The Fermionic Dark Matter Higgs Portal: an effective field theory approach

We consider fermionic (Dirac or Majorana) cold thermal relic dark-matter coupling to standard-model particles through the effective dimension-5 Higgs portal operators $\Lambda^{-1} \ \mathcal{O}_{\text{DM}} \cdot H^\dagger H$, where $\mathcal{O}_{\text{DM}}$ is an admixture of scalar $\bar\chi\chi$ and pseudoscalar $\bar\chi i\gamma_5 \chi$ DM operators. Utilizing the relic abundance requirement to fix the couplings, we consider direct detection and invisible Higgs width constraints, and map out the remaining allowed parameter space of dark-matter mass and the admixture of scalar and pseudoscalar couplings. We emphasize a subtlety which has not previously been carefully studied in the context of the EFT approach, in which an effect arising due to electroweak symmetry breaking can cause a na\"ively pure pseudoscalar coupling to induce a scalar coupling at higher order, which has important implications for direct detection bounds. We provide some comments on indirect detection bounds and collider searches.