Check of QCD based on the tau-decay data analysis in the complex q(2) plane - art. no. 093009

The thorough analysis of the ALEPH data on hadronic tau decay is performed in the framework of QCD. The perturbative calculations are performed in thr ee- and four-loop approximations. The terms of the operator product expansi on (OPE) are accounted for up to the dimension D=8. The value of the QCD co upling constant alpha (S)(m(tau)(2))=0.355 +/-0.025 is found from the hadro nic branching ratio R-tau. The V+A and V spectral functions are analyzed us ing the analytical properties of the polarization operators in the whole co mplex q(2) plane. Borel sum rules in the complex q2 plane along the rays, s tarting from the origin, are used. It is demonstrated that QCD with OPE ter ms is in agreement with the data for a coupling constant close to the lower error edge alpha (S)(m(tau)(2))=0.330. The restriction on the value of the gluonic condensate was found to be <(alpha (S)/pi )G(2)> =0.006 +/-0.012 G eV2. The analytical perturbative QCD is compared with the data. It is demon strated to be in strong contradiction with experiment. The restrictions on the renormalon contribution are found. The instanton contributions to the p olarization operator are analyzed in various sum rules. In the Borel transf ormation they appear to be small, but not in the spectral moment sum rules.