Atmospheric neutrino constraints on Lorentz invariance violation with the first six detection units of KM3NeT/ORCA

Using 1.4 years of atmospheric neutrino data from the first six detection units of the KM3NeT/ORCA detector, this study finds no evidence for isotropic Lorentz invariance violation and establishes competitive new limits on relevant coefficients.

The Gist

Imagine the universe as a giant, perfectly smooth dance floor. For nearly a century, physicists have believed that the rules of this dance (the laws of physics) are the same no matter which way you face, how fast you're moving, or where you are in the room. This rule is called Lorentz Invariance. It's the foundation of our understanding of reality, from the tiniest atoms to the vastness of space.

However, some new theories suggest that at the very smallest scales (the "Planck scale"), this dance floor might actually be made of tiny, pixelated tiles, like a video game screen. If the floor is pixelated, the rules of the dance might change slightly depending on your direction or speed. This would be a violation of Lorentz Invariance.

This paper is about a team of scientists (the KM3NeT collaboration) who went looking for these "pixels" using a giant underwater telescope.

The Detective: KM3NeT/ORCA

Think of KM3NeT/ORCA as a massive, high-tech net dropped into the deep Mediterranean Sea, 2,450 meters down near France.

• The Net: It consists of strings of light sensors (called optical modules) that look like glowing jellyfish.
• The Target: They are hunting for neutrinos. These are ghostly particles that rain down on Earth from the atmosphere. They are so light and shy that they can pass through the entire Earth without hitting anything.
• The Current Setup: At the time of this study, the net wasn't fully built yet. They only had six "detection units" (imagine six vertical strings of sensors) active. This is like trying to catch fish with a small hand-net instead of a massive trawler, but it's still enough to get some data.

The Hunt: Looking for "Glitches"

The scientists collected data for 1.4 years. They watched how these ghostly neutrinos behaved as they traveled through the Earth.

In the standard "dance" (Standard Model), neutrinos change their "flavor" (identity) as they travel. For example, a muon-neutrino might turn into a tau-neutrino. This happens in a very predictable pattern based on their energy and how far they traveled.

The scientists asked: "What if the dance floor is pixelated?"
If Lorentz Invariance is violated, the neutrinos would behave strangely. Their pattern of changing flavors would get distorted, especially at high energies. It would be like a dancer suddenly tripping or changing steps in a way that defies the music, but only when they spin very fast.

The Method: Filtering the Noise

The ocean is noisy.

1. The Background Noise: The sea is full of radioactive decay and glowing plankton (bioluminescence). It's like trying to hear a whisper in a crowded stadium.
2. The Muon Problem: The biggest troublemakers are "atmospheric muons" (particles created by cosmic rays hitting the air). They are like a thousand times more common than neutrinos.
3. The Solution: The scientists used the Earth as a shield. They only looked at neutrinos coming from below (up-going). Since the Earth is solid, muons can't pass through it, but neutrinos can. They also used smart computer algorithms (like a "boosted decision tree," which is basically a very advanced filter) to separate the real neutrino signals from the noise.

The Results: The Dance Floor is Smooth

After analyzing the data, the scientists found no evidence of any "pixels" or glitches.

• The neutrinos danced exactly as the standard rules predicted.
• They didn't trip, stumble, or change steps unexpectedly.

Because they found nothing, they didn't discover "new physics" in the sense of finding a violation. Instead, they did something just as important: They set a stricter speed limit.

They calculated the maximum size of the "pixels" the dance floor could possibly have. If the floor is pixelated, the tiles must be so incredibly small that the ORCA detector (even with just six units) couldn't see them.

Why This Matters

• New Limits: They set the tightest constraints yet on certain types of Lorentz violations, specifically for "diagonal" coefficients (a technical term for how the violation affects different types of neutrinos).
• Independence: Unlike previous experiments that had to guess the initial mix of neutrinos coming from space, this experiment used atmospheric neutrinos (created right here on Earth), making their results more robust and less dependent on assumptions.
• Future Potential: This was just the "beta test" with six units. The full KM3NeT detector will have over 100 units. As the net gets bigger, the scientists will be able to see even tinier "pixels" on the dance floor.

The Takeaway

Think of this paper as a report from a very careful inspector. They checked the universe's rulebook with a new, high-precision tool. They found that, so far, the rules hold up perfectly. The universe is still smooth, continuous, and consistent, at least down to the incredibly tiny scales they were able to probe. While they didn't find the "new physics" they were hoping for, they proved that if it exists, it's hiding even deeper than we thought.

Technical Summary

Here is a detailed technical summary of the paper "Atmospheric neutrino constraints on Lorentz invariance violation with the first six detection units of KM3NeT/ORCA."

1. Problem Statement

Lorentz invariance (LI) is a fundamental symmetry of the Standard Model and General Relativity, asserting that physical laws remain invariant for all inertial observers. However, various theories of Quantum Gravity (QG), such as string theory and loop quantum gravity, predict that LI may be violated at or near the Planck scale ($M_P \sim 10^{19}$ GeV).

The Standard Model Extension (SME) provides a comprehensive effective field theory framework to parameterize these violations. In the neutrino sector, LI violation (LIV) can modify standard oscillation probabilities, introducing energy-dependent effects that deviate from the standard $\Delta m^2/2E$ behavior. While previous experiments like Super-Kamiokande and IceCube have constrained these effects, there is a need for independent, high-precision measurements, particularly in the low-to-intermediate energy range (GeV scale) and for specific coefficient combinations that have not been fully explored.

The specific challenge addressed: To constrain isotropic LIV coefficients using atmospheric neutrinos detected by the KM3NeT/ORCA detector in its early configuration (ORCA6), focusing on both off-diagonal and diagonal coefficients across various mass dimensions ($d$).

2. Methodology

Detector and Data Sample

• Detector: The analysis utilizes the KM3NeT/ORCA (Oscillation Research with Cosmics in the Abyss) detector, a deep-sea water Cherenkov telescope located off the coast of Toulon, France.
• Configuration: The study uses data from the ORCA6 configuration, comprising the first six detection units (DUs). Each DU contains 18 Digital Optical Modules (DOMs) with 31 photomultiplier tubes (PMTs) each.
• Dataset: Data collected from January 2020 to November 2021 (1.4 years of livetime), resulting in an exposure of 433 kton-years.
• Event Selection:
  • Background Rejection: Atmospheric muons are suppressed by selecting only up-going events (using the Earth as a shield) and applying a Boosted Decision Tree (BDT) to reduce misreconstructed muons to $<2\%$.
  • Topology Classification: A second BDT separates events into High Purity Tracks (HPT), Low Purity Tracks (LPT), and Showers.
    • Tracks: Dominated by $\nu_\mu$ charged-current (CC) interactions ($\sim95\%$ purity in HPT).
    • Showers: Dominated by $\nu_e$, $\nu_\tau$, and neutral-current (NC) interactions.
  • Final Sample: The analysis uses 5,828 observed events across these three classes.

Theoretical Framework

The study employs the SME Hamiltonian for neutrino propagation:
$$H = U H_0 U^\dagger + H_M + H_{LIV}$$
Where $H_{LIV}$ contains LIV terms scaling with energy as $E^{d-3}$, where $d$ is the mass dimension of the operator.

• Isotropic Assumption: The analysis focuses on isotropic LIV, which preserves rotational symmetry in a preferred frame, simplifying the parameter space to coefficients $\mathring{k}^{(d)}_{\alpha\beta}$.
• Coefficients Analyzed:
  • Off-diagonal: $\mathring{a}^{(3)}_{e\mu}, \mathring{a}^{(3)}_{e\tau}, \mathring{a}^{(3)}_{\mu\tau}$ (Mass dimension $d=3$, CPT-odd).
  • Diagonal: Combinations $(\mathring{k}^{(d)}_{\mu\mu} - \mathring{k}^{(d)}_{\tau\tau})$ for $d=3$ to $8$. The analysis reports constraints on the combination$\mathring{k}^{(d)}{\mu\mu-\tau\tau}$because the$\mathring{k}^{(d)}{ee}$ term is largely unconstrained by this dataset due to degeneracy with flux normalization.

Analysis Strategy

• Binning: Events are binned in reconstructed energy ($\log_{10} E_{reco} \in [2 \text{ GeV}, 1 \text{ TeV}]$) and zenith angle ($\cos \theta \in [-1, 0]$).
• Statistical Approach: A binned maximum likelihood fit is performed.
  • Likelihood Function: Uses a Poisson term for event counts, a Barlow-Beeston "light" term for Monte Carlo statistical uncertainties, and Gaussian penalty terms for nuisance parameters.
  • Nuisance Parameters: 15 parameters account for systematic uncertainties, including oscillation parameters ($\Delta m^2_{31}, \theta_{23}$), flux normalization, cross-sections, detector energy scale, and atmospheric muon background.
  • Test Statistic: Confidence intervals are constructed using the likelihood ratio test statistic ($-2\Delta \log \mathcal{L}$), assuming Wilks' theorem ($\chi^2$ distribution).

3. Key Contributions

1. First Constraints on Diagonal Coefficients (Model-Independent): This work provides the first experimental upper limits on diagonal isotropic LIV coefficients ($\mathring{k}^{(d)}_{\mu\mu-\tau\tau}$) that do not rely on assumptions about the initial astrophysical neutrino flavor ratios. Previous high-energy analyses (e.g., IceCube) often required assumptions about source flavor composition to constrain diagonal terms.
2. Extended Mass Dimension Coverage: The analysis constrains diagonal coefficients for mass dimensions $d=3$ through $d=8$, demonstrating the sensitivity of the ORCA6 detector to higher-order LIV effects despite its smaller size compared to full-scale detectors.
3. Competitive Limits with Early Data: Despite using only 6 detection units and 1.4 years of data, the results are competitive with, and in some cases complementary to, limits set by Super-Kamiokande (12 years) and IceCube (2 years).
4. Phase Independence: The study demonstrates that for off-diagonal coefficients, the complex phase dependence is weak enough to fix the phase to zero without significantly affecting the sensitivity, simplifying future analyses.

4. Results

No evidence for Lorentz invariance violation was found. The analysis sets upper limits (95% and 99% Confidence Levels) on the magnitude of the LIV coefficients.

• Off-Diagonal Coefficients ($d=3$):

  • $\mathring{a}^{(3)}_{\mu\tau}$: The strongest constraint is obtained here due to the high purity of $\nu_\mu$ track events.
    • 95% CL Limit: $|\mathring{a}^{(3)}_{\mu\tau}| < 0.48 \times 10^{-23}$ GeV.
  • $\mathring{a}^{(3)}_{e\mu}$ and $\mathring{a}^{(3)}_{e\tau}$: Limits are weaker ($\sim 10^{-22}$ GeV) due to matter potential suppression for $\nu_e$ and lower sensitivity to shower-like events, respectively.

• Diagonal Coefficients ($d=3$ to $8$):

  • Limits are reported for the combination $\mathring{k}^{(d)}_{\mu\mu-\tau\tau}$.
  • $d=3$: $|\mathring{a}^{(3)}_{\mu\mu-\tau\tau}| < 1.56 \times 10^{-23}$ GeV (95% CL).
  • $d=4$: $|\mathring{c}^{(4)}_{\mu\mu-\tau\tau}| < 1.22 \times 10^{-24}$.
  • **$d=5$ to $8$:** Limits scale down with increasing dimension (e.g.,$d=8$limit is$\sim 4.69 \times 10^{-31}$GeV$^{-4}$), reflecting the$E^{d-3}$ scaling where higher dimensions become relevant at higher energies, but the dataset still provides meaningful constraints.

• Comparison: The exclusion regions derived from ORCA6 data are comparable to Super-Kamiokande and IceCube results, validating the detector's performance in the GeV energy range.

5. Significance

• Validation of KM3NeT/ORCA: This paper serves as a critical proof-of-concept for the KM3NeT/ORCA detector, demonstrating its capability to perform high-precision physics measurements (LIV constraints) even in its partial configuration (ORCA6).
• Complementarity: The results fill a gap in the global LIV search landscape. While IceCube excels at PeV energies and Super-K at sub-GeV, ORCA targets the crucial GeV range where standard oscillations are dominant, allowing for the detection of subtle LIV-induced distortions in the oscillation pattern.
• Model Independence: By avoiding assumptions about astrophysical source flavor ratios for diagonal coefficients, the constraints provided are more robust and applicable to a wider range of theoretical models.
• Future Prospects: The analysis lays the groundwork for future studies with the full KM3NeT detector (hundreds of units), which will significantly improve sensitivity to subleading LIV effects and potentially probe the Planck scale with unprecedented precision.

In conclusion, this study successfully establishes competitive, model-independent constraints on isotropic Lorentz invariance violation using early KM3NeT/ORCA data, confirming the detector's potential as a premier facility for fundamental physics tests.