Vector Freeze-In Dark Matter

• Vector freeze-in dark matter is a non-thermal production mechanism where feeble SM interactions set the relic abundance of a hidden vector particle.
• Production occurs via portals such as kinetic mixing, plasmon decay, and Higgs mediation, yielding distinct non-equilibrium phase-space distributions.
• Phenomenology includes suppressed direct detection rates and warm dark matter features, offering targets for cosmological and experimental probes.

Vector freeze-in dark matter refers to a broad class of dark matter (DM) production scenarios in which the relic abundance of a (massive) dark vector particle is set by exceedingly feeble interactions with the Standard Model (SM) bath during the early Universe. Contrasting with thermal freeze-out, where efficient interactions keep DM in equilibrium until decoupling, freeze-in relies on sub-thermal rates such that DM is never equilibrated with the SM plasma. Freeze-in scenarios utilizing vector mediators—often via abelian or non-abelian extensions (e.g., U(1)ₓ or SU(2)_D)—lead to distinctive phenomenology, cosmological signatures, and detection prospects. This production can proceed via several portals (kinetic mixing, Higgs portal, magnetic dipole), with production channels potentially including SM fermion annihilation, vector or scalar decays, and critically, in-medium plasma (plasmon) decays. The freeze-in relic density, phase space, and resulting constraints are sharply sensitive to the identity of the mediator and the detailed microphysical couplings.

1. Vector Freeze-In: Microphysical Framework

The minimal setup for vector freeze-in consists of an extension to the SM with one or more hidden gauge bosons. A classic implementation is a Dirac fermion DM (χ) interacting with a light vector mediator (V) via kinetic mixing with the SM photon or hypercharge, or with a massive Z′. The interaction Lagrangian for abelian models is typically

$$\mathcal{L} \supset g_D\,V_\mu\,\bar\chi\,\gamma^\mu\,\chi + e\,\varepsilon\,V_\mu\,J_{\rm EM}^\mu,$$

where $g_D$ is the dark gauge coupling, $\varepsilon$ is the kinetic mixing parameter, and $Q = \varepsilon\,g_D / e$ is interpreted as the millicharge of χ. The DM mass $m_\chi$ and mediator mass $m_V$ are usually in the keV–GeV range for freeze-in to be cosmologically viable (Dvorkin et al., 2019).

Non-abelian scenarios, such as an SU(2)$_D$ hidden sector spontaneously broken to U(1)$_D$, yield massive vectors ($W'^\pm$) as DM candidates, with small millicharges induced by higher-dimensional kinetic mixing operators (Tran et al., 9 Dec 2025). The phenomenology again depends on the effective millicharge and the hidden gauge coupling.

Alternative portals include the Higgs portal (interaction via scalar mixing) (Duch et al., 2017), magnetic dipole couplings (Krnjaic et al., 2022), or multi-step portals in multi-sector models (Feng et al., 29 May 2024).

2. Freeze-In Production Mechanisms

The freeze-in production of vector dark matter occurs primarily through two types of processes:

• SM fermion annihilation ($f \bar f \rightarrow \chi \bar \chi$ or $W'^+ W'^-$): Mediated by t-channel vector exchange, this channel operates efficiently as long as $T \gtrsim m_f, m_\chi$ and SM topologies and branching ratios determine the rate. In non-abelian setups, both SM–SM and $Z$ decays are relevant (Tran et al., 9 Dec 2025, Bellomo et al., 2022).
• Plasmon (in-medium photon) decay ($\gamma^* \to \chi \bar\chi$): Thermal SM photons acquire an in-medium mass $\omega_p$ and can decay into dark sector pairs when kinematically allowed. The decay rate can dominate freeze-in yields for sub-MeV DM masses, particularly for $m_\chi \lesssim 300$ keV, as found in detailed numerics (Dvorkin et al., 2019, Dvorkin et al., 2020).

For Higgs-portal models, freeze-in proceeds via Higgs boson decays ($h_1 \to XX$) or annihilations of SM Higgses and other SM particles after electroweak symmetry breaking (Duch et al., 2017).

The Boltzmann equation governing DM number density is

$$\frac{dn_\chi}{dt} + 3Hn_\chi = C_{\rm ann}(T) + C_{\rm decay}(T),$$

where each collision term is as above. For vector DM, incorporating all thermal plasma effects, including polarization sums and residues in the photon propagator (Braaten-Segel formalism), is critical for accurate relic density predictions (Dvorkin et al., 2019).

In complex hidden sectors, production may proceed in multiple steps—with an initial freeze-in to an intermediate sector, followed by further freeze-in to a more secluded ("darker") vector sector (Feng et al., 29 May 2024).

3. Relic Abundance, Phase Space, and Analytic Results

The dark matter relic yield is obtained by integrating the production terms: $$Y_\chi = \int_{T_{\rm max}}^{T_{\rm min}} \frac{dT}{s H T} \left[C_{\rm ann}(T) + C_{\rm decay}(T)\right].$$ Key results for the yield in various regimes:

• Annihilation-dominated: $Y_{\rm ann} \sim Q^2\alpha^2 M_{\rm Pl} / m_\chi$ for $m_\chi \gtrsim$ few × 100 keV (Dvorkin et al., 2019).
• Plasmon-dominated: $Y_{\rm decay} \sim 10^{-5} Q^2 (m_\chi/{\rm keV})$ for $m_\chi \lesssim$ few × 100 keV.

The required millicharge $Q$ is set by matching $\Omega_\chi h^2 \approx 0.12$. Representative values: | $m_\chi$ (keV/MeV) | $Q$ (to produce $\Omega_\chi h^2=0.12$) | |--------------------|-----------------------------------------| | 10 keV | $2 \times 10^{-12}$ | | 100 keV | $5 \times 10^{-11}$ | | 1 MeV | $3 \times 10^{-10}$ |

These requirements become more stringent (smaller $Q$) once plasmon decays are included.

The resulting DM phase-space distribution is nonthermal. Plasmon decays that dominate at low mass yield a population with a low-momentum spike, while annihilation produces a Boltzmann-like tail. The effective DM temperature is $T_\chi^{\rm eff}/T_\gamma \sim 0.4-0.7$, much hotter than conventional cold DM. This leads to warm-DM-like suppression of structure on small scales, with free-streaming scales $k_{\rm fs} \sim (m_\chi/{\rm keV})^{-0.8}$ Mpc$^{-1}$ (Dvorkin et al., 2019, Dvorkin et al., 2020).

For non-abelian DM, the yield and relic density scale as $g_D^2 \epsilon^2$, with the requirement $$g_D \epsilon \sim 10^{-14}\sqrt{(m_{W'}/{\rm GeV})(10^{10}\,{\rm GeV}/T_{\rm RH})}$$ to match the observed DM density (Tran et al., 9 Dec 2025).

4. Cosmological and Astrophysical Implications

The nonthermal vector freeze-in population affects cosmology in multiple ways:

• Structure Formation: The semi-relativistic phase-space suppresses power at sub-Mpc scales, leading to cosmological constraints $m_\chi \gtrsim 17$–$22$ keV depending on the detailed phase-space (Planck, Lyman-$\alpha$, MW satellites, stellar streams) (Dvorkin et al., 2020).
• CMB and Baryon Drag: The increased velocity dispersion of freeze-in DM weakens CMB bounds on DM-baryon scattering relative to cold DM (Dvorkin et al., 2019).
• Isocurvature: Freeze-in does not produce additional isocurvature if initial conditions are adiabatic. Any preexisting isocurvature from inflation is only power-law suppressed ($S_{\chi r}\propto x^{-9/4}$), so CMB observations place stringent constraints on primordial isocurvature contributions to freeze-in DM (Bellomo et al., 2022).

Velocity-dependent self-interactions are naturally realized for vector DM coupled via light mediators (e.g., via dark photons in non-abelian sectors or light dark Higgses in Higgs-portal scenarios). These self-interactions can address small-scale structure problems (core-cusp, too-big-to-fail), provided mediator masses are small enough and couplings satisfy bounds from structure, CMB, and indirect detection (Duch et al., 2017, Yin et al., 2023, Feng et al., 29 May 2024).

5. Detection Prospects and Experimental Constraints

Experimental and astrophysical constraints on vector freeze-in DM are governed by the extremely suppressed couplings:

• Direct Detection: The reference cross-section for χ–electron scattering (t-channel vector exchange) is $\sigma_e \propto Q^2 / v^4$. Next-generation sub-GeV experiments (SENSEI, SuperCDMS) approach, but do not yet exclude, the targets for freeze-in vector DM; plasmon decay reduces the expected event rates by an order of magnitude compared to previous estimates (Dvorkin et al., 2019, Dvorkin et al., 2020, Tran et al., 9 Dec 2025).
• Indirect and Stellar Constraints: Stellar cooling, supernovae, and white dwarf bounds restrict $Q \lesssim 10^{-14}$–$10^{-9}$ for $m_\chi \lesssim 10$ keV; the freeze-in preferred region (set by relic abundance) falls below these upper bounds (Dvorkin et al., 2019, Tran et al., 9 Dec 2025).
• CMB, AMS-02, BBN: Annihilation, decay, and self-interaction signatures must not inject excessive energy at late times—constraints from Planck and AMS-02 further restrict parameter space, especially for larger couplings and heavier mediators (Duch et al., 2017, Yin et al., 2023).
• Future Probes: Structure formation (e.g., Lyman-$\alpha$ forest, LSST subhalo counts, HERA 21cm), and proposed direct detection (oscura, superconductors) will probe deeper into the parameter space (Dvorkin et al., 2020, Tran et al., 9 Dec 2025).

6. Advanced Variants and Extensions

Recent work generalizes the vector freeze-in framework:

• Non-Abelian Freeze-In: Hidden SU(2)$_D$ sectors broken to U(1)$_D$ yield stable massive vector pairs with predictive relic densities and distinctive direct-detection prospects. These models are strongly motivated by unified dark gauge dynamics (Tran et al., 9 Dec 2025).
• Multi-Step/Darker Freeze-In: Models with sequential freeze-in into layered hidden sectors (e.g., $SM \to U(1)'_1 \to U(1)'_2$, "darker matter") allow even weaker couplings, accommodate observed relic, enable velocity-dependent self-interactions, and accommodate indirect signals such as the 511 keV line (Feng et al., 29 May 2024).
• Reheaton Scenarios: Nonthermal production of vector mediators (e.g., a $Z'$ reheaton), followed by their decay into DM before reheating completes, links vector freeze-in to inflation and preheating dynamics, and is accessible via stochastic gravitational wave backgrounds (Ghosh et al., 4 Nov 2025).
• Magnetic Dipole Portals: Vector DM coupled via magnetic dipole operators realizes freeze-in with relic $\Omega_{V}h^2 \propto \mu^2 T_{\rm RH}^n$, and yields unique experimental signatures, including loop-suppressed decays to $3\gamma$ and final-state radiation detectable in upcoming $\gamma$-ray observatories (Krnjaic et al., 2022).

These extensions further enrich the phenomenology and testability of the vector freeze-in paradigm.

7. Summary

Vector freeze-in dark matter provides a predictive, UV-robust framework for sub-thermal DM production. For realistic gauge couplings and portal strengths ($Q \sim 10^{-12}$–$10^{-10}$), freeze-in via vector mediators—often dominated by plasmon decay—achieves the observed relic abundance with a strongly nonthermal momentum distribution. This scenario predicts suppressed direct-detection rates, nontrivial small-scale cosmological signatures, and sharp, sometimes complementary experimental tests from direct, indirect, and cosmological probes. Both abelian and non-abelian models are viable, with current and future experiments poised to test essential regions of parameter space (Dvorkin et al., 2019, Tran et al., 9 Dec 2025, Dvorkin et al., 2020, Duch et al., 2017, Krnjaic et al., 2022, Feng et al., 29 May 2024, Ghosh et al., 4 Nov 2025, Bellomo et al., 2022, Yin et al., 2023).