V-A hadronic tau decays : a QCD laboratory

Recent ALEPH/OPAL data on the V-A spectral functions from hadronic tau decays are used for fixing the QCD continuum threshold at which the first and second Weinberg sum rules should be satisfied in the chiral limit, and for predicting the values of the low-energy constants f_\pi,~m_{\pi^+}-m_{\pi^0} and {L}_{10}. Some DMO-like sum rules and the $\tau$-total hadronic widths R_{\tau,V-A} are also used for extracting the values of the D=6,~8 QCD vacuum condensates and the corresponding (in the chiral limit) electroweak kaon penguin matrix elements Q^{3/2}_{8,7}\ra_{2\pi},, where a deviation from the vacuum saturation estimate has been obtained. Combining these results with the one of the QCD penguin matrix element Q^{1/2}_{6}\ra_{2\pi} obtained from a (maximal) \bar qq-gluonium mixing scheme from the scalar meson sum rules, we deduce, in the Electroweak Standard Model (ESM), the conservative upper bound for the CP-violating ratio: \epsilon'/\epsilon \leq (22\pm 9) 10^{-4}, in agreement with the present measurements.