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Particles and Fields

Eur. Phys. J. C 22, 331-340 (2001)
DOI: 10.1007/s100520100794

Analytic perturbation theory in analyzing some QCD observables

D.V. Shirkov

Bogoliubov Laboratory, JINR, 141980 Dubna, Russia

(Received: 30 July 2001 / Published online: 5 November 2001 - © Springer-Verlag / Società Italiana di Fisica 2001)

This paper is devoted to the application of the recently devised ghost-free analytic perturbation theory (APT) for the analysis of some QCD observables. We start with a discussion of the main problem of the perturbative QCD, ghost singularities, and with a resume of its resolving within the APT. By a few examples in various energy and momentum transfer regions (with the flavor number f=3,4 and 5) we demonstrate the effect of the improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution ( $\sim \alpha_{\mathrm {s}}^3$) is as a rule numerically inessential. This gives hope for a practical solution of the well-known problem of the asymptotic nature of the common QFT perturbation series. The second result is that the usual perturbative analysis of time-like events with the large $\pi^2$ term in the $\alpha_{\mathrm {s}}^3$ coefficient is not adequate at $s\leq 2\,{\rm GeV}^2 $. In particular, this relates to $\tau$ decay. Then for the "high" ( f=5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at $10\,{\rm GeV}\lower.7ex\hbox{$\;\stackrel{\textstyle <}{\sim}\;$ }s^{1/2}\lower.7ex\hbox{$\;\stackrel{\textstyle <}{\sim}\;$ }170\,{\rm
GeV}$ ) for the analysis of shape/events data contains a systematic negative error at the 1-2 per cent level for the extracted ${\bar{\alpha}_{\mathrm {s}}}^{(2)} $ values. Our physical conclusion is that the $ \bar \alpha_{\mathrm {s}}(M_Z^2)$ value averaged over the f=5 data appreciably differs, $ \langle \bar \alpha_{\mathrm {s}}(M_Z^2)\rangle _{f=5}
\simeq 0.124 $ , from the currently accepted "world average" (=0.118).

© Società Italiana di Fisica, Springer-Verlag 2001