We extract the strong coupling constant [Formula: see text] from the semileptonic τ-decay width taking into account resummation effects from the running of the strong coupling constant. In the [Formula: see text] scheme. The result reads αs=0.375±0.007 to third-order and αs=0.378±0.007 to fourth-order in the β-function, respectively, where we use the recently computed four-loop coefficient β3. These values for the coupling constant have to be compared with the value αs=0.354±0.005 derived from a third-order analysis of τ-decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.
Higgs production in bottom quark fusion: matching the 4- and 5-flavour schemes to third order in the strong coupling