$\alpha_s$ from the updated ALEPH data for hadronic $\tau$ decays

Abstract

We extract the strong coupling $\alpha_s(m_\tau^2)$ from the recently updated ALEPH non-strange spectral functions obtained from hadronic $\tau$ decays. We apply a self-consistent analysis method, first tested in the analysis of OPAL data, to extract $\alpha_s(m_\tau^2)$ and non-perturbative contributions. The analysis yields $\alpha_s^{\rm FO}(m_\tau^2)=0.296\pm0.010 $, using Fixed Order Perturbation Theory (FOPT), and $\alpha^{\rm CI}_s(m_\tau^2)= 0.310\pm0.014$, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give $\alpha_s^{\rm FO}(m_\tau^2)=0.303\pm 0.009$ and $\alpha_s^{\rm CI}(m_\tau^2)=0.319\pm 0.012$, which gives, after evolution to the $Z$ boson mass scale, $\alpha^{\rm FO}_s(m_Z^2)=0.1165\pm0.0012 $ and $\alpha_s^{\rm CI}(m_Z^2)=0.1185\pm0.0015 $, respectively. We observe that non-perturbative effects limit the accuracy with which $\alpha_s$ can be extracted from $\tau$ decay data.