Measurement of the axial-vector τ spectral functions and determination of αs(M2 τ) from hadronic τ decays

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 non-perturbative contributions at the τ mass scale is performed. The experimentally and theoretically most robust determination of αs(Mτ 2) is obtained from the (V + A) fit that yields αs (Mτ 2) = 0.334 ±0.022 giving αs (MZ 2) = 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.