The Rare Decay K^+ -> pi^+ nu nubar at the Next-to-Next-to-Leading Order in QCD

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  • 15 August 2005
Abstract
We calculate the complete next-to-next-to-leading order QCD correction of the charm quark contribution to the branching ratio for the rare decay K^+ -> pi^+ nu nubar in the standard model. The inclusion of these O(alpha_s) contributions leads to a significant reduction of the theoretical uncertainty from 10.1% down to 2.4% in the relevant parameter P_c, implying the left over scale uncertainties in BR(K^+ -> pi^+ nu nubar) and in the determination of V_td, sin(2 beta) and gamma from the K -> pi nu nubar system to be +-1.3%, +-1.0%, +-0.006 and +-1.2 deg, respectively. For the charm quark MSbar mass m_c(m_c) = (1.30 +- 0.05) GeV and |V_us| = 0.2248 the next-to-leading order value P_c = 0.37 +- 0.06 is modified to P_c = 0.37 +- 0.04 at the next-to-next-to-leading order level with the latter error fully dominated by the uncertainty in m_c(m_c). Adding the recently calculated long-distance contributions we find BR(K^+ -> pi^+ nu nubar) = (8.0 +- 1.1) x 10^-11 with the quoted error almost entirely due to the present uncertainties in m_c(m_c) and the Cabibbo-Kobayashi-Maskawa elements.

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