Production of the triply heavy $\Omega_{ccc}$ and $\Omega_{bbb}$ baryons at $e^+e^-$ colliders

Non-relativistic quantum chromodynamics (NRQCD) factorization formulism is an important approach to investigate the production of the heavy quarkonium. In this paper, we study the production of the $\Omega_{ccc}$ and $\Omega_{bbb}$ at the $e^+e^-$ collider, using the NRQCD factorization formulism. We calculate the total and differential cross sections exactly of the processes, $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{ccc}\bar{c}\bar{c}\bar{c}$ and $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{bbb}\bar{b}\bar{b}\bar{b}$, in the leading order at the $e^+e^-$ colliders with different energies. The results show that it is hard to observe them at the $e^+e^-$ collider directly.