Pion Wavefunctions and Truncation Sensitivity of QCD Sum Rules

The systematic errors inherent in the QCD sum rule approach to meson wavefunctions are examined in the context of QCD in 1+1 spacetime dimensions in the large N limit where the theory is exactly solvable. It is shown that the truncation of high momentum modes induced in a lattice discretization automatically produces a Chernyak-Zhitnitsky \cite{CZ} type meson wavefunction. Such a truncation alters the balance of leading and higher twist terms in correlators. 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 wavefunction, suggesting a doubly peaked structure of the Chernyak-Zhitnitsky type.