On the QCD perturbative expansion for e+e− → hadrons

We study the perturbative QCD series for the hadronic width of the Z boson. We sum a class of large “π2 terms” and reorganize the series so as to minimize “renormalon” effects. We also consider the renormalization schemescale ambiguity of the perturbative results. We find that, with three nontrivial known terms in the perturbative expansion, the treatment of the π2 terms is quite important, while renormalon effects are less important. The measured hadronic width of the Z is often used to determine the value of αs(M 2 Z). A standard method is to use the perturbative expansion for the width truncated at order αs in the MS scheme with scale μ = MZ . We estimate that the determined value of αs(M 2 Z) should be increased by 0.6% compared to the value extracted with this standard method. After this adjustment for π2 and renormalon effects, we estimate that the uncertainty in αs(M 2 Z) arising from QCD theory is about 0.4%. This is, of course, much less than the experimental uncertainty of about 5%. Typeset using REVTEX