Constraining axial non-standard neutrino interactions with MINOS and MINOS+

This paper demonstrates that neutral current data from the MINOS and MINOS+ experiments yield world-leading constraints on axial non-standard neutrino interactions with up and down quarks, particularly providing the first significant bounds on the theoretically motivated isospin singlet case involving tau neutrinos.

The Gist

Imagine the universe is a giant, invisible dance floor. On this floor, tiny particles called neutrinos are constantly zipping around, passing through walls, people, and planets without bumping into anything. They are the "ghosts" of the particle world.

For decades, physicists have had a rulebook for how these ghosts dance, called the Standard Model. But recently, scientists started wondering: Is there a secret dance move we haven't seen yet? Maybe there's a new kind of invisible partner or a hidden force that changes how neutrinos interact with matter. These hypothetical new moves are called Non-Standard Interactions (NSI).

This paper is like a detective story where the authors use a massive, high-tech camera to catch these ghosts in the act and see if they are doing any of these secret moves.

The Setting: The MINOS and MINOS+ Experiments

Think of the MINOS and MINOS+ experiments as a giant, two-story observation post.

• The Source: A particle accelerator in Illinois shoots a beam of neutrinos (mostly "muon neutrinos," let's call them "Muons") like a giant flashlight beam.
• The Near Detector: A camera right next to the flashlight. It sees the beam before it travels far.
• The Far Detector: A massive steel-and-scintillator camera buried deep underground in a mine in Minnesota, 450 miles away.

As the "Muons" travel 450 miles, some of them naturally change their identity (a process called "oscillation") into "Tau neutrinos" or "Electron neutrinos."

The Mystery: The "Axial" Interaction

In the Standard Model, neutrinos interact with matter in two main ways:

1. Vector: Like a gentle push.
2. Axial: Like a spin or a twist.

The authors of this paper are specifically hunting for the "Axial" twist. They suspect that neutrinos might be interacting with the up (u) and down (d) quarks (the building blocks of protons and neutrons) in a way that involves this "twist."

If this "twist" exists, it would be a new force of nature, potentially caused by a new, undiscovered particle that is lighter than the famous W boson.

The Investigation: How They Caught the Ghosts

The researchers looked at the data from the Far Detector in Minnesota. They were looking at Neutral Current (NC) events.

• Analogy: Imagine you are watching a pool game.
  • Charged Current: The cue ball hits another ball, and you see the second ball fly off. You know exactly what happened.
  • Neutral Current: The cue ball hits a ball, but the second ball stays hidden (it's a neutrino leaving the scene). You only see the cue ball bounce off and change direction slightly.

In the MINOS experiment, when a neutrino hits a nucleus in the detector, it usually bounces off and leaves a neutrino behind. The detector measures the energy of the debris left behind. The authors compared the actual number of bounces they saw against the number predicted by the Standard Model.

The Big Findings

Here is what they discovered, translated into plain English:

1. The "Tau" Twist is Constrained:
   Before this paper, scientists had very loose rules about how strong this "Axial twist" could be for Tau neutrinos (the heavy, shy cousins of the Muon). Some theories suggested the twist could be huge (as strong as the weak force itself).

   • The Result: The MINOS data says, "Nope, it can't be that big." They tightened the leash significantly. If this twist exists, it's much weaker than previously thought possible.

2. The "Isospin Singlet" Mystery:
   There is a specific theoretical scenario where the twist affects up-quarks and down-quarks exactly the same way (like a perfect mirror image). This was a "wild card" that had never been tested before.

   • The Result: This is the paper's biggest win. They put the first-ever serious limits on this specific scenario. They ruled out the idea that this twist is huge.

3. Ruling Out "Fake" Solutions:
   Previous experiments (like SNO) found some weird, disconnected mathematical solutions where the data could be explained by a huge twist.

   • The Result: The MINOS data is so precise that it completely rules out those weird, disconnected solutions. The "ghosts" aren't doing those specific secret moves.

4. The "Strangeness" of the S-Quark:
   They also looked at interactions with the Strange quark.

   • The Result: The data wasn't sensitive enough to say much about this one. The limits are still very loose (order of 1), meaning this specific interaction is still wide open for discovery.

The Future: Enter DUNE

The paper also looks ahead to a future experiment called DUNE (Deep Underground Neutrino Experiment).

• Analogy: If MINOS is a standard-definition camera, DUNE is a 4K, high-speed, slow-motion camera with a super-lens.
• The Prediction: DUNE will be able to measure these "twists" with incredible precision, potentially seeing effects that MINOS can only guess at.

The Bottom Line

This paper is a major step in "neutrino hunting." By using the existing data from MINOS and MINOS+, the authors have:

• Closed the door on some wild theories about how neutrinos interact with matter.
• Set the world's best limits on specific types of "Axial" interactions involving Tau neutrinos.
• Proved that if new physics exists in this area, it's hiding in a very small, specific corner of the universe, waiting for the next generation of experiments (like DUNE) to find it.

In short: The neutrinos are still behaving mostly as the Standard Model predicts, but the "twist" is now known to be much smaller than we hoped, narrowing the search for new physics.

Technical Summary

1. Problem Statement

The paper addresses the search for Non-Standard Interactions (NSI) of neutrinos with matter, specifically focusing on axial-vector neutral current (NC) couplings ($\epsilon^A_q$) with up ($u$) and down ($d$) quarks.

• Context: While vector NSI ($\epsilon^V$) are tightly constrained by neutrino oscillation data and Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS), axial NSI do not affect forward scattering or CE$\nu$NS. Consequently, they have historically been less constrained, particularly for the $\tau\tau$, $e\tau$, and $ee$ flavor components.
• Gap: Previous bounds on axial NSI were either weak (order of 1) or relied on specific disconnected solutions found in Solar Neutrino (SNO) data. The isospin singlet case ($\epsilon^A_u = \epsilon^A_d$) was theoretically motivated but practically unconstrained.
• Goal: To utilize the existing neutral current event data from the MINOS and MINOS+ experiments to derive world-leading constraints on these axial couplings, specifically for the $\tau\tau$, $e\tau$, and $ee$ components.

2. Methodology

The authors performed a comprehensive statistical analysis using the public data from MINOS and MINOS+.

• Data Source:

  • Used the neutrino mode data from MINOS (2005–2012) and MINOS+ (2013–2019).
  • Total exposure: $16.36 \times 10^{20}$ Protons On Target (POT).
  • Utilized 54 energy bins (27 for Near Detector, 27 for Far Detector) spanning 0 to 40 GeV, covering quasi-elastic, resonance, and Deep Inelastic Scattering (DIS) regimes.
  • Incorporated the full covariance matrix (statistical and systematic uncertainties) provided in the MINOS+ publication (Ref [22]).

• Theoretical Framework:

  • Defined the effective Lagrangian for NC NSI involving axial couplings $\epsilon^A_{q,\alpha\beta}$ (where $q \in \{u, d\}$ and $\alpha, \beta \in \{e, \mu, \tau\}$).
  • Cross-Section Calculation: Used the NuWro Monte Carlo generator to compute scattering cross-sections for $\nu_\mu$ interactions on nuclei, accounting for nuclear effects across all energy regimes.
  • Oscillation Modeling: Calculated the probability of $\nu_\mu \to \nu_\beta$ oscillations at the Far Detector (735 km baseline) using standard 3-flavor oscillation parameters (NuFIT 6.0).
  • NSI Impact:
    • For diagonal NSI, the event rate is a weighted sum of standard cross-sections modified by the NSI couplings.
    • For off-diagonal NSI (e.g., $\epsilon^A_{e\tau}$), the authors performed a basis transformation to diagonalize the interaction matrix, calculating the interference between flavor components.
    • Crucially, they noted that while NSI modifies the cross-section, it does not alter the oscillation probability in the absence of vector NSI, allowing for a clean separation of effects.

• Statistical Analysis:

  • Constructed a $\chi^2_{NC}$ statistic comparing observed events ($N^{obs}$) with predicted events ($N^{pre}$) including NSI effects.
  • Performed a Markov Chain Monte Carlo (MCMC) analysis using the Cobaya framework.
  • Marginalization: The analysis marginalized over standard oscillation parameters ($\theta_{23}, \theta_{13}, \delta, \Delta m^2_{31}$) using Gaussian priors to account for their uncertainties.
  • Scenarios: Analyzed cases with single non-zero couplings and cases with multiple non-zero couplings (including isospin singlet $\epsilon^A_u = \epsilon^A_d$ and isovector $\epsilon^A_u = -\epsilon^A_d$).

3. Key Contributions

1. First Constraints on Isospin Singlet Axial NSI: The paper provides the first experimental constraints on the isospin singlet case ($\epsilon^A_u = \epsilon^A_d$) for the $\tau\tau$ and $e\tau$ components, which were previously unconstrained.
2. Resolution of Disconnected Solutions: The authors demonstrate that MINOS(+) data rules out "non-trivial disconnected solutions" (large coupling values around $\pm 1$ to $\pm 2$) previously suggested by SNO data with high confidence.
3. World-Leading Bounds: The derived bounds on $\epsilon^A_{e\tau}$ and $\epsilon^A_{\tau\tau}$ are currently the most stringent in the world, surpassing previous limits from SNO and NuTeV.
4. Methodological Demonstration: The paper establishes a robust framework for using long-baseline NC data to probe axial NSI, a channel often overlooked in favor of oscillation-based vector NSI searches.

4. Key Results

The study presents 90% Confidence Level (C.L.) bounds on the axial couplings. Key findings include:

• Isospin Singlet Case ($\epsilon^A_u = \epsilon^A_d$):

  • $\epsilon^A_{\tau\tau}$: Constrained to $[-0.25, 0.36]$. This is a significant improvement over previous limits and rules out the previously allowed large values ($\sim 1$).
  • $\epsilon^A_{e\tau}$: Constrained to $[-0.32, 0.27]$.
  • $\epsilon^A_{ee}$: Constrained to $[-1.67, 1.8]$.
  • Note: These results are the first to constrain these specific isospin singlet parameters.

• General Cases ($\epsilon^A_u \neq \epsilon^A_d$):

  • The bounds on $\epsilon^A_{\tau\tau}$ and $\epsilon^A_{e\tau}$ for general ratios of $u/d$ couplings are significantly tighter than previous literature (Ref [19]).
  • MINOS(+) data excludes the disconnected solutions found in Ref [19] (e.g., solutions around $\epsilon \approx -2$) at high confidence.

• $\mu$-flavor Components:

  • Bounds on $\epsilon^A_{\mu\mu}$ and $\epsilon^A_{\mu\tau}$ are weaker than existing NuTeV limits but consistent with them.
  • The paper notes that future experiments like DUNE will have much higher sensitivity to these components.

• Strange Quark ($s$) Couplings:

  • Constraints on $\epsilon^A_s$ and $\epsilon^V_s$ remain weak (order $O(1)$) because the near detector normalization uncertainties mimic the NSI effects, and the collaboration did not provide a covariance matrix between NC and Charged Current (CC) bins to break this degeneracy.

• Comparison with Future Experiments:

  • The paper forecasts that the DUNE experiment, with negligible systematic errors, could improve these bounds by an order of magnitude (reaching $\sim 0.01$).

5. Significance

• Theoretical Impact: By constraining the isospin singlet axial NSI, the paper limits the parameter space for various Beyond Standard Model (BSM) theories that predict light new mediators coupled to neutrinos and quarks.
• Experimental Strategy: It highlights the importance of Neutral Current data in long-baseline experiments. Unlike Charged Current data, NC data is flavor-universal in the Standard Model, making deviations caused by NSI (which are flavor-non-universal) highly detectable.
• Phenomenological Insight: The analysis clarifies that an excess of NC events (rather than a deficit) at future experiments like DUNE would be a unique signature of axial NSI, distinguishing it from sterile neutrino oscillations (which typically predict a deficit).
• Data Utilization: The work maximizes the scientific return of the completed MINOS and MINOS+ experiments by re-analyzing their NC data for a new physics channel that was not the primary focus of the original collaborations.

In conclusion, this paper establishes MINOS(+) as the current world leader in constraining axial non-standard neutrino interactions, particularly for the $\tau$ and $e\tau$ sectors, and sets a critical baseline for future high-precision searches at DUNE.