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

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