Fermionic Dark Matter Candidate

• Fermionic dark matter is defined as stable or long-lived fermions that interact weakly or feebly via portals like the Higgs or gauge bosons.
• Key production mechanisms include thermal freeze-out, freeze-in, and gravitational production, all tuned to achieve the observed relic density.
• Experimental probes—from direct detection to collider and astrophysical observations—constrain fermionic dark matter across a wide mass range, from keV to TeV scales.

A fermionic dark matter candidate is a hypothetical, stable or cosmologically long-lived fermion—typically a neutral, weakly or feebly interacting particle—that constitutes all or part of the observed cold, warm, or even ultralight dark matter in the Universe. Theoretical realization of such candidates spans simple extensions of the Standard Model (SM), frameworks motivated by neutrino masses, portal interactions, non-Abelian sectors, and even models invoking gravitational production during cosmic inflation. Research on arXiv over the last decade has mapped out the landscape of viable masses, production mechanisms, cosmological constraints, and detection prospects for a wide range of such candidates.

1. Field-Theoretic Frameworks for Fermionic Dark Matter

Fermionic dark matter candidates emerge in a broad variety of theoretical setups. A minimal possibility is a gauge-singlet fermion stabilized by a global U(1), Z₂, or by remnant discrete symmetries following the spontaneous breaking of a larger gauge group. These singlet fermions may couple to the SM via a scalar or vector portal, or via higher-dimensional effective operators:

• Higgs-portal models: Gauge-singlet Dirac or Majorana fermions, coupling to the SM Higgs doublet or a singlet scalar mediator. Models may include renormalizable Yukawa couplings (e.g., $g_s S \bar\psi\psi$) or dimension-5 operators such as $(1/\Lambda) H^\dagger H \bar \chi \chi$, as in singlet/2HDM extensions (Fairbairn et al., 2013, Banik et al., 2013, Kim et al., 2018).
• Gauge-portal models: Extensions with new gauge groups (e.g., $U(1)_X$, $U(1)_{B-L}$, $U(1)_B$, $SU(2)_H$) yield Dirac fermion DM coupling to new $Z'$ or dark-gauge bosons, as in “dark $Z$” (Jung et al., 2020) or $SU(2)_H$ models (Banik et al., 2015), or with singlet–doublet mixing in baryon number gauge models (Taramati et al., 22 Aug 2024).
• Neutrino-mass-motivated models: Seesaw, scotogenic, or left–right symmetric models supply new SM-singlet or triplet fermions stabilized by Z₂ parities; examples include scotogenic (Singirala, 2016, Chun et al., 2023), dynamical scotogenic (Chun et al., 2023), type-III seesaw (Chaudhuri et al., 2015), and left–right frameworks (Ma, 2012).
• Hidden sector and non-Abelian models: Minimal $SU(2)$ with one fundamental fermion can yield a stable vector or pseudoscalar composite DM via gauge symmetry and accidental global symmetries (Francis et al., 2016).
• Effective Field Theory (EFT): A SM-singlet fermion coupled to SM currents via dimension-6 four-fermion vector or scalar operators is analyzed independently of mediators' UV completion (Kuday et al., 2023).
• Superconducting DM & inflationary production: Models relate DM to SM neutrino condensates or to fermions generated via vacuum gravitational effects in the early Universe (Alexander et al., 14 May 2024, Belfiglio et al., 5 Apr 2025).

2. Production Mechanisms in the Early Universe

Fermionic candidates may attain their present-day relic abundance by several cosmologically distinct processes, each highly sensitive to coupling strength and mass:

• Thermal Freeze-Out (WIMPs): A weak-scale DM fermion maintains equilibrium with the SM via portal interactions, freezing out when interaction rates drop below expansion. The canonical value $\Omega_{\chi}h^2 \simeq 0.12$ is achieved for $\langle\sigma v\rangle \simeq 3 \times 10^{-26}$ cm³/s (Fairbairn et al., 2013, Chao et al., 2015, Bellazzini et al., 2011, Kuday et al., 2023). Examples: singlet-fermion Higgs portal, singlet-doublet mixing (Taramati et al., 22 Aug 2024), triplet dark fermion (Bélanger et al., 2022).
• Freeze-In (FIMPs): The DM fermion interacts so feebly (Yukawa couplings $\lesssim 10^{-12}$) that it never equilibrates; its population is built up from decays or scatterings of thermal bath particles, as in thermal leptogenesis, or with late decaying next-to-lightest states ("superWIMP" scenario) (Bélanger et al., 2022).
• Asymmetric or nonthermal production: In left–right and $U(1)_{B-L}$ models, cosmic asymmetries or decays of heavy scalars/gauge bosons preferentially generate DM over anti-DM; in sub-keV degenerate Fermi gas models, non-thermal “two-step” freeze-in via heavy mediator decays set the abundance and velocity distribution (Choi et al., 2020).
• Inflationary gravitational production: A minimally coupled Dirac fermion (“spectator” field) can be created solely by quantum fluctuations in the perturbed metric during inflation, a process sensitive to the inflationary Hubble rate $H_I$ and the fermion mass $m$ (Belfiglio et al., 5 Apr 2025).

Model	Mass Range Allowed (GeV)	Production Channel
Higgs portal singlet	50–1000	freeze-out
Baryon gauge singlet/doublet	200–800	$Z_B$ resonance
Nonperturbative inflation GPP	$>10^8$	vacuum production
Perturbative geometric GPP	$10^5$–$10^7$	metric-perturbation
Scotogenic (vanilla)	100–2000	freeze-out, FIMP
Warm DM, keV–MeV scale	$10^{-4}$–10	asymmetric, freeze-in

3. Cosmological and Phenomenological Constraints

Fermionic dark matter models are tightly constrained by a range of cosmological, astrophysical, and experimental results:

• Cosmological bounds: Hot or warm fermionic DM ($m_{\chi}<\text{few keV}$) is limited by Lyman-alpha forest data (free-streaming), cosmic microwave background (CMB) isocurvature, and $\Delta N_{\rm eff}$ at BBN and CMB eras. Models with purely gravitational production for $m\sim10^5$–$10^7$ GeV naturally evade isocurvature via blue-tilted spectra (Belfiglio et al., 5 Apr 2025). Sub-keV models must ensure non-thermal (cold) velocity distributions at matter–radiation equality and avoid excess $\Delta N_{\rm eff}$ (Choi et al., 2020).
• Indirect detection: Thermal WIMP-scale candidates are constrained by limits on $\langle\sigma v\rangle$ from $\gamma$-ray, positron, and antiproton searches (Fermi-LAT, AMS-02, CMB). The dominant annihilation channels are typically to $b\bar b$, $WW$, or leptons; $p$-wave or CP-odd couplings can suppress present-era signals (Ghorbani, 2014, Bellazzini et al., 2011, Kuday et al., 2023).
• Direct detection: Spin-independent scattering through Higgs or $Z'$ mediators yields nucleon cross sections highly sensitive to mixing angles, portal couplings, and Majorana/Dirac nature. Next-generation detectors (LZ, XENONnT, DARWIN) probe down to $\sigma_{SI}\sim10^{-47}$–$10^{-48}$ cm² (Kim et al., 2018, Taramati et al., 22 Aug 2024). Pseudoscalar, $p$-wave, or majoron-portal DM may evade present bounds.
• BBN and CMB: Late-decaying next-to-lightest odd particles (NLOP) can dissociate light nuclei or contribute to $\Delta N_{\rm eff}$. Big Bang Nucleosynthesis imposes bounds on visible energy injection (Bélanger et al., 2022, Chun et al., 2023).

4. Predictive Features and Mass Ranges

The viable mass window for fermionic dark matter candidates is highly model-dependent:

• Ultralight and “superfluid” states: In the superconducting fluid scenario, DM is modeled as the Higgs-mode collective excitation of a neutrino or vector-like quark condensate. For natural right-handed neutrino Yukawa couplings and chemical potentials, $m_{DM}\sim10^{-19}\ \mathrm{eV}$ is realized; for vector-like quark condensates, the mass range is more flexible, scaling with the chemical potential (Alexander et al., 14 May 2024). Such DM behaves like cold DM on large scales but modifies the early-universe expansion history, potentially addressing the $H_0$ tension.
• keV–MeV “warm” regime: Models motivated by anomalies in small-scale structure (core–cusp, too-big-to-fail) propose non-thermally produced, sub-keV—few keV degenerate fermions as DM (Choi et al., 2020, Ma, 2012). The core radius in dwarf galaxies is a direct function of the DM mass, phase space density, and velocity dispersion.
• Intermediate (10 GeV–10’s TeV): WIMP-like scenarios, including singlet–doublet mixing, type-III/II seesaw, scotogenic, and non-Abelian composite models typically require masses set by portal-mixing suppression and tight couplings to relic density and direct detection. The singlet–doublet scenario in gauged baryon symmetry, for example, permits $m_{DM}\sim200$–800 GeV with optimal mixing (Taramati et al., 22 Aug 2024).
• Superheavy (“WIMPzilla”) and purely gravitational: Nonperturbative gravitational particle production (GPP) of fermions during inflation allows $m\gtrsim10^8$ GeV, but metric perturbations (perturbative “geometric” GPP) open a viable window $10^5$–$10^7$ GeV in realistic slow-roll models, closing a gap not covered by prior estimates (Belfiglio et al., 5 Apr 2025).

5. Connections to Beyond-Standard Model Physics

Fermionic dark matter models are often motivated by or tightly constrained due to their links to other open problems in particle physics and cosmology:

• Neutrino mass generation and leptogenesis: Most models introducing SM-singlet or triplet fermions explain small active neutrino masses via seesaw or loop-induced diagrams, and can accommodate thermal leptogenesis by extending the content to right-handed neutrinos (Singirala, 2016, Chun et al., 2023, Ma, 2012, Choi et al., 2020).
• Baryogenesis and phase transitions: Models with a strongly first-order electroweak phase transition and additional fermion–Higgs interactions can simultaneously account for DM and the origin of the baryon asymmetry, subject to limits from electric dipole moments (EDMs) (Chao et al., 2015, Fairbairn et al., 2013).
• Dark sector gauge structures and discrete symmetries: Hidden-sector gauge forces (e.g., $SU(2)_H$, $U(1)_B$) naturally explain DM stability, suppress dangerous decays, and can have distinctive collider and cosmological signals, including gravitational waves from a first-order phase transition (Banik et al., 2015, Taramati et al., 22 Aug 2024).

6. Experimental Probes and Future Prospects

A broad and complementary array of experiments can test fermionic dark matter frameworks:

• Direct detection: Upcoming experiments will probe parameter space corresponding to portal couplings and mixing angles in the singlet, two-Higgs-doublet, Majorana, and singlet–doublet models down to $\sigma_{SI}\sim10^{-48}$ cm² (Kim et al., 2018, Taramati et al., 22 Aug 2024).
• Collider searches: Signatures include mono-jet and mono-Higgs signals, long-lived particle (LLP) decays (e.g., at MATHUSLA), and changes to Higgs invisible branching ratios. Disappearing track signatures are expected for WIMP-like electroweak triplets (Ghorbani et al., 2016, Bélanger et al., 2022).
• Indirect detection: $\gamma$-ray searches from dwarf spheroidals, the Galactic Center, and cosmic ray antimatter provide stringent constraints on $s$-wave WIMP annihilation channels for GeV–TeV masses, but suppressed or forbidden $s$-waves allow many models to evade current limits (Ghorbani, 2014, Kuday et al., 2023).
• Cosmological/astrophysical: Measurements of the power spectrum from the Lyman-α forest, CMB anisotropies, and small-scale structure formation are crucial in constraining and distinguishing keV–MeV fermion DM (Choi et al., 2020, Ma, 2012).
• Gravitational waves: Models predicting a strongly first-order symmetry-breaking phase transition (e.g., in $U(1)_B$) are testable with future GW observatories like LISA and BBO (Taramati et al., 22 Aug 2024).

7. Outlook and Open Directions

Fermionic dark matter candidates remain at the frontier of both theoretical particle physics and phenomenology. The ongoing refinement of cosmological data, improvements in detection sensitivity, and dedicated collider searches continue to carve out and constrain their viable parameter space. Purely gravitationally produced fermions, non-thermal warm DM, and composite states constitute especially compelling directions given their minimal couplings and resilience against traditional detection strategies. Their interplay with solutions to neutrino masses, baryogenesis, and the structure-formation problems underscores their central role in a coherent picture of physics beyond the Standard Model (Belfiglio et al., 5 Apr 2025, Choi et al., 2020, Alexander et al., 14 May 2024, Chao et al., 2015).