NONLOCAL CONDENSATES AND QCD SUM-RULES FOR THE PION WAVE-FUNCTION

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 approximately 1/m(rho), so that one can substitute the original nonlocal objects such as <qBAR(0)q(z)> by constant <qBAR(0)q(0)>-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 = <qBARD2q>/<qqBAR> specifying the average virtuality of the vacuum quarks. Varying it from the most popular value lambda(q)2 = 0.4 GeV2 up to the value lambda(q)2 = 1.2 GeV2 suggested by the instanton-liquid model, we obtain <xi(2)> = 0.25-0.20, to be compared to the CZ value <xi(2)> = 0.43 obtained with lambda(q)2 = 0.