Abstract
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.
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