Attenuation of Boosted Dark Matter in Two Component Dark Matter Scenario

Boosted dark matter constitutes a small fraction of the total dark matter in the Universe, with mass ranging from eV to MeV and often exhibiting (semi)relativistic velocity. Hence the likelihood of detecting boosted dark matter in Earth-based direct detection experiments is relatively high. There is more than one explanation for the origin of the boosted dark matter including the two-component dark matter models where the heavier dark matter species(dominant) annihilates to nearly monoenergetic light dark matter particles (subdominant) in the galactic halo. If the dominant dark matter species is heavier (MeV-GeV), the subdominant light dark matter achieves (semi)relativistic velocity or {\it boost}. These boosted dark matter particles suffer from scattering with electrons and nuclei while crossing the atmosphere and the Earth's crust before reaching underground experiments and hence the kinetic energy of the dark matter is attenuated. In the two-component dark matter framework, we examine how the boost of the dark matter influences the attenuation of kinetic energy across a broad spectrum of dark matter masses. We perform a detailed study at various DM-electron and DM-nucleus cross sections including the effect of nuclear form factor and elastic and inelastic scattering (for large kinetic energy). For a 10 MeV boosted dark matter with boost $\sim$ 10-100, the effect of DM-electron scattering is found to be severe than the DM-nucleus scattering (with form factor) if DM-nucleon scattering cross section is $10^{-29}$cm$^2$. We also show how the peak position of the boosted dark matter flux shifts due to the attenuation of its kinetic energy.