Determination of $\alpha_s(M_\tau^2)$: a conformal mapping approach

Abstract

We discuss a new class of expansions in perturbative QCD, based on the technique of conformal mappings of the Borel plane, and apply them for the determination of $\alpha_s$ from the hadronic decays of the $\tau$ lepton. Using the expansion up to fifth order in the $\bar{\rm MS}$ scheme, the method leads to the prediction $\alpha_s(M_\tau^2)= 0.320\pm 0.011$.