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 $asm = 0.345 pm 0.004_{rm exp} pm 0.009_{rm th}$ 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 $alpha_s^{-1}(s)$ is found to agree with QCD at a precision of 4%. The value of asZ obtained from $tau$ decays is $asZ = 0.1215 pm 0.0004_{rm exp} pm 0.0010_{rm th} pm 0.0005_{rm evol} = 0.1215 pm 0.0012$.
تحميل البحث