The QCD-sum-rule calculation of the pion wave function by Chernyak and Zhitnitsky (CZ) implicitly assumes that the correlation length of vacuum fluctuations is large compared to the typical hadronic scale $\sim \frac{1}{m_{\rho }}$, so that one can substitute the original nonlocal objects such as $〈\overline{q}\mathrm{}\left(0\right)q\left(z\right)\mathrm{}〉$ by constant $〈\overline{q}\mathrm{}\left(0\right)q〉$-type values. We outline a formalism enabling one to work directly with the nonlocal condensates, and construct a modified sum rule for the moments $〈{\xi }^N〉$ of the pion wave function. The results are rather sensitive to the value of the parameter ${\lambda }_q^2=\frac{〈\overline{q}{D}^{2}q〉}{〈\overline{q}q〉}$ specifying the average virtuality of the vacuum quarks. Varying it from the most popular value ${\lambda }_q^2=0.4\mathrm{}$ Ge${\mathrm{V}}^2$ up to the value ${\lambda }_q^2=1.2\mathrm{}$ Ge${\mathrm{V}}^2$ suggested by the instanton-liquid model, we obtain $〈{\xi }^2〉=0.25-0.20\mathrm{}$, to be compared to the CZ value $〈{\xi }^2〉=0.43\mathrm{}$ obtained with ${\lambda }_q^2=0\mathrm{}$.

• Received 17 September 1991

DOI:https://doi.org/10.1103/PhysRevD.45.1754