Examining scalar portal inelastic dark matter with lepton fixed target experiments

Abstract: The inelastic dark matter (DM) scenarios have attracted considerable attention in contemporary particles physics. In this study, we investigate the phenomenology of sub-GeV inelastic dark matter scenarios mediated by a lepton-specific scalar portal. By solving Boltzmann equations, we obtain a thermal target curves for the set of inelastic DM mass splitting in the sub-GeV mediator mass range. We study the discovery potential of lepton fixed-target experiments, particularly NA64e and NA64$\mu$, through 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 $\phi \to \chi_1 \chi_2$, as a probe of the mediator coupling with charged leptons of Standard Model. For the viable parameters of the inelastic dark matter scenario, we derive the sensitivity projections for NA64e and NA64$\mu$, implying that boosted state $\chi_2$ decays visibly $\chi_2 \to \chi_1 e^+ e^-$ beyond the detector acceptance. Our results demonstrate the complementary roles of electron- and muon-beam experiments in exploring the sub-GeV inelastic dark matter sector mediated by the scalar portal.