Behavior of the effective QCD coupling α _τ(s) at low scales

The hadronic decays of the τ lepton can be used to determine the effective charge ατ(m _τ ²,) for a hypothetical τ lepton with a mass in the range 0<m _τ,<mτ. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of α _τ at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m _τ ², of order 1 GeV ² with a magnitude α _τ ∼0.9 ±0.1.