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 generates the non-transversity of vector current correlators. 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 <ξ2N>π (N=1, ..., 5) using the improved QCD vacuum model, including the inverse momentum π, being inaccessible if one uses the standard QCD rum rules. We construct the allowed region for Gegenbauer coefficients a2 and a4 of the pion DA for two values of the QCD vacuum nonlocality parameter, λq2=0.4 and 0.5 GeV2