On the running electromagnetic coupling constant at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_Z$\end{document} View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1999-07

AUTHORS

J.G. Körner, A.A. Pivovarov, K. Schilcher

ABSTRACT

We present a discussion on how to define the running electromagnetic coupling constant at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_Z$\end{document} or some other intermediate scale, e.g., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m_\Upsilon$\end{document}. We argue that a natural definition consistent with general requirements of the renormalization group should use Euclidean values of the momentum of the photon propagator as the appropriate scale. We demonstrate explicitly, through the evaluation of the running coupling constant at the scale of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Upsilon$\end{document}-resonance mass, that the usual definition of the hadronic contribution with a principal-value prescription is inconsistent. In the determination of the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha$\end{document} at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_Z$\end{document}, we use a Euclidean definition rather than the principal-value one, and as a result, the numerical difference is comparable in size to the errors caused by existing experimental and QCD inputs to the evaluation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha(M_Z)$\end{document}. More... »

PAGES

551-556

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s100530050498

DOI

http://dx.doi.org/10.1007/s100530050498

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1037317692


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