# Renormalization-group improvement in hadronic $τ$ decays in 2018

### Submission summary

 As Contributors: Diogo Boito Preprint link: scipost_201811_00036v2 Date accepted: 2019-01-17 Date submitted: 2018-12-12 Submitted by: Boito, Diogo Submitted to: SciPost Physics Proceedings Domain(s): Theoretical Subject area: High-Energy Physics - Phenomenology

### Abstract

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.

###### Current status:
Publication decision taken: accept

### List of changes

Comments added in Sec. 5 to clarify the use of Eq. (15) in our analysis.

### Submission & Refereeing History

Resubmission scipost_201811_00036v2 (12 December 2018)
Submission scipost_201811_00036v1 (22 November 2018)