Lepton collider imprints of Inelastic dark matter model

We explore the potential for detecting the inelastic dark model (DM) with an additional $U(1)_D$ gauge symmetry at various types of lepton colliders. The new gauge boson $Z'$ resulting from the spontaneous breaking of $U(1)_D$ can act as a portal connecting the Standard Model fermions and DM fermions $\chi$, thereby facilitating the production of $Z'$ and its decay into DM fermions. The mass difference between the excited DM fermion $\chi_2$ and the ground DM fermion $\chi_1$ induces the subsequent decays $\chi_2\to \chi_1 +\text{vis}$, where $\chi_2$ and $\chi_1$ serve as long lived particles and DM candidate, respectively. For the inelastic DM with a mass $m_{\chi_1}$ in the range of (1-100) GeV, we find that the future lepton colliders can probe many regions not accessible by current experiments and provide greater projected sensitivity than the LHC and Belle in previous studies. This suggests that future colliders can provide complementary exploration of the inelastic dark matter model.