ALEPH 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 is obtained. Taken together with the determination of from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of is found to agree with QCD at a precision of 4%. The value of obtained from τ decays is .