Mixed Freeze-In and Freeze-Out Histories and Dark-Sector Decays in a $\mathbb{Z}_4$ Two-Scalar Model

Abstract

We present a systematic non-equilibrium analysis of a renormalisable $\mathbb{Z}_4$ Higgs-portal dark sector comprising a complex scalar $S_A$ and a real scalar $S_B$. In this framework, conversion, semi-annihilation, and (when kinematically allowed) $S_B\to S_A S_A$ decays shape the coupled relic-density evolution. Imposing theoretical consistency, Higgs invisible-decay limits, and the latest LZ spin-independent bound with the standard relic-fraction rescaling, we show that the severe exclusions typical of thermal two-WIMP analyses are largely an artefact of requiring both components to thermalise with the SM bath. Mixed WIMP-FIMP (and fully feeble FIMP-FIMP) histories reopen regions excluded in thermal two-WIMP interpretations, since the total relic density can be shared while the direct-detection signal is carried only by the thermal fraction. For the unstable hierarchy $M_{S_B}>2M_{S_A}$, we identify decay-dominated regimes-SuperWIMP, injection-assisted freeze-out, and sequential freeze-in (``SuperFIMP'')-where late dark-sector injection sets the final $S_A$ abundance. These results establish the $\mathbb{Z}_4$ Higgs-portal model as a controlled benchmark for multi-component dark matter beyond the two-thermal-relic assumption.

Figures (8)

• Figure 1: Key interaction topologies governing production, depletion, and redistribution of the two dark species in the coupled relic-density evolution.
• Figure 2: Parameter space for the FIMP--FIMP regime. Left: Standard freeze-in scaling for $S_A$ in the limit where it dominates the total relic abundance, and its progressive deformation as $S_B$ becomes non-negligible. Right: Correlation between the portal couplings $\lambda_{HA}$ and $\lambda_{HB}$, colour-coded by the fractional abundance. Points near the diagonal correspond to comparable contributions from both components and populate a characteristic curved band in the $(\lambda_{HA},\lambda_{HB})$ plane.
• Figure 3: Direct-detection prospects for the mixed stable scenario with $S_B$ as a WIMP and $S_A$ as a FIMP. All points satisfy the Planck constraint on the total relic abundance, $\Omega_{\rm tot}h^2$. Left: Rescaled spin-independent cross section $\xi_{S_B}\sigma^{\rm SI}_{S_B}$ as a function of the WIMP mass. Gray points are excluded by the current LZ limit (dashed black line), while blue points remain viable. Viable points cluster around the Higgs-resonance region $M_{S_B}\simeq M_h/2$. Right: Fractional contribution of the WIMP component, $\Omega_{S_B}/\Omega_{\rm tot}$, highlighting the dilution of the direct-detection rate by the FIMP component.
• Figure 4: Parameter-space correlations for the stable mixed scenario with $S_A$ as a FIMP and $S_B$ as a WIMP.
• Figure 5: Viable parameter space for the mixed stable scenario with $S_A$ as a WIMP and $S_B$ as a FIMP. Left:$(M_{S_A},\lambda_{HA})$ plane, colour-coded by the WIMP fractional abundance $\Omega_{S_A}/\Omega_{\rm tot}$. Right:$(M_{S_B},\lambda_{HB})$ plane, colour-coded by the FIMP fractional abundance $\Omega_{S_B}/\Omega_{\rm tot}$. Relative to Fig. \ref{['fig:Z4FWS2a']}, stability ($M_{S_B}<2M_{S_A}$) combined with the Higgs-pole clustering of viable points ($M_{S_A}\simeq M_h/2$) confines $S_B$ to $M_{S_B}\lesssim M_h$.