QCD corrections to rare K- and B-decays for arbitrary top quark mass

Abstract

We calculate strong interaction O( α s) corrections to rare K- and B-decays dominated by Z 0-penguins and box-diagrams with virtual top quark exchanges for an arbitrary top quark mass. We find that the uncertainty in the branching ratios, due to the dependence of m t on the choice of the renormalization scale μ is reduced from O(25%) to O(3%) by including the O( α s) corrections. For the choice μ = m t with 100 GeV⩽ m t⩽200 GeV the corrections to K L→π 0ν ν and B→ X s ν ν are less than 4% and at most 13% for B → l l . For the choice μ = M W they can be as large as 20% for both types of decays. We also point out that the published branching ratios for B → l l miss an overall factor of 2.