Testing non-perturbative strong interaction effects via the Adler   function
  Based on the compilation of the available e^+e^- data, 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 beta-function to two-loops calculated recently. Three-loop effects, which are available as series expansions for low and high momentum transfer, are included by using Pade improvement. We discuss possible constraints on non-perturbative effects as suggested by the operator product expansion. 
S. Eidelman (BudkerINP, Novosibirsk), F. Jegerlehner (DESY Zeuthen),   A.L. Kataev (INR-ASR, Moscow), O. Veretin (DESY Zeuthen)