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. An improved way to calculate the running fine 
structure constant is presented.