Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order

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The authors calculate the complete next-to-next-to-leading order QCD corrections to the charm contribution of the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}. They encounter several new features, which were absent in lower orders. They discuss them in detail and present the results for the two-loop matching conditions of the Wilson coefficients, the three-loop anomalous dimensions, and the two-loop matrix elements of the relevant operators that enter the next-to-next-to-leading order renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the next-to-next-to-leading order QCD corrections leads to a significant reduction of the theoretical uncertainty from {+-} ... continued below

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69 pages

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Buras, Andrzej J.; Gorbahn, Martin; Haisch, Ulrich & Nierste, Ulrich March 1, 2006.

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The authors calculate the complete next-to-next-to-leading order QCD corrections to the charm contribution of the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}. They encounter several new features, which were absent in lower orders. They discuss them in detail and present the results for the two-loop matching conditions of the Wilson coefficients, the three-loop anomalous dimensions, and the two-loop matrix elements of the relevant operators that enter the next-to-next-to-leading order renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the next-to-next-to-leading order QCD corrections leads to a significant reduction of the theoretical uncertainty from {+-} 9.8% down to {+-} 2.4% in the relevant parameter P{sub c}(X), implying the leftover scale uncertainties in {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) and in the determination of |V{sub td}|, sin 2{beta}, and {gamma} from the K {yields} {pi}{nu}{bar {nu}} system to be {+-} 1.3%, {+-} 1.0%, {+-} 0.006, and {+-} 1.2{sup o}, respectively. For the charm quark {ovr MS} mass m{sub c}(m{sub c}) = (1.30 {+-} 0.05) GeV and |V{sub us}| = 0.2248 the next-to-leading order value P{sub c}(X) = 0.37 {+-} 0.06 is modified to P{sub c}(X) = 0.38 {+-} 0.04 at the next-to-next-to-leading order level with the latter error fully dominated by the uncertainty in m{sub c}(m{sub c}). They present tables for P{sub c}(X) as a function of m{sub c}(m{sub c}) and {alpha}{sub s}(M{sub z}) 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 they find {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) = (8.0 {+-} 1.1) x 10{sup -11} with the present uncertainties in m{sub c}(m{sub c}) and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. They also emphasize that improved calculations of the long-distance contributions to K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}} and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K{sup +} {yields} {pi}{sup 0}e{sup +}{nu} would be valuable in order to increase the potential of the two golden K {yields} {pi}{nu}{bar {nu}} decays in the search for new physics.

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69 pages

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  • Journal Name: JHEP 0611:002,2006; Journal Volume: 11

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  • Report No.: FERMILAB-PUB-05-512-T
  • Grant Number: AC02-07CH11359
  • DOI: 10.1088/1126-6708/2006/11/002 | External Link
  • Office of Scientific & Technical Information Report Number: 897292
  • Archival Resource Key: ark:/67531/metadc888069

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  • March 1, 2006

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  • Sept. 22, 2016, 2:13 a.m.

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  • July 25, 2017, 2:42 p.m.

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Buras, Andrzej J.; Gorbahn, Martin; Haisch, Ulrich & Nierste, Ulrich. Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order, article, March 1, 2006; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc888069/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.