On the determination of αs from hadronic τ decays with contour-improved, fixed order and renormalon-chain perturbation theory

One of the largest theoretical uncertainties assigned to the strong coupling constant αs as determined from hadronic tau decays stems from the differences in the results for Fixed Order Perturbation Theory (FOPT), Contour Improved Perturbation Theory (CIPT) and Renormalon Chain Perturbation Theory (RCPT). It is often argued that the three methods differ in the treatment of higher orders only and therefore the full difference should be treated as theoretical error. Recently other arguments either in favor of FOPT, CIPT or RCPT have been given, but none of those is able to combine all three to a single value in the strong coupling constant. In this note I will show that FOPT alone has a much larger uncertainty than previously assumed and therefore agrees within error with CIPT. Furthermore a more appropriate matching of the different schemes used in RCPT reduces the difference to the CIPT result by a factor of 6. Together with recently published results for the 4th order term K4 this reduces the theoretical error on αs by a factor of 2.5 compared to the previously assumed spread of the three perturbative approaches.