ALEPH Tau Spectral Functions and QCD
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Hadronic $τ$ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic $τ$ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong coupling constant, quark and gluon condensates. Using the ALEPH spectral functions and branching ratios, complemented by some other available measurements, and a revisited analysis of the theoretical framework, the value $\asm = 0.345 \pm 0.004_{\rm exp} \pm 0.009_{\rm th}$ is obtained. Taken together with the determination of \asZ from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of $α_s^{-1}(s)$ is found to agree with QCD at a precision of 4%. The value of \asZ obtained from $τ$ decays is $\asZ = 0.1215 \pm 0.0004_{\rm exp} \pm 0.0010_{\rm th} \pm 0.0005_{\rm evol}
= 0.1215 \pm 0.0012$.
14 pages, 5 figures, invited talk at the Tau06 International Workshop, Pisa, September 19-22 2006
14 pages, 5 figures, invited talk at the Tau06 International Workshop, Pisa, September 19-22 2006