Recent progress in hadronic tau decays

TL;DR

This paper investigates the discrepancy between two renormalisation group resummation methods, FOPT and CIPT, in determining alpha_s from hadronic tau decays, using a model based on renormalons to analyze their effectiveness.

Contribution

It introduces a model incorporating renormalon structure to compare FOPT and CIPT, showing FOPT's better alignment with the Borel sum in tau decay calculations.

Findings

FOPT approaches the Borel sum smoothly.

CIPT fails to account for the resummed series.

Model demonstrates the impact of renormalons on resummation methods.

Abstract

The determination of alpha_s from hadronic tau decays is impeded by the fact that two choices for the renormalisation group resummation, namely fixed-order (FOPT) and contour-improved perturbation theory (CIPT), yield systematically differing results. On the basis of a model for higher-order terms in the perturbative series, which incorporates well-known structure from renormalons, it is found that FOPT smoothly approaches the Borel sum for the tau hadronic width, while CIPT is unable to account for the resummed series. An example for the behaviour of QCD spectral function moments, displaying a similar behaviour, is presented as well.