Measuring $α_s(Q^2)$ in $τ$ Decays
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The decay rate of the $τ$ lepton into hadrons of invariant mass smaller than $Q\ggΛ_{\rm QCD}$ can be calculated in QCD using the OPE. Using experimental data on the hadronic mass distribution, the running coupling constant $α_s(Q^2)$ is extracted in the range $0.85~\mbox{GeV}<Q<m_τ$, where its value changes by about a factor~2. At $Q=m_τ$, the result is $α_s(m_τ^2)=0.33\pm 0.03$, corresponding to $α_s(m_Z^2)=0.119\pm 0.004$. The running of the coupling constant is in excellent agreement with the QCD prediction based on the three-loop $β$-function.
12 pages, 7 figures appended, to appear in the Proceedings of Les Rencontres de Physique de la Vallée d'Aoste (La Thuile, Italy, March 1996), and Second Workshop on Continuous Advances in QCD (Minneapolis, Minnesota, March 1996)
12 pages, 7 figures appended, to appear in the Proceedings of Les Rencontres de Physique de la Vallée d'Aoste (La Thuile, Italy, March 1996), and Second Workshop on Continuous Advances in QCD (Minneapolis, Minnesota, March 1996)