$\tau$ spectral functions, QCD applications and chiral sum rules

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. The spectral functions of the dominant two- and four-pion vector tau decay modes are compared to published results of e/sup +/e/sup $/annihilation experiments applying isospin symmetry. A precise measurement of alpha /sub s/ along with a determination of nonperturbative contributions at the tau mass scale is performed. The experimentally and theoretically most robust determination of alpha /sub s/ (M/sub tau //sup 2/) is obtained from the (V+A) fit that yields alpha /sub s/(M/sub tau //sup 2/)=0.334+or-0.022 giving alpha /sub s/(M zeta 2)=0.1202+or-0.0027 after the extrapolation to the mass of the Z boson. In addition, the approach of the Operator Product Expansion (OPE) is tested experimentally by studying the evolution of the tau hadronic widths to masses smaller than the tau mass. An analysis based on finite energy chiral sum rules provides a precise determination of the L/sub 10/ constant of the chiral lagrangian. (41 refs).