Constraining sub-GeV dark matter from Migdal and Boosted effects

Given the current strong constraints on WIMPs, search for sub-GeV Dark Matter (DM) now is an essential task in direct detections. In order to overcome the limitation of low recoils, enhancing ionization rate of electron from Migdal effect and modifying the velocity distribution of DM from interaction of DM and cosmic rays are two important ways. In this work, we find that these two ways are complementary to probe sub-GeV DM. The former can cover heavier DM, while the latter can cover the lighter DM. Both of them can cover DM with a mass of 20 MeV to 200 MeV. Including momentum transfer effect can greatly improve the existing bounds.