Signatures of Earth-scattering in the direct detection of Dark Matter

Direct detection experiments search for the interactions of Dark Matter (DM) particles with nuclei in terrestrial detectors. But if these interactions are sufficiently strong, DM particles may scatter in the Earth, affecting their distribution in the lab. We present a new analytic calculation of this 'Earth-scattering' effect in the regime where DM particles scatter at most once before reaching the detector. We perform the calculation self- consistently, taking into account not only those particles which are scattered away from the detector, but also those particles which are deflected towards the detector. Taking into account a realistic model of the Earth and allowing for a range of DM-nucleon interactions, we present the EARTHSHADOW code, which we make publicly available, for calculating the DM velocity distribution after Earth-scattering. Focusing on low-mass DM, we find that Earth-scattering reduces the direct detection rate at certain detector locations while increasing the rate in others. The Earth's rotation induces a daily modulation in the rate, which we find to be highly sensitive to the detector latitude and to the form of the DM-nucleon interaction. These distinctive signatures would allow us to unambiguously detect DM and perhaps even identify its interactions in regions of the parameter space within the reach of current and future experiments.