Analytic Perturbation Theory in analyzing some QCD observables

The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD – ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f=3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution $\sim \alpha_s^3$) is as a rule numerically inessential. This gives raise a hope for practical solution of the well-known problem of asymptotic nature of common QFT perturbation series. The second result is that a usual perturbative analysis of time-like events with the big ${\pi }^2$ term in the ${\alpha }_s^3$ coefficient is not adequate at $s\le 2{\text{GeV}}^2$. 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 $10 \GeV\lesssim\sqrt{s}\lesssim 170 \GeV$) for analysis of shape/events data contains a systematic negative error of a 1–2 per cent level for the extracted ${\overline{alpha}}_s^{(2)}$ values. Our physical conclusion is that the ${\overline{alpha}}_s(M_Z^2)$ value averaged over the f=5 data appreciably differs $<bar{alpha}_s(M_Z^2){>}_{f=5}\simeq 0.124$ from the currently accepted “world average” (=0.118).}