Dark Photon mediated Inelastic Dark Matter in Cosmology, Astrophysics and Colliders

We provide a systematic discussion of the phenomenology of Dark Photon iDM (A$^{\prime}$iDM) where the Standard Model (SM) is extended by a dark sector containing an additional $U(1)_D$ gauge symmetry under which all SM particles are neutral, and that couples to the SM hypercharge gauge boson through a kinetic mixing parameter $\epsilon$. The model contains two Majorana states $\chi_1$ and $\chi_2$ with $\delta=M_{\chi_2}-M_{\chi_1}>0$ and $\chi_1$ the dark matter candidate, and a dark photon $A^{\prime}$ with mass $M_{A^{\prime}}$. Our analysis represents an integration of existing ones, where only specific benchmarks of the A$^{\prime}$iDM scenario have been discussed. In particular, we fix the $U(1)_D$ coupling $\alpha_D$ equal to the electromagnetic one $\alpha_{EM}$ and $\epsilon$ to its experimental upper bound, and perform a complete scan of the remaining parameters $(M_{\chi_1},\delta, M_{A^{\prime}})$, discussing the $\chi_1$ relic abundance, its direct and indirect searches, as well as potential signals from astrophysics and accelerators. Our systematic scan shows that $\alpha_D$ = $\alpha_{EM}$ is not disfavored, as some previous analyses, limited to specific benchmarks, may suggest. We also find that when the $\chi_1$ relic density matches observation direct and indirect searches are not kinematically accessible. On the other hand we find that the projected luminosity of FASER, a detector searching for Long Lived Particles (LLP) decay at the LHC, can probe or rule out the parameters space of the model for $M_{\chi_1}\lesssim$ 7 GeV, 100 MeV $\lesssim \delta\lesssim$ 300 MeV and $M_{A^{\prime}}\lesssim$ 25 GeV. This range of parameter could be significantly extended by the FASER 2 upgrade proposed for the High-Luminosity phase at the LHC. The parameter space probed by LLP seaches partially overlaps with that probed by $\chi_1$ capture in neutron stars.