Analytic perturbation theory in analyzing some QCD observables

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 () 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 term in the coefficient is not adequate at . In particular, this relates to decay. Then for the “high” () region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at ) for the analysis of shape/events data contains a systematic negative error at the 1–2 per cent level for the extracted values. Our physical conclusion is that the value averaged over the data appreciably differs, , from the currently accepted “world average” (=0.118). Received: 30 July 2001 / Published online: 5 November 2001