Measurement of the Strong Coupling Constant and the Vector and Axial-Vector Spectral Functions in Hadronic Tau Decays

TL;DR

This paper measures the spectral functions in hadronic tau decays to determine the strong coupling constant alpha_s and non-perturbative parameters, comparing different theoretical approaches and testing QCD sum rule saturation.

Contribution

It provides a precise measurement of alpha_s at tau and Z mass scales using OPAL data and compares various perturbative methods within the Operator Product Expansion framework.

Findings

Alpha_s(mtau^2) = 0.348 ± 0.009 ± 0.019

Alpha_s(mz^2) = 0.1219 ± 0.0010 ± 0.0017

Different perturbative methods yield slightly different alpha_s values.

Abstract

The spectral functions of the vector current and the axial-vector current have been measured in hadronic tau decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant alpha_s, the non-perturbative operators of dimension 6 and 8 and of the gluon condensate has been performed. Different perturbative descriptions have been compared to the data. The Contour Improved Fixed Order Perturbation Theory gives alpha_s(mtau**2) = 0.348 +- 0.009 +- 0.019 at the tau-mass scale and alpha_s(mz**2) = 0.1219 +- 0.0010 +- 0.0017 at the Z-mass scale. The values obtained for alpha_s(mz**2) using Fixed Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1% smaller, respectively. The running of the strong coupling between s_0 ~1.3 GeV**2 and s_0 = mtau**2 has been tested from direct fits to the integrated differential hadronic decay rate R_tau. A test of the saturation of QCD sum rules at the tau-mass scale has been performed.