THE NONPERTURBATIVE WAVE-FUNCTIONS, TRANSVERSE-MOMENTUM DISTRIBUTION AND QCD VACUUM-STRUCTURE

It is shown that there is one-to-one correspondence between two, apparently different problems: (1) The determination of the mean values Of transverse moments [k(perpendicular-to)2n] for the nonperturbative pion wave function psi(k(perpendicular-to)2, x) and (2) The evaluation of the mixed vacuum condensates [qG(munu)(n)qBAR]. Arguments in favor of a large magnitude of the mixed vacuum condensate [q(igsigma(munu)G(munu)2q]BAR are given. The analysis is based on the dispersion relations and PCAC. Because of the large values of the condensates we found a noticeable fluctuation of the momentum [k(perpendicular-to)4] > [k(perpendicular-to)2]2. We also found some general properties of the condensates [q(igsigma(munu)G(munu))(n)qBAR] for arbitrary n. This information is used for the analysis of the higher moments [k(perpendicular-to)2n] in the limit when the space-time dimension d --> infinity. As a byproduct, it is proven that the standard assumption on factorizability of the psi(k(perpendicular-to)2, x) = psi(k(perpendicular-to)2)phi(x) does contradict the very general properties of the theory. We define and model psi(k(perpendicular-to)2, x), satisfying all these constraints.