Lr. Surguladze et Ma. Samuel, ON THE RENORMALIZATION-GROUP AMBIGUITY OF PERTURBATIVE QCD FOR R(S) IN E(-) ANNIHILATION AND R(TAU) IN TAU-DECAY()E(), Physics letters. Section B, 309(1-2), 1993, pp. 157-162
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 th
e three known approaches for resolving the scheme-scale ambiguity and
we fix the scale for which all of the criteria tested are satisfied. W
e find the four-loop R(s) within the new scheme with flavor independen
t 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 estim
ated at 4%. The results of the analysis of R(tau) in tau-decay are pre
sented.