Dark photon and U(1)${}_{B-L}$ gauge boson from dark Higgs boson decays at FASER and SHiP

We study the sensitivity to dark photons and U(1)${}_{B-L}$ gauge bosons produced via dark Higgs boson decays at the FASER and SHiP experiments. In addition to pair production of these vector bosons from both on-shell and off-shell dark Higgs boson decays, a new production process of single vector boson associated with the standard model particles is taken into account. Constraints on the parameter space of dark photon are derived with including the latest results from the FASER experiment. The expected sensitivity regions to the dark photon and U(1)${}_{B-L}$ gauge boson of the future FASER2 and SHiP experiments are presented. The sensitivity to the U(1)${}_{B-L}$ model with freeze-in sterile neutrino dark matter is also discussed.