# Measurement of the strong coupling constant \(\alpha_{\rm s}\) and the vector and axial-vector spectral functions in hadronic tau decays

DOI: 10.1007/s100529901061

- Cite this article as:
- The OPAL Collaboration & Ackerstaff et al., K. Eur. Phys. J. C (1999) 7: 571. doi:10.1007/s100529901061

## Abstract.

The spectral functions of the vector current and the axial-vector current have been measured in hadronic \(\tau\) decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant \(\alpha_{\rm s}\), the non-perturbative operators of dimension 6 and 8 and of the gluon condensate has been performed. Different perturbative descriptions have been compared to the data. The Contour Improved Fixed Order Perturbation Theory gives \(\alpha_{\rm s}(m_\tau^2) = 0.348 \pm 0.009_{\rm exp} \pm 0.019_{\rm theo}\) at the \(\tau\)-mass scale and \(\alpha_{\rm s}(m^2_{\rm Z}) = 0.1219 \pm 0.0010_{\rm exp} \pm 0.0017_{\rm theo}\) at the \({\rm Z}^0\)-mass scale. The values obtained for \(\alpha_{\rm s}(m^2_{\rm Z})\) using Fixed Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1% smaller, respectively. The ‘running’ of the strong coupling between \(s_0 \simeq 1.3 {\rm GeV}^2\) and \(s_0 = m_\tau^2\) has been tested from direct fits to the integrated differential hadronic decay rate \(R_\tau(s_0)\). A test of the saturation of QCD sum rules at the \(\tau\)-mass scale has been performed.