Non-Perturbative Expansion Technique and Threshold Resummation for the Inclusive τ -decay and e +e − Annihilation into Hadrons Processes

Abstract

The method of non-perturbative a-expansion, which gives a self-consistent description of both spacelike and timelike regions, is applied to describe the D-functions corresponding to the inclusive τ-decay and e+e- annihilation into hadrons data. Thresholds effects are taken into account via a new relativistic Coulomb-like resummation factor. It is shown the method proposed leads to good agreement with experimental data down to the lowest energy scale.