On the role of the quark mass thresholds in extrapolations of the running αs

The accuracy of the conventional treatment of quark mass thresholds in the QCD running coupling constant αs, based on the step approximation to the β-function, is investigated. The errors of extrapolating αs(μ) from low energies to μ = Mz, implied by this approximation, are shown to be of the same magnitude as the typical next-to-next-to-leading order contributions to αs and tend to increase the resulting αs. The importance of the proper choice of matching points is emphasized.