Exploring properties of long-lived particles in inelastic dark matter models at Belle II

The inelastic dark matter model is one kind of popular models for the light dark matter (DM) below $O(1)$ GeV. If the mass splitting between DM excited and ground states is small enough, the co-annihilation becomes the dominant channel for thermal relic density and the DM excited state can be long-lived at the collider scale. We study scalar and fermion inelastic dark matter models for $\mathcal{O}(1)$ GeV DM at Belle II with $U(1{)}_D$ dark gauge symmetry broken into its $Z_2$ subgroup. We focus on dilepton displaced vertex signatures from decays of the DM excited state. With the help of precise displaced vertex detection ability at Belle II, we can explore the DM spin, mass and mass splitting between DM excited and ground states. Especially, we show scalar and fermion DM candidates can be discriminated and the mass and mass splitting of DM sector can be determined within the percentage of deviation for some benchmark points. Furthermore, the allowed parameter space to explain the excess of muon $(g-2{)}_{\mu }$ is also studied and it can be covered in our displaced vertex analysis during the early stage of Belle II experiment.