Determining $α_s$ from hadronic $τ$ decay: the pitfalls of truncating the OPE

Abstract

We discuss sum-rule determinations of $α_s$ from non-strange hadronic $τ$-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. [1-3]. Here, we test this strategy by applying the strategy to the $R$-ratio obtained from $e^+e^-$ data, which extend beyond the $τ$ mass, and, based on the outcome of these tests, we demonstrate the failure of this strategy.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 $α_s$, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.

15 pages, 4 figures, contribution to the proceedings for the 15th International Workshop on Tau Lepton Physics, Amsterdam, The Netherlands, Sept. 2018