Rare decay K+ → π+ν(ν)over-bar at the next-to-next-to-leading order in QCD -: art. no. 261805

We calculate the charm quark contribution to the rare decay K+->pi(+)nu(nu) over bar in the next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P-c from +/- 10.1% down to +/- 2.4%, corresponding to scale uncertainties of +/- 1.3%, +/- 1.0%, +/- 0.006, and +/- 1.2 degrees in B(K+->pi(+)nu(nu) over bar) and in vertical bar V-td vertical bar, sin2 beta, and gamma extracted from the K ->pi nu(nu) over bar system. The error in P-c = 0.37 +/- 0.04 is now fully dominated by the current uncertainty of +/- 3.8% in the charm quark mass m(c). We find B(K+->pi(+)nu(nu) over bar) = (8.0 +/- 1.1)x10(-11), where the quoted error stems almost entirely from the present uncertainties in m(c) and the Cabibbo-Kobayashi-Maskawa elements.