Fermion and scalar two-component dark matter from a Z₄ symmetry

We revisit a two-component dark matter model in which the dark matter particles are a singlet fermion ($\psi$) and a singlet scalar ($S$), both stabilized by a single $Z_4$ symmetry. The model, which was proposed by Y. Cai and A. Spray, is remarkably simple, with its phenomenology determined by just five parameters: the two dark matter masses and three dimensionless couplings. In fact, $S$ interacts with the Standard Model particles via the usual Higgs-portal, whereas $\psi$ only interacts directly with $S$, via the Yukawa terms $\overline{\psi^c}(y_s+y_p\gamma^5)\psi\,S$. We consider the two possible mass hierarchies among the dark matter particles, $M_S<M_\psi$ and $M_\psi<M_S$, and numerically investigate the consistency of the model with current bounds. The main novelties of our analysis are the inclusion of the $y_p$ coupling, the update of the direct detection limits, and a more detailed characterization of the viable parameter space. For dark matter masses below $1.3$ TeV or so, we find that the model not only is compatible with all known constraints, but that it also gives rise to observable signals in future dark matter experiments. Our results show that both dark matter particles may be observed in direct detection experiments and that the most relevant indirect detection channel is due to the annihilation of $\psi$. We also argue that this setup can be extended to other $Z_N$ symmetries and additional dark matter particles.