Neutrino Electromagnetic Properties

This Annual Review article, “Neutrino Electromagnetic Properties” (Giunti, Kouzakov, Li, Studenikin, 2025), addresses a central question in neutrino physics: what electromagnetic interactions can neutrinos have, how are these interactions parameterized in a general theory, and what do current laboratory and astrophysical data imply about the corresponding neutrino electromagnetic form factors. The question matters because neutrinos are electrically neutral in the Standard Model (SM) at tree level, yet they are massive and therefore can acquire tiny electromagnetic properties through radiative corrections. Any measured deviation from the SM expectations would be evidence for physics beyond the SM (BSM), potentially linked to the origin of neutrino masses, sterile neutrinos, and other new sectors.

The review’s significance is twofold. First, it provides a unified theoretical framework for neutrino electromagnetic form factors in the one-photon approximation, distinguishing charge, anapole, magnetic, and electric form factors and clarifying how these depend on whether neutrinos are Dirac or Majorana particles. Second, it synthesizes phenomenology and experimental constraints across multiple processes and energy regimes: elastic neutrino–electron scattering (EνES), coherent elastic neutrino–nucleus scattering (CEνNS), radiative processes in high-energy colliders, and energy-loss arguments in stars and cosmology. The paper also extends the discussion to astrophysical electromagnetic processes (e.g., plasmon decay, neutrino radiative decay, spin light) and to the “neutrino magnetic moment portal” (dipole portal) in the presence of sterile neutrinos.

Methodologically, the paper is a review rather than a new empirical study. Its “method” is the construction and use of a general effective electromagnetic vertex for massive neutrinos, followed by mapping those form factors onto observable cross sections and decay rates, and then compiling existing bounds from the literature. The theoretical backbone is an effective interaction Hamiltonian in the one-photon approximation, with an effective neutrino electromagnetic current and a vertex function decomposed into form factors. Gauge invariance and hermiticity constrain the structure: for neutrinos, the charge, magnetic, and electric form factors are Hermitian matrices; for antineutrinos, they change sign appropriately; and for Majorana neutrinos, the charge, magnetic, and electric form factor matrices are antisymmetric, implying vanishing diagonal values in the mass basis. In the low-momentum-transfer limit relevant to scattering, the charge form factor’s first derivative at zero momentum transfer is interpreted as an effective charge radius via $$F_{fi}^Q(q^2)\simeq F_{fi}^Q(0)+\frac{q^2}{6}⟨r_{fi}^2⟩.$$ For ultrarelativistic neutrinos, the review emphasizes helicity coherence: charge and charge-radius terms conserve helicity and thus interfere coherently with the SM weak amplitude, whereas magnetic-moment terms flip helicity and contribute incoherently.

The review’s key quantitative results are primarily SM predictions and current experimental/phenomenological bounds. For magnetic moments, the SM (minimal Dirac extension) predicts diagonal magnetic moments proportional to neutrino masses: $${\mu }_{kk}^{\mathrm{D}}\simeq \frac{3e{G}_F{m}_k}{8\sqrt{2}{\pi }^2}\simeq 3\times 10^{-19}\left(\frac{m_k}{\mathrm{eV}}\right){\mu }_B.$$ Transition magnetic moments are further suppressed by additional factors (including charged-lepton mass effects), with representative estimates on the order of $10^{-23}{\mu }_B$ times mass combinations (e.g., $|{\mu }_{12}^{\mathrm{D}}|\simeq 1.1\times 10^{-23}\left(\frac{m_1+m_2}{\mathrm{eV}}\right){\mu }_B$). For Majorana neutrinos, diagonal magnetic moments vanish in the mass basis and only (imaginary) transition moments can exist; in minimal extensions they remain similarly suppressed, though non-minimal BSM models can enhance them by many orders of magnitude.

The review compiles laboratory upper limits on effective magnetic moments from short-baseline experiments using EνES and CEνNS, and from astrophysical arguments using stellar cooling and cosmology. While the paper reproduces bounds in tables rather than a single headline number, it highlights the scale separation: current experimental sensitivity is many orders of magnitude above the minimal SM expectations. For example, it notes that the simplest SM extensions predict magnetic moments far below current bounds (the conclusions state that current upper limits are more than seven orders of magnitude larger than simplest SM-extension predictions). Astrophysical constraints are often more stringent but carry larger systematic uncertainties.

For charge radii, the SM radiative corrections yield flavor-diagonal charge radii (in the flavor basis) of order $10^{-32}{\mathrm{cm}}^2$, with explicit values: $$⟨r_{{\nu }_e}^2{⟩}^{\mathrm{SM}}=-0.83\times 10^{-32}{\mathrm{cm}}^2,⟨r_{{\nu }_{\mu }}^2{⟩}^{\mathrm{SM}}=-0.48\times 10^{-32}{\mathrm{cm}}^2,⟨r_{{\nu }_{\tau }}^2{⟩}^{\mathrm{SM}}=-0.30\times 10^{-32}{\mathrm{cm}}^2.$$ The review emphasizes that current laboratory bounds on flavor charge radii are only about one order of magnitude larger than these SM predictions (as stated in the conclusions), making charge radii a particularly promising target for near-future precision experiments.

For electric charges (“millicharges”), the review discusses constraints from charge conservation and scattering, distinguishing Dirac and Majorana cases. It notes that Majorana neutrinos cannot have diagonal electric charges (in the mass basis), while Dirac neutrinos can have a common diagonal charge in the mass basis $Q_{kk}={\mathcal{Q}}_{\nu }$ due to flavor mixing and charge conservation. It then compiles bounds on effective flavor charges from neutrality of matter, scattering experiments, and astrophysical mechanisms such as the “neutrino star turning” (νST) scenario. A key practical point is that some extremely tight bounds in the literature rely on controversial assumptions (e.g., no cancellations among species), and the review treats such bounds cautiously.

The review also provides important methodological caveats and limitations. First, many experimental bounds depend on modeling assumptions about neutrino electromagnetic form factors, such as neglecting unknown momentum-transfer dependence beyond the leading low-$q^2$ terms. Second, for charge-radius extractions, degeneracies arise when both diagonal and transition charge radii are allowed: in CEνNS, a diagonal charge-radius contribution can cancel against transition contributions, so analyses that assume the absence of transition charge radii can yield different results than more general analyses. Third, astrophysical bounds depend on stellar and cosmological modeling (e.g., plasma conditions, energy-loss mechanisms, and assumptions about the temperature at which right-handed neutrinos are produced), introducing systematic uncertainties.

Practical implications follow directly from these findings. The review argues that (i) charge radii are close enough to SM expectations that improved precision in EνES and CEνNS could plausibly reveal them first; (ii) magnetic moment searches remain motivated because many BSM models predict enhanced moments, and laboratory control of systematics is crucial; and (iii) CEνNS in modern dark-matter detectors provides a powerful new avenue for both magnetic moments and charge radii, with the added benefit of flavor composition and timing/energy information in some experiments (e.g., COHERENT) that can help disentangle contributions from different neutrino flavors.

Who should care? Neutrino experimentalists designing low-energy scattering programs (reactor/accelerator CEνNS and EνES), theorists modeling neutrino mass generation and sterile-neutrino portals, and astrophysicists using stellar cooling and supernova constraints all benefit. The review also points to future experiments and analysis strategies—such as improved semiconductor detector sensitivity, next-generation CEνNS measurements, and refined treatments of momentum-transfer-dependent radiative corrections—as the route to turning these electromagnetic properties from theoretical curiosities into measurable probes of new physics.