Messung der starken Kopplungskonstanten $\alpha_{s}$ und der hadronischen Spektralfunktionen in $\tau$-Zerfällen

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 /sub 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 /sub s/(m/sub tau //sup 2/)=0.348+or-0.009/sub exp/+or-0.019/sub theo/ at the tau - mass scale and alpha /sub s/(m/sub Z//sup 2/)=0.1219+or-0.0010/sub exp/+or-0.0017/sub theo/ at the Z/sup 0/-mass scale. The values obtained for alpha /sub s/(m/sub Z//sup 2/) using fixed order perturbation theory or renormalon chain resummation are 2.3and 4.1 smaller, respectively. The `running' of the strong coupling between s /sub 0/ equivalent to 1.3 GeV/sup 2/ and s/sub 0/=m/sub tau //sup 2/ has been tested from direct fits to the integrated differential hadronic decay rate R/sub tau /(s/sub 0/). A test of the saturation of QCD sum rules at the tau -mass scale has been performed. (86 refs) .