Analytic Perturbation Theory and New Analysis of some QCD observables

Here, we report briefly two topics: 1) The latest version of “Analytic Perturbation Theory” (APT) devised recently for the QCD observables both in the Euclidean and Minkowskian regions. 2) Results of the APT–based calculation for some physical processes. 1 The APT — a closed theoretical scheme The new APT version [1, 2] mutually relates two ghost–free formulations of modified perturbation expansions for observables. The first one, initiated about two decades ago [3, 4], changes the standard power expansion in the time-like region Rpt(s) = 1 + rpt(s) ; rpt(s) = ∑ k≥1 rk αs (s; f) into a nonpower one rpt(s) → rπ(s) = ∑ k≥1 dk Ak(s, f) . Here, αs(s) is a common, e.g., 3–loop QCD invariant/running coupling (usually in the MS scheme – see eq.(9.5a) in Ref. [5]); and Ak, some integral images of the αs powers: Ak(s) = R [