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 ~1m_ρ, so that one can substitute the original nonlocal objects such as 〈q̄(0)q(z)〉 by constant 〈q̄(0)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 〈ξN〉 of the pion wave function. The results are rather sensitive to the value of the parameter λq²=〈q̄D²q〉〈q̄q〉 specifying the average virtuality of the vacuum quarks. Varying it from the most popular value λq²=0.4 GeV² up to the value λq²=1.2 GeV² suggested by the instanton-liquid model, we obtain 〈ξ²〉=0.25-0.20, to be compared to the CZ value 〈ξ²〉=0.43 obtained with λq²=0.
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Михайлов et al. (1992) studied this question.