A TEST OF OPTIMIZED PERTURBATIVE QCD TO O(ALPHA(2)(S)) AND O(ALPHA(3)(S)) FROM Z(0) AND TAU-DECAYS, AND A METHOD TO DEAL WITH THE RENORMALIZATION SCALE AMBIGUITY

A QCD analysis of the published LEP data on 11 observables measured in the Z(0) and tau decays is performed in order to probe the renormaliz ation scale optimization of perturbative QCD to Scriptive O alpha(s)(2 )) and Scriptive O(alpha(s)(3)). The explicit dependence of the fundam ental QCD parameter Lambda(<(MS)over bar>) on the renormalization scal e mu(2) is extracted from the data. The theoretical predictions for th e optimized scale are calculated using various QCD-inspired procedures , and are compared to the experimental results. An experimental proced ure is presented to deal with the renormalization scale ambiguity in t he determination of alpha(s). Applying this procedure to 11 observable s, we obtain alpha(s)(M(2)0) = 0.114 +/- 0.004 as our final result.