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

TL;DR

This paper analyzes a $ ext{Z}_4$ symmetric two-scalar dark sector model, revealing that mixed freeze-in and freeze-out histories can evade traditional thermal relic constraints, offering new multi-component dark matter scenarios.

Contribution

It introduces a systematic non-equilibrium analysis of a $ ext{Z}_4$ Higgs-portal model, highlighting novel dark matter relic-density evolution regimes and relaxing thermal relic constraints.

Findings

Mixed WIMP-FIMP histories reopen excluded parameter regions.

Late dark-sector injection can dominate the final relic abundance.

The model serves as a benchmark for multi-component dark matter beyond thermal relics.

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.