The strong coupling from the revised ALEPH data for hadronic $\tau$ decays

TL;DR

This paper refines the measurement of the strong coupling constant from hadronic tau decays using revised ALEPH data, compares analysis methods, and discusses the impact of non-perturbative effects and systematic errors.

Contribution

It applies a novel analysis approach to updated ALEPH data, critiques previous methods, and highlights the limitations due to non-perturbative effects in extracting the strong coupling.

Findings

Determined α_s(m_τ^2) ≈ 0.30 with combined data.

Critiqued previous analysis methods for underestimating systematic errors.

Showed non-perturbative effects limit the precision of α_s extraction.

Abstract

We apply an analysis method previously developed for the extraction of the strong coupling from the OPAL data to the recently revised ALEPH data for non-strange hadronic $\tau$ decays. Our analysis yields the values $\alpha_s(m_\tau^2)=0.296\pm 0.010$ using fixed-order perturbation theory, and $\alpha_s(m_\tau^2)=0.310\pm 0.014$ using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find $\alpha_s(m_\tau^2)=0.303\pm 0.009$, respectively, $\alpha_s(m_\tau^2)=0.319\pm 0.012$. We present a critique of the analysis method employed previously, for example in analyses by the ALEPH and OPAL collaborations, and compare it with our own approach. Our conclusion is that non-perturbative effects limit the accuracy with which the strong coupling, an inherently perturbative quantity, can be extracted at energies as low as the $\tau$ mass. Our results further indicate that systematic errors on the determination of the strong coupling from analyses of hadronic $\tau$-decay data have been underestimated in much of the existing literature.