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

Abstract

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.

20 pages

References in corpus (5)

• Measurements of the Cross Section for e+e- -> hadrons at Center-of-Mass Energies from 2 to 5 GeV
• The check of QCD based on the tau-decay data analysis in the complex q^2-plane
• The V-A sum rules and the Operator Product Expansion in complex q^2-plane from tau-decay data
• New analytic running coupling in spacelike and timelike regions
• Investigation of a new analytic running coupling in QCD

Cited by in corpus (6)

• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Vector and axial-vector correlators in a nonlocal chiral quark model
• QCD vacuum condensates from tau-lepton decay data
• Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD
• Chiral sum rules and vacuum condensates from tau-lepton decay data
• Calculation of gluon and four-quark condensates from the operator expansion