Active-Sterile Neutrino Polarizability

• Active–sterile neutrino polarizability is defined by effective operators that couple active neutrinos to sterile states through electromagnetic fields.
• The interactions involve dimension-5 transition dipole moments and dimension-7 Rayleigh operators, driving phenomena like Primakoff upscattering and neutrino-induced photon production.
• Astrophysical observations and accelerator experiments impose stringent limits, guiding BSM models with implications for supernova cooling, oscillation signatures, and neutrino-nucleus scattering.

Active–sterile neutrino polarizability encompasses higher-dimensional electromagnetic interactions between Standard Model (SM) active neutrinos and hypothetical sterile neutrinos, parameterized via effective operators coupling neutrino bilinears to the photon field strength and its dual. Such couplings manifest either as transition dipole moments (dimension-5), relevant for magnetic moment portals, or as dimension-7 polarizability operators, leading to distinct physical effects in laboratory, astrophysical, and cosmological environments. The phenomenon plays a key role in constraining physics beyond the SM (BSM), with powerful bounds stemming from supernova energetics, particle accelerators, and dedicated oscillation searches.

1. Effective Operators and Theoretical Foundations

The active–sterile neutrino polarizability is realized at low energies via effective operators. Two primary structures are relevant:

1. Transition magnetic moment (dipole portal): After electroweak symmetry breaking, the dimension-5 Majorana transition dipole operator is

$$\mathcal{L}_\text{dipole} \supset \sum_\alpha d_\alpha \, \overline{N} \, \sigma_{\mu\nu} \nu_{L\alpha} F^{\mu\nu} + \text{h.c.}$$

where $N$ is the sterile neutrino, $\nu_{L\alpha}$ denotes an active neutrino of flavor $\alpha$, $F_{\mu\nu}$ is the electromagnetic field strength, $\sigma^{\mu\nu} = (i/2)[\gamma^\mu,\gamma^\nu]$, and $d_\alpha$ is the (possibly flavor-universal) transition dipole moment (Chauhan et al., 2 Feb 2024).

2. Dimension-7 polarizability (Rayleigh operator): In the Standard Model Effective Field Theory (SMEFT), integrating out new heavy states yields

$$\mathscr{L}_\text{pol} = d_{as}\; \overline{N} \, \nu_a \, F^{\mu\nu} \widetilde{F}_{\mu\nu} + \text{h.c.}$$

where $d_{as}$ carries dimension $[{\rm GeV}^{-3}]$, $$\widetilde F_{\mu\nu} = \frac{1}{2} \epsilon_{\mu\nu\rho\sigma} F^{\rho\sigma}$$, and $\nu_a$ is an active neutrino of flavor $a$ (Gehrlein et al., 8 Dec 2025). CP-even and CP-odd combinations exist, distinguished by the replacement $\widetilde F_{\mu\nu} \to F_{\mu\nu}$.

Physically, these operators mediate processes such as $\nu_a + \gamma \to \nu_s + \gamma$, coherent $\nu$-nucleus scattering with photon emission, and other transitions involving active and sterile neutrinos and external photons. The structure is analogous to Rayleigh polarizability in atomic physics, except realized in the neutrino sector.

2. Astrophysical and Experimental Signatures

Active–sterile neutrino polarizability has several distinct experimental consequences:

• Supernova cooling and energy deposition:

Transition dipole moments enable copious sterile neutrino production in hot, dense supernova cores ($T \sim 10$–30 MeV, $\rho\sim10^{14}\,$g cm$^{-3}$), primarily via Primakoff upscattering ($\nu+f\to N+f$, $f=e,p$) and inverse decay ($\nu + \gamma \to N$), where Pauli suppression and chemical potential effects determine the dominant channel as a function of $M_N$ (Chauhan et al., 2 Feb 2024). Energy loss and trapping analyses using integrated luminosity provide stringent limits based on observables such as SN1987A cooling ($E_\text{cool} < 10^{52}\,$erg) and underluminous Type IIP supernova explosion energies ($E_\text{dep} < 10^{50}\,$erg).

• Photon scattering and neutrino-induced polarization:

Forward $\gamma$–$\nu$ scattering, mediated by weak interactions, induces a parity-violating polarizability tensor. When a linearly polarized laser traverses a neutrino beam, the antisymmetric part of this tensor converts linear to circular polarization. The rate of newly circular-polarized photons tracks the surviving active flux and thus oscillates with baseline in presence of active–sterile mixing, providing an in-situ interferometric probe of oscillation parameters (Bakhti et al., 2014).

• Neutrino-nucleus scattering with single-photon production:

The dimension-7 Rayleigh operator generates “neutrino-induced inverse Primakoff” ($\nu IIP$) events: $\nu_a N \to \nu_s N \gamma$. The cross section receives a $Z^2$ enhancement from coherence and is highly sensitive to the polarizability coupling $d_{as}$, growing rapidly with $E_\nu$. This process features distinctive single-photon final states—relevant to MiniBooNE and future SBN/DUNE detectors (Gehrlein et al., 8 Dec 2025).

3. Constraints from Laboratory, Astrophysical, and Cosmological Probes

Astrophysical environments and terrestrial experiments set complementary bounds:

Observable	Parameter Constrained	Exclusion Level
SN1987A cooling	$|d|$ (transition dipole)	$\,\lesssim$few $\times\,10^{-10}$–$10^{-9}$ GeV$^{-1}$ for $M_N<300$ MeV (Chauhan et al., 2 Feb 2024)
Type IIP explosion energy	$|d|$	$\lesssim 10^{-11}$ GeV$^{-1}$ for $30\,{\rm MeV} < M_N < 600$ MeV (Chauhan et al., 2 Feb 2024)
NOMAD (accelerator)	$d_{\mu s}$	$\gtrsim 5\times10^{-7}$ GeV$^{-3}$ for $m_N\lesssim 1\,\rm GeV$ (Gehrlein et al., 8 Dec 2025)
JUNO-TAO (reactor)	$d_{e s}$	$\lesssim 5\times10^{-6}$ GeV$^{-3}$ for $m_N \lesssim 8$ MeV (Gehrlein et al., 8 Dec 2025)
MiniBooNE (accelerator)	$d_{\mu s}$, $m_N$, $m_\phi$	See Fit Regions (see below)

The constraints from supernova physics are orders of magnitude tighter than present direct laboratory bounds for the dipole portal. For polarizability operators, current and near-future short- and long-baseline neutrino experiments are crucial, especially in the MeV–GeV regime.

Notably, the “neutrino-induced inverse Primakoff” mechanism with an intermediate light pseudoscalar mediator can fit the MiniBooNE low-energy excess for $m_N\approx 350$ MeV, $m_\phi\approx 50$ MeV, and $$c_{\nu}^{\mu s}g_{\phi\gamma}\simeq2.5\times10^{-6}$$ GeV$^{-1}$, without violating extant SN 1987A and beam-dump constraints (Gehrlein et al., 8 Dec 2025).

4. Modeling, Amplitudes, and Channel Dependence

The characteristic physical processes associated with active–sterile polarizability and dipole portals depend sensitively on the neutrino and mediator masses, environmental degeneracy, and the nature of the coupling:

• Primakoff upscattering: For sterile neutrinos with $M_N \lesssim 50$ MeV, production via upscattering off protons dominates due to strong electronic Pauli suppression in supernova cores (Chauhan et al., 2 Feb 2024).
• Inverse decay: At intermediate $M_N$ ($\sim$50–200 MeV), $\nu+\gamma\to N$ becomes prominent, unsuppressed by degeneracy or blocking, exploiting the high chemical potential of active neutrinos (Chauhan et al., 2 Feb 2024).
• Opacity and trapping: In the trapping regime (large $d$ or high $M_N$), $N \to \nu \gamma$ decays set the sterile-neutrino mean free path. The integrated-luminosity approach demonstrates that even strongly interacting (trapped) sterile neutrinos can leak energy until their decay length shortens below the core size.
• Rayleigh-like $\nu$ polarizability: For dimension-7 operators, single-photon production cross sections scale as $Z^2\alpha d_{as}^2 E_\nu^4$ in the coherent regime. The momentum dependence is controlled by $q^2$ and nuclear form factors (Gehrlein et al., 8 Dec 2025).
• Forward $\gamma$–$\nu$ scattering: The evolution of the photon polarization density matrix is governed by the induced polarizability tensor $\Pi_{ij}$, whose antisymmetric part enables conversion of linear to circular polarization in the presence of parity violation (Bakhti et al., 2014).

5. Ultraviolet Completions and Model Realizations

A range of BSM theories can yield active–sterile polarizability operators at low energies:

• Light-mediator models: Introduction of a singlet pseudoscalar $\phi$ coupling to both neutrinos and photons yields, upon integrating out $\phi$, the operator $$d_{as}\overline{N}\nu_a F^{\mu\nu}\widetilde{F}_{\mu\nu}$$ with $d_{as} = c_\nu^{as}g_{\phi\gamma}/2m_\phi^2$ (Gehrlein et al., 8 Dec 2025). For $|q^2|\sim m_\phi^2$, the amplitude acquires a propagator factor and the single-photon angular spectrum is broadened.
• One-loop SM and scalar-mediated models: Four-Fermi neutrino-lepton interactions, with charged-lepton loops attached to two photons, generate polarizability at the level of $d_{as}\sim 10^{-12}$ GeV$^{-3}$ for GeV-scale neutrinos—numerically inaccessible to current experiments (Gehrlein et al., 8 Dec 2025). Enhanced effects arise in extended models introducing new charged scalar fields with appropriate Yukawa couplings (e.g., $S^+$ loops).
• Active–sterile mixing models: Standard oscillation-based frameworks (e.g., $3+1$) control the magnitude of observable effects through mixing angles $|U_{\alpha 4}|^2=\sin^2\theta_{\alpha 4}$ and mass-squared splittings. Polarizability signals in photon–neutrino interactions are modulated by oscillatory depletion of the active neutrino flux over baseline $L$ (Bakhti et al., 2014).

6. Experimental Prospects and Implications for BSM Physics

The discovery reach for active–sterile neutrino polarizability is advancing along multiple experimental frontiers:

• Short-baseline neutrino facilities: SBND, ICARUS, and DUNE ND can probe dimension-7 polarizability coefficients $d_{as}$ down to $10^{-9}$–$10^{-10}$ GeV$^{-3}$, particularly through single-photon final state searches and associated kinematic signatures (Gehrlein et al., 8 Dec 2025).
• Intense laser–neutrino setups: Polarization experiments using overlapping laser and neutrino beams enable baseline-dependent measurements, extracting mixing parameters with sensitivities to $\sin^2(2\theta)$ at the $10^{-2}$ level, and $\Delta m^2_{41}$ in the $0.1$–$10$ eV$^{2}$ range (Bakhti et al., 2014).
• Astrophysical observations: Supernova energetics remain uniquely sensitive to magnetic and polarizability portals: any BSM scenario predicting large transition moments or Rayleigh coefficients is strongly disfavored for sterile neutrino masses in the 30 MeV–600 MeV range if $d$ exceeds $10^{-11}\,$GeV$^{-1}$ (Chauhan et al., 2 Feb 2024).

A plausible implication is that further improvements in single-photon event reconstruction, coherence enhancement, and joint use of accelerator and astrophysical data may either discover new active–sterile electromagnetic structures or further close parameter space for relevant BSM models.

7. Summary

Active–sterile neutrino polarizability constitutes a well-motivated and experimentally accessible class of neutrino-photon interactions lying beyond the Standard Model. Transition dipole and dimension-7 Rayleigh-type operators permit active–sterile couplings to the electromagnetic field, mediating phenomena such as enhanced production in stellar environments, photon-induced oscillation signals, and distinctive single-photon signatures at accelerators. Bounds from supernovae are exceptionally strong, while laboratory experiments at the intensity frontier continue to probe unexplored regions of parameter space. The prospect of explaining anomalies such as MiniBooNE via active–sterile polarizability underscores the operator’s relevance in BSM model-building. Collectively, these studies define rigorous constraints and guide the search for new physics in the neutrino sector (Chauhan et al., 2 Feb 2024, Bakhti et al., 2014, Gehrlein et al., 8 Dec 2025).