On the role of the quark mass thresholds in extrapolations of the running \alpha_s

Abstract

The accuracy of the conventional treatment of quark mass thresholds in the QCD running coupling constant ${\alpha }_s$, based on the step approximation to the $\beta$--function, is investigated. The errors of extrapolating $\text{ase}(\mu )$ from low energies to $\mu =M_Z$, implied by this approximation, are shown to be of the same magnitude as the typical next--to--next--to--leading order contributions to \as and tend to increase the resulting \as. The importance of the proper choice of matching points is emphasized.

Comments: latex, 7 pages, 2 uuencoded figures