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Ultra-high-energy event KM3-230213A constraints on Lorentz Invariance Violation in neutrino sector

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read If extragalactic, the 220 PeV neutrino's survival puts the LIV scale above 1.1×10^30 GeV.

desk verdict A clean, correctly executed application of the known neutrino-splitting width to KM3-230213A gives new n=1 and n=2 LIV bounds, but the 'conservative 68% CL' label overstates the robustness because it hinges on an assumed 10 Mpc source distance and a loose survival criterion. read the letter →

arxiv 2502.09548 v3 pith:I4M6ETAR submitted 2025-02-13 hep-ph astro-ph.HE

Petr Satunin This is my paper · ORCID
classification hep-phastro-ph.HE
keywords Lorentzinvarianceviolationsuperluminalneutrinosneutrinosplittingultra-high-energyKM3-230213ALIVmassscalequantumgravityphenomenologydecay
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses the detection of the 220 PeV neutrino event KM3-230213A as a new probe of Lorentz Invariance Violation (LIV) in the neutrino sector. The reasoning is that a superluminal neutrino of that energy would lose energy by splitting into three neutrinos, so the event's survival through propagation means the decay did not happen fast enough. Assuming an extragalactic source at about $L=10$ Mpc, the absence of neutrino splitting bounds the LIV mass scale at $\Lambda \ge 1.1\times 10^{30}$ GeV for linear ($n=1$) LIV and $\Lambda \ge 1.1\times 10^{19}$ GeV for quadratic ($n=2$) LIV. For the quadratic case this is more than an order of magnitude stronger than the previous limit. This matters because it constrains quantum-gravity-motivated departures from Lorentz invariance at energies far beyond what accelerators can reach.

What carries the argument

The load-bearing object is the neutrino-splitting width formula $\Gamma_{\nu\to\nu\bar{\nu}\nu}\simeq (G_F^2 E^5/6\pi^3)\,(E/\Lambda)^{3n}\,c(\nu)$ with $c(\nu)\approx 0.024$, computed in the collinear approximation and neglecting neutrino masses. It is used through the relation $L=\Gamma^{-1}$, so setting the mean free path equal to the assumed source distance converts the event's existence into a lower bound on $\Lambda$ via eq. (7). The distance enters as $L^{1/3}$ for $n=1$ and $L^{1/6}$ for $n=2$, which is why the result depends only mildly on the unknown source distance. The same process, neutrino splitting $\nu\to\nu\bar{\nu}\nu$, is the observable whose absence during propagation is being probed.

What would settle it

Identify the source distance of KM3-230213A, for example through a multi-messenger counterpart search. A confirmed galactic association would lower the central $n=1$ and $n=2$ bounds to roughly $5.3\times10^{29}$ GeV and $1.1\times10^{19}$ GeV, and the headline eq. (14) would no longer follow. Alternatively, observing a UHE neutrino whose energy spectrum or cascade pattern matches $\nu\to\nu\bar{\nu}\nu$ energy loss would contradict the no-splitting premise directly.

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Extended reading notes

Core claim

On its own terms, the paper's claim is that KM3-230213A's survival, combined with an assumed extragalactic propagation distance $L=10$ Mpc, turns one observed event into the strongest available constraint on superluminal LIV in the neutrino sector. Starting from the collinear-approximation width $\Gamma_{\nu\to\nu\bar{\nu}\nu}\simeq (G_F^2 E^5/6\pi^3)\,(E/\Lambda)^{3n}\,c(\nu)$ with $c(\nu)\approx 0.024$, and requiring the mean free path $\Gamma^{-1}$ to exceed $L$, the paper solves for $\Lambda$. With $E=220$ PeV it obtains $\Lambda\simeq 5.3\times 10^{30}$ GeV for $n=1$ and $\Lambda\simeq 3.4\times 10^{19}$ GeV for $n=2$; taking the lower edge of the 68% CL interval gives the conservative bounds $\Lambda\ge 1.1\times 10^{30}$ GeV and $\Lambda\ge 1.1\times 10^{19}$ GeV. The paper also checks competing processes and finds neutrino pair production to be subleading, while the pion-decay production constraint is about an order of magnitude weaker.

Load-bearing premise

The headline bounds assume the neutrino travelled about $L=10$ Mpc from an extragalactic source; if the true distance were a galactic 10 kpc, the limits would weaken by roughly an order of magnitude.

Editorial extensions

If this is right

  • For an extragalactic source at 10 Mpc, the conservative 68% CL bounds are $\Lambda\ge 1.1\times10^{30}$ GeV ($n=1$) and $\Lambda\ge 1.1\times10^{19}$ GeV ($n=2$), exceeding the previous $n=2$ bound of $1.4\times10^{17}$ GeV by more than an order of magnitude.
  • Adopting a galactic distance (10 kpc) softens the central values to about $5.3\times10^{29}$ GeV and $1.1\times10^{19}$ GeV, while a cosmogenic distance (100 Mpc) raises them to about $1.2\times10^{31}$ GeV and $5.0\times10^{19}$ GeV.
  • The $\nu\to\nu e^+e^-$ pair-production channel is subleading at these parameters; the pion-decay production constraint ($\Lambda\approx 5.3\times10^{17}$ GeV for $n=2$) is about an order of magnitude weaker than the splitting bound.
  • Because the bound scales as $L^{1/3}$ ($n=1$) or $L^{1/6}$ ($n=2$), better distance estimates for the source sharpen the constraint even without new events.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If future multi-messenger observations identify the source of KM3-230213A, the true distance replaces the assumed 10 Mpc in eq. (7) and the same formula immediately gives the sharpened limit; this is a direct update path the paper leaves implicit.
  • At $n=1$ the quoted bound exceeds the Planck mass by many orders of magnitude, so any viable linear superluminal LIV scenario must be extremely suppressed; this weighs against models that identify $\Lambda$ with the Planck scale.
  • A future sample of UHE neutrinos could test the no-splitting assumption statistically: if any event shows the energy-loss signature of $\nu\to\nu\bar{\nu}\nu$, the core premise of the bound would fail.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper uses the KM3NeT ultra-high-energy event KM3-230213A to constrain superluminal Lorentz Invariance Violation (LIV) in the neutrino sector. Assuming the event is a neutrino of energy 220 PeV and that neutrino splitting would occur if the LIV scale is below some value, the author solves the Carmona et al. width formula for the neutrino splitting width, setting the mean free path equal to the assumed source distance. For an extragalactic distance L = 10 Mpc, the lower edges of the propagated 68% energy interval give Lambda >= 1.1e30 GeV for n = 1 and Lambda >= 1.1e19 GeV for n = 2 (Eq. 14). The paper also gives constraints for galactic (L = 10 kpc) and cosmogenic (L = 100 Mpc) distance assumptions, discusses the subleading neutrino pair-production and pion-decay processes, and compares with the previous IceCube bound.

Significance. If the assumptions hold, these are among the strongest constraints on superluminal LIV in the neutrino sector, several orders of magnitude more stringent than the previous IceCube limit. The derivation is transparent: the algebra from the width formula (Eq. 6) to the bounds (Eqs. 7-10) is correct, the dependence on the assumed distance is written out explicitly, and the author acknowledges the main limitations (unknown source distance, neglect of continuous energy losses) within the manuscript. The main weaknesses are statistical and interpretational rather than technical, and they are fixable within the scope of the paper.

major comments (2)
  1. [Section f, Eq. (14)] The headline bounds in Eq. (14) depend on the assumed extragalactic distance L = 10 Mpc, which is not established for this event. The text cites Ref. [2] to argue that galactic origin is unlikely, but that reference does not exclude L = 10 kpc. Since Eq. (7) gives Lambda prop to L^{1/(3n)}, the galactic-scale values in Eq. (8) are lower by a factor of roughly 10 for n = 1 and 2.5 for n = 2. Calling the extragalactic lower edge a 'conservative 68% CL bound' is therefore misleading, because the bound is not conservative with respect to the dominant systematic uncertainty. I recommend presenting the constraint as a function of L, or explicitly stating that the quoted values require the extragalactic-origin assumption.
  2. [Section f, Eqs. (8)-(10)] The statistical interpretation of Eqs. (8)-(10) is not a 68% confidence level. Setting the mean free path equal to the source distance (L = Gamma^{-1}) in Eq. (7) corresponds to a survival probability exp(-1) = 0.37, i.e., a one-sided confidence of about 63%, not 68%. The asymmetric errors in Eqs. (8)-(10) are obtained by propagating the 68% interval of the measured energy E through Eq. (7), but this does not account for the exponential probability of no splitting over the propagation distance. To quote a confidence level, one should invert the survival probability at the chosen CL; for example, 90% confidence would require Gamma L = -ln(0.1) = 2.3, changing Lambda by a factor of a few for these power laws.
minor comments (5)
  1. [Section d, Eq. (11)] The threshold formula as written has incorrect dimensions: it should be Lambda_thr = E^2 / (sqrt(6) m_e), not E^2 / sqrt(6 m_e). The numerical value quoted in the text corresponds to the corrected expression.
  2. [Section c, after Eq. (10)] The sentence 'Splitting cannot produce significant excess at lower energy in a spectrum decreasing with energy like ~ E^-2. In fact, splitting of a neutrino of energy E into 3 particles of energy E/3 adds 3 particles to the spectrum which consists of (E/(E/3))^2 = 9 particles' is unclear and not a rigorous statement about differential fluxes; please rewrite or remove it.
  3. [Footnote 2] The phrase 'cf. other ultra high energy events came from that distance [12]' is vague; please specify which events are meant or give a more precise justification for choosing L = 10 Mpc as the reference extragalactic distance.
  4. [Section b, after Eq. (4)] The sentence 'the sign before the LIV term is different for neutrino and antineutrino' should be completed with an explicit statement that the superluminal case analyzed here corresponds to the plus sign for neutrinos in Eq. (4), which is the sign that leads to neutrino splitting.
  5. [References] Reference [12] is missing the publication year; it should read 'JCAP 04 (2024) 042' or the year should be supplied.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the bounds are obtained by inverting an external decay-width formula for an assumed propagation distance; no fitted parameter is renamed as a prediction.

full rationale

The derivation chain is self-contained and non-circular. The central constraint follows by solving the external Carmona et al. width formula, Eq. (6), for the LIV scale Lambda after setting the neutrino mean free path L equal to the assumed source distance, Eq. (7). Both inputs - the event energy E and the distance L - are scenario parameters, not quantities fitted so as to reproduce the output bound. The paper explicitly treats L as an assumption and presents separate constraints for galactic (L = 10 kpc), extragalactic (L = 10 Mpc), and cosmogenic (L = 100 Mpc) origins, so the headline value is conditional rather than circular. Reference [2] is used only to argue that galactic origin is unlikely and thereby to select the lower edge of the extragalactic interval as the quoted bound; it does not supply the width formula, the kinematics, or the numerical value of Lambda. Reference [12] supplies the assumed distance scale, but it is an external astrophysical input, not a prior result of this author, and the L-dependence is explicitly shown in Eq. (7). No self-citation chain is load-bearing, no fitted parameter is renamed as a prediction, and no quantity is defined in terms of the quantity it is claimed to constrain. The noted statistical issue - the '68% CL' label corresponding to exp(-1) survival rather than a full likelihood - is a correctness or presentation concern, not a circularity of the derivation.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The derivation rests on the assumed source distance (a free input), the published width formula, and the identification of the detected event as a propagating neutrino. No new particles or forces are introduced.

free parameters (1)
  • propagation distance L = 10 Mpc (extragalactic; also 10 kpc and 100 Mpc considered)
    The distance to the source of KM3-230213A is unknown. The paper assumes L=10 Mpc for the headline extragalactic bound, following ref. [12] that nearby UHECR sources exist at that distance. The bound scales as L^{1/3} (n=1) and L^{1/6} (n=2) in eq. (7), so the distance choice directly sets the constraint.
assumptions (4)
  • domain assumption Superluminal LIV dispersion relation (1) with n=1 or n=2 and positive sign
    The paper restricts to superluminal neutrino LIV, the scenario in which vacuum Cherenkov-like decays occur; subluminal LIV is not constrained by this argument. Stated in the introduction.
  • domain assumption Carmona et al. width formula (6) for neutrino splitting in the collinear approximation neglecting masses
    The central constraint is obtained by solving this formula for Lambda. The formula is taken from ref. [8] and not re-derived; the paper relies on its validity at E=220 PeV.
  • domain assumption The KM3-230213A event is a neutrino that propagated from a source at distance L without decaying
    The 'absence of neutrino splitting' is inferred from the detection of a 220 PeV neutrino; this requires the mean free path to be at least the source distance. If the event has a different origin or is misidentified, the conclusion fails.
  • domain assumption Neutrino splitting is the dominant LIV decay channel for the parameters considered
    The paper estimates the pair production channel Nu -> Nu e+ e- is subleading and the pion-decay constraint is weaker; this follows from prior literature and the paper's own threshold estimate in section d.

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Cite this review

Pith. "Pith review of Ultra-high-energy event KM3-230213A constraints on Lorentz Invariance Violation in neutrino sector." pith.science (2026). https://pith.science/paper/I4M6ETAR

@misc{pith2026250209548,
  author       = {Pith},
  title        = {Pith review of: Ultra-high-energy event KM3-230213A constraints on Lorentz Invariance Violation in neutrino sector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I4M6ETAR}},
  note         = {Machine review of arXiv:2502.09548}
}
abstract

We discuss the constraints on superluminal neutrino Lorentz Invariance Violation (LIV) parameters from the observation of the ultra-high-energy event KM3-230213A by KM3NeT collaboration in cases of linear $n=1$ and quadratic $n=2$ LIV scenarios. Assuming extragalactic origin of the event, we obtain the constraints on LIV mass scale $\Lambda_{n=1} = 1.1 \times 10^{30}\, \mbox{GeV}$ and $\Lambda_{n=2} = 1.1 \times 10^{19}\, \mbox{GeV}$ from the absence of neutrino splitting.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Highest-Energy Neutrino Event Constrains Dark Matter-Neutrino Interactions

    hep-ph 2025-06 conditional novelty 6.0 of 10

    KM3-230213A limits dark matter-neutrino scattering to below about 1e-22 cm^2/GeV at 220 PeV, but most simple dark matter models are excluded by unitarity above MeV masses.

  2. `Dark' Matter Effect as a Novel Solution to the KM3-230213A Puzzle

    hep-ph 2025-05 conditional novelty 6.0 of 10

    Dark matter scattering in the Earth, sourced by a flaring blazar, can explain the KM3-230213A event while yielding few or no IceCube events in a viable parameter space.

  3. Interpreting the KM3-230213A PeV Neutrino Event via Vector Dark Matter Decay and Its Multi-Messenger Signatures

    hep-ph 2025-07 conditional novelty 4.0 of 10

    A U(1)_X vector dark matter model explains the KM3-230213A PeV neutrino via DM decay and predicts a cosmic string gravitational wave background consistent with PTA observations, but with several parameters fitted to the data.

Reference graph

Works this paper leans on

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