Elastic and Inelastic Scattering of Cosmic-Rays on Sub-GeV Dark Matter

We revisit the signatures from collisions of cosmic-rays on sub-GeV dark matter (DM) in the Milky Way. In addition to the upscattered DM component that can be probed by existing DM and neutrino experiments widely discussed, we examine the associated signals in $\gamma$-rays and neutrinos that span a wide energy range due to the inelastic scatterings. Assuming a simple vector portal DM model for illustration, we compute both the upscattered DM flux by cosmic-ray protons, and the resulting emission of secondary $\gamma$-rays and high-energy neutrinos from proton excitation, hadronization, and the subsequent meson decay. We derive limits on coupling constants in the vector portal model using data from the $\gamma$-ray and high-energy neutrino telescopes including Fermi, H.E.S.S. and IceCube. These limits are compared to those obtained by considering the upscattered DM signals at the low-energy DM/neutrino detectors XENON1T/MiniBooNE and the IceCube. For this particular model, the limits are set predominantly by non-detection of the upscattered DM events in XENON1T, for most of the DM mass range due to the large scattering cross section at low energies. Nevertheless, our study demonstrates that the $\gamma$-ray and neutrino signals, traditionally considered as indirect probes for DM annihilation and decay, can also be directly used to constrain the DM--nucleon interaction in complementary to the direct search experiments.