QCD MATCHING CONDITIONS AT THRESHOLDS

The use of MS-like renormalization schemes in QCD requires an implemen tation of nontrivial matching conditions across thresholds, a fact oft en overlooked in the literature. We shortly review the use of these ma tching 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 a ppropriate matching conditions are taken into account.