The case for duality violations in the analysis of hadronic $\tau$ decays

Abstract

We discuss why, in the determination of ${\alpha }_s(m_{\tau }^2)$ from hadronic $\tau$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of Duality Violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion is expected to be an asymptotic, rather than a convergent expansion. There is not only experimental and theoretical evidence for DVs, but they also affect the extraction of ${\alpha }_s(m_{\tau }^2)$.

Comments: Invited contribution to the workshop "Determination of the Fundamental Parameters in QCD" (MITP/Mainz, 7-11 March 2016). 15 pages 13 figures