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One of the largest theoretical uncertainties assigned to the strong couplingconstant alpha_s as determined from hadronic tau decays stems from thedifferences in the results for Fixed Order Perturbation Theory (FOPT), ContourImproved Perturbation Theory (CIPT) and Renormalon Chain Perturbation Theory(RCPT). It is often argued that the three methods differ in the treatment ofhigher orders only and therefore the full difference should be treated astheoretical error. Recently other arguments either in favor of FOPT, CIPT orRCPT have been given, but none of those is able to combine all three to asingle value in the strong coupling constant. In this note I will show thatFOPT alone has a much larger uncertainty than previously assumed and thereforeagrees within error with CIPT. Furthermore a more appropriate matching of thedifferent schemes used in RCPT reduces the difference to the CIPT result by afactor of 6. Together with recently published results for the 4th order termK_4 this reduces the theoretical error on alpha_s by a factor of 2.5 comparedto the previously assumed spread of the three perturbative approaches.

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