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Renormalization-group improvement in hadronic $τ$ decays in 2018
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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
Padé approximants as a model-independent and robust method to extract
information about the higher-order terms. We show that in hadronic
\tau
τ
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.
Title: Renormalization-group improvement in hadronic $τ$ decays in 2018
Description:
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
Padé approximants as a model-independent and robust method to extract
information about the higher-order terms.
We show that in hadronic
\tau
τ
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.
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