Resolved photoproduction of the $B_c$ meson in electron-proton collisions

Abstract

We present a systematic study of $B_c$ meson photoproduction at electron--proton colliders within the framework of nonrelativistic QCD (NRQCD) factorization. In addition to the dominant direct channel $\gamma +g\to B_c+X$, we include resolved contributions initiated by $g+g$ and $q+\bar{q}(q=u,d,s)$ subprocesses. Total cross sections and transverse-momentum distributions are calculated for several collider configurations, including HERA, LHeC, FCC-$ep$, and EIC. The numerical results show that the direct $\gamma +g$ channel provides the leading contribution over the entire kinematic range. However, the resolved $g+g$ channel yields a non-negligible correction, reaching the level of $\mathcal{O}(10\%)$ in the low-$p_T$ region where most events are produced, and it becomes increasingly important at higher collision energies. The $q+\bar{q}$ channel is found to be numerically insignificant.