A general upper bound on the light dark matter scattering rate in materials

Combining an effective theory description of spin-1/2 dark matter (DM)-electron interactions in materials with linear response theory provides a powerful framework to model the scattering of DM, including in-medium effects, in detectors used for direct searches. Within this framework, we show that the rate of DM-induced electronic transitions in detector materials admits a theoretical upper bound under general assumptions on the underlying DM-electron coupling. In particular, our theoretical upper bound applies to models where DM couples to the electron density as well as the spin, paramagnetic and Rashba currents in materials, and arises from the Kramers-Kronig relations that constrain the analytic properties of the scattering rate. We evaluate our maximum rate formula numerically for Ar, Xe, Ge, and Si targets and find that Ge and Si detectors are closer to saturate this theoretical upper bound, but still far from saturation when DM couples to densities or currents which are different from the electron density. This motivates the exploration of a different class of materials to effectively probe such coupling forms.