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Considering the possibility to build an $e^+ e^-$ collider at the energies around the $Z^0$-boson resonance with a planned luminosity so high as ${\cal L}\propto 10^{34}\sim 10^{36}cm^{-2}s^{-1}$ (super $Z$-factory), we make a detailed discussion on the $(c\bar{b})$-quarkonium production through $e^{+}+e^{-}\rightarrow (c\bar{b})[n]+b+\bar{c}$ within the framework of non-relativistic QCD.
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