FIMPs in a two-component dark matter model with $Z_2 \times Z_4$ symmetry

TL;DR

This work investigates a two-component dark matter framework stabilized by $Z_2 \times Z_4$ symmetry, featuring a feebly interacting singlet scalar $S$ and a Majorana fermion $χ$ with mass generated after spontaneous symmetry breaking via a second singlet $S_0$. In the decoupling limit, the relic densities of both components arise through Freeze-in, and the authors solve the associated Boltzmann equations to map viable regions of the six-parameter space $(m_{χ}, m_S, m_2, y_{sf}, λ_{ds}, λ_{dh})$ that reproduce the Planck relic density. They find that the scenario remains viable over wide ranges of masses and couplings, including $λ_{ds}$ as small as $O(10^{-20})$, with the heavy Higgs $h_2$ often dominating DM production. The results underscore the robustness of FIMPs in multi-component DM models and point to distinctive Higgs-portal signatures for future exploration.

Abstract

We consider the FIMPs scenario in a two-component dark matter model with $Z_2 \times Z_4$ symmetry, where a singlet scalar $S$ and a Majorana fermion $χ$ 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. The model admits six free parameters in the decoupling limit: three masses and three dimensionless parameters. Depending on the mass hierarchies between dark matter particles with half of the new Higgs mass, the DM relic density will be determined by different channels, where $χ$ and $S$ production can be generated individually. We numerically study the relic density as a function of the model's free parameters and determine the regions consistent with the dark matter constraint for four possible cases. Our results show that this scenario is viable over a wide range of couplings and dark matter masses, where the coupling $λ_{ds}$ can be as tiny as $\mathcal{O}(10^{-20})$ level. We stress that even for such tiny couplings, the new Higgs can still play a dominant role in determining dark matter production.

Figures (10)

• Figure 1: Evolution of $\Omega_{\chi}h^2$ (left) and $\Omega_Sh^2$ (right) with $m_{\chi}$, where we have fixed $\lambda_{dh}=10^{-10},\lambda_{ds}=10^{-10},m_S= 400$ GeV. The different colored lines represent $y_{sf}$ taking different values and the solid (dashed) lines correspond to the results of $m_2=1$ TeV ($m_2=2$ TeV) respectively.
• Figure 2: Evolution of $\Omega_Sh^2$ with $m_S$, where we fixed $y_{sf}=10^{-11}$. In Fig. \ref{['fig2']}(a), we set $\lambda_{dh}=10^{-11}$ and $m_{\chi}=100$ GeV, while lines with different colors represent $\lambda_{ds}$ taking different values. The solid lines are results of $m_2=1$ TeV while the dashed lines are $m_2=2$ TeV. In Fig. \ref{['fig2']}(b), we fix $\lambda_{ds}=10^{-11}$ and vary $\lambda_{dh}$ ranging from $[10^{-20},10^{-8}]$ while other parameter are same with the Fig. \ref{['fig2']}(a), and the lines with different colors correspond to $\lambda_{dh}$ taking different values. In Fig. \ref{['fig2']}(c), we fix $\lambda_{ds}=10^{-11}$ and vary $m_{\chi}$ ranging from $[1 \mathrm{GeV},1000\mathrm{GeV}]$ while other parameter are same with the Fig. \ref{['fig2']}(a), and the lines with different colors correspond to $m_{\chi}$ taking different values.
• Figure 3: Evolution of $\Omega_{\chi}h^2$ with $m_{\chi}$ by setting $y_{sf}=2.5 \times 10^{-6}$, where the black dashed line corresponds to the observed DM relic density.
• Figure 4: Evolution of $\Omega_Sh^2$ with $m_S$ by fixing $\lambda_{dh}=10^{-14}$ and $m_2=1$ TeV, where in the left figure we set $y_{sf}=2.5 \times 10^{-6}$ as well as $m_{\chi}=501$ GeV and we fix $y_{sf}=10^{-11}$ and $m_{\chi}=1$ GeV in the right figure. The black dashed lines represent the current observed DM relic density of $\Omega h^2=0.12$ and other colored lines correspond to the results of $\lambda_{ds}$ taking different values.
• Figure 5: Same as Fig. \ref{['fig4']} but $m_2=2$ TeV.