Dark matter: Red or blue?

We report the first calculation of light scattering on heavy dark matter (DM) particles. We show that despite the fact that DM has no direct coupling to photons, the light-DM($\gamma \chi$) ($m_{\chi }\sim 1$ TeV) cross-section is non-vanishing, albeit small. The cross section, calculated within the Standard Model (SM) framework (no BSM extensions),is particularly large in the case of heavy Weakly Interacting Massive Particles (WIMP). Combined with astrophysical observation, these results can constrain existing WIMP DM models in favor of lighter DM, $M_{\chi }<<M_{\mathrm{Planck}}$, (axions, composite DM, etc.) or non-weakly interacting pure gravitational DM. We also show that the energy dependence of light scattering on dark matter should make the DM colored - red in the case of weak-DM and blue for the gravitational-DM, when a white background light is passing through. Gravitational scattering of light on DM particles also leads to non-trivial polarization effects, which might be easier to detect than the deflection of light from the scattering on DM particles, $\gamma \chi \to \gamma \chi$.