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

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 $\alpha_s(m_{\tau}^2)$.