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

ALEPH Collaboration:     R. Barate - et al.

doi:doi:10.1007/s100520050217

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2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 4, 409-431
DOI 10.1007/s100529800895

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

ALEPH Collaboration

R. Barate et al.

Laboratoire de Physique des Particules (LAPP), IN²P³-CNRS, F-74019 Annecy-le-Vieux Cedex, France

Received: 26 January 1998 / Published online: 15 June 1998

Abstract
An analysis based on 124000 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.