. The scale- and scheme-invariant combinations of spectral two-point functions and corresponding Wilson coefficients are constructed and analyzed. For ΔS = 1, the QCD corrections to the CP-conserving part, dominated by current-current operators, are 40–120% at q2 = (1–3 GeV)2, whereas the corrections to the imaginary part, mainly coming from the penguin operator Q6, are 100–240%. The large size of the gluonic corrections to current-current operators provides a qualitative understanding of the observed enhancement of ΔI = 1/2 transitions. In the ΔS = 2 sector the QCD corrections are quite moderate (≈−20%).