Self-resonant dark matter with $Z_4$ gauged symmetry

We present a new model for two-component scalar dark matter (DM), consisting of two complex scalar fields. In this model, both the DM components are stable due to the remaining $Z_4$ gauge symmetry, which is the remnant of the $U(1)^\prime$ local symmetry. When the resonance condition for DM masses is fulfilled, we show that the elastic co-scattering processes between two components of dark matter ($u$-channel processes) are enhanced due to the Yukawa potential with a small effective mass for the lighter DM mediator, so we can use such co-scattering processes for dark matter to explain the small-scale problems at galaxies. Moreover, there are also semi-annihilation processes that two components of dark matter annihilate into one dark matter particle and a dark photon/Higgs, which are enhanced by the $u$-channel Sommerfeld factor. Focusing on some benchmark models for two-component dark matter satisfying the observed relic density, we obtain the bounds for the dark photon portal couplings from the direct detection for boosted dark matter, which is produced from the semi-annihilation processes at the galactic center.