IS PERTURBATIVE QCD IN TROUBLE?

In a recent paper, Preparata, Ratcliffe and Verpelli have examined two related experimental quantities: R{sub e{sup +}} e{sup {minus}} and {Gamma}{sup Z{sup 0}}{sub hadronic} and compared their values with the predictions of perturbative QCD. They conclude that a strong-interaction correction roughly twice the magnitude of that calculated within the framework of perturbative QCD is needed. Their calculation includes only terms up to O({alpha}{sup 2}{sub s}). In this paper the authors keep terms up to O({alpha}{sup 3}{sub s}) and show that their conclusion is too drastic. In fact, we find good agreement between experiment and perturbative QCD.