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Probing Lorentz Invariance Violation in Cosmogenic Neutrino Propagation with KM3-230213A

This paper investigates superluminal Lorentz invariance violation in cosmogenic neutrinos using the KM3-230213A event as a benchmark, demonstrating that while current statistics preclude formal constraints, the model predicts a distinct spectral sensitivity to LIV coefficients between $10^{-24}$ and $10^{-22}\,\mathrm{eV}^{-1}$ that depends critically on cosmic-ray source properties.

Original authors: Rodrigo Sasse, Rodrigo Guedes Lang, Rita de Cássia dos Anjos

Published 2026-09-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rodrigo Sasse, Rodrigo Guedes Lang, Rita de Cássia dos Anjos

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the fabric of our universe, there is a rule that physicists have trusted for over a century: nothing can travel faster than light. This principle, known as Lorentz invariance, is a cornerstone of modern physics, acting as the speed limit for all matter and energy. However, some theories about how gravity works at the tiniest scales suggest this rule might not be absolute. They propose that at energies far beyond what we can create in laboratories, particles might occasionally break this speed limit. While we cannot test these ideas with current machines, the universe itself offers a natural laboratory. High-energy particles from deep space, traveling for billions of years, could carry subtle signs of this violation. If such a rule-breaking effect exists, it would not just be a minor glitch; it would fundamentally change how these particles behave over vast cosmic distances, potentially revealing a new layer of reality hidden within the laws of physics.

A recent study takes a fresh look at this possibility using a specific type of cosmic messenger: neutrinos. These are ghostly, nearly massless particles that rarely interact with anything, allowing them to travel unimpeded from the most violent events in the cosmos to detectors on Earth. The researchers focused on "cosmogenic" neutrinos, which are created when ultra-high-energy cosmic rays—protons and atomic nuclei traveling at near-light speeds—collide with background light filling the universe. These collisions produce a steady, predictable stream of neutrinos that should arrive at Earth with a specific energy pattern. The team used a massive neutrino detector in the Mediterranean Sea, known as KM3NeT, which recently recorded a single, incredibly energetic event. They asked a simple but profound question: could the properties of this event, and the lack of other similar events, tell us if neutrinos are secretly breaking the speed limit?

To answer this, the researchers built a detailed simulation of how these cosmic rays travel through the universe and turn into neutrinos. They started with the most accepted models of where these cosmic rays come from and how they are composed, mixing different types of atomic nuclei to match what we observe from Earth. Then, they introduced a hypothetical scenario where neutrinos travel slightly faster than light. In this scenario, the laws of physics change in a way that makes these fast-moving neutrinos unstable. Instead of traveling all the way to Earth, they would spontaneously split into three smaller neutrinos, a process that is impossible if the speed limit holds true. This splitting would drain energy from the highest-energy neutrinos and dump it into a lower energy range, creating a distinct "pile-up" of particles at intermediate energies while leaving a gap at the very top.

The team ran their simulations to see how this splitting would change the number of neutrinos we should expect to see. They found that if neutrinos were indeed traveling faster than light, the pattern of arrivals would shift dramatically. The highest energies would be suppressed, while the energy range around a few hundred thousand trillion electron volts would see a significant increase in activity. They compared these predictions against the actual data from the KM3NeT detector and other observatories like IceCube and the Pierre Auger Observatory. The single event recorded by KM3NeT, while exciting, was not enough on its own to prove or disprove the theory. However, the study revealed a specific window of possibility. The simulations showed that if the speed-limit violation exists, it would likely be strongest for neutrinos with a specific type of energy coefficient, roughly between 10 to the power of minus 24 and 10 to the power of minus 22 inverse electron volts.

This range is crucial because it represents a sweet spot where the predicted increase in neutrinos at the energy of the KM3NeT event is noticeable, but not so large that it contradicts the strict limits set by other detectors. If the violation were any stronger, the models would predict far too many neutrinos at higher energies, which we simply do not see. Conversely, if the effect were weaker, it would be too small to explain any deviation from the standard rules. The researchers also found that the answer depends heavily on what the cosmic rays are made of. If the cosmic rays are mostly protons, the effect is more pronounced; if they are heavier nuclei, the effect is more subtle. This means that understanding the source of cosmic rays is just as important as understanding the neutrinos themselves.

Ultimately, this work does not claim to have found proof that the speed of light can be broken. Instead, it maps out exactly where to look for such a discovery. The study demonstrates that the current data is sensitive enough to test these ideas, but the statistics are not yet high enough to make a final call. The single event from KM3NeT serves as a valuable benchmark, showing that future detectors with larger collecting areas and more data could either confirm this subtle violation or rule it out completely. By refining the models and waiting for more cosmic messengers to arrive, scientists are closing in on a definitive test of one of the most fundamental rules of our universe. The search continues, guided by the precise predictions of how a broken speed limit would rewrite the story of the cosmos.

Technical Summary: Probing Lorentz Invariance Violation in Cosmogenic Neutrino Propagation with KM3-230213A

Problem Statement
The detection of the ultra-high-energy (UHE) neutrino event KM3-230213A (estimated energy $220^{+570}_{-110}$ PeV) by the KM3NeT collaboration presents a tension with standard cosmogenic neutrino flux predictions derived from UHE cosmic-ray (UHECR) models that successfully describe observed spectra and composition. While the origin of KM3-230213A remains debated, the event serves as a unique probe for non-standard neutrino physics. Specifically, the authors investigate superluminal Lorentz Invariance Violation (LIV) in the neutrino sector. In superluminal scenarios ( $v > c$ ), neutrinos become kinematically unstable, opening decay channels such as vacuum pair emission and neutrino splitting ( $\nu \to 3\nu$ ) that are forbidden in the Standard Model. These decays can substantially modify the observed neutrino flux at Earth, potentially resolving the tension between the KM3-230213A event and standard cosmogenic flux upper limits established by the Pierre Auger Observatory and IceCube.

Methodology
The study employs a simulation framework based on the CRPropa 3.2 toolkit to model UHECR propagation and the subsequent production of cosmogenic neutrinos.

Source Models: Five representative primary nuclei (H, He, N, Si, Fe) are simulated with abundances weighted to match Pierre Auger Observatory best-fit composition parameters. Two primary scenarios are tested: a "Best Fit" composition dominated by intermediate-mass nuclei, and a "Proton-Enhanced" scenario adding a 10% pure proton component with a softer spectrum and higher rigidity cutoff. Source evolution is parameterized by $\Psi(z) \propto (1+z)^m$ , with $m$ ranging from 0.0 to 2.0.
LIV Implementation: The authors implement a Modified Dispersion Relation (MDR) for superluminal neutrinos ( $\delta_{\nu, n} > 0$ ). Unlike complex cascade calculations required for photons or cosmic rays, the neutrino propagation is treated analytically. The survival probability $P_{surv}$ is calculated by integrating the energy-dependent decay rate for the dominant neutrino splitting channel ( $\nu \to 3\nu$ ) over cosmological distances.
Flux Reconstruction: A reweighting scheme is applied to the standard flux ( $\Phi_{std}$ ) to account for LIV. The modified flux ( $\Phi_{LIV}$ ) is constructed as the sum of the surviving primary flux and the redistributed secondary flux from decays, where daughter neutrinos carry approximately $1/3$ of the parent energy. This approach models the spectral suppression at high energies and the "pile-up" enhancement at lower energies.
Benchmarking: The KM3-230213A event is used as a benchmark to evaluate sensitivity. The analysis compares predicted LIV-modified fluxes against observational constraints from the Pierre Auger Observatory, IceCube (EHE limits), and the Glashow resonance event.

Key Results

Spectral Modifications: Superluminal LIV induces a characteristic spectral distortion: suppression of the flux at the highest energies (where neutrinos become unstable) and a corresponding enhancement (pile-up) at intermediate energies (PeV scale).
Parameter Sensitivity: The study identifies a specific region of observational sensitivity for the linear LIV coefficient $\delta_{\nu, 1}$ . Coefficients in the range $10^{-24} \text{ eV}^{-1} \lesssim \delta_{\nu, 1} \lesssim 10^{-22} \text{ eV}^{-1}$ maximize the expected event rate within the reconstructed energy range of KM3-230213A (72 PeV – 1 EeV) without violating upper limits from IceCube and Pierre Auger at higher energies.
Composition Dependence: The results are strongly dependent on the assumed UHECR source composition. The "Proton-Enhanced" scenario yields higher baseline fluxes and provides the most conservative constraints. In the conservative "Best Fit" (Auger-only) scenario, the standard flux at 6 PeV is negligible, and LIV coefficients large enough to enhance the flux to the level of KM3-230213A would likely conflict with other constraints.
Detection Probability: For the proton-enhanced scenario, the introduction of superluminal LIV systematically increases the probability of detecting at least one cosmogenic neutrino event in KM3NeT/ARCA. The optimal detection probability occurs in the $\delta_{\nu, 1} \sim 10^{-24} - 10^{-22} \text{ eV}^{-1}$ band.
Statistical Significance: The authors calculate the statistical significance ( $\sigma$ ) of the KM3-230213A event under various LIV assumptions. While LIV can increase the significance, the available statistics (a single event) do not allow for a formal constraint. The significance exhibits non-monotonic behavior, dipping at specific coefficient values before plateauing.

Significance and Claims
The paper claims to identify a "region of observational sensitivity" to superluminal LIV in the neutrino sector, offering testable predictions for future neutrino telescopes.

Clean Probe: The authors emphasize that cosmogenic neutrinos provide a "clean" probe of fundamental physics because they propagate without further interactions, allowing LIV effects to be incorporated via direct analytic modification of the dispersion relation without the need for complex cascade simulations.
Energy Scale: The constrained LIV energy scale ( $E_{LIV} \sim 10^{22} - 10^{24}$ eV) lies approximately five to six orders of magnitude below the Planck scale. The authors note this is consistent with certain quantum-gravity frameworks (e.g., loop quantum gravity, string theory compactifications) where LIV effects may appear with additional suppression factors.
Modest Conclusion: The authors explicitly state that the KM3-230213A event, while used as a benchmark, lacks the statistical significance to formally constrain the LIV parameter space (yielding a variation of only $\sim 0.5\sigma$ ). The primary contribution is demonstrating the methodology's sensitivity and highlighting the potential of this approach. The results suggest that as statistics increase with future facilities (e.g., IceCube-Gen2, GRAND, POEMMA), cosmogenic neutrinos will provide increasingly stringent tests of Lorentz invariance.
No Conflict with Other Sectors: The study notes that these constraints apply specifically to the neutrino sector and do not conflict with tighter bounds on LIV in the hadronic and photonic sectors derived from UHECR spectra and gamma-ray transparency.

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