Asymmetric Two-Component Scalar FIMP Dark Matter

Abstract: We propose a two-component asymmetric FIMP (feebly interacting massive particle) dark matter (DM) model in which both DM candidates are real scalar fields. The model is an extension of the Standard Model (SM) by two scalar DM components and a heavy scalar mediator, stabilized by a $\mathbb{Z}<em>2 \times \mathbb{Z}_2&#39;$ symmetry. DM is produced via the freeze-in mechanism through the Higgs portal, while the out-of-equilibrium decay of the heavy mediator generates an asymmetry in the first component, which is partially transferred to the second component via quartic interactions. By solving the Boltzmann equations numerically, we compute the relic density and perform a detailed scan over the parameter space. The observed relic density $Ω</em>{\text{DM}} h² = 0.12 \pm 0.001$ is successfully reproduced for benchmark parameters $m_{φ<em>1}=0.1$~GeV, $m</em>{φ<em>2}=0.5$~GeV, $λ</em>{1H}=7\times10<sup>{-11}$, and $η=0.01$, with the second component contributing only about $5\%$ to the total abundance. We also examine phenomenological constraints. The DM self-interaction cross section lies orders of magnitude below the Bullet cluster bound ($σ/m &lt; 0.47$~cm$<sup>2$/g) and the more stringent double radio relic limit ($σ/m &lt; 0.22$~cm$<sup>2$/g). The invisible Higgs decay branching ratio is $\sim 4\times10<sup>{-19}$, well below the LHC upper limit, and direct detection prospects are negligible due to the small Higgs portal couplings. Our model establishes a novel connection between two-component DM, the freeze-in mechanism, and DM asymmetry.

• The paper introduces an asymmetric two-component scalar FIMP dark matter model that employs freeze-in production to generate the relic density.
• It uses a heavy scalar mediator and soft U(1) breaking to induce a primordial asymmetry, linking dark matter production with CP-violation.
• Numerical Boltzmann analysis demonstrates quadratic sensitivity to portal couplings and linear dependence on asymmetry, consistent with Planck data.

Asymmetric Two-Component Scalar FIMP Dark Matter: Model, Dynamics, and Phenomenology

Model Construction and Theoretical Motivation

This work introduces a scalar FIMP (Feebly Interacting Massive Particle) dark matter (DM) framework incorporating two real singlet scalar fields, $\phi_1$ and $\phi_2$, along with a heavy real scalar mediator $S$, all uncharged under the Standard Model (SM) gauge group and stabilized by a $\mathbb{Z}_2 \times \mathbb{Z}_2'$ symmetry. The symmetry assignment ensures the absolute stability of both DM components, as each is odd under a distinct $\mathbb{Z}_2$ factor, while all SM fields and $S$ remain even.

The model is further endowed with a soft breaking of a global $U(1)$ dark number via a trilinear term $\mu_{12} S \phi_1^2$, enabling the decay of $S$ to produce a primordial asymmetry in $\phi_1$ through CP-violating decays, a characteristic aligning this setup with asymmetric DM scenarios. Quartic scalar couplings facilitate the partial transfer of this asymmetry to $\phi_2$0. Notably, all portal couplings linking the dark and visible sectors are chosen extremely small ($\phi_2$1), ensuring that both DM candidates are produced dominantly via the freeze-in mechanism, never attaining equilibrium with the cosmic plasma.

Freeze-In Production and Boltzmann Analysis

The freeze-in mechanism underpins the relic density generation for both $\phi_2$2 and $\phi_2$3. Production is dominated by decays of the SM Higgs boson $\phi_2$4, given the small DM masses ($\phi_2$5 GeV, $\phi_2$6 GeV) considered in the parameter scan. The portal couplings control the overall production rate, and the characteristic yield from freeze-in scales as $\phi_2$7.

Asymmetric production is implemented via a nonzero initial asymmetry parameter $\phi_2$8, injected at a high initial temperature, and preserved since symmetric processes are negligible due to feeble couplings. The Boltzmann equations tracking both particle and antiparticle yields for each DM component are numerically integrated from an initial temperature ($\phi_2$9 GeV) to the present day, incorporating all source and dilution effects.

Figure 1: Total DM abundance $S$0 as a function of temperature $S$1 for various Higgs portal couplings $S$2. Freeze-in production is Higgs-dominated and controlled by $S$3.

The parametric dependence, as visualized in Figure 1, confirms that the build-up of DM abundance freezes in as the temperature drops below $S$4 GeV, corresponding to the decoupling regime of the parent (Higgs) abundance.

Figure 2: Total DM abundance $S$5 for varying initial asymmetry $S$6. Larger asymmetry results in higher freeze-in yields, manifesting as a linear scaling of final abundance with $S$7.

The impact of $S$8 is transparent: the asymmetric component augments the total DM abundance linearly, thereby providing a tunable mechanism to match the observed relic density for smaller portal couplings.

Relic Density Results and Parameter Dependencies

The numerical scan reveals that the total DM relic density, $S$9, is a sum of individual contributions from $\mathbb{Z}_2 \times \mathbb{Z}_2'$0 and $\mathbb{Z}_2 \times \mathbb{Z}_2'$1, with the first component dominant under the chosen benchmarks. The observed cosmological density, $\mathbb{Z}_2 \times \mathbb{Z}_2'$2 (Planck), can be precisely accommodated for $\mathbb{Z}_2 \times \mathbb{Z}_2'$3 and $\mathbb{Z}_2 \times \mathbb{Z}_2'$4, with $\mathbb{Z}_2 \times \mathbb{Z}_2'$5 contributing only $\mathbb{Z}_2 \times \mathbb{Z}_2'$6.

Figure 3: Relic density $\mathbb{Z}_2 \times \mathbb{Z}_2'$7 as a function of portal coupling $\mathbb{Z}_2 \times \mathbb{Z}_2'$8 for different values of the asymmetry $\mathbb{Z}_2 \times \mathbb{Z}_2'$9. The Planck value is indicated by a gray band.

These results Figure 3 illustrate the quadratic sensitivity of the relic density to portal couplings, and its linear scaling with asymmetry, allowing the model to evade under- and over-production issues across a broad parameter swath.

Figure 4: Relic density $\mathbb{Z}_2$0 as a function of the initial asymmetry parameter $\mathbb{Z}_2$1, for several portal couplings $\mathbb{Z}_2$2. Only a narrow stripe—constrained in both $\mathbb{Z}_2$3 and $\mathbb{Z}_2$4—reproduces the Planck relic density.

Phenomenological Constraints

Self-Interactions

Scalar self-couplings $\mathbb{Z}_2$5 and $\mathbb{Z}_2$6 lead to quartic contact interactions. The model's predicted DM self-interaction cross sections per unit mass are orders of magnitude below observational upper limits from merging clusters. Concretely, for benchmark points even at maximal ($\mathbb{Z}_2$7) perturbative values, $\mathbb{Z}_2$8 cm$\mathbb{Z}_2$9/g, easily satisfying the Bullet Cluster ($S$0 cm$S$1/g) and double radio relic ($S$2 cm$S$3/g) constraints.

Figure 5: Allowed parameter region in the $S$4 plane under self-interaction constraints from the Bullet Cluster and double radio relic observations.

Invisible Higgs Decay and Direct Detection

The Higgs portal-mediated invisible decay widths for $S$5 are exceedingly suppressed, yielding branching ratios $S$6—vastly below experimental sensitivities of ATLAS and CMS. Likewise, DM-nucleon elastic scattering, being proportional to $S$7, is also far below the detection thresholds of current and foreseeable direct detection experiments (LUX-ZEPLIN, XENONnT).

Implications and Outlook

The interplay of asymmetry and multiple FIMP components enables the polymorphic matching of the DM abundance, decoupled from the usual annihilation cross section constraints of thermal WIMPs. The asymmetric double-scalar FIMP scenario here not only conforms to all astrophysical and collider constraints, but also offers a dynamical route to linking DM and baryon asymmetries in the freeze-in paradigm—previously explored primarily in WIMP-ADM settings.

The model's flexibility in accommodating the observed relic abundance, while naturally suppressing dangerous signals in invisible Higgs decay and direct detection channels, represents an essential feature. Given the sub-GeV DM masses, attention to cosmological and astrophysical probes (e.g., structure formation, cosmic microwave background) is warranted in future studies. The framework also motivates further exploration of multi-scalar freeze-in models, transfer mechanisms of asymmetry, and possible connections to baryogenesis.

Conclusion

This two-component asymmetric FIMP model, stabilized by discrete symmetries and producing relic abundance through freeze-in, satisfies the cosmological dark matter density while evading all direct, indirect, and collider constraints. The model’s combination of a heavy asymmetric mediator, rich phenomenology, and decoupling from thermal equilibrium dynamics opens further lines of theoretical investigation, particularly in understanding the linkage between dark and visible sector relics and the signatures of non-thermal multi-scalar dark sectors.