Maximally self-interacting dark matter: models and predictions

We study self-interacting dark matter (SIDM) scenarios, where the $s$-wave self-scattering cross section almost saturates the Unitarity bound. Such self-scattering cross sections are singly parameterized by the dark matter mass, and are featured by strong velocity dependence in a wide range of velocities. They may be indicated by observations of dark matter halos in a wide range of masses, from Milky Way's dwarf spheroidal galaxies to galaxy clusters. We pin down the model parameters that saturates the Unitarity bound in well-motivated SIDM models: the gauged $L_{\mu} - L_{\tau}$ model and composite asymmetric dark matter model. We discuss implications and predictions of such model parameters for cosmology like the $H_{0}$ tension and dark-matter direct-detection experiments, and particle phenomenology like the beam-dump experiments.