Analytic perturbation theory for QCD observables

We investigate the connection between ghost-free formulations of the RG-inv ariant QCD perturbation theory in the spacelike and timelike regions. Our b asic tool is the "double spectral representation," similar to the represent ation for the Adler function, which stems from the first principles of loca l QFT and relates real functions in the Euclidean and Minkowskian (i.e., ti melike) regions. On this base, ive establish a simple relation between the approach (known from the early 1080s) of resumming the pi (2) terms for the invariant coupling function <(<alpha>)over tilde>(s) and QCD observables i n the timelike region and the invariant analytic approach (devised a few ye ars ago) leading to the "analyticized" coupling function alpha (an) (Q(2)) and nonpower expansion for observables in the spacelike domain. The functio n alpha (an)(Q2) and the expansion are free of unphysical singularities. Th e formulated self-consistent scheme, analytic perturbation theory (APT), re lates renorm-invariant, effective coupling functions alpha (an) (Q(2)) and <(<alpha>)over tilde>(s), as well as nonpower perturbation expansions for o bservables in the Euclidean and Minkowskian domains, free of extra singular ities and with better convergence in the infrared region. We present a glob al generalization of the new APT scheme in the case of real QCD, including the domain with various numbers of active quarks. Preliminary estimates ind icate that calculations in the framework of the global scheme can produce r esults quite different from the usual ones for a,,, even in the five-quark region. Numerical examples are given.