Scalar-Mediated Neutrino Self-Interactions

• Scalar-mediated neutrino self-interactions are defined by neutrinos exchanging a scalar boson, which modifies scattering processes and early universe dynamics.
• They influence sterile neutrino dark matter production and alter cosmic signals, including modifications to the CMB anisotropies and neutrino free-streaming.
• Laboratory and astrophysical constraints, from meson decays to spectral distortions, decisively narrow the allowed parameter space for both light and heavy mediator models.

Scalar-mediated neutrino self-interactions (νSI) are a class of new-physics scenarios in which Standard Model (SM) neutrinos interact with each other via the exchange of a light or heavy scalar boson. Such interactions, often termed "secret" or "hidden" neutrino interactions, fundamentally alter the dynamics of the neutrino sector in the early universe, impact laboratory observables, and provide novel mechanisms for sterile neutrino dark matter production. These models are tightly constrained by current experimental and cosmological observations, but they continue to attract attention due to their possible connection to outstanding cosmological anomalies, such as the Hubble tension.

1. Theoretical Framework

Scalar-mediated νSI are constructed by extending the SM with a singlet scalar field φ of mass $m_\phi$ and with dimensionful Yukawa couplings $g_{\alpha\beta}$ to the neutrino bilinears. The typical Lagrangian in four-component notation reads (Sen, 2021, Brdar et al., 2020): $$\mathcal{L} \supset \frac{1}{2} g_{\alpha\beta} \,\bar\nu_\alpha \nu_\beta\, \phi + \textrm{h.c.} + \textrm{kinetic~terms} - \frac{1}{2}m_\phi^2 |\phi|^2$$ where $\nu_\alpha$ are the active (possibly Majorana) neutrino fields and $g_{\alpha\beta}=g_{\beta\alpha}$ (for Majorana). In flavor-diagonal scenarios, $$g_{\alpha\beta} = \lambda_\phi\,\delta_{\alpha\beta}$$ is commonly adopted for phenomenological constraints.

The scalar mediator can be either real or complex, and the coupling matrix can be chosen to produce flavor-universal or flavor-specific models, or to mediate interactions between active and sterile neutrinos or sterile–sterile neutrino interactions (An et al., 2023, Astros et al., 2023).

At energies $E \ll m_\phi$, integrating out the scalar yields a four-fermion effective operator: $$\mathcal{L}_{\rm eff} = - (g_{ij}g_{kl}/m_\phi^2) (\bar\nu_i\nu_j) (\bar\nu_k\nu_l)$$ leading to $G_{\rm eff} = g^2/m_\phi^2$ for contact interactions (Deppisch et al., 2020).

2. Scattering Amplitudes, Cross Sections, and Rates

The leading process is elastic neutrino–neutrino scattering via t- and/or s-channel φ exchange (Sen, 2021, An et al., 2023, Astros et al., 2023). For t-channel exchange between (Majorana) neutrinos of flavors α and β: $$\nu_\alpha(p_1) + \nu_\beta(p_2) \rightarrow \nu_\alpha(p_3) + \nu_\beta(p_4)$$ the differential cross section (for identical flavors) is: $$\frac{d\sigma}{d\Omega} = \frac{|g_{\alpha\beta}|^4}{128\pi (s(1-\cos\theta)+2m_\phi^2)^2} (1+\cos^2\theta)$$ with full expressions involving logarithmic terms upon angular integration.

For s-channel exchange (relevant for high-energy astrophysical neutrinos), the resonant cross section takes the Breit–Wigner form (Dhuria, 2023, Venzor et al., 2023): $$\sigma(s) = \frac{g^4}{4\pi} \frac{s}{(s-m_\phi^2)^2 + (m_\phi \Gamma_\phi)^2}$$ where $\Gamma_\phi$ is the width of the mediator. The cross section exhibits significant enhancement near the resonance $s \approx m_\phi^2$.

The thermally averaged scattering rate per neutrino in the early universe scales as (Choudhury et al., 2020, Bostan et al., 2023): $\Gamma_\nu \sim G_{\rm eff}^2 T_\nu^5$

3. Cosmological and Astrophysical Impacts

Scalar-mediated νSI alter the behaviour of the neutrino plasma in the early universe and have multiple consequences:

• Sterile Neutrino Dark Matter Production: νSI enhance the production of keV-scale sterile neutrinos via the Dodelson–Widrow mechanism without violating X-ray and structure-formation constraints (Sen, 2021, An et al., 2023, Astros et al., 2023). Quantum damping and modified thermal matter potentials suppress or modify active–sterile mixing, changing the momentum spectrum and relic density.
• Modification of the Cosmological Boltzmann Hierarchy: Self-interactions delay neutrino free-streaming, modifying the source of anisotropic stress in the photon–baryon plasma, which affects the CMB TT, TE, EE, and lensing spectra (Choudhury et al., 2020, Bostan et al., 2023, Venzor et al., 2023, Poudou et al., 13 Mar 2025). In the "relaxation time approximation," collision terms introduce damping to multipole moments $\ell\geq2$:

  $$\dot\Psi_\ell \sim \ldots + \alpha_\ell \dot\tau_\nu \Psi_\ell,$$

  with $\dot\tau_\nu = - a G_{\rm eff}^2 T_\nu^5$ and coefficients $\alpha_\ell$ determined by the nature of the mediator (Bostan et al., 2023).

• Spectral Distortions in the CMB: Radiative neutrino–neutrino scattering mediated by a scalar (followed by photon emission via charged lepton loops) injects energy during the $\mu$- and $y$-distortion epoch, constrained by COBE/FIRAS and future PIXIE missions (Natwariya et al., 30 Jun 2025). For $E_\nu=1\,\text{PeV}$, couplings $g_{\nu_\mu}\gtrsim 3\times10^{-5}$ are excluded for $m_\phi \lesssim 15$ MeV.
• Allowed Parameter Space for the Hubble Tension: Strong or moderately strong νSI have been invoked to delay or damp neutrino free-streaming, shifting the inferred $H_0$ to higher values. However, CMB polarization and LSS data have progressively disfavored the strong-coupling regime, particularly for flavor-universal or $\nu_e$–coupled models (ruled out by double beta decay) (Deppisch et al., 2020, Collaboration et al., 17 Nov 2025). Only $\nu_\mu$ or $\nu_\tau$–specific interactions in the "moderately interacting" range remain viable (Bostan et al., 2023, Poudou et al., 13 Mar 2025).
• Supernova Cooling Constraints: Energy loss via scalar-mediated neutrino self-scattering and sterile-neutrino production in core-collapse supernova cores constrains $g \lesssim 10^{-4}$ for $m_\phi \lesssim 30$ MeV (Chen et al., 2022).

4. Laboratory and Astrophysical Constraints

Laboratory experiments provide complementary constraints to cosmology and astrophysics:

• Z and Higgs Invisible Decays: Three-body and loop-induced corrections to the invisible width of the $Z$ boson constrain $|g|\lesssim 10^{-2}$ for $m_\phi < m_Z$ for flavor-diagonal couplings (Brdar et al., 2020). The strongest limits for $\nu_e$ and $\nu_\mu$ apply for $m_\phi \sim$ 0.1–10 GeV.
• Meson Decays: Searches for $K\to\mu \nu\phi$ and similar rare decays constrain $|g|\lesssim 10^{-3}–10^{-5}$ in the sub–100 MeV mediator mass range (Sen, 2021, Wu et al., 2023, Dhuria, 2023).
• Beta Decay and Double Beta Decay: KamLAND-Zen and PandaX-4T provide the most stringent laboratory limits on $g_{ee}$ for $m_\phi < 2\,\mathrm{MeV}/c^2$, with $g_{ee} \lesssim 1.1\times10^{-5}$ (90% CL) for $m_\phi\to 0$ (Collaboration et al., 17 Nov 2025, Deppisch et al., 2020).
• Solar and Reactor Experiments: Future detection of solar antineutrinos via inverse-beta decay in large detectors (JUNO, Hyper-K, THEIA) will probe $g$ at the $10^{-2}-10^{-1}$ level for $m_\phi\sim10$ MeV, overlapping cosmologically relevant regions (Wu et al., 2023).
• IceCube and High-Energy Neutrinos: Lack of spectral dips in astrophysical neutrino spectra (NGC 1068, GRB221009A) sets $g \lesssim 10^{-1}-1$ for $m_\phi \sim 1-10$ MeV for flavor-universal or tau–specific couplings (Hyde, 2023, Dhuria, 2023).

5. Parameter Space, Regimes, and Phenomenological Signatures

Distinct production and phenomenological regimes arise depending on the mediator mass and flavor structure (Astros et al., 2023):

• Light Mediator ($m_\phi \lesssim 100$ MeV): In this regime, self-interactions are long-range, the contact interaction approximation breaks down, and labels like “strongly” or “moderately” interacting must be defined in terms of the scattering rate relative to $H$ at $T_\nu\sim$ eV–MeV scales. Cosmological and lab signatures depend on whether the mediator thermalizes or decays after BBN, with implications for $\Delta N_{\rm eff}$.
• Heavy Mediator ($m_\phi \gg T_\nu$): The interaction becomes point-like, probing $G_\text{eff}$ through its effect on the neutrino decoupling and the CMB anisotropy power spectra. Cosmological constraints on $G_\text{eff}$ (flavor-universal or flavor-specific) are at the $10^{-4}$ MeV$^{-2}$ level (Bostan et al., 2023, Choudhury et al., 2020, Poudou et al., 13 Mar 2025).
• Resonant Regime: For $T_\nu \sim m_\phi$, s-channel resonant enhancement leads to strong damping of anisotropic stress over a finite epoch, which can produce observable effects in the CMB and allow for maximal impact on the $H_0$ parameter at weaker couplings than the contact limit (Venzor et al., 2023).
• Sterile Neutrino Production and Dark Matter: For sterile neutrino dark matter, four regimes are identified: (i) non-resonant with light mediators, (ii) partial thermalization and cooling, (iii) resonance near $m_\phi\sim1$ GeV, and (iv) sharp/fine-tuned resonance for $m_\phi \gg$ GeV (Astros et al., 2023). Only light-mediator/weak-coupling windows remain viable after the combination of X-ray, structure, and lab bounds.
• Solar Antineutrinos: Scalar-mediated νSI generically lead to solar $\bar\nu_e$ emission at rates testable in future detectors. Absence of such events would place strong constraints on the SI/MI parameter space (Wu et al., 2023).

6. Comparison and Synthesis of Constraints

The allowed region is a function of mediator mass, flavor structure, and the cosmological/astrophysical observable in question. The following table provides a synthesized view of leading limits for selected scenarios:

Observable/Constraint	Flavor	$m_\phi$ Range	Bound on $g$
Double $\beta$ decay (PandaX-4T)	$\nu_e$	$0-2$ MeV	$<1.1\times10^{-5}$
Meson decays ($K$, $D$)	$\nu_{e,\mu}$	$10-100$ MeV	$<10^{-3}-10^{-5}$
Z/Higgs decays	all	$<45$ GeV	$<10^{-2}$
CMB/LSS (Planck, BAO, DESI)	$\nu_\tau|\nu_\mu$	$0.01~10^3$ MeV	$g/m_\phi\lesssim2\times10^{-2}$ MeV$^{-1}$
Supernova cooling	$e, \mu, \tau$	$1-100$ MeV	$<10^{-4}-10^{-3}$
CMB spectral distortion (PIXIE)	$\nu_\mu$	$<15$ MeV	$<3\times10^{-5}$

Electron-flavor νSI at Hubble-tension-relevant couplings are now strongly excluded (Deppisch et al., 2020, Collaboration et al., 17 Nov 2025). Only flavor-specific (τ, μ) or dark radiation–coupled models may remain viable.

7. Implications for Cosmology and Future Prospects

While early claims that scalar-mediated strong νSI could resolve the Hubble tension have been weakened by CMB, double beta decay, and LSS data, the residual "moderately interacting" window for $\nu_\mu$ or $\nu_\tau$-specific models persists within reach of next-generation probes (Bostan et al., 2023, Poudou et al., 13 Mar 2025). Solar antineutrino searches, CMB Stage-IV, spectral distortion missions (PIXIE), and precision laboratory studies (e.g., KATRIN, beam-dump experiments) will further test the remaining parameter space (Wu et al., 2023, Natwariya et al., 30 Jun 2025).

Models featuring rapid active-to-dark radiation conversion after BBN but before recombination may evade direct constraints by suppressing terrestrial couplings relative to cosmological interaction scales (Das et al., 9 Jun 2025). These "masquerading" scenarios may relax cosmological mass bounds and will be testable with upcoming probes of the absolute neutrino mass and rare decay signatures.

In summary, scalar-mediated neutrino self-interactions constitute a rich theoretical and phenomenological framework, interfacing particle physics, cosmology, and astrophysics, with strong present constraints but promising discovery or exclusion potential with next-generation experimental and observational data.