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

Abstract

We discuss why, in the determination of $α_s(m_τ^2)$ from hadronic $τ$ 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 $α_s(m_τ^2)$.

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