Renormalization Scheme and Higher Loop Stability in Hadronic $τ$ Decay within Analytic Perturbation Theory

Abstract

We apply an analytic description to the inclusive decay of the $τ$ lepton. We argue that this method gives not only a self-consistent description of the process both in the timelike region by using the initial expression for $R_τ$ and in the spacelike domain by using the analytic properties of the hadronic correlator, but also leads to the fact that theoretical uncertainties associated with unknown higher-loop contributions and renormalization scheme dependence can be reduced dramatically.