Calculation of gluon and four-quark condensates from the operator expansion

The magnitudes of gluon and four-quark condensates are found from the analysis of vector mesons consisting of light quarks (the families of $\rho$ and $\omega$ mesons) in the 3 loops approximation. The QCD model with infinite number of vector mesons is used to describe the function $R(s)$. This model describes well the experimental function $R(s)$. Polarization operators calculated with this model coincide with the Wilson operator expansion at large $Q^2$. The improved perturbative theory, such that the polarization operators have correct analytical properties, is used. The result is $<0 | (\alpha_s/\pi) G^2 | 0 > = 0.062 \pm 0.019 GeV^4$. The electronic widths of $\rho(1450)$ and $\omega(1420)$ are calculated.Comment: 18 pages, latex, changed content slightl

Hadronic τ\tau decay, the renormalization group, analiticity of the polarization operators and QCD parameters

The ALEPH data on hadronic tau-decay is throughly analysed in the framework of QCD. The perturbative calculations are performed in 1-4-loop approximation. The analytical properties of the polarization operators are used in the whole complex q^2 plane. It is shown that the QCD prediction for R_{tau} agrees with the measured value R_{tau} not only for conventional Lambda^{conv}_3 = (618+-29) MeV but as well as for Lambda^{new}_3 = (1666+-7) MeV. The polarization operator calculated using the renormgroup has nonphysical cut [-Lambda^2_3, 0]. If Lambda_3 = Lambda^{conv}_3, the contribution of only physical cut is deficient in the explanation of the ALEPH experiment. If Lambda_3 = Lambda^{new}_3 the contribution of nonphysical cut is very small and only the physical cut explains the ALEPH experiment. The new sum rules which follow only from analytical properties of polarization operators are obtained. Basing on the sum rules obtained, it is shown that there is an essential disagreement between QCD perturbation theory and the tau-lepton hadronic decay experiment at conventional value Lambda_3. In the evolution upwards to larger energies the matching of r(q^2) (Eq.(12)) at the masses J/psi, Upsilon and 2m_t was performed. The obtained value alpha_s(-m^2_z) = 0.141+-0.004 (at Lambda_3 = Lambda^{new}_3) differs essentially from conventional value, but the calculation of the values R(s) = sigma(e+e- -> hadrons)/sigma(e+e- -> mu+mu-), R_l = Gamma(Z -> hadrons)/Gamma(Z -> leptons), alpha_s(-3 GeV^2), alpha_s(-2.5 GeV^2) does not contradict the experiments.Comment: 20 page