ON THE RENORMALIZATION-GROUP AMBIGUITY OF PERTURBATIVE QCD FOR R(S) IN E(+)E(-) ANNIHILATION AND R(TAU) IN TAU-DECAY

The O(alpha(s)3) perturbative QCD result for R(s) in e+e- annihilation is given with explicit dependence on the scale parameter. We apply the three known approaches for resolving the scheme-scale ambiguity and we fix the scale for which all of the criteria tested are satisfied. We find the four-loop R(s) within the new scheme with flavor independent perturbative coefficients: R(s)=3 SIGMA(f) Q(f)2[1 + alpha(s)/pi + 1/12(alpha(s)/pi)2-(alpha(s)/pi)3 (16.2+/-0.5)] + O(alpha(s)4). We find a remarkable cancellation of the Riemann zeta-functions at the 3-loop level. The theoretical uncertainty of the QCD effect in R(s) is estimated at 4%. The results of the analysis of R(tau) in tau-decay are presented.