QCD corrections to FCNC decays mediated by Z-penguins and W-boxes

Abstract

QCD corrections are evaluated to FCNC processes like $B \to X_s ν\barν$, $K \to πν\barν$, $B \to l^+ l^-$ or $K_L \to μ^+ μ^-$, i.e. to processes mediated by effective operators containing neutrino currents or axial leptonic currents. Such operators originate from $W$-box and $Z$-penguin diagrams in the Standard Model. QCD corrections to them are given by two-loop diagrams. We confirm results for those diagrams which are already present in the literature. However, our analytical expressions for the Wilson coefficients disagree, due to a subtlety in regulating spurious IR divergences. The numerical effect of the disagreement is rather small. The size of the perturbative QCD corrections compared to the leading terms depends on the renormalization scheme used at the leading order. It varies from 0 to around 15% for a reasonable class of schemes. The uncertainty originating from uncalculated higher-order (three-loop) QCD corrections is expected to be around 1% .