Adler function from Re+e- (s) measurements: Experiments vs QCD theory

An experimentally motivated QCD analysis of the behaviour of the Adler D-function in the Euclidian region is described. It is stressed that by taking account of b-quark mass-dependent αs2-effects one obtains better agreement between theoretical predictions and experimentally motivated behaviour of the D-function at large Euclidean momentum transfer. A more detailed analysis of QCD predictions, including information on quark and gluon condensates, requires more precise data on e+e- → hadrons, particularly in the energy regions E < MJ/Ψ and MJ/Ψ < E < 3.6 GeV. Use of experimental determination of the D-function to test the generalized Crewther relation is outlined. (author)