alpha_s and the tau hadronic width

TL;DR

This paper compares fixed-order and contour-improved perturbation theory in extracting alpha_s from tau decays, showing FOPT aligns better with the Borel sum and providing a precise alpha_s value.

Contribution

It introduces a model based on renormalons to analyze higher-order terms, demonstrating FOPT's advantage over CIPT in approximating the resummed series.

Findings

FOPT approaches the Borel sum more accurately than CIPT.

Determined alpha_s(M_tau)=0.316 ± 0.006 and alpha_s(M_Z)=0.1180 ± 0.0008.

CIPT cannot fully account for the resummed series.

Abstract

Different choices exist for the renormalisation group resummation in the determination of $\alpha_s$ from hadronic $\tau$ decays: namely fixed-order (FOPT) and contour-improved perturbation theory (CIPT). The two approaches lead to systematic differences in the resulting $\alpha_s$. 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 while CIPT is unable to account for the fully resummed series, FOPT smoothly approaches the Borel sum. Employing the model to determine $\alpha_s$ yields $\alpha_s(M_\tau)=0.316 \pm 0.006$, which after evolution leads to $\alpha_s(M_Z) = 0.1180 \pm 0.0008$.