Condensates in Quantum Chromodynamics

Abstract

The paper presents the short review of our to-day knowledge of vacuum condensates in QCD. The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determination of physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of quark condensate, connected with the existence of baryon masses is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic tau-decay. In the theoretical analysis the terms of perturbation theory (PT) up to alpha^3_s are accounted, in the operator product expansion (OPE) - those up to dimension 8. The total probability of the decay tau->hadrons (with zero strangeness) and of the tau-decay structure functions are best described at alpha_s(m^2_tau) = 0.330+-0.025. It is shown that the Borel sum rules for tau-decay structure functions along the rays in the q^2-complex plane are in agreement with the experiment with the accuracy ~2% at the values of the Borel parameter |M^2|> 0.8 GeV^2. The magnitudes of dimensions 6 and 8 condensates were found and the limitations on gluonic condensates were obtained. The sum rules for the charmed quark vector currents polarization operator was analysed in 3 loops (i.e., in order alpha^2_s). The value of charmed quark mass (in MS-bar regularization scheme) was found to be: m_c(m_c) = 1.275+-0.015 GeV and the value of gluonic condensate was estimated: <(alpha_s/pi)G^2> = 0.009+-0.007 GeV^4. The general conclusion is: QCD described by PT + OPE is in a good agreement with experiment at Q^2 >~ 1 GeV^2.