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

### Submission summary

 As Contributors: Santiago Peris Preprint link: scipost_201901_00045v2 Date accepted: 2019-02-14 Date submitted: 2019-02-11 01:00 Submitted by: Peris, Santiago Submitted to: SciPost Physics Proceedings Proceedings issue: The 15th International Workshop on Tau Lepton Physics (Amsterdam, 2018-09) Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We discuss sum-rule determinations of $\alpha_s$ from non-strange hadronic $\tau$-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.~\cite{Pich,Aleph, Opal}. Here, we test this strategy by applying the strategy to the $R$-ratio obtained from $e^+e^-$ data, which extend beyond the $\tau$ 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 $\alpha_s$, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.

Published as SciPost Phys. Proc. 1, 053 (2019)