The status of the strong coupling from tau decays in 2016

Abstract

While the idea of using the operator product expansion (OPE) to extract the strong coupling from hadronic $τ$ decay data is not new, there is an ongoing controversy over how to include quark-hadron "duality violations" (i.e., resonance effects) which are not described by the OPE. One approach attempts to suppress duality violations enough that they might become negligible, but pays the price of an uncontrolled OPE truncation. We critically examine a recent analysis using this approach and show that it fails to properly account for non-perturbative effects, making the resulting determination of the strong coupling unreliable. In a different approach duality violations are taken into account with a model, avoiding the OPE truncation. This second approach provides a self-consistent determination of the strong coupling from $τ$ decays.