The 15th International Workshop on Tau Lepton Physics
One of the main sources of theoretical uncertainty in the extraction of the strong coupling
from hadronic tau decays stems from the renormalization group improvement of the series. Perturbative
series in QCD are divergent but are (most likely) asymptotic expansions. One needs knowledge
about higher orders to be able to choose the optimal renormalization-scale setting procedure.
Here, we discuss the use of Pad\'e approximants
as a model-independent and robust method to extract information about the higher-order terms. We show that
in hadronic \boldmath $\tau$ decays
the fixed-order expansion, known as fixed-order perturbation theory (FOPT), is the most reliable mainstream
method to set the scale.
This fully corroborates previous conclusions based on the available knowledge about the leading renormalon
singularities of the perturbative series.