Diurnal Effect of Sub-GeV Dark Matter Boosted by Cosmic Rays

We point out a new type of diurnal effect for the cosmic ray boosted dark matter (DM). The DM-nucleon interactions not only allow the direct detection of DM with nuclear recoils but also allow cosmic rays to scatter with and boost the nonrelativistic DM to higher energies. If the DM-nuclei scattering cross sections are sufficiently large, the DM flux is attenuated as it propagates through the Earth, leading to a strong diurnal modulation. This diurnal modulation provides another prominent signature for the direct detection of boosted sub-GeV DM, in addition to signals with higher recoil energy.