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