Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1994-08-30
Nucl.Phys.Proc.Suppl. 39BC (1995) 312-317
Physics
High Energy Physics
High Energy Physics - Phenomenology
revised version and improved version of CERN.TH-7400/94, LATEX 10 pages, six-loop estimates for R(s) in Table 2 are revised, t
Scientific paper
10.1016/0920-5632(95)00094-P
We consider the further development of the formalism of the estimates of higher-order perturbative corrections in the Euclidean region, which is based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We present the estimates of the order $O(\alpha^{4}_{s})$ QCD corrections to the Euclidean quantities: the $e^+e^-$-annihilation $D$-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross--Llewellyn Smith sum rule. The results for the $D$-function are further applied to estimate the $O(\alpha_s^4)$ QCD corrections to the Minkowskian quantities $R(s) = \sigma_{tot} (e^{+}e^{-} \to {\rm hadrons}) / \sigma (e^{+}e^{-} \to \mu^{+} \mu^{-})$ and $R_{\tau} = \Gamma (\tau \to \nu_{\tau} + {\rm hadrons}) / \Gamma (\tau \to \nu_{\tau} \overline{\nu}_{e} e)$. The problem of the fixation of the uncertainties due to the $O(\alpha_s^5)$ corrections to the considered quantities is also discussed.
Kataev Andrei L.
Starshenko Valery V.
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