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 equation of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments \langle \xi 2N\rangle \pi (N=1, . . . , 5) using the improved QCD vacuum model, including the inverse moment \langle x-1\rangle \pi , being inaccessible if one uses the standard QCD sum 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, \lambda q2 = 0.4 and 0.5 GeV2.
PACS numbers: 11.15.Bt, 12.38.Bx, 12.38.Cy
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