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 reevaluating these constraints in the context of specific models.