Looking forward to inelastic DM with electromagnetic form factors at FASER and beam dump experiments

Inelastic Dark Matter (iDM) is an interesting thermal DM scenario that can pose challenges for conventional detection methods. However, recent studies demonstrated that iDM coupled to a photon by electric or magnetic dipole moments can be effectively constrained by intensity frontier experiments using the displaced single-photon decay signature. In this work, we show that by utilizing additional signatures for such models, the sensitivity reach can be increased towards the short-lived regime, $\gamma c\tau \sim O(1)\,$m, which can occur in the region of the parameter space relevant to successful thermal freeze-out. These processes are secondary iDM production taking place by upscattering in front of the decay vessel and electron scattering. Additionally, we consider dimension-6 scenarios of photon-coupled iDM - the anapole moment and the charge radius operator - where the leading decay of the heavier iDM state is $\chi_1 \to \chi_0 e^+ e^-$, resulting in a naturally long-lived $\chi_1$. We find that the decays of $\chi_1$ at FASER2, MATHUSLA, and SHiP will constrain these models more effectively than the scattering signature considered for the elastic coupling case, while secondary production yields similar constraints as the scattering.