Constraints on Lorentz invariance violation using HAWC observations above 100 TeV

H. Mart\'inez-Huerta; J. Lundeen (for the HAWC Collaboration); J. T. Linnemann; S. Marinelli

REVIEW 1 major objections 6 minor 1 cited by

Constraints on Lorentz invariance violation using HAWC observations above 100 TeV

T0 review · 1 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that the absence of a hard cutoff in HAWC's spectra of seven TeV gamma-ray sources pushes the Lorentz invariance violation energy scale above $10^{31}$ eV, more than 800 times the Planck scale.

desk verdict Preliminary HAWC limit on LIV from photon decay is a genuine step forward, but the headline E_LIV > 10^31 eV depends on energy-scale systematics that are explicitly deferred; treat as promising, not final. read the letter →

arxiv 1908.09614 v1 pith:OUZCGCA7 submitted 2019-08-26 astro-ph.HE

H. Martínez-Huerta , S. Marinelli , J. T. Linnemann , J. Lundeen (for the HAWC Collaboration) This is my paper · ORCID

classification astro-ph.HE

keywords LorentzinvarianceviolationLIVphotondecayveryhighenergygammaraysHAWCobservatorymodifieddispersionrelationhardspectralcutoffquantumgravityscalegamma-rayastronomy

topics Quantum Gravity

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 claims that the absence of a hard cutoff in HAWC's highest-energy gamma-ray spectra rules out Lorentz invariance violation (LIV) at an energy scale above $10^{31}$ eV, more than 800 times the Planck scale. In superluminal LIV scenarios, energetic photons would decay into electron-positron pairs over astrophysical distances, so a source spectrum should terminate abruptly above a threshold energy; HAWC sees no such termination in seven bright TeV sources. The most restrictive source, 2HWC J1825-134, gives a 95% confidence lower limit on the cutoff energy of 253 TeV, which Eq. (2.2) converts into $E^{(1)}_{LIV} > 1.55 \times 10^{31}$ eV. This improves the best previous bound by a factor of about 60. The result matters because it shows that wide-field ground-based observatories can test quantum-gravity physics purely from the survival of very-high-energy photons.

What carries the argument

The machinery is a modified dispersion relation of the form $E_a^2 - p_a^2 = m_a^2 \pm |\alpha_{a,n}| A^{n+2}_a$, which parameterizes LIV as an energy-dependent correction to the usual special-relativistic relation. In the superluminal case, the correction opens the decay $\gamma \to e^+e^-$ above a threshold energy given by Eq. (2.2), so any astrophysical source should show a hard cutoff above that threshold. The paper searches for the cutoff by fitting each source with a profile log-likelihood in which the cutoff energy $E_c$ is a free parameter, using HAWC's neural-network energy reconstruction to reach photon energies above 100 TeV. The observed spectrum is modeled as the true cutoff smeared by detector energy resolution, and the Lorentz-invariant case is recovered as $E_c \to \infty$; the likelihood crossing at $2\Delta\ln L = 2.71$ gives the 95% CL lower limit on $E_c$.

What would settle it

Recompute the profile likelihood for 2HWC J1825-134 after shifting the reconstructed energy scale down by 20% and including the expected systematic uncertainties; if the 95% CL lower limit on $E_c$ falls below the highest confidently reconstructed photon energy from that source, the claimed $E^{(1)}_{LIV} > 10^{31}$ eV would not survive. Alternatively, an independent instrument with better energy resolution that measures a spectral break around 250 TeV in 2HWC J1825-134 matching an intrinsic source cutoff would undermine the LIV interpretation.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is a null result converted into a limit: a dedicated search for the LIV photon-decay cutoff in seven sources, including the Crab Nebula, finds no evidence for such a cutoff, and the non-detection becomes a lower limit on where the cutoff cannot be. The spectrum of 2HWC J1825-134 remains consistent with a cutoff energy $E_c$ whose 95% CL lower limit is 253 TeV; interpreting that value through the threshold relation (2.2) yields limits on the LIV coefficients $\alpha_0$, $\alpha_1$, $\alpha_2$ and energy scales $E^{(1)}_{LIV} = 1.55 \times 10^{31}$ eV and $E^{(2)}_{LIV} = 6.26 \times 10^{22}$ eV. All seven sources have p-values consistent with the Lorentz-invariant null hypothesis, so the data do not prefer any LIV cutoff. The paper presents the result as preliminary because detailed systematic uncertainties in the source spectra and detector response are not yet included.

Load-bearing premise

The whole limit rests on the assumption that HAWC's reconstructed energies above 100 TeV are calibrated well enough that the 253 TeV cutoff lower limit reflects the true photon energies; the paper does not yet fold in systematic uncertainties in the detector response or source spectral shapes.

Editorial extensions

If this is right

If the central claim holds, any LIV model with leading-order superluminal photon decay must have a suppression scale above $1.55 \times 10^{31}$ eV, ruling out a broad class of quantum-gravity dispersion relations.
The 253 TeV lower limit from 2HWC J1825-134 means photons of that energy survived propagation from a Galactic source, so superluminal photon-decay thresholds below that energy are excluded for this line of sight.
The null result across all seven sources independently reinforces the Lorentz-invariant interpretation: no bright TeV source prefers a cutoff, so the observed spectral shapes remain compatible with standard propagation.
With the same analysis method, future HAWC observations that push reconstructed photon energies higher or add more sources will directly translate into stronger or equally strong LIV limits.

Reading between the lines

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

The same cutoff likelihood could be applied jointly to all seven sources rather than taking the single most restrictive source; a combined fit would sharpen the limit if the sources share a common LIV scale.
Because the strongest bound comes from a source whose intrinsic spectral cutoff is unknown, disentangling an astrophysical break from a LIV cutoff will require either a model-independent multi-source consistency check or a source with a harder, better-measured spectrum.
The limit's translation into $E_{LIV}$ assumes the photon-decay channel is the dominant LIV signature; models in which LIV enters only through other operators, such as vacuum Cherenkov radiation, would need separate treatment.
A calibrated energy-scale shift of even tens of percent would move the derived $E_{LIV}$ scale by the same relative amount, so the headline 'over 800 times the Planck scale' should be read as a preliminary central value pending the systematics study the authors announce.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The one thing to know: this is a conference proceedings, and it reads like one—clear, short, honest about its limitations. The new bit is the application of the known photon-decay cutoff method to HAWC's first >100 TeV source spectra, yielding a 95% CL lower limit on the first-order LIV scale above 1.5×10^31 eV for 2HWC J1825-134. That's about 60 times stronger than the old HEGRA bound, and it does land above 800 times the Planck scale. If it holds up, it starts to bite on EFT models that predict photon decay.

The analysis itself is straightforward: fit source spectra with a hard cutoff softened by detector resolution, profile likelihood for the cutoff, and convert the 95% lower limit via the threshold relation. The p-values are all comfortably non-significant, meaning none of the seven sources prefer a cutoff; the limits come from how far up you can still confirm photons. The paper is appropriately labeled preliminary, and Section 4 says the systematics will come later.

Now the soft spots. The main one, as your stress-test note says, is that E_LIV^(1) scales as E_c^3. The headline 10^31 eV corresponds to E_c = 253 TeV, and a ~13% downward shift in the energy scale takes you below that headline. HAWC's energy reconstruction above 100 TeV is new, and the detector-response and energy-scale systematics are explicitly deferred to a future publication. That doesn't kill the result, but it means the categorical statement in the abstract is not yet supported. The spectral model choices (log-parabola for Crab, power-law with exp cutoff for the others) are also fixed, and no systematics on those shapes are included. Again, this is a proceedings paper, and the authors flag it; I'm not holding that against them as a flaw so much as a boundary on interpretation.

The citation pattern looks fine. The method relies on earlier work by Martínez-Huerta and Pérez-Lorenzana, which is properly cited, and the comparison limits are all there. No circularity issue.

Who should read this? Anyone working on LIV constraints or TeV-PeV gamma-ray astronomy will want it for the result and the method demonstration. It deserves a serious referee if it develops into a journal paper; as a proceedings, it's acceptable as a preliminary limit if the caveats are respected. I'd cite it only with a note that systematics are pending.

My advice: engage with it, treat the headline as conditional, and watch for the full systematic analysis. If the ~13% energy-scale question is resolved, the 60x improvement will be a solid result.

Referee Report

1 major / 6 minor

Summary. The paper searches for Lorentz invariance violation (LIV) in the photon sector using HAWC observations of seven gamma-ray sources. The authors assume that superluminal LIV causes photon decay above a threshold energy, producing a hard cutoff in the observed spectrum. For each source, they fit the spectrum with a profile likelihood that includes a free cutoff energy E_c, fold in the detector energy resolution, and test whether a cutoff is favored over the Lorentz-invariant (LI) hypothesis. No source shows a significant preference for a cutoff, so they derive 95% CL lower limits on E_c. The strongest limit, from 2HWC J1825-134, is E_c > 253 TeV, which is converted via Eq. (2.2) into limits on LIV parameters. The headline result is E_LIV^(1) > 1.55 × 10^31 eV, claimed to be over 800 times the Planck scale and 60 times stronger than previous limits. The results are labeled 'Prel.' in Table 1, and Section 4 states that a study including detailed systematic uncertainties will be addressed in a future publication.

Significance. The analysis is technically sound in its use of profile likelihood and the threshold condition from Eq. (2.2). A notable strength is that it uses real HAWC data and reports limits for seven sources, with the strongest constraint coming from a Galactic plane source rather than the Crab. If the result is robust, a limit on E_LIV^(1) above 10^31 eV would be a major advance, exceeding the Planck energy scale by more than two orders of magnitude and improving previous photon-decay limits by roughly a factor of 100. The paper is clearly labeled as preliminary by the authors, which mitigates some concerns, but the abstract presents the result as a firm limit without that qualification.

major comments (1)

[Section 4 and Table 1] The abstract and Section 3 state that HAWC limits E_LIV^(1) to greater than 10^31 eV (specifically 1.55 × 10^31 eV from Table 1), but the paper explicitly defers all systematic uncertainties in the source spectra and HAWC detector response to a future publication, and Table 1 labels the results 'Prel.'. This omission is load-bearing for the central claim. Because Eq. (2.2) implies E_LIV^(1) ∝ E_c^3 for n = 1, a downward systematic shift of about 13% in the 2HWC J1825-134 cutoff limit (253 TeV) reduces the derived E_LIV^(1) to roughly 1.0 × 10^31 eV, and a 20% shift brings it below the headline value. The analysis does fold in the detector energy resolution (Fig. 1a), but energy-scale miscalibration is a different effect and is not addressed. To support the categorical claim in the abstract, the paper must either include a systematic uncertainty budget for the energy scale and detector response or clearly present the abstract result as a preliminary constraint pending that study.

minor comments (6)

[Abstract and Table 2] The abstract states the limit is 'over 60 times more constraining than the best previous value,' but Table 2 lists the previous HEGRA n=1 limit as 0.15 × 10^30 eV, which makes the improvement approximately 103 times; please reconcile this factor.
[Section 2, Eq. (2.2)] The relation α_n = E_LIV^(-n) should be stated when Eq. (2.2) is introduced; the footnote on page 2 defines it only later, making the table entries harder to interpret on first reading.
[Section 3] The source selection criterion 'significant high energy emission above 56 TeV' is not quantified; specify the statistical significance threshold and whether it applies to reconstructed energy or fitted flux.
[Figure 1(b) and Table 1] The likelihood curve in Fig. 1(b) is for the Crab, but the strongest limit is from 2HWC J1825-134; showing the likelihood curve for the limiting source would be more informative.
[Table 1] The p-values are reported to three decimal places with several entries of 0.999–1.000; reporting the test statistic D or a truncated p-value (e.g., >0.99) would be clearer.
[Section 4] The final sentence states 'new and stringent limits to LIV' without an explicit 'preliminary' qualifier; adding the qualifier in the same sentence would better match the first sentence of the conclusions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the LIV energy scale is derived from a data-driven cutoff limit through an in-paper threshold formula, not fitted or self-referential.

full rationale

The derivation chain is self-contained. The paper derives the photon-decay threshold condition, Eq. (2.2), directly from the modified dispersion relation, Eq. (2.1), rather than importing it as an unexamined input. The LIV parameter is not fitted to the HAWC data; instead, a profile likelihood is used to obtain a 95% CL lower limit on the spectral cutoff energy Ec for each source, with the Lorentz-invariant scenario recovered as Ec approaches infinity. The resulting limit, e.g., Ec = 253 TeV for 2HWC J1825-134, is then converted to limits on the LIV coefficients through Eq. (2.2). This is a one-way theoretical mapping from a data-derived quantity, not an equivalence between input and output. Self-citations, such as Refs. [4], [11], and [16], provide supporting phenomenology for photon decay and threshold calculations, but the present paper re-derives the relevant threshold from Eq. (2.1), and the central limits are set by the energy-reconstruction data, not by those citations. The paper explicitly defers detailed systematic uncertainties in source spectra and detector response to future work (Section 4); that is a legitimate robustness caveat, not a circularity. No step in the argument reduces by construction to its own input, and no fitted LIV parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new entities are introduced; LIV is a pre-existing hypothetical framework. The free parameters are the fitted cutoff energy and the nuisance spectral parameters. The axioms are theoretical and modeling assumptions from effective field theory and the HAWC detector characterization, none of which are independently derived in this paper.

free parameters (3)

E_c (spectral cutoff energy) for each source = e.g., 253 TeV for 2HWC J1825-134 (Table 1)
E_c is a free parameter in the profile likelihood; the 95% CL lower limit on E_c is the input to the LIV limit via Eq. (2.2).
Source spectral shape parameters (normalization, index, log-parabola coefficients, exponential cutoff) = not given in the paper
The spectral models are fit to HAWC data and the likelihood ratio depends on these nuisance parameters. Values are not listed but are fitted in the analysis.
Source morphology parameters (Gaussian widths for extended sources) = fixed at best-fit values from 2HWC catalog [17]
Chosen from prior catalog fits, not fit in this analysis. They affect the source flux and thus the E_c limits.

assumptions (4)

domain assumption Modified dispersion relation (Eq. 2.1) and the photon decay threshold condition (Eq. 2.2) describe superluminal LIV induced photon decay.
The entire limit is predicated on this effective field theory framework; it is assumed without derivation in this paper (referenced to prior work).
domain assumption The intrinsic spectra of the seven sources have no sharp cutoff above the observed energies, so any observed cutoff would be due to LIV.
The test compares LIV cutoff models against a smooth LI spectral model; if a source intrinsically had a cutoff, the derived LIV limit would be invalid. The paper does not justify this for each source.
domain assumption The HAWC detector energy response is correctly described by the neural-network energy reconstruction and the smearing model.
The expected observed spectrum with a true cutoff (Fig. 1a) depends on the energy resolution. This is referenced to prior work [1,13] but not detailed in this paper.
domain assumption The spectral models (log-parabola for Crab, power-law with exponential cutoff for the six galactic sources) and fixed source morphologies from the 2HWC catalog are adequate descriptions.
The E_c limits are extracted by fitting these models; mis-modeling could bias the limits. Values are taken from previous HAWC analyses.

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Cite this review

Pith. "Pith review of Constraints on Lorentz invariance violation using HAWC observations above 100 TeV." pith.science (2026). https://pith.science/paper/OUZCGCA7

@misc{pith2026190809614,
  author       = {Pith},
  title        = {Pith review of: Constraints on Lorentz invariance violation using HAWC observations above 100 TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OUZCGCA7}},
  note         = {Machine review of arXiv:1908.09614}
}

abstract

Due to the high energies and long distances involved, astrophysical observations provide a unique opportunity to test possible signatures of Lorentz Invariance Violation (LIV). Superluminal LIV enables the decay of photons at high energy over relatively short distances, giving astrophysical spectra which have a hard cutoff above this energy. The High Altitude Water Cherenkov (HAWC) observatory is the most sensitive currently-operating gamma-ray observatory in the world above 10 TeV. Together with the recent development of an energy-reconstruction algorithm for HAWC using an artificial neural network, HAWC can make detailed measurements of gamma-ray energies above 100 TeV. With these observations, HAWC can limit the LIV energy scale greater than $10^{31}$ eV, over 800 times the Planck energy scale. This limit on LIV is over 60 times more constraining than the best previous value for $\rm E_{LIV}^{(1)}$.

Figures

Figures reproduced from arXiv: 1908.09614 by the authors.

**Figure 1.** Left (a). True spectrum with LIV hard cutoff at some energy Ec and the expected observer spectrum due to the detector energy resolution [13]. Right (b). Likelihood curve as a function of the LIV Energy cutoff in the Crab analysis; the lower point (green) shows the lower limit at 95% CL. be addressed by the following expression1 , E 2 a − p 2 a = m 2 a ±|αa,n|A n+2 a , (2.1) where a stands for the particle type. A ca… view at source ↗

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Forward citations

Cited by 1 Pith paper

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

The Spectrum of the Crab Nebula and Highest Energy Photons Measured by HAWC
astro-ph.HE 2019-08 conditional novelty 5.0 of 10

HAWC's new energy estimator yields a Crab spectrum beyond 100 TeV and 95% confidence lower limits on the cutoff energy above 200 TeV for the hardest Galactic source.

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · cited by 1 Pith paper

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

A. U. Abeysekara et al. Measurement of the Crab Nebula at the Highest Energies with HAWC. 2019

work page 2019

[2] [2]

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J. T. Linnemann. Highest Energy Photons Ever Observed and High-Energy Crab Spectrum. In Proceedings, 36th International Cosmic Ray Conference (ICRC2019): Madison, WI, U.S.A., July 24th - August 1st, 2019. , 2019. PoS ICRC 2019, 723

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Martínez-Huerta and A

H. Martínez-Huerta and A. Pérez-Lorenzana. Restrictions from Lorentz invariance violation on cosmic ray propagation. Phys. Rev., D95(6):063001, 2017

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[5] [5]

Hohensee, Ralf Lehnert, David F

Michael A. Hohensee, Ralf Lehnert, David F. Phillips, and Ronald L. Walsworth. Limits on isotropic Lorentz violation in QED from collider physics. Phys. Rev., D80:036010, 2009

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Vasileiou, A

V . Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, and F. Longo. Constraints on Lorentz Invariance Violation from Fermi-Large Area Telescope Observations of Gamma-Ray Bursts. Phys. Rev., D87(12):122001, 2013

work page 2013