QCD (Quantum chromodynamics) at low energies

The modern status of basic low energy QCD parameters is reviewed. It is demonstrated that the recent data allow one to determine the light quark mass ratios with an accuracy of 10-15%. The general analysis of vacuum condensates in QCD is presented, including those induced by external fields. The QCD coupling constant αs(mτ2) is found from the τ-lepton hadronic decay rate. The contour improved perturbation theory includes the terms up to αs4. The influence of instantons on αs(mτ2) determination is estimated. V−A spectral functions of the τ-decay are used for construction of the V−A polarization operator ΠV−A(s) in the complex s-plane. The operator product expansion (OPE) is used up to dimension D=10 and the sum rules along the rays in the complex s-plane are constructed. This makes it possible to separate the contributions of operators of different dimensions. The best values of the quark condensate and αs〈0|q̄q|0〉2 are found. The value of the quark condensate is confirmed by considering the sum rules for baryon masses. The value of the gluon condensate is found in four ways: by considering the V+A polarization operator based on the τ-decay data and by studying the sum rules for polarization operator momenta in charmonia in the vector, pseudoscalar and axial channels. All of these determinations are in agreement and result in 〈(αs/π)G2〉=0.005±0.004GeV4. Valence quark distributions in the proton are calculated in QCD using the OPE in the proton current virtuality. The quark distributions agree with those found from the deep inelastic scattering data. The same value of the gluon condensate is favoured.