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.
