The uncertainty in αs (MZ2) determined from hadronic tau decay measurements Original Research Article

We show that QCD Minkowski observables such as the e+e− R-ratio and the hadronic tau decay Rτ are completely determined by the effective charge (EC) beta-function, ϱ(x), corresponding to the Euclidean QCD vacuum polarization Adler D-function, together with the next-to-leading order (NLO) perturbative coefficient of D. An efficient numerical algorithm is given for evaluating R, Rτ from a weighted contour integration of D (seiΘ around a circle in the complex squared energy s-plane, with ϱ(x) used to evolve in s around the contour. The EC beta-function can be truncated at next-to-NLO (NNLO) using the known exact perturbative calculation or the uncalculated N3 LO and higher terms can be approximated by the portion containing the highest power of b, the first QCD beta-function coefficient. The difference between the R, Rτ constructed using the NNLO and “leading-b” resummed versions of ϱ(x) provides an estimate of the uncertainty due to the uncalculated higher order corrections. Simple numerical parametrizations are given to facilitate these fits. For Rτ we estimate an uncertainty Δαs(mτ2) ≅ 0.01, corresponding to Δαs(Mz2) ≅ 0.002. Thus there is no necessary implication that the uncalculated higher order corrections contribute a large uncertainty in αs (MZ2) as had been claimed by other authors based on analogous all-orders resummations. We show that these earlier estimates are dependent on the renormalization scheme chosen, a difficulty which is avoided in our formulation.