Determination of ${\alpha }_s(M_{\tau }^2)$: a conformal mapping approach

Abstract

We discuss a new class of expansions in perturbative QCD, based on the technique of conformal mappings of the Borel plane, and apply them for the determination of ${\alpha }_s$ from the hadronic decays of the $\tau$ lepton. Using the expansion up to fifth order in the $\overline{\mathrm{MS}}$ scheme, the method leads to the prediction ${\alpha }_s(M_{\tau }^2)=0.320\pm 0.011$.

6 pages, 2 figures. Talk given at the 11th International Workshop on Tau Lepton Physics, Manchester, UK, 13-17 September 2010

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• Expansions of $\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior
• Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior
• Strong coupling from the tau hadronic width by non-power QCD perturbation theory
• Determination of the strong coupling from hadronic tau decays using renormalization group summed perturbation theory
• Non-global logarithms up to four loops at finite-N${}_c$ for V/H+jet processes at hadron colliders
• A new determination of higher-order QCD corrections to hadronic $\tau$ decays