Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE

Abstract

We discuss sum-rule determinations of \alpha_sαs from non-strange hadronic \tauτ-decay data. We investigate, in particular, the reliability of the assumptions underlying the “truncated OPE strategy,” which specifies a certain treatment of non-perturbative contributions, and which was employed in Refs. . Here, we test this strategy by applying the strategy to the RR-ratio obtained from e^+e^-e+e− data, which extend beyond the \tauτ mass, and demonstrate that the assumptions underlying this strategy are not, in general, valid. We then present a brief overview of new results on the form of duality-violating non-perturbative contributions, which are conspicuously present in the experimentally determined spectral functions. As we show, with the current precision claimed for the extraction of \alpha_sαs, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.