Non-Standard Neutrino Interactions at Neutrino Experiments and Colliders

This paper compares the sensitivity of neutrino experiments and high-energy colliders to non-standard neutrino interactions by analyzing specific simplified models, finding that collider searches generally provide stronger constraints than neutrino measurements, with notable exceptions for muon-philic leptoquarks and certain heavy neutral leptons.

The Gist

Imagine the universe is a giant, bustling party. For decades, physicists have been watching the guests (particles) interact, trying to figure out the rules of the game. They have a "Rulebook" called the Standard Model, which explains almost everything they see.

But there's a shy guest at the party: the Neutrino. It's a ghost-like particle that barely talks to anyone. It zips through walls, stars, and even you, without leaving a trace. Recently, scientists started wondering: What if the neutrino is actually whispering secrets to other particles that we can't hear yet?

This paper is a detective story about those whispers, called Non-Standard Interactions (NSIs). The authors, Ayres Freitas and Matthew Low, are trying to figure out: Are these whispers real, and if so, where should we look for them?

Here is the breakdown of their investigation, using some everyday analogies.

1. The Two Ways to Catch a Whisper

The authors compare two different "detective teams" trying to find these new neutrino interactions:

• Team Neutrino (The Microscope): These are experiments like DUNE or COHERENT. They shoot beams of neutrinos at detectors and watch how they bounce off atoms. They are looking for tiny deviations in how the neutrinos behave.
  • Analogy: Imagine trying to hear a whisper in a library. You have to be very quiet and listen closely to the specific sound waves.
• Team Collider (The Sledgehammer): These are giant machines like the Large Hadron Collider (LHC). They smash particles together at incredible speeds to create heavy, new particles that might be the "messengers" of these whispers.
  • Analogy: Instead of listening for a whisper, you smash two cars together to see if a hidden compartment pops open. If the compartment exists, you'll see it immediately.

2. The Big Question: Who is Better?

For a long time, people thought the "Microscope" (neutrino experiments) was the only way to find these subtle whispers. But the authors asked: What if the "Sledgehammer" (colliders) is actually better at finding the source of the whisper?

They tested three different types of "messengers" (new particles) that could carry these whispers:

1. New Force Carriers (Z' Bosons): Like a new type of invisible glue holding particles together.
2. Leptoquarks: A weird hybrid particle that is half-lepton (like an electron) and half-quark (like a proton).
3. Heavy Neutral Leptons (HNLs): A heavy, invisible cousin of the neutrino.

3. The Verdict: The Sledgehammer Wins (Mostly)

After running the numbers, the authors found a surprising result: In almost every case, the Colliders (Team Sledgehammer) are much better at finding these new particles than the Neutrino Experiments (Team Microscope).

• The LHC is already looking: The data from the LHC has already ruled out many of the places where the neutrino experiments were hoping to find these particles. It's like the LHC found the thief's footprints before the library detectives even started listening.
• The Future is Brighter for Colliders: Even with future upgrades (like the High-Luminosity LHC or a new Muon Collider), the colliders will likely set stricter limits than any neutrino experiment ever could.

4. The Exceptions: Where the Microscope Might Win

There are two specific scenarios where the "Microscope" (Neutrino experiments) might still have a chance to win the race:

• The "Muon-Loving" Leptoquark: If the new particle only likes to talk to muons (a heavy cousin of the electron), the DUNE experiment might be able to see it if the particle is very heavy (over 2 TeV).
• The "Electron-Mixing" Heavy Neutrino: If the heavy neutrino mixes specifically with electron-neutrinos, the DUNE experiment might see a signal that current collider data misses.

However, there's a catch: The authors warn that the "Microscope" is very sensitive to noise. If the DUNE experiment has even a small amount of "static" (systematic errors) in its data, its ability to find these whispers drops dramatically. The colliders are much more robust.

5. The "Fine-Tuning" Loophole

The authors also looked at a clever trick: What if the new physics is so subtle that it only shows up in "dimension-8" operators (a fancy math way of saying "very, very weak interactions")? This would allow the new particles to hide from the colliders.

• The Analogy: Imagine the thief is wearing a cloak that makes them invisible to the security cameras (colliders) but leaves a faint footprint on the floor (neutrino experiments).
• The Reality: To make this cloak work, the universe would have to be "fine-tuned" with incredible precision—like balancing a pencil on its tip while riding a rollercoaster. The authors found that even with this trick, the colliders are still very good at catching the thief because the "footprints" left behind are still too big to ignore.

Summary

Think of this paper as a report from a detective agency. They investigated whether we need to build more sensitive listening devices (neutrino experiments) or bigger smashing machines (colliders) to find new physics.

Their conclusion: For most scenarios, bigger smashing machines are the way to go. The LHC and future colliders are already doing a better job of hunting down these "non-standard" neutrino interactions than the specialized neutrino experiments. While the neutrino experiments have a few narrow windows where they might still find something, the colliders are the heavy hitters that will likely define the future of this search.

The only thing that could change this verdict is if the neutrino experiments can perfectly eliminate all their "static" (systematic errors), but even then, the colliders are likely to stay ahead.

Technical Summary

1. Problem Statement

Neutrino Non-Standard Interactions (NSIs) are a generic framework to parametrize Beyond the Standard Model (BSM) physics affecting neutrino propagation and scattering. These are typically described by low-energy effective field theory (EFT) using dimension-6 four-fermion operators.

• The Conflict: While neutrino experiments (oscillations, scattering) are sensitive to these low-energy effects, the same BSM physics often generates contributions to processes involving charged leptons (e.g., $q\bar{q} \to \ell^+\ell^-$) at high-energy colliders.
• The Gap: Previous studies often compared neutrino constraints using EFT with collider constraints using the same EFT. However, at high-energy colliders (like the LHC), the EFT description often breaks down because the mediator mass is within the kinematic reach. Furthermore, specific UV-complete models may generate dimension-8 operators (which affect neutrinos but not charged leptons at tree level) to evade charged-lepton constraints, but such scenarios require fine-tuning.
• Objective: The authors aim to rigorously compare the discovery reach of current and future neutrino experiments against high-energy colliders (LHC, future $e^+e^-$, and $\mu^+\mu^-$ colliders) using explicit UV-complete simplified models rather than just effective operators.

2. Methodology

The authors analyze three classes of minimal BSM models that generate NSIs at tree-level via dimension-6 operators, and one scenario involving dimension-8 operators.

A. Models Studied

1. Spin-1 Mediators (Gauge Bosons):
   • $Z'_{B-L}$: A $U(1)_{B-L}$ gauge boson coupling universally to quarks and leptons.
   • Axial-Vector $Z'$: A $U(1)$ extension with specific charges to generate significant axial-vector NSIs (which are invisible to oscillations but visible in inelastic scattering).
2. Spin-0 Mediators (Scalar Leptoquarks):
   • An electroweak doublet scalar leptoquark $\Omega(3, 2, 1/6)$.
   • Two specific flavor scenarios: Muon-philic ($\lambda_{\mu d} \neq 0$) and Tau-philic ($\lambda_{\tau d} \neq 0$).
3. Spin-1/2 Mediators (Heavy Neutral Leptons - HNLs):
   • SU(2) singlet pseudo-Dirac fermions mixing with SM neutrinos.
   • Scenarios: Mixing exclusively with $\nu_e$, $\nu_\mu$, or $\nu_\tau$.
4. Dimension-8 Operators:
   • A "toy model" with both scalar and vector leptoquarks to generate dimension-8 operators (Eq. 9) while canceling dimension-6 contributions via fine-tuning, specifically to evade charged-lepton constraints.

B. Experimental Inputs & Constraints

• Neutrino Experiments:
  • Current: Global fits of oscillation data (MINOS, T2K, NO$\nu$A) + Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) from COHERENT. NuTeV scattering data for muon neutrinos.
  • Future: Projections for DUNE Near Detector (ND) scattering (both statistical and systematic uncertainties), KM3NeT/ORCA, and JUNO/TAO.
• Colliders:
  • LHC: Direct searches for resonances ($Z' \to \ell\ell$, Leptoquark pair/single production) and Drell-Yan deviations ($pp \to \ell\ell$). Data from ATLAS/CMS (13 TeV) and projections for HL-LHC (14 TeV, 3 ab$^{-1}$).
  • Future Lepton Colliders: FCC-ee ($e^+e^-$ at 240 GeV) and a 3 TeV Muon Collider ($\mu^+\mu^-$).
  • Electroweak Precision (EWPT): Constraints on $Z$-width and Fermi constant ($G_F$) modifications.

C. Computational Tools

• CalcHEP and MadGraph 5 were used to calculate cross-sections and asymmetries for collider processes, including initial-state radiation and specific kinematic cuts.
• The analysis maps collider limits directly to the parameter space ($g/M$ or $\lambda/M$) of the specific models, rather than relying on generic EFT bounds.

3. Key Results

A. General Trend: Colliders Dominate

For the vast majority of the models studied, collider searches provide significantly stronger constraints than neutrino experiments.

• $Z'$ Models: Existing LHC Drell-Yan limits ($pp \to \ell^+\ell^-$) already exclude the parameter space where DUNE or future neutrino experiments would have sensitivity. The HL-LHC and Muon colliders will further tighten these bounds.
• Tau-philic Leptoquarks: LHC pair-production limits ($m_\omega > 990$ GeV) and Drell-Yan constraints far exceed current and projected neutrino bounds.

B. Notable Exceptions (Where Neutrino Experiments Compete)

The authors identify two specific scenarios where neutrino experiments could be competitive or superior, contingent on systematic uncertainties:

1. Muon-philic Leptoquarks:
   • If DUNE ND systematic uncertainties are negligible, the statistical sensitivity of neutrino scattering could surpass the HL-LHC reach for leptoquark masses $m \gtrsim 2$ TeV.
   • However, a 10% systematic uncertainty on detection efficiency degrades the DUNE reach significantly, making it less competitive than the HL-LHC.
2. Heavy Neutral Leptons (HNLs) mixing with $\nu_e$:
   • LHC direct searches for HNLs are weak for this mixing pattern.
   • DUNE ND scattering (statistical only) can probe mixing angles $|\theta_e|$ smaller than current LEP electroweak precision data.
   • Caveat: Future FCC-ee electroweak precision measurements are projected to be even more constraining than DUNE.

C. Dimension-8 Operators and Fine-Tuning

• The paper investigates models where dimension-8 operators dominate to avoid charged-lepton constraints.
• Result: Achieving this requires a fine-tuned cancellation between two different mediators (e.g., scalar and vector leptoquarks) to suppress dimension-6 operators.
• Collider Impact: Even with this cancellation, the LHC Drell-Yan bounds are only weakened by a factor of $\sim 1.5$ for high masses ($M=5$ TeV). The viable parameter space remains strongly constrained by collider data, often more so than by neutrino experiments, because the NSI signal itself is suppressed by the dimension-8 nature.

4. Significance and Conclusions

• Model-Dependence is Crucial: The paper demonstrates that comparing neutrino and collider sensitivities requires explicit model building. EFT comparisons can be misleading at high energies where the mediator is on-shell.
• Systematics are the Deciding Factor: The potential for neutrino experiments (specifically DUNE ND) to outperform colliders hinges entirely on the control of systematic uncertainties. If systematics are high (e.g., 10%), colliders win; if they are negligible, neutrino experiments can probe higher mass scales for specific models (muon-philic leptoquarks).
• Complementarity: While colliders generally dominate, neutrino experiments offer a unique probe for specific flavor structures (like $\nu_e$-HNL mixing) where collider direct searches are blind or weak, provided electroweak precision data does not rule them out first.
• UV Completion Constraints: The study reinforces that "natural" models generating NSIs are heavily constrained by charged-lepton observables. Models attempting to evade these via dimension-8 operators require fine-tuning and still face significant collider constraints.

In summary, the paper concludes that high-energy colliders are generally the most powerful tool for constraining NSI mediators, but neutrino experiments retain a niche capability to probe specific, high-mass, or flavor-specific scenarios if experimental systematics can be minimized.