This paper is devoted to the study of leading twist light cone wave functions of the J/Psi meson. The moments of these wave functions have been calculated within three approaches: potential models, nonrelativistic QCD, and QCD sum rules. Using the results obtained within these approaches the models for the light cone wave functions of leading twist have been proposed. Similarly to the wave function of the eta(c) meson, the leading twist light cone wave functions of the J/Psi meson have very interesting properties at scales mu > m(c): improvement of the accuracy of the model, appearance of a relativistic tail, and violation of nonrelativistic QCD velocity scaling rules. The last two properties are the properties of true leading twist light cone wave functions of the J/Psi meson.
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