The rare decays K → πν(ν)over-bar, B → Xν(ν)over-bar and B l+l-:: an update

We update the Standard Model predictions for the rare decays K+ --> pi(+)nu<(nu)over bar> and K-L --> pi(0)nu<(nu)over bar>. In view of improved limits on B-s-(B) over bar(s), mixing we derive a stringent and theoretically clean Standard Model upper limit on B(K+ --> pi(+)nu<(nu)over bar>), which is based on the ratio of B-d-(B) over bar(d) to B-s-(B) over bar(s) mixing, Delta M-d/Delta M-s, alone. This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix. We find B(K+ --> pi(+)nu<(nu)over bar>) < 1.67 x 10(-10), which can be further improved in the future. In addition we consider the extraction of \V-td\ from a future measurement of B(K+ --> pi(+)nu<(nu)over bar>), discussing the various sources of uncertainties involved. We also investigate theoretically clean constraints on B(K-L --> pi(0)nu<(nu)over bar>). We take the opportunity to review the next-to-leading order (NLO) QCD corrections to K --> pi nu<(nu)over bar>, K-L --> mu(+)mu(-), B --> X nu<(nu)over bar> 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. (C) 1999 Elsevier Science B.V. All rights reserved.