HADRONIC QUARK DISTRIBUTION AMPLITUDES FROM QCD SUM-RULE MOMENTS

We discuss the reliability of hadronic wave functions (quark distribut ion amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncerta inty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large os cillations of the model function. In particular, the freedom in the mo ments left by QCD sum rules leads to a nonconverging polynomial expans ion. This remains true even if additional constraints on the wave func tions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to th e true wave function. The differences among the model wave functions p ersist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by mea ns of such model wave functions are in general very unreliable. As spe cific examples, we examine the pion and nucleon wave functions and sho w that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.