Non-Standard Neutrino Interactions

• Non-standard neutrino interactions (NSI) are deviations from Standard Model neutrino behavior, described by effective dimension-6 four-fermion operators in the SMEFT framework.
• NSI modify neutrino propagation by altering matter effects and can induce unexpected oscillation phenomena that complicate the extraction of standard mixing parameters.
• Collider experiments and neutrino measurements together constrain NSI parameters, with collider searches often setting stringent limits on the mediators responsible for these interactions.

Non-standard neutrino interactions (NSI) refer to deviations from the Standard Model (SM) predictions for neutrino interactions with charged leptons and quarks, parametrized as effective four-fermion operators. These interactions, which are not contained in the SM, provide a model-independent framework for exploring the low-energy consequences of high-scale new physics and can affect both neutrino propagation in matter and neutrino production or detection processes. NSI have become a critical focus in contemporary neutrino physics for interpreting oscillation data, constraining new-physics models, and understanding the complementarity between precision neutrino measurements and high-energy collider searches.

1. Effective Operator Formalism for Non-Standard Neutrino Interactions

In the low-energy regime (energies much below the electroweak scale), NSI are described by dimension-6 operators in the Standard Model Effective Field Theory (SMEFT) framework. For neutral-current interactions relevant to neutrino propagation and scattering, the effective Lagrangian takes the form: $$\mathcal{L}_\text{NC} = -2\sqrt{2}\, G_F\, \sum_{\alpha,\beta,f,P}\, \epsilon^{(fP)}_{\alpha\beta}\ (\overline{\nu}_\alpha \gamma^\mu P_L \nu_\beta)\ (\overline{f} \gamma_\mu P f)$$ where:

• $\alpha,\beta$ are neutrino flavor indices,
• $f=u,d$ (or $e$) is the matter fermion,
• $P=P_L, P_R$ denotes chirality,
• $\epsilon^{(fP)}_{\alpha\beta}$ are dimensionless NSI parameters.

Such operators can arise after electroweak symmetry breaking from the dimension-6 SMEFT operators

$$O_{Lq}^{(1)} = (\overline{L}_\alpha \gamma^\mu L_\beta)(\overline{q} \gamma_\mu q)\,,\quad O_{Lq}^{(3)} = (\overline{L}_\alpha \gamma^\mu \tau^a L_\beta)(\overline{Q} \gamma_\mu \tau_a Q)\,,$$

and

$$O_{HL}^{(1)} = (H^\dagger i\overset{\leftrightarrow}{D}_\mu H) (\overline{L}_\alpha \gamma^\mu L_\beta)\,,\quad O_{HL}^{(3)} = (H^\dagger i\overset{\leftrightarrow}{D}_\mu \tau_a H)(\overline{L}_\alpha \gamma^\mu \tau^a L_\beta)\,.$$

After matching and including the Higgs vacuum expectation value, these generate vector NSI coefficients, for example

$$\epsilon^q_{\alpha\alpha} \equiv \epsilon^{(qL)}_{\alpha\alpha} + \epsilon^{(qR)}_{\alpha\alpha}$$

which are probed in oscillation and scattering experiments.

For charged-current NSI, similar operators involving $(\overline{\nu}_\alpha \gamma^\mu P_L \ell_\beta)$ arise with potentially significant phenomenological consequences for neutrino production and detection.

2. Phenomenological Implications and Experimental Signatures

NSI affect neutrino phenomenology in multiple ways:

• Propagation: The effective potential for neutrinos in matter is modified, leading to a flavor-dependent potential in the oscillation Hamiltonian. This induces alterations to resonance effects, modifies the mapping between mixing angles in vacuum and in matter, and can mimic or obscure measurements of standard oscillation parameters.
• Production and Detection: NSI of charged-current type can modify the flavor composition of the produced and detected neutrino states. These effects can induce “zero-distance” flavor transitions in oscillation experiments.
• Scattering Rates: In neutrino-nucleus, neutrino-electron, and neutrino-nucleon scattering, NSI lead to measurable deviations in cross sections.
• Degeneracy and Parameter Extraction: NSI parameters enter linearly in the Hamiltonian, leading to degeneracies with standard parameters such as the Dirac CP phase or the mass ordering.

Key experimental channels sensitive to NSI include long-baseline oscillations (DUNE, Hyper-Kamiokande), coherent elastic neutrino-nucleus scattering (CE$\nu$NS, e.g., COHERENT), and deep inelastic scattering (CHARM, NuTeV, future collider-based neutrino detectors).

3. Neutrino Versus Collider Constraints and Complementarity

There is a fundamental complementarity between low-energy (neutrino) and high-energy (collider) probes of NSI:

• Neutrino Experiments: These provide direct sensitivity to the low-energy effective operators by measuring deviations in oscillation probabilities, cross sections, and coherent scattering rates. Oscillation experiments are especially sensitive to specific combinations of NSI parameters (e.g., $\epsilon_{ee} - \epsilon_{\mu\mu}$ for long-baseline appearance probabilities), while CE$\nu$NS and inelastic scattering can measure absolute magnitudes.
• Collider Searches: High-energy colliders (LHC, HL-LHC, FCC-ee, muon colliders) probe the mediators responsible for NSI, either through direct production (resonances) or through contact-interaction effects at finite momentum transfer. When the mediator mass is within collider reach, the effective field theory treatment breaks down and explicit models must be considered. Collider limits become especially strong for models where the same mediator couples to charged leptons, as this leads to signatures (e.g., dilepton production) tightly constrained by existing data.

Empirical comparisons indicate that, except in cases where NSI arise dominantly in neutrino-specific channels (e.g., muon-philic leptoquarks, heavy neutral leptons with large electron or muon neutrino mixing), collider bounds are typically more stringent than those from current or anticipated neutrino measurements (Freitas et al., 2 May 2025).

4. Realizations in Simplified New Physics Models

The landscape of explicit new physics models producing NSI includes several representative classes:

Model Type	Mediator Signature	Produced NSI	Example Constraint
U(1) Gauge Bosons	$Z'$ (e.g. $B-L$ or axial)	Vector, Axial	$\epsilon_{\ell\ell}^q \propto g_{Z’}^2/m_{Z’}^2$
Scalar Leptoquarks	Leptoquark (doublet, singlet)	Scalar, Vector	$$\epsilon_{\ell\ell}^d \propto |\lambda_{\ell d}|^2/(4\sqrt{2} G_F m_\omega^2)$$
Heavy Neutral Leptons	SM singlet, mass mixing	All (via mixing)	NSI param. linear in mixing angles $\theta_\alpha$

In gauge boson models, collider constraints on di-lepton production robustly limit the parameter space accessible to neutrino experiments unless the mediator couples almost exclusively to neutrinos. For leptoquarks, LHC data from pair and single leptoquark production typically eliminate significant regions where large NSI would arise, apart from specialized flavor scenarios. Heavy neutral leptons can enhance NSI if the mixing with light neutrinos is sizable for electron or muon flavors; in these cases near detector measurements (e.g., DUNE ND) may set unique bounds.

The effective NSI coefficients in these models are functions of mediator couplings, masses, and mixing angles, as specified by explicit matching to the SMEFT or UV Lagrangians.

5. EFT Limitations and Higher-Dimensional Operator Effects

The effective operator approximation that links collider and neutrino experiment sensitivities relies on the assumption that the scale of new physics $\Lambda$ is much larger than the experimental momentum transfers. When mediators are within collider kinematics, the EFT breaks down, and collider bounds must be interpreted within the context of simplified models with explicit propagators.

Efforts to build models where neutrino NSIs arise dominantly via dimension-8 operators—thus avoiding strong charged-lepton constraints at colliders—encounter significant theoretical obstacles. UV completions which produce dimension-8 operators without also generating detectable dimension-6 operators require fine-tuned cancellations (for instance, between scalar and vector leptoquark contributions), and even then collider constraints remain relevant due to residual production or interference effects.

6. Future Directions and Theoretical Considerations

Future large-scale neutrino experiments (DUNE, Hyper-Kamiokande, new muon collider detectors) will reach NSI sensitivity as low as $|\epsilon|\sim 10^{-3}$ for certain channels, probing scales up to tens of TeV. Nonetheless, for most reasonable UV completions, high-energy collider bounds are expected to remain leading except in exotic scenarios precisely engineered to evade them.

The discriminating power of neutrino experiments will be at its strongest for:

• Flavored new physics where the mediator couples predominantly to specific neutrino flavors,
• Models where the mediator is effectively “neutrinophilic” (e.g., heavy neutral leptons coupled to only one flavor),
• New phenomena not coupled to charged leptons (dimension-8 or loop-induced scenarios where SM fermions other than neutrinos are not involved at tree level).

Exploration of correlated signals in multiple channels (charged-current, neutral-current, and charged lepton flavors) and combined analyses of neutrino plus collider data will be essential for disentangling the structure of any observed NSI from more mundane systematic effects or other new physics signals.

7. Summary Table: NSI Sensitivity in Selected Models and Experiments

Model/Scenario	Neutrino Sensitivity	Collider Sensitivity	Dominant Bound
U(1) $B$–$L$/$Z'$ vector	$\epsilon \sim 10^{-3}$	$g_{Z’}/m_{Z’}$ from di-lepton/di-jet	Collider bound
Scalar leptoquark (tau-philic)	$\epsilon \sim 10^{-2}$	$m_\omega,\lambda_{\ell d}$ from LQ production	Collider bound
Scalar leptoquark (muon-philic)	$\epsilon \sim 10^{-4}$ (DUNE ND)	Similar, but less stringent	Potentially neutrino bound
Heavy neutral lepton (νe, νμ)	$\epsilon \sim 10^{-4}$ (DUNE ND)	Weak, unless EW precision	Potentially neutrino bound
Heavy neutral lepton (ν_τ)	Limited	$Z$-width, EW precision	Collider bound

This demonstrates that, with the exception of select flavor scenarios (muon-philic or large mixing with νe/νμ), collider searches currently set the most stringent constraints on non-standard neutrino interactions (Freitas et al., 2 May 2025).

---

This comprehensive overview reflects the interplay between neutrino physics and collider probes in the ongoing search for evidence of non-standard neutrino interactions and the extension of the Standard Model.