The Check of QCD based on the tau - decay data analysis in the complex q**2 - plane

The thorough analysis of the ALEPH data [1] on hadronic -decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D = 8. The value of the QCD coupling constant s(m 2 )=0 :355 0:025 was found from hadronic branching ratio R .T heV + A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q 2 plane. Borel sum rules in the complex q 2 plane along the rays, starting from the origin, are used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge s(m 2 )=0 :330. The restriction on the value of the gluonic condensate was found h s G 2 i =0 :006 0:012 GeV 2 .T he analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.