{"id":"6b58777b-66b9-4b79-8a45-8a176a39209a","arxiv_id":"1908.09614","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using the lack of a spectral cutoff in seven bright gamma-ray sources, HAWC constrains the Lorentz-violating energy scale E_LIV^(1) to be above 1.5e31 eV, 60 times stronger than prior limits.","lead":"HAWC's observations of very high-energy gamma rays (above 100 TeV) set new limits on Lorentz invariance violation, ruling out superluminal photon decay up to an energy scale over 10^31 eV. These are preliminary results, and the actual limit depends on energy reconstruction and source modeling assumptions.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Energy-scale systematics at >100 TeV are deferred; because E_LIV^(1) scales as E_c^3, a ~13% downward energy shift drops the 253 TeV cutoff limit below the headline 10^31 eV.","rationale":"The paper is a conference proceeding presenting a preliminary LIV constraint. After checking the main technical steps, I find no internal inconsistency in the threshold condition (Eq. 2.2), the likelihood procedure, or the single-source limit quoted. The finite-distance/lifetime question is not a serious concern because the photon's effective invariant mass near threshold makes the decay extremely fast for the energies and LIV scales involved. The most vulnerable point is exactly the one the reader identified: the analysis does not include detector-response or source-spectrum systematics, and the paper openly defers this to future work. I sharpen that concern by quantifying the required accuracy: E_LIV^(1) scales as E_c^3, so the headline 10^31 eV claim demands the 253 TeV lower limit to be reliable to within roughly 13% in energy. A neural-network energy estimator above 100 TeV can plausibly carry such a systematic. This does not demonstrate that the limit is wrong, but it makes the claim conditional on an unperformed systematic study. Therefore the reader's CONDITIONAL verdict remains appropriate, and no change to the verdict is needed.","tokens_in":5321,"tokens_out":17889,"duration_ms":188806,"concrete_test":"Reproduce the profile-likelihood fit for 2HWC J1825-134 in Table 1 with a ±15% energy-scale systematic, for example by profiling over a nuisance parameter with a 15% prior on reconstructed energy or by shifting all reconstructed energies down by 15%, and recompute the 95% CL lower limit on E_c. If the lower limit falls below ~219 TeV, the claimed E_LIV^(1) > 10^31 eV is not robust to this systematic; if it remains above ~219 TeV, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the 95% CL lower limit E_c = 253 TeV for 2HWC J1825-134 (Table 1) being a faithful bound on the true photon cutoff, which is then converted to E_LIV^(1) via Eq. (2.2). The load-bearing assumption is that HAWC's energy reconstruction above 100 TeV is accurate enough that this 253 TeV value is not biased low by detector-response or energy-scale systematics. Because E_LIV^(1) is proportional to E_c^3, a 10^31 eV limit corresponds to E_c ≈ 219 TeV; a downward systematic shift of only ~13% in the energy scale would take the claimed limit below the headline value. The paper's Section 4 explicitly states that detailed systematic uncertainties in the source spectra and HAWC detector response will be addressed in a future publication, and Table 1 labels the results 'Prel.'. Until the energy-scale and energy-resolution systematics at these energies are quantified, the 253 TeV lower limit and the derived 1.55 × 10^31 eV exclusion are not robust enough to support the categorical claim in the abstract.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":5573,"tokens_out":10816,"duration_ms":107594,"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":[{"comment":"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.","section":"Section 4 and Table 1"}],"minor_comments":[{"comment":"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":"Abstract and Table 2"},{"comment":"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":"Section 2, Eq. (2.2)"},{"comment":"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.","section":"Section 3"},{"comment":"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.","section":"Figure 1(b) and Table 1"},{"comment":"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":"Table 1"},{"comment":"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.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"This appears to be a conference proceedings paper submitted for review. Applying a journal standard, the central claim is not fully supported because the authors themselves defer all systematic uncertainties. The authors are aware of the limitation, so the missing work is not an oversight. The main editorial question is whether the venue accepts 'preliminary' results; for a traditional journal, a major revision that either adds the systematic study or substantially qualifies the abstract is warranted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nNow 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.\n\nThe 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.\n\nWho 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.\n\nMy 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.","headline":"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.","tokens_in":6151,"tokens_out":2548,"would_cite":true,"duration_ms":25316,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["Lorentz invariance violation","LIV photon decay","very high energy gamma rays","HAWC observatory","modified dispersion relation","hard spectral cutoff","quantum gravity energy scale","gamma-ray astronomy"],"falsifier":"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.","tokens_in":5124,"feed_emoji":"🌌","tokens_out":9320,"duration_ms":89699,"temperature":0.7,"pith_summary":"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.","feed_headline":"Highest-energy photons push Lorentz violation scale past 10^31 eV","feed_subtitle":"No spectral cutoff shows up in seven TeV sources, ruling out superluminal photon decay far beyond the Planck scale.","key_machinery":"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 $E_c$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"supplies the neural-network energy-reconstruction algorithm and the Crab measurement above 100 TeV that make the search possible","marker":"[1]"},{"why":"derives the LIV photon-decay phenomenology and threshold used to predict the hard cutoff, and provides a previous HEGRA comparison limit","marker":"[4]"},{"why":"provides the detector-resolution smearing treatment that turns a true hard cutoff into the observed spectrum shape used in the likelihood","marker":"[13]"},{"why":"gives the photon emission and decay rates that justify the fast, effective decay above threshold","marker":"[16]"},{"why":"supplies the HAWC gamma-ray catalog and the fixed source morphologies and spectral shapes used for the seven analyzed sources","marker":"[17]"}],"fun_headline_variants":["HAWC null test bounds Lorentz violation at 10^31 eV","No photon decay seen; LIV scale limit 800x Planck","HAWC 100 TeV spectra rule out LIV cutoffs, set best bound","LIV energy scale constrained beyond 10^31 eV by HAWC","Seven sources, zero cutoffs: HAWC's tightest LIV limit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["HAWC null test bounds Lorentz violation at 10^31 eV","No photon decay seen; LIV scale limit 800x Planck","HAWC 100 TeV spectra rule out LIV cutoffs, set best bound","LIV energy scale constrained beyond 10^31 eV by HAWC","Seven sources, zero cutoffs: HAWC's tightest LIV limit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001107,"raw_usage":{"total_tokens":4610,"prompt_tokens":933,"completion_tokens":3677,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":549,"completion_tokens_details":{"reasoning_tokens":3582}},"tokens_in":549,"tokens_out":3677,"duration_ms":29458,"temperature":1.0,"reasoning_tokens":3582,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:05:25.557646+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the neural-network energy-reconstruction algorithm and the Crab measurement above 100 TeV that make the search possible"},{"cited_title":"Martínez-Huerta and A","cited_arxiv_id":null,"evidence_quote":"derives the LIV photon-decay phenomenology and threshold used to predict the hard cutoff, and provides a previous HEGRA comparison limit"},{"cited_title":"Marinelli","cited_arxiv_id":null,"evidence_quote":"provides the detector-resolution smearing treatment that turns a true hard cutoff into the observed spectrum shape used in the likelihood"},{"cited_title":"Martínez-Huerta and A","cited_arxiv_id":null,"evidence_quote":"gives the photon emission and decay rates that justify the fast, effective decay above threshold"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the HAWC gamma-ray catalog and the fixed source morphologies and spectral shapes used for the seven analyzed sources"}],"review_version":1}