| Abstrakt: |
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 $10 {\rm GeV}\lesssim s^{1/2}\lesssim 170 {\rm GeV}$) 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). [ABSTRACT FROM AUTHOR] |
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