Estimates of the O(alpha_s^4) corrections to sigma_{tot}(e^+e^- \rightarrow hadrons), Gamma(\tau\rightarrow \nu_{\tau} +hadrons) and deep inelastic scattering sum rules

Abstract

We present the estimates of the order $O({\alpha }_s^4)$ QCD corrections to $R(s)$, $R_{\tau }$ and to the deep-inelastic scattering sum rules, namely to the non-polarized and polarized Bjorken sum rules and to the Gross-Llewellyn Smith sum rule. The estimates are obtained in the $\overline{MS}$-scheme using the principle of minimal sensitivity and the effective charges approach.

Comments: CERN-TH.7190/94, to appear in Proc. of the Workshop "QCD at LEP: Determinations of ${\alpha }_s$ from Inclusive Observables", Aachen, Germany 11 April, LATEX, 11 pages; extended version submitted for publication. Some misprints in the previous version corrected, thanks to F. Le Diberder for pointing them, PMS results in Tables 1-4 are affected. Changes do not affect main results