Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
We calculate the complete NNLO QCD corrections to 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...
| Main Authors: | , , , |
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| Format: | Journal article |
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2006
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| _version_ | 1826294965988229120 |
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| author | Buras, A Gorbahn, M Haisch, U Nierste, U |
| author_facet | Buras, A Gorbahn, M Haisch, U Nierste, U |
| author_sort | Buras, A |
| collection | OXFORD |
| description | We calculate the complete NNLO QCD corrections to 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. |
| first_indexed | 2024-03-07T03:53:50Z |
| format | Journal article |
| id | oxford-uuid:c22e58f1-83d5-41b4-a63e-7a90bfbceb8d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:53:50Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:c22e58f1-83d5-41b4-a63e-7a90bfbceb8d2022-03-27T06:07:07ZCharm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading OrderJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c22e58f1-83d5-41b4-a63e-7a90bfbceb8dSymplectic Elements at Oxford2006Buras, AGorbahn, MHaisch, UNierste, UWe calculate the complete NNLO QCD corrections to 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. |
| spellingShingle | Buras, A Gorbahn, M Haisch, U Nierste, U Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order |
| title | Charm Quark Contribution to K+ -> pi+ nu anti-nu at
Next-to-Next-to-Leading Order |
| title_full | Charm Quark Contribution to K+ -> pi+ nu anti-nu at
Next-to-Next-to-Leading Order |
| title_fullStr | Charm Quark Contribution to K+ -> pi+ nu anti-nu at
Next-to-Next-to-Leading Order |
| title_full_unstemmed | Charm Quark Contribution to K+ -> pi+ nu anti-nu at
Next-to-Next-to-Leading Order |
| title_short | Charm Quark Contribution to K+ -> pi+ nu anti-nu at
Next-to-Next-to-Leading Order |
| title_sort | charm quark contribution to k gt pi nu anti nu at next to next to leading order |
| work_keys_str_mv | AT burasa charmquarkcontributiontokgtpinuantinuatnexttonexttoleadingorder AT gorbahnm charmquarkcontributiontokgtpinuantinuatnexttonexttoleadingorder AT haischu charmquarkcontributiontokgtpinuantinuatnexttonexttoleadingorder AT niersteu charmquarkcontributiontokgtpinuantinuatnexttonexttoleadingorder |