Abstract
We analyze tau lepton decay observables, namely moments of the hadronic spectral density in the finite energy interval (0,M_τ), within finite order perturbation theory including α_s^4 corrections. The start of asymptotic growth of perturbation theory series is found at this order in a scheme invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables.
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