On the running electromagnetic coupling constant at $M_Z$

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

doi:doi:10.1007/s100520050556

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2024 Impact factor 4.8

Particles and Fields

Eur. Phys. J. C 9, 551-556
DOI 10.1007/s100529900061

On the running electromagnetic coupling constant at M_Z

J.G. Körner¹ - A.A. Pivovarov^1,2 - K. Schilcher¹

¹ Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
² Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia

Received: 19 February 1999 / Published online: 30 June 1999

Abstract
We present a discussion on how to define the running electromagnetic coupling constant at M_Z or some other intermediate scale, e.g., $m_\Upsilon$ . 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 $\Upsilon$ -resonance mass, that the usual definition of the hadronic contribution with a principal-value prescription is inconsistent. In the determination of the value of $\alpha$ at M_Z, 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 $\alpha(M_Z)$ .