Analytic Perturbation Theory in analyzing some QCD observables

D. V. Shirkov

doi:10.1007/s100520100794

paper

Analytic Perturbation Theory in analyzing some QCD observables

arXiv:hep-ph/0107282 · doi:10.1007/s100520100794

Abstract

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 $\sim α_{s}^{3}$ ) 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 $π^{2}$ term in the $α_{s}^{3}$ coefficient is not adequate at $s\leq 2 \GeV^2$. In particular, this relates to $τ$ 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 $a l p ha ˉ_{s}^{(2)}$ values. Our physical conclusion is that the $a l p ha ˉ_{s} (M_{Z}^{2})$ value averaged over the f=5 data appreciably differs $< ba r a l p ha_{s} (M_{Z}^{2}) >_{f = 5} ≃ 0.124$ from the currently accepted "world average" (=0.118).}

19 pages, LaTeX2e, 3 figures

Analytic Perturbation Theory in analyzing some QCD observables

Abstract

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