Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu   nu-bar
  We compute the leading-log QED, the next-to-leading-log QED-QCD, and the electroweak corrections to the charm quark contribution relevant for the rare decay K+ -> pi+ nu nu-bar. The corresponding parameter P_c(X) is increased by up to 2% with respect to the pure QCD estimate to P_c(X) = 0.372 +- 0.015 for m_c(m_c)= (1.286 +- 0.013) GeV, alphas(M_Z) = 0.1176 +- 0.0020 and |V_us| = 0.2255. For the branching ratio we find B(K+ -> pi+ nu nu-bar) = (8.5 +- 0.7)*10^{-11}, where the quoted uncertainty is dominated by the CKM elements. 
Joachim Brod, Martin Gorbahn