Photoproduction of the $B_c^{(\ast )}$ Meson at the LHeC

Abstract

We make a detailed study on the photoproduction mechanism of the doubly heavy flavored $B_c^{(\ast )}$ meson at the purposed Large Hadron Electron Collider (LHeC) within the framework of nonrelativistic QCD. In addition to the photoproduction mechanism via the gluon-induced channel $\gamma +g\to B_c^{(\ast )}+b+\bar{c}$, the extrinsic heavy quark mechanism via the two channels $\gamma +c\to B_c^{(\ast )}+b$ and $\gamma +\bar{b}\to B_c^{(\ast )}+\bar{c}$ has also been studied. Those two extrinsic channels are generally suppressed by the heavy quark distribution functions in proton, which however provide significant contributions in low and intermediate $p_T$ region. A detailed comparison of those channels together with the theoretical uncertainties has been presented. By summing up all the mentioned photoproduction channels, we observe that about $(1.04_{-0.53}^{+0.90})\times 10^5$ $B_c$ and $(4.86_{-2.30}^{+3.72})\times 10^5$ $B_c^{\ast }$ events can be generated at the LHeC in one operation year with the proton-electron collision energy $\sqrt{S}=1.30$ TeV and the luminosity $\mathcal{L}\simeq 10^{33}$ ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Here the errors are for $m_c=1.50\pm 0.20$ GeV and $m_b=4.9\pm 0.40$ GeV. Thus, in addition to the hadronic experiments, the LHeC shall provide another helpful platform for studying the $B_c^{(\ast )}$ meson properties, especially to test the extrinsic heavy quark mechanism.