Determination of the QCD Coupling from ALEPH $\tau$ Decay Data

TL;DR

This paper analyzes various theoretical methods to determine the strong coupling constant from tau decay data, achieving a consistent and reliable value with quantified uncertainties, and compares different approaches for robustness.

Contribution

It introduces novel approaches and critically evaluates existing methods for extracting the QCD coupling from tau decay data, enhancing the reliability of the results.

Findings

Consistent determination of alpha_s(m_tau^2) = 0.328 ± 0.013

Agreement between CIPT and FOPT methods within uncertainties

Derived alpha_s(M_Z^2) = 0.1197 ± 0.0015

Abstract

We present a comprehensive study of the determination of the strong coupling from $\tau$ decay, using the most recent release of the experimental ALEPH data. We critically review all theoretical strategies used in previous works and put forward various novel approaches which allow to study complementary aspects of the problem. We investigate the advantages and disadvantages of the different methods, trying to uncover their potential hidden weaknesses and test the stability of the obtained results under slight variations of the assumed inputs. We perform several determinations, using different methodologies, and find a very consistent set of results. All determinations are in excellent agreement, and allow us to extract a very reliable value for $\alpha_s(m_\tau^2)$. The main uncertainty originates in the pure perturbative error from unknown higher orders. Taking into account the systematic differences between the results obtained with the CIPT and FOPT prescriptions, we find $\alpha_{s}^{(n_f=3)}(m_\tau^2) = 0.328 \pm 0.013$ which implies $\alpha_{s}^{(n_f=5)}(M_Z^{2}) = 0.1197\pm 0.0015$.