Exclusive \it \Omega_ccc^++\bar\it \Omega_ccc^-- Production from Z^0/\gamma^* Decays

Based on the quark model the cross section for the e^+e^-\to Z^0/\gamma^*\to\it \Omega_ccc^++\bar\it \Omega_ccc^-- exclusive process is investigated at the tree level. Compared with the Z^0\to\it \Omega^-\bar\it \Omega^+ decay, our result shows that the Z^0 boson favors decaying into charmed baryon pairs. The results are also compared with the calculation of inclusively charmed baryon production.