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 nonstrange 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 ${\alpha }_s(m_{\tau }^2)=0.303\pm 0.009$ and ${\alpha }_s(m_{\tau }^2)=0.319\pm 0.012$, respectively. 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 nonperturbative 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.

• Received 21 October 2014

DOI:https://doi.org/10.1103/PhysRevD.91.034003