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

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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 q² plane. It is shown that the QCD prediction for Rtau agrees with the measured value Rtau not only for conventional Lambdaconv₃ = (618+-29) MeV but as well as for Lambdanew₃ = (1666+-7) MeV. The polarization operator calculated using the renormgroup has nonphysical cut [-Lambda²₃, 0]. If Lambda₃ = Lambdaconv₃, the contribution of only physical cut is deficient in the explanation of the ALEPH experiment. If Lambda₃ = Lambdanew₃ 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 Lambda₃. In the evolution upwards to larger energies the matching of r(q²) (Eq.(12)) at the masses J/psi, Upsilon and 2mₜ was performed. The obtained value alphaₛ(-m²z) = 0.141+-0.004 (at Lambda₃ = Lambdanew₃) differs essentially from conventional value, but the calculation of the values R(s) = sigma(e+e- -> hadrons)/sigma(e+e- -> mu+mu-), Rₗ = Gamma(Z -> hadrons)/Gamma(Z -> leptons), alphaₛ(-3 GeV²), alphaₛ(-2.5 GeV²) does not contradict the experiments.