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Tau Spectral Functions and QCD

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 αS(m 2 τ ) = 0.345± 0.004exp ± 0.009th is obtained. Taken together with the determination of αS(M 2 Z) 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 (s) is found to agree with QCD at a precision of 4%. The value of αS(M 2 Z) obtained from τ decays is αS(M 2 Z) = 0.1215 ± 0.0004exp ± 0.0010th ± 0.0005evol = 0.1215 ± 0.0012 .