Spin-Dependent Scattering of Sub-GeV Dark Matter: Models and Constraints

Abstract: We calculate the scattering rate of sub-GeV dark matter in solid-state targets for spin-dependent dark matter -- nucleon interactions. For dark matter particles with mass below 100 MeV, the scattering occurs predominantly through incoherent phonon production. For dark matter heavier than 100 MeV, we match onto the nuclear recoil calculation. To compare the sensitivity of future direct detection experiments with existing constraints, we consider three models with interactions which are mediated by spin-0 or spin-1 particles. This allows us to derive bounds on the cross section from searches for the mediating particle, including bounds from stellar cooling, beam dump experiments, meson factories and dark matter self-interactions. The existing bounds are very stringent, though for $m_\chi\gtrsim 100$ MeV there is parameter space which may be accessible with direct detection, depending on the exposure and background rates.