Boosted self-interacting dark matter in a multi-component dark matter model

In models of multi-component dark matter, the lighter component of dark matter can be boosted by annihilations of the heavier state if mass splitting is large enough. Such relativistic dark matter can be detectable via large neutrino detectors such as Super-Kamiokande and IceCube. Moreover, if the process is inelastic scattering and decay length of the produced particle is short enough, another signature coming from the decay can also be detectable. In this paper, we construct a simple two-component dark matter model with a hidden U(1)_D gauge symmetry where the lighter component of dark matter has a potential to improve the so-called small scale structure problems with large self-interacting cross section. We estimate number of multi-Cherenkov ring events due to both of the boosted dark matter and subsequent decay of the particle produced by inelastic scattering at Hyper-Kamiokande future experiment. Some relevant constraints, such as dark matter direct detection and cosmological observations, are also taken into account. The numerical analysis shows that some parameter space which can induce large self-interacting cross section can give a few multi-Cherenkov ring events per year at Hyper-Kamiokande.