On the QCD perturbative expansion for e^+ e^- --> hadrons

Abstract

We study the perturbative QCD series for the hadronic width of the Z boson. We sum a class of large ``pi^2 terms'' and reorganize the series so as to minimize ``renormalon'' effects. We also consider the renormalization scheme-scale ambiguity of the perturbative results. We find that, with three nontrivial known terms in the perturbative expansion, the treatment of the pi^2 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 alpha_s(M_Z^2). A standard method is to use the perturbative expansion for the width truncated at order alpha_s^3 in the MS-bar scheme with scale mu = M_Z. We estimate that the determined value of alpha_s(M_Z^2) should be increased by 0.6% compared to the value extracted with this standard method. After this adjustment for pi^2 and renormalon effects, we estimate that the uncertainty in alpha_s(M_Z^2) arising from QCD theory is about 0.4%. This is, of course, much less than the experimental uncertainty of about 5%.

23 pages, REVTEX3.0, uses epsf.tex to insert figures; with 6 figures in encapsulated postscript form

References in corpus (11)

• Observation of Top Quark Production in Pbar-P Collisions
• Observation of the Top Quark
• Renormalization group analysis of the tau-lepton decay within QCD
• The Large Quark Mass Expansion of Gamma (Z^0 -> hadrons) and Gamma(tau^- -> nu_tau + hadrons) in the Order alpha_s^3
• Quark Mass Effects in Fermionic Decays of the Higgs Boson in $O({\alpha }_s^2)$ Perturbative QCD
• A Study of Ultraviolet Renormalon Ambiguities in the Determination of $\as$ from $\tau$ Decay
• Radiation of Heavy Quarks
• The ${\alpha }_s^3$ Corrections to the Effective Neutral Current and to the Z Decay Rate in the Heavy Top Quark Limit
• Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes
• Status of Higher-Order Corrections in the Standard Electroweak Theory
• Top Quark Contribution to Hadronic Decays of the Z-Boson at Alpha_s^2 in QCD

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