On the Direct Detection of Dark Matter Annihilation

We investigate the direct detection phenomenology of a class of dark matter (DM) models in which DM does not directly interact with nuclei, {but rather} the products of its annihilation do. When these annihilation products are very light compared to the DM mass, the scattering in direct detection experiments is controlled by relativistic kinematics. This results in a distinctive recoil spectrum, a non-standard and or even absent annual modulation, and the ability to probe DM masses as low as a $\sim$10 MeV. We use current LUX data to show that experimental sensitivity to thermal relic annihilation cross sections has already been reached in a class of models. Moreover, the compatibility of dark matter direct detection experiments can be compared directly in $E_{{\rm min}}$ space without making assumptions about DM astrophysics, mass, or scattering form factors. Lastly, when DM has direct couplings to nuclei, the limit from annihilation to relativistic particles in the Sun can be stronger than that of conventional non-relativistic direct detection by more than three orders of magnitude for masses in a 2-7 GeV window.