Self-consistent Gaussian model of nonperturbative QCD vacuum

We show that the minimal Gaussian model of nonlocal vacuum quark and quark-gluon condensates in QCD violates the transverse character of the correlator of two vector currents. We suggest the improved Gaussian model of the nonperturbative QCD vacuum, which respects QCD equations of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments 〈ξ^2N 〉_π (N = 1, ..., 5) using the improved QCD vacuum model, including the inverse moment 〈x ^?1〉_π, being inaccessible if one uses the standard QCD SR. We construct the allowed region for Gegenbauer coefficients a ₂ and a ₄ of the pion DA for two values of the QCD vacuum nonlocality parameter, λ _q ² = 0.4 and 0.5 GeV².