Searching for inelastic dark matter with future LHC experiments

We consider a dark sector containing a pair of almost degenerate states coupled to the Standard Model through a dark photon mediator. This set-up constitutes a simple realization of the inelastic dark matter scenario. The heaviest dark state is long-lived, in the limit of a small kinetic mixing among the dark photon and the Standard Model hypercharge gauge boson, and/or of a small mass splitting among the dark states. We study the prospects for detection of this scenario at proposed LHC experiments dedicated to search for long-lived particles, namely FASER, MATHUSLA, CODEX-b, AL3X, MAPP, ANUBIS and FACET. We consider both the cases of fermionic and scalar inelastic dark matter. We show that these experimental facilities can probe unexplored regions of the parameter space of this model, and we highlight their complementary roles.