QCD corrections to inclusive $\Delta S=1,2$ transitions

Abstract

The talk summarises a calculation of the two-point functions for $\Delta S=1$ current-current and QCD-penguin operators, as well as for the $\Delta S=2$ operator, at the next-to-leading order. The size of the gluonic corrections to current-current operators is large, providing a qualitative understanding of the observed enhancement in $\Delta I=1/2$ transitions. In the $\Delta S=2$ sector the QCD corrections are quite moderate ($\approx -20\%$). This work has been done in collaboration with Antonio Pich.