Analytic Perturbation Theory for QCD observables
Abstract
The connection between ghostfree formulations of RGinvariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function, that stems from first principles of local QFT. It relates real functions defined in the Euclidean and Minkowskian regions. On this base we establish a simple relation between  The trick of resummation of the $\pi^2$terms (known from early 80s) for the invariant QCD coupling and observables in the timelike region and  Invariant Analytic Approach (devised a few years ago) with the "analyticized" coupling $\alpha_{\rm an}(Q^2)$ and nonpower perturbative expansion for observables in the spacelike domain which are free of unphysical singularities . As a result, we formulate a selfconsistent scheme, Analytic Perturbation Theory (APT), that relates a renorminvariant, effective coupling functions $\alpha_{an}(Q^2) $ and $\tilda{alpha}(s),$ as well as nonpower perturbation expansions for observables in both space and timelike domains, that are free of extra singularities and obey better convergence in the infrared region. Then we consider the quark threshold crossing and devise a global APT scheme for the data analysis in the whole accessible spacelike and timelike domain with various numbers of active quarks. Preliminary estimates indicate that this global scheme produces results a bit different, sometimes even in the fiveflavour region, on a few per cent level for $\bar{\alpha}_s$  from the usual one, thus influencing the total picture of the QCD parameter correlation.
 Publication:

arXiv eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:hepph/0012283
 Bibcode:
 2000hep.ph...12283S
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 19 pages, LaTeX2e