| Summary: | Abstract Using the spectral functions measured in τ decays, we investigate the actual numerical impact of duality violations on the extraction of the strong coupling. These effects are tiny in the standard α s ( m τ 2 $$ {m}_{\tau}^2 $$ ) determinations from integrated distributions of the hadronic spectrum with pinched weights, or from the total τ hadronic width. The pinched-weight factors suppress very efficiently the violations of duality, making their numerical effects negligible in comparison with the larger perturbative uncertainties. However, combined fits of α s and duality-violation parameters, performed with non-protected weights, are subject to large systematic errors associated with the assumed modelling of duality-violation effects. These uncertainties have not been taken into account in the published analyses, based on specific models of quark-hadron duality.
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