The ups and downs of inelastic dark matter: Electron recoils from terrestrial upscattering

The growing interest in the interactions between dark matter particles and electrons has received a further boost by the observation of an excess in electron recoil events in the XENON1T experiment. Of particular interest are dark matter models in which the scattering process is inelastic, such that the ground state can upscatter into an excited state. The subsequent exothermic downscattering of such excited states on electrons can lead to observable signals in direct detection experiments and gives a good fit to the XENON1T excess. In this work, we study terrestrial upscattering, i.e. inelastic scattering of dark matter particles on nuclei in the Earth, as a plausible origin of such excited states. Using both analytical and Monte Carlo methods, we obtain detailed predictions of their density and velocity distribution. These results enable us to explore the time dependence of the flux of excited states resulting from the rotation of the Earth. For the case of XENON1T, we find the resulting daily modulation of the electron recoil signal to be at the level of 10% with a strong dependence on the dark matter mass.