Dark Matter scattering in low threshold detectors

The scattering of sub-GeV dark matter in direct detection experiments happens at characteristic wavelengths comparable or larger than the interparticle spacing. Collective effects in the target material must therefore be accounted for when calculating the scattering rate. For dark matter-nucleon couplings, this implies matching onto the appropriate phonon effective theory and calculating single and multi-phonon scattering amplitudes. For dark matter-electron couplings, we make use of the energy loss formalism to predict the scattering rate. Combining both techniques allows us to derive a formula for the Migdal effect in crystals, which differs from prior calculations performed in atomic systems.