Decay widths and total cross sections in perturbative QCD

Abstract

The current status of analytic higher-order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is reviewed. Important issues are the methodology of renormalization-group evaluations, the ambiguities of the renormalization scheme and its scale, and the technical challenge of calculating many-loop diagrams. As examples, the authors consider the quantities ${\ensuremath{\sigma}}_{\mathrm{tot}}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons})$ and $\ensuremath{\Gamma}({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}+\mathrm{hadrons})$ up to $O({\ensuremath{\alpha}}_{s}^{3})$ as well as $\ensuremath{\Gamma}(H\ensuremath{\rightarrow}\mathrm{hadrons})$ up to $O({\ensuremath{\alpha}}_{s}^{2})$. The evaluation of the four-loop QED beta function is also described. The problem of theoretical uncertainty estimates in perturbative calculations is briefly discussed.