Sequence transformations applied to the fixed-order QCD series for hadronic tau decays produce estimates c5,1 = 298 ± 15, c6,1 = 3431 ± 256, c7,1 = 2.29 ± 0.29 × 10^4 and a predicted δ^(0)_FOPT = 0.2119 ± 0.0040.
Determination of $\alpha_s(M_\tau^2)$: a conformal mapping approach
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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 $\bar{\rm MS}$ scheme, the method leads to the prediction $\alpha_s(M_\tau^2)= 0.320\pm 0.011$.
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Hadronic tau decays at higher orders in QCD
Sequence transformations applied to the fixed-order QCD series for hadronic tau decays produce estimates c5,1 = 298 ± 15, c6,1 = 3431 ± 256, c7,1 = 2.29 ± 0.29 × 10^4 and a predicted δ^(0)_FOPT = 0.2119 ± 0.0040.