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preprints:2006:ttp06-06 [2016/03/17 11:03] (current)
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 +====== TTP06-06 Charm Quark Contribution to K^+ -> pi^+ nu anti-nu at Next-to-Next-to-Leading Order ====== 
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 +   <​hidden TTP06-06 ​ Charm Quark Contribution to K^+ -> pi^+ nu anti-nu at Next-to-Next-to-Leading Order > the charm contribution of the rare decay K+ -> pi+ nu nu-bar. We 
 + ​encounter several new features, which were absent in lower orders. We 
 + ​discuss them in detail and present the results for the 2-loop matching 
 + ​conditions of the Wilson coefficients,​ the 3-loop anomalous dimensions,​ 
 + and the 2-loop matrix elements of the relevant operators that enter the 
 + NNLO renormalization group analysis of the Z-penguin and the electroweak 
 + box contribution. The inclusion of the NNLO QCD corrections leads to a 
 + ​significant reduction of the theoretical uncertainty from 9.8% down to 
 + 2.4% in the relevant parameter Pc, implying the leftover scale 
 + ​uncertainties in BR(K+ -> pi+ nu nu-bar) and in the determination of 
 + ​|V_td|,​ sin(2 beta), and gamma from the K -> pi nu nu system to be 1.3%, 
 + 1.0%, 0.006, and 1.2 degrees, respectively. For the charm quark MSbar 
 + mass mc=(1.30+-0.05) GeV and |V_us|= 0.2248 the NLO value Pc=0.37+-0.06 
 + is modified to Pc=0.38+-0.04 at the NNLO level with the latter error 
 + fully dominated by the uncertainty in mc. We present tables for Pc as a 
 + ​function of mc and alphas(MZ) and a very accurate analytic formula that 
 + ​summarizes these two dependences as well as the dominant theoretical 
 + ​uncertainties. Adding the recently calculated long-distance 
 + ​contributions we find BR(K+ -> pi+ nu nu-bar)=(8.0+-1.1)*10^-11 with the 
 + ​present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements 
 + being the dominant individual sources in the quoted error. We also 
 + ​emphasize that improved calculations of the long-distance contributions 
 + to K+ -> pi+ nu nu-bar and of the isospin breaking corrections in the 
 + ​evaluation of the weak current matrix elements from K+ -> pi0 e+ nu 
 + would be valuable in order to increase the potential of the two golden K 
 + -> pi nu nu decays in the search for new physics. ​  
 + </​hidden>​ 
 +|**Andrzej J. Buras, Martin Gorbahn, Ulrich Haisch, Ulrich Nierste** ​ |  
 +|**  JHEP   0611 002 2006  **  | 
 +| {{preprints:​2006:​ttp06-06.pdf|PDF}} {{preprints:​2006:​ttp06-06.ps|PostScript}} [[http://​arxiv.org/​abs/​hep-ph/​0603079|arXiv]] ​  | 
 +| |