ALEPH Tau Spectral Functions and QCD

Hadronic tau decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic tau 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 alpha(s) (m(tau)(2)) = 0.345 +/- 0.004(exp) +/- 0.009(th) is obtained. Taken together with the determination of as (M-Z(2)) from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of alpha(-1)(S) 1 (s) is found to agree with QCD at a precision of 4%. The value of alpha(s)(M-z(2)) obtained from tau decays is as(M-Z(2)) = 0.1215 0.0004(CXP) +/- 0.0010(th) +/- 0.0005(evol) = 0.1215 +/- 0.0012