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REVIEW 3 major objections 4 minor 59 references

Earth's rotation turns neutrino arrival time into a geometric probe: with time-resolved visibility, roughly 14–16 ultra-high-energy events would let a Mediterranean neutrino telescope confirm or rule out a dark-matter origin for KM3-230213A

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-01 09:51 UTC pith:Y5GSVIQF

load-bearing objection The timing idea is nice and the single-event analysis is solid, but the forecast's isotropic alternative is unphysical, so the headline 14–16 event thresholds are not trustworthy. the 3 major comments →

arxiv 2607.20608 v1 pith:Y5GSVIQF submitted 2026-07-22 hep-ph astro-ph.HE

Earth rotation turns event timing into a geometric probe of UHE neutrino origin

Andrew Cheek , Jo\~ao Paulo Pinheiro , Jordi Salvado This is my paper
classification hep-ph astro-ph.HE
keywords ultra-high-energy neutrinosKM3-230213Adark matter decayneutrino telescope visibilityEarth opacityevent timingtest statisticGalactic Centre
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether the record-energy neutrino KM3-230213A could come from decaying dark matter even though it arrived from a direction opposite the Galactic Centre. It argues that the usual directional answer is incomplete: above PeV energies the Earth is opaque, so a neutrino telescope sees only a thin band near the horizon that rotates with the Earth. That makes the arrival time of each event an independent geometric observable. Building a per-event test statistic from the time-dependent dark-matter sky map, the authors find that retaining arrival times cuts the number of events needed to exclude the dark-matter origin from ~33–43 (geometry only) and ~22–27 (time-averaged) to ~14–16. With just the single observed event, the dark-matter hypothesis is disfavoured but not excluded (p ≈ 0.13–0.15).

Core claim

The central discovery is that for an equatorial ultra-high-energy neutrino telescope the detection time of an event labels which slice of sky was below the horizon, hence visible, at that instant. Because the neutrino-nucleon cross-section grows with energy, the Earth becomes opaque above ~PeV and the visible region is a thin, rotating band near the horizon. The authors encode this in a visibility function and define a per-event statistic that combines the time-dependent probability that dark-matter decay produces the event with its angular distance to the Galactic Centre. When the full time-resolved visibility is used, a stacked sample of ~14–16 events would exclude the decaying-dark-matter

What carries the argument

The key object is the visibility function V(E, nhat, t) — the probability that a neutrino of energy E from direction nhat at time t produces a detectable up-going lepton — factorised into survival through the Earth (exponential in the column depth) and interaction in the detector's target segment. It turns the detector's latitude and Earth's rotation into an explicit daily modulation of which sky directions are observable. The test statistic is the per-event score TSi = -log P_DM(t_i, δ_i, α_i) × ψ_GC, where P_DM is the time-dependent, visibility-weighted dark-matter sky map and ψ_GC is the angular distance to the Galactic Centre; Monte-Carlo pseudo-experiments convert the summed score into

Load-bearing premise

The exclusion thresholds assume the alternative isotropic hypothesis is adequately represented by mock events drawn uniformly over the observable sky, rather than by an astrophysical isotropic flux weighted by the same energy- and time-dependent visibility; if a physically weighted isotropic flux populated the visible band differently, the required event counts could move.

What would settle it

Re-run the forecast using an isotropic astrophysical flux convolved with the same V(E,n,t) and recompute the p < 0.05 event thresholds; if the time-resolved threshold does not drop below roughly 22 events, the central claim that timing is worth a ~40% reduction fails. Alternatively, watch the arrival-time distribution of the next ~14–16 detected ultra-high-energy neutrinos: if their times are spread uniformly across the sidereal day rather than peaking when the Galactic Centre transits the visible band, the dark-matter hypothesis as modelled would be disfavoured.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If KM3NeT collects roughly 14–16 ultra-high-energy events of the same flavour class, the decaying-dark-matter origin of KM3-230213A could be excluded at p < 0.05 in favour of an isotropic signal, assuming the mock-event model of isotropy.
  • The timing gain is largest for harder decay spectra such as b bbar, because higher-energy neutrinos see a more opaque Earth, a narrower visible band, and a deeper daily modulation.
  • The single observed event becomes slightly more dark-matter-compatible once its arrival time is used, not less, so the anti-Galactic-Centre tension is partly a visibility artifact.
  • The method is generic to equatorial neutrino telescopes and can be applied to any anisotropic flux hypothesis, not only dark-matter decay.
  • Time-resolved directional information can be more decisive than spectral information for distinguishing Galactic dark matter from astrophysical backgrounds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the same timing-as-geometry logic should apply to any anisotropic signal at an equatorial detector, so the test could be recycled for point-source versus diffuse discrimination without new machinery.
  • Editorial inference: if a physical isotropic astrophysical flux is used instead of uniform-sky mock events, the claimed thresholds may shift; checking this would either strengthen or bound the timing gain.
  • Editorial inference: the single-point visibility model omits atmospheric-muon rejection cuts and background sources; folding in the real detector efficiency could change the event-number thresholds in either direction.
  • Editorial inference: the trend that harder spectra reach the threshold sooner suggests that combining channels with energy weights might extract even more information than timing alone.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper develops a per-event test statistic to assess whether the UHE neutrino KM3-230213A observed by KM3NeT could originate from Galactic plus extragalactic dark-matter decay, and to forecast how many additional events would be needed to exclude this hypothesis in favor of an isotropic astrophysical signal. The central ingredient is a time-dependent detector visibility function arising from Earth opacity and KM3NeT's equatorial location, which makes the arrival time of each event an independent geometric observable. The authors compare three levels of information: geometry-only (V=1), time-averaged exposure, and fully time-resolved visibility. They find single-event p-values of 0.065/0.070, 0.072/0.080, and 0.133/0.149 for the restrictive/permissive halo profiles respectively, and forecast that the number of events needed for p<0.05 exclusion falls from ~33–43 (geometry-only) to ~22–27 (time-averaged) to ~14–16 (time-resolved), a claimed ~40% gain from timing information alone. They argue the result is robust to decay channel and halo-profile choices.

Significance. If the central forecast is correct, the paper introduces a genuinely useful idea: for equatorial UHE neutrino telescopes, the event arrival time tags which part of the sky was instantaneously visible, so timing becomes a geometric probe even for quasi-stationary signal models such as DM decay. The paper's strengths include a well-specified, if simplified, visibility model (Eq. 3.2 and App. A), bracketing of halo-profile uncertainty with simulation-based profiles, a Monte Carlo p-value procedure that avoids analytic distributional assumptions, explicit robustness checks on the test-statistic weighting (App. B), and the use of externally determined cross sections and benchmark DM parameters rather than fitting to the observation. These are real merits. However, the headline thresholds and the claimed timing gain rest on the definition of the isotropic alternative hypothesis, which as implemented is not a physical isotropic astrophysical flux under the detector response. That issue is load-bearing and needs to be addressed before the quantitative conclusions can be accepted.

major comments (3)
  1. [Sec. 4 (H_iso definition, after Eq. 4.3)] The alternative hypothesis is implemented as mock events 'drawn uniformly over the observable sky.' This is not the event distribution of a physical isotropic astrophysical flux under the same detector response used for H_DM. For an isotropic flux phi_iso(E), the expected event density is proportional to ∫dE V(E,t,δ,α) phi_iso(E), not uniform over the region where V>0. Since V in Eq. (3.2) is strongly peaked near the horizon and energy-dependent, uniform sampling over the visible band overweights low-V, low-P_DM, large-ψ_GC directions, inflating the TS distribution under H_iso and making the DM hypothesis appear easier to reject. The thresholds in Table 1 and the claimed 40% timing gain in Sec. 5.3 are therefore not yet demonstrated against a realistic isotropic alternative. Please specify the exact sampling procedure (including the definition of 'observable sky', the time sampling, and
  2. [Eq. (4.1)] The definition of P_DM(t,δ,α) = (1/Φν) dΦν(t,δ,α)/dΩ with Φν(t,δ,α) = ∫dE V(E,t,δ,α) ϕ_tot(E,δ,α) is not a normalized probability density as written: the denominator is still a function of (δ,α), whereas normalization requires an integral over solid angle. The sentence following the equation says 'the flux integrated numerically over the remaining variables,' but the equation should read Φν(t) = ∫dE dΩ V ϕ_tot and P_DM = V ∫dE ϕ_tot / Φν(t) (or an explicit equivalent). This is not a purely cosmetic issue: the normalization choice determines how the 'instantaneously visible sky' enters P_DM and hence all TS values and p-values. Please rewrite Eq. (4.1) unambiguously.
  3. [Sec. 5.3 / Table 1] The thresholds 14–16 events are quoted as exact integers with no Monte Carlo uncertainty. The p-values are obtained from pseudo-experiments, so the number of events at which the median p-value crosses 0.05 has a statistical error that depends on the number of trials and the width of the TS distributions. Since the central quantitative claim is a reduction from 33–43 to 14–16, the paper should report the number of pseudo-experiments and an uncertainty on each threshold (e.g., from bootstrap or larger MC samples). At present it is unclear whether the 1–2 event differences between channels and halo profiles are significant or within MC noise.
minor comments (4)
  1. [Sec. 5.2 and Fig. 5] There is an inconsistency in the threshold values: the text and Table 1 state ~22 (restrictive) events for the time-averaged case, but Fig. 5(b) is titled 'νν, 21 events' and already shows p_DM^res < 0.050. Please clarify whether the thresholds include the observed event and correct the figure/text/table consistently.
  2. [Sec. 3 / App. A] The paper explicitly states that atmospheric-muon rejection cuts and background sources are not included and the detector is treated as a single point. This is a stated limitation, but the forecast assumes zero background. A quantitative statement of the expected background rate in the visible band above ~10 PeV (or an argument for why it is negligible at these energies) would strengthen the forecast; currently the thresholds assume an ideal background-free detector.
  3. [Sec. 4 / Fig. 4–6] The description of the H_iso MC is too terse: it is not specified how event times are generated for the isotropic mock events in the time-resolved scenario, nor how the 'observable sky' region is defined (e.g., threshold on V, solid-angle cut, or mask). This makes the forecasts difficult to reproduce and is connected to the major comment on H_iso.
  4. [Throughout] Typos and minor wording: Abstract 'can readily be applied other relics' should be 'applied to other relics'; Sec. 5.3 contains 'the the p-value'; Fig. 5 caption says '22 and 27' while the inset says '21' (see above); the '1σ Asimov expectation' in Sec. 5.1 is not defined. Please proofread.

Circularity Check

0 steps flagged

No significant circularity; the H_iso uniform-sky and background-free assumptions are modeling limitations, not circular steps.

full rationale

The derivation is not circular. The DM probability density P_DM (Eq. 4.1) is built from externally imported inputs—benchmark masses/lifetimes from Ref. [48], halo profiles from Refs. [49–57], HDMSpectra [58], and cross-section parameterizations [61,67–69]—and the overall normalization 1/(M_DM tau_DM) cancels in P_DM, so no parameter is fitted to KM3-230213A in this paper. The per-event statistic (Eq. 4.2) and the Monte-Carlo p-values are computed from the null model H_DM; the single-event p-values are tail probabilities under that model, not restatements of the input. The forecast thresholds are a power study against the stated alternative H_iso, and the paper explicitly defines H_iso as mock events "drawn uniformly over the observable sky" (Sec. 4). That definition is a modeling limitation—a physical isotropic astrophysical flux would be V-weighted and could shift the 14–16 event thresholds—but it is not circular because H_iso is an input assumption rather than a derived prediction, and the time-resolved gain is not obtained by equating the forecast to the input. The psi_GC weighting is shown in App. B not to drive the thresholds. The self-citations (Refs. [46,61]) supply a geometric-compatibility framework and cross-section fits; they are not used as uniqueness theorems, and the central time-resolved claim does not reduce to them. The background-free idealization is flagged by the authors themselves (Sec. 3) and is a correctness/robustness concern, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

No invented physical entities. The paper imports benchmark DM masses/lifetimes from a fit to the same event (Ref [48]), halo-profile inputs, and cross-section fits; its own free choices are the form of the test statistic and the definition of H_iso.

free parameters (3)
  • DM decay benchmark masses/lifetimes = M_DM = [0.2,1,100] EeV; τ_DM = [4,7,4]×10^26 s
    Adopted from Ref [48] best-fit to KM3-230213A for νν, ττ, bb channels. They set the spectral shape and Earth-opacity behavior entering P_DM and the timing gain; normalization cancels in P_DM.
  • NFW halo parameters for fiducial map = r_s=25 kpc, ρ_s=0.23 GeV/cm^3
    Standard NFW parameters from Ref [48] used for the fiducial sky map; sensitivity is bracketed by restrictive/permissive profiles from Ref [49].
  • Test-statistic angular weight ψ_GC^n exponent = n=1
    The statistic TSi = -log P_DM × ψ_GC is hand-chosen; App. B shows n=0,1/2,1,2 give no better discrimination, so thresholds are mildly conservative.
axioms (5)
  • standard math Standard probability and Monte Carlo tail-count p-values.
    p-values defined as fraction of pseudo-experiments with TS≥observed (Sec. 4).
  • domain assumption The restrictive/permissive halo profiles bracket the true Milky Way DM distribution.
    D-factor sky maps use simulation-derived profiles from Refs [49–53] and astrometric constraints [54,55]; if the true halo is outside the bracket, P_DM and thresholds change.
  • domain assumption PREM Earth model and UHE neutrino-nucleon cross-section fits accurately describe opacity.
    The visibility V(E,n,t) of Eq. (3.2) and App. A uses PREM [63] and power-law fits from [61]; these set the width of the visible band and hence the timing information.
  • ad hoc to paper H_iso is represented by events drawn uniformly over the observable sky.
    Sec. 4 defines the isotropic alternative this way; a physical isotropic flux would V-weight the mock events. This is the weakest assumption behind the 14–16 threshold.
  • domain assumption Pseudo-experiment MC results are converged and stable.
    No number of trials, seed, or convergence criterion is reported; p-values and thresholds are quoted without MC uncertainty.

pith-pipeline@v1.3.0-alltime-deepseek · 16133 in / 18473 out tokens · 155045 ms · 2026-08-01T09:51:16.136799+00:00 · methodology

0 comments
read the original abstract

It has been proposed that the ultra-high-energy (UHE) event $\rm KM3-230213A$ detected by KM3NeT could be explained by dark matter (DM) decay. Prima facie this seems unlikely because the arrival direction of the event is opposite to the Galactic Centre. We develop a per-event test statistic to quantitively assess this possibility and forecast the required future events to exclude the DM hypothesis in favour of an isotropic signal. For the single event observed, the DM decay hypothesis is disfavoured but not excluded ($p\text{-value}_{\rm DM}\simeq0.13$--$0.15$). We emphasise how including the time-averaged detector visibility helps discrimination despite reducing the proportion of visible sky, reducing the number of events for exclusion from $\sim33$--$43$ to $\sim22$--$27$. Moving beyond this, we perform a fully time-resolved forecast and find that the required number of events for exclusion reduces by $40\%$, $\sim14$--$16$. The time variation in the signal provides vital information allowing one to exclude or confirm the DM hypothesis with much fewer events. Our results are robust against DM decay channels and halo distributions and can readily be applied to other relics distributed similarly. Our framework allows one to turn event timing into a probe of signal geometry and is generic to any UHE equatorial neutrino telescopes.

discussion (0)

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Reference graph

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