Violations of quark-hadron duality in low-energy determinations of αs
Antonio Pich, Antonio Rodríguez–Sánchez
Abstract
A bstract 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 ( $$ {m}_{\tau}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ) 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.