${\alpha }_s$ 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 ${\alpha }_s^{\mathrm{FO}}(m_{\tau }^2)=0.296\pm 0.010$, using Fixed Order Perturbation Theory (FOPT), and ${\alpha }_s^{\mathrm{CI}}(m_{\tau }^2)=0.310\pm 0.014$, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give ${\alpha }_s^{\mathrm{FO}}(m_{\tau }^2)=0.303\pm 0.009$ and ${\alpha }_s^{\mathrm{CI}}(m_{\tau }^2)=0.319\pm 0.012$, which gives, after evolution to the $Z$ boson mass scale, ${\alpha }_s^{\mathrm{FO}}(m_Z^2)=0.1165\pm 0.0012$ and ${\alpha }_s^{\mathrm{CI}}(m_Z^2)=0.1185\pm 0.0015$, respectively. We observe that non-perturbative effects limit the accuracy with which ${\alpha }_s$ can be extracted from $\tau$ decay data.

Comments: 5 pages, Talk given at the 18th International Conference in Quantum Chromodynamics (QCD 15, 30th anniversary), 29 june - 3 july 2015, Montpellier, France