EPJ

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EPJ C - Particles and Fields
Particles and Fields
Eur. Phys. J. C 12, 461-467
DOI 10.1007/s100529900279

Asymptotic structure of perturbative series
for $\tau$ lepton observables

J.G. Körner1 - F. Krajewski1 - A.A. Pivovarov1,2

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, Moscow 117312, Russia

Received: 6 September 1999 / Published online: 21 December 1999

Abstract
We analyze $\tau$ lepton decay observables, namely the moments of the hadronic spectral density in the finite energy interval $(0,M_\tau)$, within finite order perturbation theory including $\alpha_{\mathrm {s}}^4$ corrections. The start of the asymptotic growth of the perturbation theory series is found at this order in a scheme-invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables.

Copyright Springer-Verlag 2000

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