Charmonium polarization in e^+e^- and heavy ion collisions

In e^+e^- annihilation at \sqrt{s}=10.6 GeV Belle Collaboration found, that J/psi mesons are predominantly produced in association with an extra \bar{c}c pair. The possible mechanisms of J/psi production are discussed and the probability of the associate production of \bar{c}c pair is estimated. The choice between these mechanisms can be done by measuring J/psi polarization. It is suggested, that in case of heavy ion collisions one may expect remarkable transverse polarization of produced J/psi, if quark-gluon plasma if formed. The measurement of asymmetry of e^+e^-(\mu^+\mu^-) angular distribution in J/psi-> e^+e^-(\mu^+\mu^-) decay is a useful tool for detection of quark-gluon plasma formation in heavy ion collisions.