Production of the $B_c$ meson at the CEPC
In this paper, we make a detailed study on the production of the $B_c$, $B_c^*$, $B_c(2\,^1S_0)$, and $B^*_c(2\,^3S_1)$ mesons via the three planned running modes ($Z$, $W$, and $H$) at the future Circular Electron-Positron Collider (CEPC). The fragmentation-function and full nonrelativistic QCD approaches are adopted to calculate the production cross sections. Considering the excited states shall decay to the ground $B_c$ state (e.g. $1^1S_0$-state) with almost $100\%$ probability, our numerical results show that up to next-to-leading order QCD corrections, there are about $1.4\times 10^8$ $B_c$ events to be accumulated via the $Z$ mode ($\sqrt{s}=m_{_Z}$) of the CEPC, but only about $1.6\times 10^4$ and $1.1\times 10^4$ $B_c$ events to be accumulated via the $W$ ($\sqrt{s}=160\,{\rm GeV}$) and $H$ ($\sqrt{s}=240\,{\rm GeV}$) modes, respectively. Since the $Z$ mode is the best mode among the three planned modes of the CEPC for studying the production of the $B_c$, $B_c^*$, $B_c(2\,^1S_0)$, and $B^*_c(2\,^3S_1)$ mesons and the differential distributions of these mesons may be measured precisely at this mode, we further present the differential cross sections $dσ/(dz\,d{\rm cos}θ)$ and $dσ/dz$ via the $Z$ mode of the CEPC.