The Pion Wave Function and QCD Sum Rules with Nonlocal Condensates

The QCD sum rule calculation of the pion wave function by Chernyak and Zhitnitsky is implicitly assuming that the correlation length of vacuum fluctuations is large compared to the typical hadronic scale ~ 1/m(sub)p, so that one can substitute the orginal nonlocal objects like (q-bar(0)q(z)) by constant (q-bar(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^2(sub)q = (q-barD^2q)/(q-bar q) specifying the average virtuality of the vacuum quarks.Varying it from the most popular value lambda^2(sub)q = 0.4 GeV^2 up to the value lamba^2(sub)q = 1.2 GeV^2 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^2(sub)q = 0