The rare decays K+ → π+νν and KL → μ+μ- beyond leading logarithms

Gerhard Buchalla, Andrzej J. Buras

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177 Scopus citations


We analyze the branching ratio for the FCNC mode K+ → π+νν in the standard model with QCD effects taken into account consistently to next-to-leading order. This involves a two-loop renormalization group analysis for the charm contribution, presented in this paper, and the calculation of O(αS) corrections to all orders in mt/MW for the top-quark case that we have described elsewhere. The inclusion of next-to-leading corrections reduces considerably the theoretical uncertainty due to the choice of the renormalization scales, inherent in any calculation to finite order in perturbation theory. For K+ → π+νν this point has not been discussed previously. In particular, the related uncertainty in the determination of |Vtd| from B(K+ → π+νν) is reduced from ∼ 30% to ∼ 7% for typical values of the parameters. Simultaneously also the dependence of B(K+ → π+νν) on the choice of mc is considerably reduced. We also give the next-to-leading order expression for the short-distance part of KL → μ+μ-. Impacts of our calculations on the determination of the unitarity triangle are presented.

Original languageEnglish
Pages (from-to)106-142
Number of pages37
JournalNuclear Physics, Section B
Issue number1-2
StatePublished - 17 Jan 1994


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