The rare decays K → πνν−, B → Xνν− and B → l+l−: an update Original Research Article

We update the Standard Model predictions for the rare decays K+ → π+νν− and KL → π0νν−. In view of improved limits on Bs−B−s mixing we derive a stringent and theoretically clean Standard Model upper limit on B(K+ → π+νν−, which is based on the ratio of Bd−B−dto Bs−B−s mixing, ΔMd/ΔMs, alone. This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix. We find B(K+ → π+νν− < 1.67 × 10−1, which can be further improved in the future. In addition we consider the extraction of |Vtd| from a future measurement of B (K+ → π+νν−), discussing the various sources of uncertainties involved. We also investigate theoretically clean constraints on B(KL → π0νν−). We take the opportunity to review the next-to-leading order (NLO) QCD corrections to K → πνν−, KL → μ+μ−, B → Xνν−and B → l+l−, including a small additional term that had been missed in the original publications. The phenomenological impact of this change is negligible, the corresponding numerical shift being essentially within the small perturbative uncertainties at the NLO level.