Recent progress in QCD at low energies

Abstract

The recent results in QCD at low energies are reported. The theoretical analysis of hadronic tau-decay is performed in complex q^2-plane. The terms of perturbation theory (PT) up to alpha^3_s are accounted, the terms of operator product expansion (OPE) -- up do dimension 8. The momenta of charmed quark vector current polarization operator are analyzed in 3 loops with account of dimension 4 and 6 OPE terms. The main conclusion is that in the range of low-energy phenomena under consideration PT and OPE are in good agreement with experiment starting from Q^2=-q^2 ~ 1 GeV^2. The values of alpha_s(m^2_tau), alpha_s<qq>^2, <(alpha_s/pi)G^2> and m_c(m_c)were found.