Measurement of the axial-vector spectral functions and determination of from hadronic decays

.   An analysis based on 124 000 selected pairs recorded by the ALEPH detector at LEP provides the vector and axial-vector spectral functions of hadronic decays together with their total widths. This allows the evaluation of finite energy chiral sum rules that are weighted integrals over the spectral functions. In addition, a precise measurement of along with a determination of nonperturbative contributions at the mass scale is performed. The experimentally and theoretically most robust determination of is obtained from the fit that yields giving 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 hadronic widths to masses smaller than the mass.