Light Thermal Dark Matter Models

• Light thermal dark matter is a thermal relic candidate with sub-GeV to ∼10 GeV masses, whose cosmic abundance is established by freeze-out annihilations into Standard Model or dark sector particles.
• The topic includes two key frameworks—the family non-universal U(1) (gauged Lμ-Lτ) model and the family universal dark U(1) model—each offering distinct annihilation channels and detection signatures.
• Recent constraints from experiments like DAMIC-M restrict the viable parameter space, emphasizing the significance of resonant enhancement and dark sector self-interactions in addressing astrophysical anomalies.

Light thermal dark matter is defined as a thermal relic dark matter candidate with a mass in the sub-GeV to ∼10 GeV regime whose cosmic abundance is set by standard freeze-out dynamics through annihilations to Standard Model (SM) or dark sector states. Models of this type have attracted extensive theoretical and experimental scrutiny due to their distinctive detection prospects, their ability to address small-scale structure issues, and their potential to remain viable in the face of stringent bounds from laboratory, astrophysical, and cosmological searches. Recent work (Borah et al., 19 Sep 2025) systematically analyzes the viability of two main classes of light thermal dark matter models—the family non-universal U(1) extension (notably the gauged $L_\mu-L_\tau$ model) and the family universal dark U(1)—in direct confrontation with new stringent constraints from the DAMIC-M experiment.

1. Model Classes: Family Non-Universal vs. Universal U(1) Extensions

Two representative frameworks are detailed:

a) Family Non-Universal U(1) (Gauged $L_\mu-L_\tau$) Model

• The SM gauge group is extended by $U(1)_{L_\mu-L_\tau}$, under which only muons, taus, and their corresponding neutrinos carry charge; electrons and quarks are neutral.
• A Dirac fermion singlet $\chi$ (charge $q_\chi=1/2$) serves as the dark matter candidate and communicates with the SM via a new gauge boson $Z_{\mu\tau}$ with coupling $g_{\mu\tau}$.
• The annihilation channel setting the relic abundance is $\chi\bar\chi\to Z_{\mu\tau}^{*}\to f\bar f$, where $f$ is a muon, tau, or their neutrinos. The cross section is resonantly enhanced near $M_{Z_{\mu\tau}}\simeq 2 m_\chi$, which is required for sub-GeV dark matter to yield the observed relic density.
• Direct electron couplings are loop-induced: kinetic mixing with the photon arises at one loop, with $\epsilon_A\simeq -g_{\mu\tau}/70$ for small momentum transfer.
• The model Lagrangian contains $$-\mathcal{L}\supset g_{\mu\tau}Z_{\mu\tau}^\lambda(J^{\mu\tau}_\lambda+q_\chi\bar\chi\gamma_\lambda\chi)$$, where $J^{\mu\tau}_\lambda$ is the SM $\mu-\tau$ current.

b) Family Universal Dark U(1) ($U(1)_X$) Model

• All SM fermions are neutral under $U(1)_X$, which is spontaneously broken. The DM candidate $\chi$ is a Dirac fermion charged under $U(1)_X$, coupling to a dark photon $X^\mu$ with gauge coupling $g_d$ and mass $M_X$.
• The dark photon kinetically mixes with the SM hypercharge gauge boson via a free parameter $\epsilon$, not loop-suppressed.
• The dominant annihilation channel setting the relic is $\chi\bar\chi\to X X$ (into pairs of dark photons), yielding

$$\langle \sigma v\rangle_{\chi\chi\to XX} = \frac{g_d^4}{16\pi m_\chi^2}\sqrt{1-\left(\frac{M_X}{m_\chi}\right)^2}$$

• Because the mediator is light and couples strongly to the dark sector, significant DM self-interactions arise, characterized by a Yukawa potential $V(r)=\pm\frac{\alpha_d}{r}e^{-M_X r}$.

These two constructions typify mechanisms where: (i) the relic is set by resonant annihilation into SM final states via a family non-universal portal, and (ii) dark matter predominantly annihilates into light mediators, producing strong self-interactions.

2. Experimental and Cosmological Constraints: DAMIC-M and Complementarity

Recent results from the DAMIC-M silicon-based detector have set stringent limits on the cross section for DM-electron elastic scattering, particularly for sub-GeV dark matter. In both model classes, compatibility with these bounds depends on suppression mechanisms:

• $L_\mu-L_\tau$: The coupling between DM and electrons is suppressed by the one-loop induced $\epsilon_A\simeq -g_{\mu\tau}/70$, reducing the cross section for DM-electron interactions in the direct detection regime. This allows the model to evade DAMIC-M constraints while attaining the observed relic via resonant enhancement of annihilation.
• $U(1)_X$: The DM-nucleon and DM-electron scattering rate is controlled by the free kinetic mixing parameter $\epsilon$ and can be chosen small enough to satisfy direct detection bounds. The relic density is set by $\chi\bar\chi\to XX$, and the mediator can remain light, evading electron coupling constraints.

Other constraints arise from:

• Accelerator/fixed-target searches: NA64, BABAR, LHCb, and other facilities limit the strength and mass of the $Z_{\mu\tau}$ and $X$ bosons.
• Muon $g-2$: The $L_\mu-L_\tau$ model can partially address the muon $g-2$ anomaly in the $M_{Z_{\mu\tau}}\sim10-200$ MeV region, but the viable parameter space is narrowed by DAMIC-M and related bounds.
• Cosmology: CMB and BBN constraints on additional relativistic degrees of freedom ($\Delta N_\text{eff}$) and late-time s-wave annihilation.
• Indirect detection: CMB constraints are particularly severe for s-wave annihilation channels open at late times, requiring relic freeze-out to occur predominantly through p-wave or forbidden processes, or into invisible (neutrino or dark sector) final states.

3. Self-Interactions and Small-Scale Structure

A central result is that the universal $U(1)_X$ model with light mediator can feature large DM self-interactions:

$$\sigma/m_\chi \sim \mathcal{O}(1~\text{cm}^2/\text{g})$$

for $\alpha_d \sim 0.01$ and $M_X\ll m_\chi$. This helps to address small-scale structure anomalies such as the core-cusp, missing satellites, and too-big-to-fail problems observed in $\Lambda$CDM cosmology.

The transfer cross section is velocity-dependent owing to the lightness of the mediator, naturally suppressing self-interactions at the cluster scale while maintaining sizable effects in dwarf galaxies and halos, consistent with astrophysical constraints (Borah et al., 19 Sep 2025). In the $L_\mu-L_\tau$ model, dark matter self-interactions are not significant due to the heavier, less strongly coupled $Z_{\mu\tau}$.

4. Detection Prospects and Remaining Parameter Space

After assimilating the new DAMIC-M and previous direct detection results, the remaining viable parameter space is considerably narrowed but not excluded:

• $L_\mu-L_\tau$: Viability is confined to a narrow resonance region with $m_\chi\simeq M_{Z_{\mu\tau}}/2$ and $g_{\mu\tau}\lesssim10^{-3}$. Planned and ongoing muon beam fixed-target experiments (NA64-μ, SHiP), improved rare meson searches, and upgraded direct detection experiments will further probe or close this window.
• $U(1)_X$: The parameter space is still open for small enough $\epsilon$ and $M_X\lesssim$ few MeV, as large self-interactions suppress electron recoil signals below current experiment thresholds. Next-generation low-threshold detectors, future beam dump experiments, and cosmological probes (including CMB and $N_\text{eff}$ measurements) are poised to test the remaining allowed regions.

Model	Relic Annihilation Channel	Direct Detection Coupling	Astrophysical Impact
$L_\mu-L_\tau$	$$\chi\bar\chi\to Z_{\mu\tau}^{*}\to \nu_\mu,\nu_\tau, \mu, \tau$$	loop-suppressed via $\epsilon_A$	minimal self-interaction
Universal $U(1)_X$	$\chi\bar\chi \to XX$	controlled by $\epsilon$	strong, velocity-dependent self-int.

The ongoing interplay between relic abundance, direct detection, indirect constraints, and cosmological signatures outlines a multifaceted search strategy for both model classes.

5. Implications for Light Thermal Dark Matter Model Building

The synthesis of new experimental bounds—particularly those from DAMIC-M—reinforces several general lessons for viable light thermal dark matter:

• Resonant Enhancement: In family non-universal scenarios, only a narrow resonance region can yield observed relics without violating direct/indirect constraints.
• Decoupling Relic and Direct Detection: The $U(1)_X$ framework illustrates that if the relic is set via annihilation to light mediators, constraints from electron/nucleon scattering can be largely decoupled from the relic calculation, as the two couplings ($g_d$ and $\epsilon$) are independent.
• Self-interaction as a Required Feature: Strong, velocity-dependent self-interactions—arising naturally for light mediators—provide not only a phenomenologically viable region still consistent with data but may also help address core astrophysical issues in $\Lambda$CDM.
• Experimental Probes Remain Powerful: The remaining allowed parameter space in both classes is highly testable: through direct detection (lower thresholds and larger exposures), accelerator searches, cosmological and astrophysical observations (e.g., CMB-S4, indirect gamma/X-ray line searches), and improved studies of small-scale structure.

6. Summary and Outlook

The current landscape for sub-GeV thermal relic dark matter models, as rigorously examined with the latest DAMIC-M constraints (Borah et al., 19 Sep 2025), is characterized by a sharp reduction in viable parameter space, yet both the family non-universal ($L_\mu-L_\tau$) and universal ($U(1)_X$) scenarios retain windows that satisfy all existing laboratory, astrophysical, and cosmological limits. The $L_\mu-L_\tau$ case is cornered into a narrow resonance region for annihilation, while $U(1)_X$ models with substantial dark sector self-interactions remain open even with extreme bounds on DM-electron scattering. The next generation of low-mass dark matter direct detection, rare process searches, and cosmological measurements—all anticipated within this decade—will provide decisive tests of these scenarios, making light thermal dark matter a robust and highly constrained area of ongoing research.