Based on the quark model the cross section for the e^+e^-→ Z^0/r~*→Ω_(ccc)^(++)Ω_(ccc)^(--) exclusive process is investigated at the tree level. Compared with the Z^0→Ω^-Ω^+ 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.
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