Mixed WIMP-FIMP scenario in a two-component dark matter model

We consider the mixed WIMP-FIMP scenario in a two-component dark matter model with $Z_2 \times Z_4$ symmetry, where a singlet scalar $S$ and a Majarano fermion $\chi$ are introduced as dark matter candidates. We also introduce another singlet scalar $S_0$ with a non-zero vacuum expectation value to the SM so that the fermion dark matter can obtain mass after spontaneous symmetry breaking. Either $S$ or $\chi$ relic density can be generated via the "Freeze-out" mechanism. In contrast, the other DM candidate relic density is obtained by the "Freeze-in" mechanism, and we therefore have two different cases. In the case of $\chi$ as WIMP and $S$ as FIMP, we perform random scans to estimate the allowed parameter space consistent with the dark matter constraint. The results show that this case is viable over a wide range of dark matter masses with the Yukawa coupling of $S_0$ and $\chi$ should be larger than 1. Instead, for the case of $S$ as WIMP and $\chi$ as FIMP, the viable parameter space is more constrained by the direct detection experiements, and we have two regions with $m_S \approx 62.5$ GeV and $m_S>400$ GeV under the constraints, which is consistent with the singlet scalar DM result but the scalar DM mass can be as low as a few hundred GeV for the heavy mass region in the model.