Attenuation of Cosmic Ray Electron Boosted Dark Matter

We consider a model of boosted dark matter (DM), where a fraction of DM is upscattered to relativistic energies by cosmic ray electrons. Such interactions responsible for boosting the DM also attenuate its flux at the Earth. Considering a simple model of constant interaction cross-section, we make analytical estimates of the variation of the attenuation ceiling with the DM mass and confirm it numerically. We then extend our analysis to a $Z'$-mediated leptophilic DM model. We show that the attenuation ceiling remains nearly model-independent for DM and mediator particles heavier than the electron, challenging some previous discussions on this topic. Using the XENONnT direct detection experiment, we illustrate how constraints based on energy-dependent scattering can significantly differ from those based on an assumed constant cross-section. This highlights the importance of re-evaluating these constraints in the context of specific models.