Testing non-perturbative strong interaction effects via the Adler function

Based on the compilation of the available e+e− data [S.I. Eidelman, F. Jegerlehner, Z. Phys. C 67 (1995) 585; F. Jegerlehner, Nucl. Phys. B (Proc. Suppl.) 51C (1996) 131], we present a non-perturbative estimation of the Adler function derived from the electromagnetic current correlator, and compare it with theoretical predictions from perturbative QCD (pQCD). The comparison is presented for the Euclidean region where pQCD is supposed to work best. We emphasize that such a comparison only makes sense if one takes into account the exact mass dependence of the perturbative predictions, which are available for the leading and next to leading (two-loop) order. In order to have the correct physical mass dependence in the evolution of the strong coupling as well, we utilize the MOM scheme β-function to two-loops calculated recently [F. Jegerlehner, O.V. Tarasov, DESY 98-093, hep-ph/9809485, and references therein]. Three-loop effects, which are available as series expansions for low [K.G. Chetyrkin et al., Nucl. Phys. B 482 (1996) 213; B 505 (1997) 40] and high [K.G. Chetyrkin et al., Nucl. Phys. B 503 (1997) 339] momentum transfer, are included by using Padé improvement. We discuss possible constraints on non-perturbative effects as suggested by the operator product expansion.