Two-Component Dark Matter in the Type-I 2HDM

Abstract: We investigate a two-component dark matter scenario in the type-I two-Higgs-doublet model. The dark sector contains a real scalar $s$ and a Dirac fermion $χ$, whose stability is ensured by a $Z_4$ symmetry together with kinematic conditions. The scalar interacts with the visible sector through Higgs-portal couplings, while the fermion interacts with the scalar via Yukawa interactions. In this framework, we analyze the thermal freeze-out production of both candidates, accounting for annihilation, conversion, and semi-annihilation processes. A comprehensive scan over the multidimensional parameter space is performed in terms of physical masses, mixing angles, and portal couplings, imposing theoretical requirements such as perturbativity and vacuum stability. We confront the model with current experimental constraints, including the observed relic abundance, invisible Higgs decays, direct detection limits on spin-independent scattering cross sections, and electroweak precision observables. We find that viable regions of parameter space can satisfy all dark matter constraints, but collider bounds strongly constrain the scalar sector, narrowing the allowed regions and creating tension with those favored by dark matter phenomenology, particularly in the sub-TeV mass regime.

• The paper demonstrates that a Z4-stabilized scalar singlet and vector-like fermion can jointly reproduce the observed relic abundance through semi-annihilation, conversion, and Higgs-portal annihilation.
• The model’s viable parameter space satisfies relic-density, invisible-Higgs, direct-detection, and electroweak constraints, with semi-annihilation dominant below roughly 700 GeV and scalar abundance fractions reaching 10–100% in selected regimes.
• Collider, flavor, and precision constraints strongly compress the sub-TeV parameter space, creating tension between dark-matter-favored freeze-out solutions and the extended Higgs-sector masses required by current searches.

This paper by Escalona, Neto, Neves, Ramos, and Suarez (2603.18158) studies a two-component dark matter (DM) scenario built on a CP-conserving type-I two-Higgs-doublet model (2HDM). The dark sector consists of a real scalar singlet $s$ and a vector-like Dirac fermion $\chi$, both stabilized by a $Z_4$ symmetry supplemented with the kinematic condition $m_s < 2m_\chi$. The scalar couples to the visible sector through Higgs-portal interactions with both CP-even states $h$ and $H$, while the fermion couples only to the scalar via Yukawa couplings. The central result is that viable parameter space exists that reproduces the observed relic abundance while satisfying invisible Higgs decay, direct detection, and electroweak precision constraints — but collider bounds on the extended scalar sector create substantial tension with the regions favored by DM phenomenology, particularly below the TeV scale.

Model structure and theoretical consistency

The model extends the type-I 2HDM potential with a $Z_2^{\text{2HDM-I}}$ symmetry (which suppresses flavor-changing neutral currents, following the Glashow–Weinberg–Paschos theorem) and a $Z_4^{\text{DM}}$ under which $s \to -s$ and $\chi \to i\chi$. The soft-breaking term $\chi$0 avoids the domain wall problem. After EWSB, the spectrum contains two CP-even scalars ($\chi$1, $\chi$2), one physical pseudoscalar $\chi$3, one charged pair $\chi$4, plus the inert singlet $\chi$5 and fermion $\chi$6. The analysis is performed in the exact alignment limit, in either regime: heavy partner ($\chi$7 GeV) or light partner ($\chi$8 GeV). Two effective portal couplings, $\chi$9 and $Z_4$0-analogous $Z_4$1, mediate all interactions of $Z_4$2 with the SM; $Z_4$3 has no direct coupling to visible-sector fields.

The scan is performed over a twelve-dimensional input basis of physical masses, mixing angles ($Z_4$4, $Z_4$5), portals $Z_4$6, and Weyl-decomposed Yukawa couplings $Z_4$7, $Z_4$8. Perturbativity is imposed at $Z_4$9, together with copositivity-type vacuum stability conditions on the full three-field potential.

Dark matter production mechanisms

The thermal history depends sharply on the size of the portals and Yukawa couplings. For portals below roughly $m_s < 2m_\chi$0, the dark sector never equilibrates and freeze-in or dark freeze-out applies; for Yukawa couplings above roughly $m_s < 2m_\chi$1, both candidates thermalize and standard freeze-out governs their abundances. The paper focuses on the latter regime with $m_s < 2m_\chi$2, where the coupled Boltzmann equations must include three classes of processes beyond ordinary annihilation:

• Semi-annihilation: $m_s < 2m_\chi$3 and $m_s < 2m_\chi$4-type channels, enabled by the $m_s < 2m_\chi$5 charge assignment;
• Conversion: $m_s < 2m_\chi$6 processes that redistribute abundance between components;
• Annihilation: $m_s < 2m_\chi$7 through both Higgs portals into SM and additional 2HDM final states.

The resulting phenomenology is richer than in the analogous SM-singlet extension (Yaguna et al., 2021). In the $m_s < 2m_\chi$8 regime, points with a light Higgs partner can exhibit "bouncing" behavior — an exponential growth of the scalar yield before freeze-out driven by the semi-annihilation $m_s < 2m_\chi$9. Notably, the light-partner regime admits viable points in mass-ratio regions excluded in the single-Higgs-portal setup, and the second portal raises the achievable scalar relic fraction by approximately one order of magnitude relative to prior work.

Constraints and numerical results

The scan imposes the Planck relic density window $h$0, invisible Higgs branching ratio $h$1, spin-independent direct detection limits from XENONnT and LZ (with projected DARWIN sensitivity), and the Peskin–Takeuchi oblique parameters from a global electroweak fit. Direct-detection cross sections are rescaled by fractional abundance; the scalar scatters at tree level while the fermion scatters only at one loop through the $h$2-$h$3 portal combination.

Several quantitative findings stand out. In the $h$4 regime, the fermion fraction can be as small as $h$5 for $h$6 GeV, rising to $h$7 at $h$8 TeV, so the scalar dominates almost everywhere. In the opposite hierarchy, the scalar fraction typically lies between $h$9 and $H$0, but points with a light Higgs portal can reach 10–100% scalar abundance. Semi-annihilation dominates DM production for $H$1 GeV unless near-degeneracy ($H$2) makes conversion and annihilation dominant instead.

The constraint interplay is decisive. Invisible Higgs decays exclude essentially all viable points with $H$3 and a heavy Higgs partner. Direct detection most severely constrains the light-partner regime and the $H$4 case (where the scalar lacks abundance suppression); the most resilient configuration is $H$5 with a heavy Higgs partner. Electroweak precision tests force approximate degeneracy among the extra scalar states, which drastically shrinks the surviving sample. Four benchmark points spanning all four regimes (light/heavy partner crossed with lighter/heavier scalar) survive all DM-level constraints, with masses ranging from sub-GeV pseudoscalars to nearly TeV-scale fermions.

Collider tension

The dominant collider constraints come not from missing-energy searches — which have limited sensitivity at these DM masses — but from direct searches for the extended scalar sector. Flavor physics excludes charged Higgs masses up to about 900 GeV for $H$6, ruling out benchmarks III and IV. LEP excludes $H$7 GeV and requires $H$8 GeV. Full Run-2 LHC searches in $H$9, $Z_2^{\text{2HDM-I}}$0, $Z_2^{\text{2HDM-I}}$1, $Z_2^{\text{2HDM-I}}$2, $Z_2^{\text{2HDM-I}}$3, $Z_2^{\text{2HDM-I}}$4, and resonant $Z_2^{\text{2HDM-I}}$5 channels collectively make a fully light sub-TeV scalar spectrum difficult to accommodate unless parameters sit close to alignment with approximate mass degeneracies closing cascade channels, or production rates are Yukawa-suppressed. This creates the paper's central tension: the sub-TeV region preferred by WIMP-like freeze-out is precisely where collider bounds bite hardest.

Escaping to heavier scalar spectra relaxes collider and direct-detection pressure, but maintaining a 125 GeV SM-like Higgs then demands increasingly large quartic couplings, driving the model toward perturbativity breakdown or fine-tuning. The authors conclude that the sub-TeV region remains the most natural regime, under significant pressure from current data.

Limitations and open questions

The analysis carries several stated caveats. It assumes exact (rather than approximate) alignment and a standard radiation-dominated thermal history with freeze-out production; non-standard cosmologies or alternative production mechanisms could reopen excluded regions. The exclusion logic applies individual experimental bounds sequentially rather than through a combined likelihood, which the authors note overstates the stringency of intersecting constraints. Collider sensitivity is assessed qualitatively against published searches rather than through a dedicated recasting of the benchmark points. The self-coupling $Z_2^{\text{2HDM-I}}$6, relevant for structure formation and Bullet Cluster constraints, is set aside as phenomenologically irrelevant for the relic density. Finally, alternative 2HDM Yukawa types (II, X, F) could modify both DM phenomenology and some collider bounds, though electroweak precision and perturbativity constraints would persist; whether such variants substantially enlarge the viable space remains untested here.

Conclusion

The paper demonstrates that a $Z_2^{\text{2HDM-I}}$7-stabilized scalar-plus-fermion two-component DM sector embedded in the type-I 2HDM supports a rich freeze-out dynamics involving semi-annihilation, conversion, and dual Higgs portals, including bouncing solutions absent from single-portal models. All cosmological and astrophysical constraints can be satisfied simultaneously across four distinct mass-hierarchy regimes. However, the combined weight of electroweak precision observables, flavor physics, and Run-2 Higgs-sector searches compresses the viable parameter space severely, leaving the sub-TeV model either highly constrained or dependent on fine-tuning. The framework's ultimate viability hinges on questions this work leaves open: whether a combined statistical treatment softens the apparent exclusions, and whether non-standard thermal histories or alternative Yukawa structures can reconcile the DM-favored and collider-allowed regions.