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

D. Boito; M. Golterman; K. Maltman; S. Peris

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arXiv · 1811.01581

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

D. Boito·M. Golterman·K. Maltman·S. Peris

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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. [1-3]. 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, 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 $\alpha_s$, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.

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D. Boito, M. Golterman, K. Maltman, S. Peris. 2018-11-05. Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE. https://arxiv.org/abs/1811.01581

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