Everything You Always Wanted to Know About Dark Matter Elastic Scattering Through Higgs Loops But Were Afraid to Ask

We consider a complete list of simplified models in which Majorana dark matter particles annihilate at tree level to $hh$ or $hZ$ final states, and calculate the loop-induced elastic scattering cross section with nuclei in each case. Expressions for these annihilation and elastic scattering cross sections are provided, and can be easily applied to a variety of UV complete models. We identify several phenomenologically viable scenarios, including dark matter that annihilates through the $s$-channel exchange of a spin-zero mediator or through the $t$-channel exchange of a fermion. Although the elastic scattering cross sections predicted in this class of models are generally quite small, XENON1T and LZ should be sensitive to significant regions of this parameter space. Models in which the dark matter annihilates to $hh$ or $hZ$ can also generate a gamma-ray signal that is compatible with the excess observed from the Galactic Center.