Accelerated Light Dark Matter-Earth Inelastic Scattering in Direct Detection

The Earth-stopping effect plays a crucial role in the direct detection of sub-GeV dark matter. Besides the elastic scattering process, the quasi-elastic and deep inelastic scatterings between dark matter and nucleus that are usually neglected can dominate the interaction, especially in the accelerated dark matter scenarios, which may affect the dark matter detection sensitivity significantly for the underground experiments. We calculate such inelastic scattering contributions in the Earth-stopping effect and illustrate the essence of our argument with the atmospheric dark matter. With the available data, we find that the resulting upper limits on the atmospheric dark matter-nucleus scattering cross-section can differ from those only considering the elastic scattering process by one order of magnitude.