Scalar Non-Standard Interactions (SNSI)

• Scalar Non-Standard Interactions (SNSI) are defined as hypothetical neutrino interactions mediated by new scalar or pseudoscalar fields that modify the neutrino mass matrix in a density-dependent, energy-independent manner.
• SNSI introduce a unique correction to oscillation physics by making the probabilities explicitly dependent on absolute neutrino mass scales alongside standard mass-squared differences.
• The practical study of SNSI spans reactor, accelerator, and solar neutrino experiments, offering insights into neutrino mass ordering, CP violation, and potential deviations from the Standard Model.

Searching arXiv for papers on scalar non-standard neutrino interactions to ground the article in the literature. Scalar Non-Standard Interactions (SNSI), also written as sNSI in part of the literature, are hypothetical neutrino interactions mediated by a new scalar or pseudoscalar field beyond the Standard Model. In neutrino oscillation phenomenology, their defining feature is that they induce a medium-dependent correction to the neutrino mass matrix rather than a vector-like matter potential. As a result, the scalar matter effect is energy independent, scales with ambient density, and can make oscillation observables depend explicitly on the absolute neutrino mass scale in addition to the usual mass-squared differences and mixing parameters (Ge et al., 2018, Denton et al., 2024).

1. Field-theoretic definition and parametrization

The standard effective description introduces Yukawa couplings of a new scalar mediator to neutrinos and to background fermions. A representative effective interaction is

$$\mathcal{L}_{\rm eff}^{\rm S} = \frac{y_f\,y_{\alpha\beta}}{m_\phi^2} (\bar{\nu}_\alpha \nu_\beta)(\bar f f),$$

where $y_{\alpha\beta}$ denotes the neutrino-scalar Yukawa coupling, $y_f$ the scalar coupling to a Standard Model fermion $f$, and $m_\phi$ the scalar mass (Ge et al., 2018).

In propagation through matter, this interaction is encoded as a correction $\delta M$ to the neutrino mass matrix. A widely used phenomenological parametrization is

$$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$

with dimensionless SNSI coefficients

$$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$

In this parametrization the diagonal entries $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$ are real, while off-diagonal entries such as $\eta_{e\mu},\eta_{e\tau},\eta_{\mu\tau}$ are complex and satisfy the Hermiticity condition $y_{\alpha\beta}$0 (ESSnuSB et al., 2023).

This formulation is used across reactor, solar, atmospheric, and accelerator studies. In the simplest analyses one often activates a single parameter, especially $y_{\alpha\beta}$1, but more general treatments allow all entries to be nonzero simultaneously (Choubey et al., 5 Feb 2026, Dutta et al., 2024).

2. Oscillation Hamiltonian and the distinctive scalar signature

With SNSI, the propagation Hamiltonian is modified to

$y_{\alpha\beta}$2

so the new physics enters through the mass term rather than through an additional matter potential (Medhi et al., 2021).

This distinction from vector NSI is structurally important. Vector NSI alter the matter potential and scale with density and neutrino energy, whereas scalar NSI alter the mass matrix and scale with density only. The scalar effect is therefore energy independent in the sense emphasized throughout the oscillation literature, and its phenomenology is not equivalent to a reparameterized vector matter effect (Ge et al., 2018, Denton et al., 2024).

A second distinctive consequence is the appearance of explicit absolute-mass dependence in oscillation probabilities. Analytic expressions derived with the Cayley-Hamilton theorem show SNSI contributions proportional to combinations such as $y_{\alpha\beta}$3, $y_{\alpha\beta}$4, $y_{\alpha\beta}$5, $y_{\alpha\beta}$6, and $y_{\alpha\beta}$7. This dependence is absent in standard oscillations and in vector NSI treatments (Bezboruah et al., 2024).

For global analyses, an alternative mass-basis parametrization writes the effective mass-squared matrix as $y_{\alpha\beta}$8 plus complex shifts $y_{\alpha\beta}$9. That construction was introduced to allow all nonzero scalar NSI parameters to be examined simultaneously and to connect oscillation sensitivities directly to light-scalar model parameters (Dutta et al., 2024).

3. Reactor and medium-baseline phenomenology: KamLAND and JUNO

The reactor sector has played a central role in exposing SNSI degeneracies. In a one-parameter analysis with only $y_f$0, fits to KamLAND showed that the inferred values of $y_f$1 and $y_f$2 can deviate significantly from their standard best-fit values; KamLAND allows $y_f$3, and the main conclusion was that global fits to SNSI and standard oscillation parameters are necessary before addressing three-flavor questions such as mass ordering or CP violation (Gupta et al., 2023).

At JUNO, the effect can be more severe. For $y_f$4, the effective solar angle is modified according to

$y_f$5

with

$y_f$6

A resonance occurs when

$y_f$7

at which point $y_f$8. This “SNSI resonance” is analogous to the MSW resonance but is induced by the scalar NSI correction rather than the standard matter potential (Choubey et al., 5 Feb 2026).

For inverted ordering with lightest neutrino mass $y_f$9 eV, JUNO’s neutrino-mass-ordering sensitivity falls below $f$0 for $f$1 and for $f$2. For $f$3, the mass-ordering sensitivity is completely lost. At resonance, the $f$4 survival probabilities for normal and inverted ordering become exactly degenerate throughout the measured energy range, implying $f$5 (Choubey et al., 5 Feb 2026).

The first reactor antineutrino oscillation results from JUNO, based on 59.1 days of data and a spectral $f$6 fit, already yield a constraint $f$7. That analysis also found strong correlations with the solar oscillation parameters $f$8 and $f$9 (Flores et al., 25 Mar 2026).

4. Long-baseline accelerator experiments and parameter degeneracies

In long-baseline settings, SNSI modify appearance and disappearance channels in ways that are not reducible to standard matter effects. A detailed DUNE study found that positive $m_\phi$0 can enhance CP-violation sensitivity, while negative $m_\phi$1 can severely degrade it; for the true value $m_\phi$2, the sensitivity can drop below the $m_\phi$3 threshold. The same work emphasized that scalar NSI effects are energy independent and scale linearly with matter density, and that they alter several oscillation parameters through the effective mass matrix (Medhi et al., 2021).

ESSνSB studies extended this picture to all six independent SNSI parameters. Projected $m_\phi$4 C.L. bounds include $m_\phi$5, $m_\phi$6 at $m_\phi$7, $m_\phi$8 at $m_\phi$9, and $\delta M$0 at $\delta M$1. More significantly, ESSνSB identified blind spots where the $\delta M$2 appearance probability becomes independent of $\delta M$3, notably near $\delta M$4 and $\delta M$5. In these regions the $\delta M$6 for distinguishing $\delta M$7 from $\delta M$8 drops essentially to zero (ESSnuSB et al., 2023).

A comparative analysis of P2SO and DUNE found similar sensitivities to $\delta M$9 and $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$0, with DUNE slightly better for $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$1. It also concluded that mass-ordering and CP-violation sensitivities are mostly affected by $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$2, while octant sensitivity is mostly affected by $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$3 and $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$4. In the same study, the precision of $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$5 deteriorates significantly in the presence of $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$6 and $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$7, whereas the precision of $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$8 remains comparatively robust (Singha et al., 2023).

A later DUNE analysis using the mass-basis $$\delta M = \sqrt{|\Delta m_{31}^2|} \begin{pmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{pmatrix},$$9 parametrization found that once all scalar NSI parameters are allowed to vary simultaneously, the light-scalar parameter space to which DUNE is sensitive is predominantly excluded by non-oscillation probes, except in scenarios with very light mediator mass (Dutta et al., 2024).

5. Solar neutrinos and the absolute neutrino mass scale

Solar neutrinos provide the strongest oscillation constraints on scalar NSI because the scalar effect scales with density rather than with density and neutrino energy. A global analysis combining Borexino and SNO solar data with KamLAND derived constraints on all sNSI parameters and on the absolute neutrino mass scale, and found solar neutrinos to be more than one order of magnitude more sensitive to sNSI than terrestrial probes (Denton et al., 2024).

In the solar-density normalization used in that work and for $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$0, the $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$1 C.L. Solar+KamLAND interval for $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$2 is $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$3. The same analysis reported limits on all diagonal and off-diagonal parameters, including separate bounds on the real and imaginary parts of $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$4, $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$5, and $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$6 (Denton et al., 2024).

The dependence on absolute neutrino mass is not merely formal. A DUNE-based study showed that SNSI can be used to constrain the lightest neutrino mass through oscillation measurements. For normal hierarchy, the lightest mass can be constrained with $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$7 irrespective of the octant of $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$8 and the value of $$\eta_{\alpha\beta} = \frac{y_{\alpha\beta}}{\sqrt{|\Delta m_{31}^2|}\,m_\phi^2} \sum_f N_f y_f.$$9. For $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$0 and true $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$1 eV, the allowed region restricts $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$2 eV at $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$3 (Medhi et al., 2023).

These results clarify a central point of the SNSI framework: once the matter correction enters the mass matrix, oscillation observables can no longer be expressed solely in terms of mass-squared splittings. This is the basis for the repeated claim in the literature that SNSI open a route to absolute-mass information from oscillation data (Bezboruah et al., 2024).

6. Broader phenomenology in dense media, quantum correlations, and astrophysical neutrinos

SNSI effects extend beyond standard oscillation fits. In DUNE-oriented studies of quantum correlations, scalar NSI were shown to affect both spatial non-locality, quantified by CHSH inequalities, and temporal non-locality, quantified by Leggett-Garg type inequalities. The strongest effect was found for the off-diagonal parameter $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$4, while diagonal parameters such as $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$5 were found to have negligible impact. For $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$6 GeV, LGtI violation can be amplified by up to $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$7 relative to the standard oscillation scenario (Yadav et al., 2024).

Supernovae provide a particularly dense environment in which new scalar effects can dominate flavor conversion. One study of flavor-conserving SNSI found that nonzero $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$8 or $\eta_{ee},\eta_{\mu\mu},\eta_{\tau\tau}$9 can invert the neutrino mass eigenstate in which flavor states are produced inside the supernova core, significantly modifying the electron-neutrino flux reaching Earth. In that framework, the early $\eta_{e\mu},\eta_{e\tau},\eta_{\mu\tau}$0 signal at DUNE becomes degenerate between normal ordering with SNSI and inverted ordering without SNSI, while the $\eta_{e\mu},\eta_{e\tau},\eta_{\mu\tau}$1 distribution at Hyper-Kamiokande can break the degeneracy (Das et al., 22 Aug 2025).

A complementary Galactic-supernova analysis emphasized that, in the supernova environment, SNSI induce a density-squared-dependent contribution to the mass-squared differences. This alters resonant flavor conversion and the neutronization burst, and for a given mass ordering supernova neutrinos can improve the sensitivity to SNSI parameters by up to four orders of magnitude compared to solar or terrestrial neutrino sources (Dutta et al., 22 Aug 2025).

High-energy astrophysical neutrinos furnish another extension of the framework. In a scenario where a Majorana-type scalar interaction with the relic neutrino background induces tiny active-sterile mass splittings, SNSI lead to pseudo-Dirac behavior, modifying both the flavor composition and the energy distribution of astrophysical neutrino fluxes. Joint flavor and spectral analyses with IceCube data and IceCube-Gen2 projections were used to translate these effects into limits on the underlying Yukawa couplings and scalar mass for ultra-light mediators (Verma et al., 23 Jun 2026).

A related supernova literature considers scalar or pseudoscalar nonstandard neutrino self-interactions rather than matter-induced SNSI in the oscillation Hamiltonian. In that setting, the effective interaction vanishes in the ultrarelativistic limit for Dirac neutrinos but not for Majorana neutrinos; flavor-preserving self-interactions suppress collective oscillations, whereas flavor-violating self-interactions promote them (Yang et al., 2018).