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 $O(\alpha^{4}_{s})$ 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.