Pion Wave Function from QCD Sum Rules with Nonlocal Condensates

Abstract

We investigate a model QCD sum rule for the pion wave function ${\phi }_{\pi }(x)$ based on the non-diagonal correlator whose perturbative spectral density vanishes and $\Phi (x,M^2)$, the theoretical side of the sum rule, consists of condensate contributions only. We study the dependence of $\Phi (x,M^2)$ on the Borel parameter $M^2$ and observe that $\Phi (x,M^2)$ has a humpy form, with the humps becoming more and more pronounced when $M^2$ increases. We demonstrate that this phenomenon reflects just the oscillatory nature of the higher states wave functions, while the lowest state wave function ${\phi }_{\pi }(x)$ extracted from our QCD sum rule analysis,has no humps, is rather narrow and its shape is close to the asymptotic form ${\phi }_{\pi }^{as}(x)=6x(1-x)$.

Talk at the Workshop "Continuous Advances in QCD", 11 pages + appended uuencoded ps file with 8 figures, Latex, CEBAF-TH-94-13