Color-octet mechanism and J/psi polarization at LEP

Polarized heavy quarkonium productions in $Z^0$ decays are considered. We find that polarizations of the produced quarkonia are independent of that of the parent Z^0 provided that one considers the energy distribution or the total production rate. Produced J/psi's via the color-octet and the color- singlet mechanisms are expected to be 19% and 29% longitudinally polarized, respectively. The energy dependence of eta_{1,8}(x)=\frac{dGamma_{1,8}^L}{dx} /\frac{dGamma_{1,8}}{d x} is very sensitive to the production mechanism, and therefore the measurement of \eta(x)_exp will be an independent probe of the color-octet mechanism.