Measurement of the spectral functions of axial - vector hadronic tau decays and determination of alpha(S)(M**2(tau))

An analysis based on 124 000 selected τ pairs recorded by the ALEPH detector at LEP provides the vector (V) and axial-vector (A) spectral functions of hadronic τ 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 αs along with a determination of nonperturbative contributions at the τ mass scale is performed. The experimentally and theoretically most robust determination of αs(M2τ) is obtained from the (V+A) fit that yields αs(M2τ)=0.334±0.022 giving αs(M2Z)=0.1202±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 τ hadronic widths to masses smaller than the τ mass.