Color-octet heavy quarkonium productions in Z0 decays at LEP

We consider the energy and the polar angle distributions of J/\psi's produced via the color-singlet and the color-octet (^3S_1^{(8)}) mechanisms in Z^0 \to J/\psi +X at LEP. Since both distributions of the J/\psi produced via color-octet mechanism are significantly different from those via color-singlet mechanism, these observables can be used as tests of color-octet production mechanism for heavy quarkonia. We also discuss Z^0 \rightarrow \Upsilon + X and W \to J/\psi ( or \Upsilon) + X in brief.