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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]] | | ||

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