Measurement of the axial-vector $\tau$ spectral functions and determination of $\alpha_s(M_\tau^2)$ from hadronic $\tau$ decays

Abstract.

An analysis based on 124 000 selected $\tau$ pairs recorded by the ALEPH detector at LEP provides the vector $(V)$ and axial-vector $(A)$ spectral functions of hadronic $\tau$ decays together with their total widths. This allows the evaluation of finite energy chiral sum rules that are weighted integrals over the $(V-A)$ spectral functions. In addition, a precise measurement of $\alpha_s$ along with a determination of nonperturbative contributions at the $\tau$ mass scale is performed. The experimentally and theoretically most robust determination of $\alpha_s(M_\tau^2)$ is obtained from the $(V+A)$ fit that yields $\alpha_s(M_\tau^2)=0.334\pm 0.022$ giving $\alpha_s(M_{\rm Z}^2)=0.1202\pm 0.0027$ after the extrapolation to the mass of the Z boson. The approach of the Operator Product Expansion (OPE) is tested experimentally studying the evolution of the $\tau$ hadronic widths to masses smaller than the $\tau$ mass.