Resolved photoproduction of the B c meson in electron-proton collisions

We present a systematic study of prompt B c meson photoproduction at electron-proton colliders within the framework of nonrelativistic QCD factorization. In addition to the dominant direct channel γ + g → B c + X , we include resolved contributions initiated by g + g and q + q ¯ ( q = u , d , s ) subprocesses. The production of the 1 S , 2 S , and 1 P color-singlet B c states is calculated, and the feeddown contributions from the excited states are included in the prompt- B c yield. Total cross sections and transverse-momentum distributions are presented for several collider configurations, including HERA, LHeC, FCC- e p , and EIC. The numerical results show that the direct γ + g channel provides the leading contribution over the entire kinematic range. The resolved g + g channel gives a non-negligible correction, reaching the level of O ( 10 % ) in the low- p T region where most events are produced, and it becomes increasingly important at higher collision energies.