QCD Matching Conditions at Thresholds

Abstract

The use of MS-like renormalization schemes in QCD requires an implementation of nontrivial matching conditions across thresholds, a fact often overlooked in the literature. We shortly review the use of these matching conditions in QCD and check explicitly that the prediction for ${\alpha }_s(M_Z)$, obtained by running the strong coupling constant from the $M_{\tau }$ scale, does not substantially depend on the exact value of the matching point chosen in crossing the $b$-quark threshold when the appropriate matching conditions are taken into account.

Comments: 9 pages and 2 postscript figures added after the TeX file, LaTeX, CERN-TH.6899/93