Manifestation of quark-hadron duality via the Adler D-function

Abstract

Analyzing the hadronic contributions to various physical quantities within the method based on the variational perturbation theory we obtain that the suggested method allows us to describe well the Adler function corresponding to the e+e− annihilation and the τ-decay into hadrons, the hadronic contributions to the lepton anomalous magnetic moment, and to the running electromagnetic fine structure constant. A common feature of all these quantities is that their theoretical description contains the vector current correlator and includes the low-energy region with the scale about 1 GeV and less in which the standard perturbation theory cannot be applied. We discuss the reason for such good agreement and formulate a criterion that is satisfied by the considered quantities. It is shown that such consent may be understood if we use the concept of quark-hadron duality. If the method supports the required analytic properties, the criterion obtained ensures the equivalence of the transition from the timelike to the spaselike region.