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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Diogo Boito,
- 2 Pere Masjuan,
- 1 Fabio Oliani
- 1 Universidade de São Paulo / University of Sao Paulo [USP]
- 2 Universitat Autònoma de Barcelona / Autonomous University of Barcelona [UAB]
- Conselho Nacional de Desenvolvimento Científico e Tecnológico / National Council for Scientific and Technological Development [CNPq]
- Fundação de Amparo à Pesquisa do Estado de São Paulo / São Paulo Research Foundation [FAPESP]
- Generalitat de Catalunya / Government of Catalonia
- Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])