Examining scalar portal inelastic dark matter with lepton fixed target experiments

Inelastic dark matter scenarios have attracted considerable attention in contemporary particle physics. In this study, we investigate the phenomenology of sub-GeV inelastic dark matter interacting via a lepton-specific scalar portal. By solving the Boltzmann equations, we obtain thermal target curves for several inelastic DM mass splittings in the sub-GeV mediator-mass range. We study the discovery potential of lepton fixed-target experiments, particularly NA64e, LDMX, and NA64$\mu$, via their missing-energy signatures. Our analysis focuses on the $\phi$-strahlung process, $l N \to l N \phi$, followed by the invisible decay of the scalar mediator into Majorana dark matter particles $\phi \to \chi_1 \chi_2$. We use this channel to probe the mediator coupling to charged leptons of the Standard Model. For phenomenologically viable parameters of the inelastic dark matter scenario, we derive projected sensitivities for NA64e, LDMX, and NA64$\mu$, assuming that the boosted state $\chi_2$ decays visibly via $\chi_2 \to \chi_1 e^+ e^-$ outside the detector acceptance. Our results demonstrate the complementary roles of electron- and muon-beam experiments in exploring the sub-GeV inelastic dark matter sector interacting via a scalar portal.