Measurement of αs and the non-strange spectral functions in hadronic τ decays with OPAL

Abstract

The spectral functions of the vector current and the axial-vector current have been measured in hadronic τ decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant α 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 α s( m τ 2) = 0.348 ± 0.009 exp ± 0.019 theo at the τ-mass scale and α s( m Z 2) = 0.1219 ± 0.0010 exp ± 0.0017 theo at the Z 0-mass scale. The values obtained for α s( m Z 2) 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 ≅ 1.3 GeV 2 and s 0 = m τ 2 has been tested from direct fits to the integrated differential hadronic decay rate R τ ( s 0). A test of saturation of QCD sum rules at the τ-mass scale has been performed.