Pion wave functions and truncation sensitivity of QCD sum rules

Abstract

The systematic errors inherent in the QCD sum rule approach to meson wave functions are examined in the context of QCD in 1+1 spacetime dimensions in the large $N$ limit where the theory is exactly solvable. The systematic sensitivity of the sum rules reconstruction of meson wave functions to the input data at large ${Q}^{2}$ is studied in this model. We find that the reliable extraction of (a few) higher moments is possible provided a reasonably accurate uniform approximation to the Euclidean correlator over a suitable ${Q}^{2}$ range is available, but that the extracted values are particularly sensitive to the balance of lower and higher twist contributions. Underestimates of lower twist contributions or overestimates of the highest twist term may lead to too high values for the second and fourth moments of the pion wave function, suggesting a doubly peaked structure of the Chernyak-Zhitnitsky-type. Lattice discretization is shown to lead to similar distortions in the balance of lower and higher twist terms.