Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions

TL;DR

This paper analyzes the perturbative series of tau hadronic spectral function moments to improve the extraction of the strong coupling constant alpha_s, highlighting the stability of certain moments and advocating for fixed-order perturbation theory.

Contribution

It classifies spectral function moments based on their perturbative behavior and recommends optimal methods for alpha_s extraction, considering renormalon effects.

Findings

Certain moments are perturbatively unstable and should be avoided.

Fixed-order perturbation theory is preferred for well-behaved moments.

Evidence supports a small number of leading renormalon singularities in the Adler function.

Abstract

Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling alpha_s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and Adler function series. Some moments that are commonly employed in alpha_s analyses from tau decays should be avoided because of their perturbative instability. This conclusion is corroborated by a simplified alpha_s extraction from individual moments. Furthermore, under reasonable assumptions for the higher-order behaviour of the perturbative series, fixed-order perturbation theory (FOPT) provides the preferred framework for the renormalization group improvement of all moments that show good perturbative behaviour. Finally, we provide further evidence for the plausibility of the description of the Adler function in terms of a small number of leading renormalon singularities.