On Dark Matter Self-interaction via Single Neutrino Exchange Potential

Neutrinos -- amongst the lightest known particles -- can mediate a force driving dark matter self-interaction and the small scale structure of the universe. We explore such a possibility in the simplest neutrino portal dark sector model where neutrino has a Yukawa coupling with a scalar $\phi$ and fermion $\chi$ that are degenerate in mass and together comprise 100\% of dark matter in the universe. We derive the non-relativistic potential generated by single-neutrino exchange which is of the monopole-dipole form and explore $\chi\phi\to\chi\phi$ scattering based on phase shift analysis. Our result shows that Born approximation continues to be valid in the low energy regime and the scattering cross section scales as $1/v^2$ over a wide range of dark matter velocities. Such a velocity-dependent self-interacting cross section can be large enough to explain the shallow density of dwarf galaxy cores and consistent with the upper limit from colliding galaxy clusters. The $1/v^2$ behavior persists down to rather low velocities $v\sim m_\nu/m$ where $m$ is the dark matter mass, leaving the opportunity for further astrophysical probes. Through the neutrino portal, the self-interacting dark matter parameter space can be tested by searches for $Z$-boson and light mesons decaying into the dark sector, as well as low-mass dark matter direct detection experiments.