Adler function for light quarks in analytic perturbation theory - art. no.016005

The method of analytic perturbation theory, which avoids the problem of gho st-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler fu nction corresponding to the nonstrange vector channel of the inclusive deca y of the tau lepton. The role of threshold effects is investigated. The beh avior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed l eads to good agreement with the "experimental" Adler function down to the l owest energy scale.