Fermion and scalar two-component dark matter from a $Z_4$ 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—proposed by Cai and 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 not only is the model compatible with all known constraints, but 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.

Figure 1

Dark matter semiannihilation (top) and conversion (bottom) processes.

Figure 2

$a_2{|}_{yp=0}/a_2{|}_{ys=0}$ as a function of $M_S$ for different mass ratios $M_{\psi }/M_S$.

Figure 3

Total relic density as a function of $M_{\psi }$ (left) or $M_S$ (right) for different sets of parameters. In the left (right) panel, $M_S$ ($M_{\psi }$) is fixed to 300 GeV. The benchmark model (solid green) features $y_s=y_p={\lambda }_{SH}=1$. The other lines differ from the benchmark only in the value of the coupling shown in the key.

Figure 4

$\psi$ and $S$ relic densities as functions of $M_S$ for $M_{\psi }/M_S=1.2$ (left) and $M_{\psi }/M_S=1.8$ (right). The benchmark model (solid green) features $y_s=y_p={\lambda }_{SH}=1$. The other lines differ from the benchmark only in the value of the coupling shown in the key.

Figure 5

$\psi$ and $S$ relic densities as functions of $M_{\psi }$ for $M_S/M_{\psi }=1.2$ (left) and $M_S/M_{\psi }=1.8$ (right). The benchmark model (solid green) features $y_s=y_p={\lambda }_{SH}=1$. The other lines differ from the benchmark only in the value of the coupling shown in the key.

Figure 6

Diagrams leading to the elastic scattering of dark matter particles off nuclei at the one-loop level for the fermion (left panel) and at tree level for the scalar (right panel).

Figure 7

Sample of viable models for $M_{\psi }<M_S$ and $y_p=0$ (scalar portal) projected onto different planes. The different panels show the couplings ${\lambda }_{SH}$ (top left) and $y_s$ (top right), the ratio of dark matter masses (center), and the direct-detection prospects of $\psi$ (bottom left) and $S$ (bottom right). In the bottom panels the lines correspond, from top to bottom, to the current limit from XENON1T, and the expected sensitivities of LZ and DARWIN.

Figure 8

Sample of viable models for $M_{\psi }<M_S$ and $y_s=0$ (pseudoscalar portal) projected onto different planes. The different panels show the couplings ${\lambda }_{SH}$ (top left) and $y_s$ (top right), the ratio of dark matter masses (center), and the direct-detection prospects of $\psi$ (bottom left) and $S$ (bottom right). In the bottom panels the lines correspond, from top to bottom, to the current limit from XENON1T, and the expected sensitivities of LZ and DARWIN.

Figure 9

Sample of viable models for $M_{\psi }<M_S$ projected onto different planes. The different panels show the $\psi$ and $S$ contributions to the dark matter density (top left), the ratio of dark matter masses (top right), and the different couplings (center and bottom panels).

Figure 10

Direct (top) and indirect (bottom) dark matter detection rates for our sample of models in the regime $M_{\psi }<M_S$. In the top panels the lines correspond, from top to bottom, to the current limit from XENON1T, and the expected sensitivities of LZ and DARWIN. In the bottom panel, the lines indicate the Fermi-LAT limit (solid) and the expected sensitivity of CTA (dashed).

Figure 11

Sample of viable models for $M_S<M_{\psi }$ projected onto different planes. The different panels show the $\psi$ and $S$ contributions to the dark matter density (top left), the ratio of dark matter masses (top right), and the allowed ranges of variation for the three couplings (center and bottom panels).

Figure 12

Detection prospects in our sample of viable models for $M_S<M_{\psi }$. The top panels show the direct-detection cross sections for the fermion (left) and scalar (right). From top to bottom, the lines correspond to the current limit from XENON1T and the expected sensitivities of LZ and DARWIN. The bottom panel illustrates the indirect-detection signal due to the process $\psi +\psi \to S+h$. The lines correspond to the Fermi-LAT limit (solid) and the expected sensitivity of CTA (dashed).