Estimates of the higherorder QCD corrections: theory and applications
Abstract
We consider the further development of the formalism of the estimates of higherorder perturbative corrections in the Euclidean region, which is based on the application of the schemeinvariant methods, namely the principle of minimal sensitivity and the effective charges approach. We present the estimates of the order O( α _{s}^{4}) QCD corrections to the Euclidean quantities: the e^{+}e^{}annihilation Dfunction and the deep inelastic scattering sum rules, namely the nonpolarized and polarized Bjorken sum rules and to the GrossLlewellyn Smith sum rule. The results for the Dfunction are further applied to estimate the O( α _{s}^{4}) QCD corrections to the Minkowskian quantities R( s) = σ _{tot}( e^{+}e^{} → hadrons)/ σ( e^{+}e^{} → μ^{+}μ^{}) and R _{τ} = Γ( τ → ν _{τ} + hadrons)/Γ( τ → ν _{τ}ν¯ _{e}e ). The problem of the fixation of the uncertainties due to the O( α _{s}^{5}) corrections to the considered quantities is also discussed.
 Publication:

Nuclear Physics B Proceedings Supplements
 Pub Date:
 March 1995
 DOI:
 10.1016/09205632(95)00094P
 arXiv:
 arXiv:hepph/9408395
 Bibcode:
 1995NuPhS..39..312K
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 revised version and improved version of CERN.TH7400/94, LATEX 10 pages, sixloop estimates for R(s) in Table 2 are revised, thanks to J. Ellis for pointing numerical shortcomings (general formulae are nonaffected). Details of derivations of sixloop estimates for R_tau are presented