Scalar-Mediated SIDM Models

• Scalar-mediated SIDM models are frameworks where a light scalar mediator enables dark matter to self-interact with a strong velocity dependence, addressing small-scale structure anomalies.
• The models feature distinct scattering regimes—Born, classical, and resonant—that tune the momentum-transfer cross section to match observations from dwarf galaxies to clusters.
• They link cosmological relic abundance, laboratory detection, and astrophysical signatures through precise mediator properties, offering testable predictions for dark matter experiments.

Scalar-mediated Self-Interacting Dark Matter (SIDM) models constitute a theoretically robust and phenomenologically rich class of extensions to standard cold dark matter, wherein the dominant dark matter component acquires sizable, velocity-dependent self-interactions via the exchange of a light scalar mediator. These models are motivated by the small-scale structure anomalies of $\Lambda$CDM cosmology—namely, the core–cusp, missing satellites, and too-big-to-fail problems—while preserving consistency with large-scale structure, cosmic microwave background (CMB), and collider constraints. Scalar mediators in the MeV–GeV range yield the required transfer cross sections and allow for predictive links to both laboratory and astrophysical observations (Kaplinghat et al., 2013, Wang, 22 Dec 2025, Kao et al., 2020, Jia, 2019).

1. Theoretical Structure and Scalar-Mediated Yukawa Potential

Scalar-mediated SIDM scenarios extend the Standard Model with at least one real or complex scalar field $\phi$ (the mediator), which couples to dark matter particles $\chi$ through a Yukawa-type interaction of the form

$V(r) = \pm\,\frac{\alpha_\chi}{r}\,e^{-m_\phi r}$

where $\alpha_\chi = g_\chi^2/(4\pi)$ is the dark fine-structure constant, $m_\chi$ and $m_\phi$ are the dark matter and mediator masses, and the sign depends on the DM sector symmetry (attractive $\chi\bar\chi$ or repulsive $\chi\chi$) (Kaplinghat et al., 2013).

The class of models includes:

• Simple singlet-fermion or singlet-scalar extensions (Kainulainen et al., 2015, Bernal et al., 2018),
• Models with additional leptonic or neutrinophilic interactions (Kao et al., 2020, Rajaraman et al., 2018),
• Pseudo-Dirac or inelastic dark matter (Wang, 22 Dec 2025),
• Extended Higgs sectors (e.g. NMSSM, 3-3-1) where the mediator emerges naturally (Li et al., 2021, Lan et al., 2020),
• Stabilizing discrete symmetries ($\mathbb Z_2, Z_4$ etc.) to ensure mediator or DM stability (Duch et al., 2019),
• Higgs portal couplings enabling direct detection and cosmological decay channels (Xu et al., 28 Oct 2024, Jia, 2019, Dutta, 2023).

The effective coupling to Standard Model states (quarks, leptons, or neutrinos) controls both mediator decay properties and the viability of detection through terrestrial, astrophysical, and cosmological signatures.

2. Transfer Cross Section, Velocity Dependence, and Scattering Regimes

Self-interacting dark matter phenomenology is governed by the momentum-transfer (or viscosity) cross section,

$$\sigma_T = \int d\Omega\,(1-\cos\theta)\,\frac{d\sigma}{d\Omega}$$

which encapsulates the thermalization efficiency per halo. Its behavior sharply depends on the relation between $\alpha_\chi$, $m_\chi$, and $m_\phi$, and the typical relative velocities $v$ of the system (Kaplinghat et al., 2013, Jia, 2019, Rajaraman et al., 2018, Li et al., 2021):

• Born (perturbative) regime: $\alpha_\chi m_\chi / m_\phi \ll 1$,

$$\sigma_T^{\text{Born}} = \frac{8\pi \alpha_\chi^2}{m_\chi^2 v^4}\left[\ln\left(1+\frac{m_\chi^2 v^2}{m_\phi^2}\right) - \frac{m_\chi^2 v^2}{m_\phi^2 + m_\chi^2 v^2}\right]$$

• Classical regime: $\alpha_\chi m_\chi / m_\phi \gtrsim 1$ and $m_\chi v / m_\phi \gg 1$, the cross section is typically parameterized using a function of $\beta = 2\alpha_\chi m_\phi/(m_\chi v^2)$, exhibiting a strong velocity dependence:

$$\sigma_T \simeq \begin{cases} (4\pi/m_\phi^2)\beta^2\ln(1+\beta^{-1}), & \beta \lesssim 0.1 \ (8\pi/m_\phi^2)\beta^2/(1+1.5\beta^{1.65}), & 0.1 \lesssim \beta \lesssim 10^3 \ (\pi/m_\phi^2)[\ln \beta + 1/2], & \beta \gtrsim 10^3 \end{cases}$$

• Resonant/Quantum regime: For $\alpha_\chi m_\chi / m_\phi \gtrsim 1$ and $m_\chi v / m_\phi \lesssim 1$, the cross section exhibits quantum mechanical resonances linked to the formation of (meta-)stable DM bound states, requiring numerical or analytic solution (e.g., Hulthén potential) for $\sigma_T$ (Kaplinghat et al., 2013, Li et al., 2021, Wang, 22 Dec 2025).

These regimes can be realized at different $m_\chi$, $m_\phi$, and $v$ values corresponding to dwarf galaxies ($v\sim 30$ km/s), Milky Way-like galaxies ($v\sim 200$ km/s), and clusters ($v\sim 1000$ km/s).

3. Astrophysical Parameter Space and Small-Scale Structure Phenomenology

Successful scalar-mediated SIDM models predict cross sections in the range

$$0.1~\mathrm{cm}^2/\mathrm{g} \lesssim \left\langle \frac{\sigma_T}{m_\chi} \right\rangle \lesssim 10~\mathrm{cm}^2/\mathrm{g}$$

at dwarf galaxy-scale velocities, with $$\sigma_T/m_\chi \lesssim 1~\mathrm{cm}^2/\mathrm{g}$$ at cluster scales to satisfy Bullet Cluster and halo shape constraints (Kaplinghat et al., 2013, Jia, 2019, Wang, 22 Dec 2025).

Preferred model parameters, as established across multiple benchmarks, include (Kaplinghat et al., 2013, Jia, 2019, Kao et al., 2020, Xu et al., 28 Oct 2024):

• Mediator mass: $m_\phi \approx 1$–$100$ MeV,
• Dark matter mass: $m_\chi \approx 10$ GeV–$1$ TeV,
• Coupling: $\alpha_\chi \sim 10^{-5}$–$10^{-1}$, subject to relic density constraints and direct detection bounds.

Nontrivial velocity dependence, realized through either classical or quantum resonance regimes, is essential for resolving both the core–cusp and cluster limits. Inelastic models further introduce kinematic thresholds suppressing $\sigma_T$ in ultra-faint satellites while enabling resonant enhancement in dwarfs (Wang, 22 Dec 2025).

Scalar-mediated SIDM halos yield Burkert-like cores rather than NFW cusps, resolving the observed diversity and density anomalies in rotation curves of local galaxies (Lan et al., 2020). N-body and hydrodynamical simulations confirm the development of $\mathrm{kpc}$-scale cores and substructure depletion in this regime (Lan et al., 2020, Kaplinghat et al., 2013).

4. Relic Abundance, Early-Universe Evolution, and Cosmological Constraints

Thermal freeze-out of dark matter via $\chi\chi \to \phi\phi$ is typically $p$-wave suppressed (scalar mediation), resulting in velocity-dependent annihilation cross sections. The requirement $\Omega_\chi h^2 \simeq 0.12$ fixes the combination $g_\chi(m_\chi, m_\phi)$ (Kaplinghat et al., 2013, Jia, 2019, Dutta, 2023, Xu et al., 28 Oct 2024). If the annihilation is too rapid (as occurs for large $g_\chi$), the relic density can be restored via non-thermal mechanisms, entropy dilution, or late-time decays of heavier states (e.g., in singlet-doublet models) (Dutta, 2023, Borah et al., 2021).

Restrictive bounds arise from:

• CMB: Scalar-mediated models with $p$-wave suppressed annihilation avoid strong CMB limits that otherwise affect $s$-wave models, while bound-state formation or off-shell contributions are negligible for typical $m_\phi,m_\chi$ (Wang, 22 Dec 2025).
• BBN: Decay of $\phi$ to $e^+e^-$ must occur before $t\sim 1$ s; this imposes a lower limit on the mediator–SM coupling (e.g., kinetic mixing $$\epsilon \gtrsim 10^{-10}\sqrt{10~\mathrm{MeV}/m_\phi}$$) (Kaplinghat et al., 2013, Xu et al., 28 Oct 2024, Wang, 22 Dec 2025).
• $\Delta N_{\text{eff}}$: Mediators that remain coupled to neutrinos or other light degrees of freedom must decouple early enough to avoid overproduction of dark radiation, often setting $m_\phi\gtrsim 20~\mathrm{MeV}$ (Kao et al., 2020).

Cosmological histories with nonstandard expansion (e.g., early matter domination) or significant entropy injection can open viable regions otherwise forbidden by over-efficient annihilation (Dutta, 2023, Bernal et al., 2018).

5. Direct and Indirect Detection, Laboratory Signatures

Direct detection signatures depend sensitively on the portal coupling of $\phi$ to the SM:

• Nuclear recoils: The cross section is often suppressed at large recoil due to the light mediator propagator,

$f(q^2) = \frac{m_\phi^4}{(m_\phi^2+q^2)^2}$

resulting in several orders of magnitude suppression for $q \gtrsim m_\phi$ typical in xenon-based detectors (Kaplinghat et al., 2013, Jia, 2019).

• Electron recoils: Scenarios with sub-GeV SIDM and MeV scalar mediators can generate detectable signals in low-threshold electron-recoil experiments if the mediator–SM mixing $\sin\theta$ is sufficiently large ($\sin\theta\gtrsim10^{-3}$), but astrophysical and beam-dump constraints strongly limit this possibility (Xu et al., 28 Oct 2024).
• Inelastic up-scatters: In models where a transition dipole connects two nearly degenerate DM states, the low-energy nuclear recoil spectrum is sharply peaked at the inelastic threshold with $1/E_R$ scaling, providing a distinct signature for future low-threshold direct detection (Wang, 22 Dec 2025).
• Constraints: Beam-dump, supernova, BBN, and electroweak precision tests further restrict mediator–SM couplings, typically forcing $$10^{-10}\lesssim\epsilon(\sin\theta)\lesssim10^{-7}$$ for $m_\phi\sim10$–$100$ MeV, leaving a narrow direct-detection window (Kaplinghat et al., 2013, Xu et al., 28 Oct 2024).

Indirect detection (gamma-ray, positron, neutrino signals) are typically suppressed in scalar-mediated SIDM, particularly in models with invisible final states (e.g., dominant $\chi\chi\to\phi\phi$ annihilation with $\phi$ decaying invisibly, or models where DM annihilation proceeds via $p$-wave transitions) (Duch et al., 2019, Wang, 22 Dec 2025). In neutrinophilic scenarios, $\phi\to\nu\nu$ decays could generate a neutrino line, but these are generally below detectability (Rajaraman et al., 2018).

Collider signatures can arise from Higgs-portal couplings ($h\to\phi\phi$ decay), lepton-jet production, or soft unclustered energy patterns (SUEP) in multi-scalar extensions, depending on specific NMSSM or other nonminimal scenarios (Li et al., 2021).

6. Model Extensions, Variants, and Benchmark Realizations

Numerous realizations of the scalar-mediated SIDM paradigm address distinct phenomenological and model-building objectives:

• Inelastic SIDM: Pseudo-Dirac DM with small mass splittings yields unique kinematic thresholds for self-scattering, reconciling strong core creation in dwarfs with suppression in satellites (Wang, 22 Dec 2025).
• Sterile Neutrino Portal: Introducing a light sterile neutrino enables prompt mediator decay compatible with BBN, while maintaining strong self-interaction (Kainulainen et al., 2015).
• Complex Dark Sectors and Multi-Component Models: Models with stable scalar mediators as subdominant DM, off-diagonal couplings, or additional symmetry-protected sectors permit expanded phenomenology—including late-time relic injection, nontrivial cosmological histories, and radiative neutrino mass generation in scotogenic frameworks (Kao et al., 2020, Duch et al., 2019, Borah et al., 2021).

The table below summarizes select parameter ranges and constraints for benchmark models grounded in the referenced literature:

Model/Ref.	$m_\chi$ [GeV]	$m_\phi$ [MeV]	Coupling	$\sigma_T/m_\chi$ [cm$^2$/g]	Direct detection reach
Kaplinghat et al. (Kaplinghat et al., 2013)	10–10000	1–100	$\alpha_\chi=10^{-5}$–$10^{-1}$	$0.1–10$ (dwarf), $<1$ (cluster)	$10^{-46}-10^{-44}$ cm$^2$
Duch et al. (Duch et al., 2019)	5–500	2–50	$g_Y=0.03-0.3$	$0.1–10$ (dwarf)	$\sim10^{-48}$–$10^{-46}$ cm$^2$
Wang (Wang, 22 Dec 2025)	40	20	$\alpha_S\sim10^{-2}$	$10$ at 60 km/s	1/$E_R$ inelastic, $R<10^{-3}$ t$^{-1}$y$^{-1}$
Kaō–Tsai–Wong (Kao et al., 2020)	300–1200	200–800	$\alpha_\chi\sim10^{-3}-10^{-1}$	$0.1-10$	near/XENON1T floor
NMSSM (Li et al., 2021)	1.7–20	7–23	$\kappa=0.08-0.24$	$0.1-10$	$y_\chi \theta \lesssim 10^{-7}$

7. Outlook and Synthesis

Scalar-mediated SIDM models, leveraging light pseudo-scalar or scalar force carriers, yield predictive, testable signatures in small-scale structure, astroparticle probes, and direct and indirect detection experiments. Models constrained to $m_\phi\sim10$–$100$ MeV and $m_\chi\sim 10$ GeV–TeV can simultaneously satisfy astrophysical observations, cosmological relic abundance, and laboratory limits (Kaplinghat et al., 2013, Wang, 22 Dec 2025, Kainulainen et al., 2015, Xu et al., 28 Oct 2024). Careful treatment of quantum resonances, non-perturbative scattering, and unique direct detection signatures in inelastic or multi-component realizations is essential to fully mapping and probing the remaining viable parameter space.

Further research directions include improved simulation of SIDM-induced galactic dynamics, deeper exploration of cosmological histories (early matter domination, entropy injection), refinement of nuclear and electron recoil modeling for light mediators, and collider-oriented searches sensitive to small mixing angles or multi-scalar cascades. The interplay of astrophysical, cosmological, and laboratory observables will continue to drive advances in model exclusion and possible discovery of SIDM with scalar mediators.