Simple But Efficient Tests of QCD from Tau Decays${}^{\ast )}$

Abstract

We review the determinations of the QCD coupling ${\alpha }_s$ from the inclusive and exclusive modes of $\tau$-decays. The most recent $\tau$-data provide the average value ${\alpha }_s\left(M_{\tau }^2\right)\simeq 0.347\pm 0.030$ corresponding to ${\alpha }_s\left(M_Z^2\right)\simeq 0.121\pm 0.003\pm \mathrm{0.001.}$ The values of the QCD vacuum condensates extracted from the inclusive weighted-moment distributions are consistent with the ones from QCD spectral sum rules. Accurate estimates and further precision tests should be reached in the next $\tau$C/B-factory machines. The $M_{\tau }$-stability test from the $e^{+}{e}^{-}⟶I=1$ hadron data is also discussed.

Comments: revised and updated version of hep-ph 9404211. CERN-TH 7188/94 (4 figures available on requests) Talk given at the Symposium {\it ``Symmetry and simplicity in physics"} on the occasion of {\it Sergio Fubini's 65th birthday}, Turin, 24--26 February 1994 and at the QCD--LEP meeting on ${\alpha }_s$, Aachen, 11 April 1994. To appear in the ``Atti dell'Accademia delle Science di Torino" and in the Aachen proceedings