{"id":"32bdda3f-1ffa-432e-acfc-4adf09e8cc02","arxiv_id":"2412.09595","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"MeV-mass axion-like particles from galactic supernovae can form a diffuse flux detectable via a p -> p gamma in water Cherenkov detectors, and Super-Kamiokande data exclude a new region of the ALP parameter space.","lead":"This paper calculates a steady, galaxy-wide flow of heavy axion-like particles coming from many past supernova explosions, and shows that water Cherenkov neutrino detectors could catch these particles bumping into protons. Using Super-Kamiokande data, the authors rule out a swath of the ALP coupling/mass plane that previous supernova cooling limits could not reach.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The detection cross section in Eq. (14) appears to omit the 2-to-2 phase-space Jacobian; if so, the event rates and the new SK/HK exclusion are not reliable.","rationale":"The paper's new physics result is an exclusion region in the trapping regime of MeV ALPs, derived from the expected rate of a p -> p gamma events in Super-Kamiokande. The flux calculation is carefully laid out, and the progenitor-profile limitation is explicitly acknowledged; it affects the absolute normalisation but is not the most fragile step. The most load-bearing ingredient is the detection cross section in Eq. (14). A standard two-body phase-space treatment shows that converting the angular delta function to a photon-energy distribution requires the Jacobian |d cos(theta0)/dE_gamma|. That factor is not present in the published formula. If the factor is truly missing, every event rate in the paper is rescaled by an energy-dependent factor, and the claimed exclusion region, the projected HK sensitivity, and the comparison with cooling bounds are all called into question. The Reader noted that the cross section was not independently checked, but did not identify it as the weakest assumption; this stress-test does. Because the issue is a concrete algebraic correction that can be verified in a few hours, a conditional verdict is appropriate pending that check.","tokens_in":15971,"tokens_out":17732,"duration_ms":180118,"concrete_test":"Re-derive dsigma/dE_gamma for a p -> p gamma from the lab-frame two-body phase space, including the Jacobian |d cos(theta0)/dE_gamma|, and compare it with Eq. (14) at a benchmark point, e.g. m_a = 30 MeV, E_a = 50 MeV, E_gamma = 35 MeV. Then recompute the expected SK event spectrum in Fig. 3 with the corrected formula and rerun the profiled log-likelihood to see whether the exclusion contour in Fig. 4 survives. If the event rate changes by more than 10%, the published SK and HK bounds need to be redrawn.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on the event rate in Eq. (13), which multiplies the diffuse ALP flux by the differential cross section dsigma/dE_gamma from Eq. (14). Equation (14) has the form dsigma/dE_gamma = (1/32pi) integral dcos(theta) |M|^2 / (|p_a|^2 m_p) delta(cos(theta) - cos(theta0)). After the delta integration this is simply proportional to |M|^2, with no Jacobian from changing variables between the scattering angle and the photon energy. For a 2-to-2 process, the correct transformation requires dsigma/dE_gamma = dsigma/dcos(theta) * |d cos(theta0)/dE_gamma|, where, from Eq. (16), |d cos(theta0)/dE_gamma| = (2 m_p E_a + m_a^2) / (2 E_gamma^2 sqrt(E_a^2 - m_a^2)). This factor is absent from Eq. (14). Since Eq. (13) integrates this cross section over the ALP spectrum, an O(1) missing Jacobian directly changes the predicted photon counts and shifts the exclusion contours in Fig. 4. The effect can be much larger than the progenitor-profile uncertainty the Reader emphasised, because the cross-section normalisation enters every event rate. The same form is used in Appendix A for the subdominant photoproduction channel, so the issue does not cancel in the signal estimate. The claim that SK excludes a new region of ALP parameter space is therefore not secure until Eq. (14) is checked against a standard phase-space derivation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that MeV-scale axion-like particles (ALPs) produced in the trapping regime of core-collapse supernovae build up a diffuse galactic flux, and that this flux can be detected in water Cherenkov detectors through a p -> p gamma interactions. Using an 18 solar-mass proto-neutron-star profile at 1 s after bounce, an emission window of 0.5-2 s, and the galactic supernova distribution, the authors compute the diffuse ALP flux. They then use Super-Kamiokande DSNB search data (SK-I through SK-IV, reconstructed energies 16-80 MeV) to set a 95% C.L. exclusion in the (gap, ma) plane, and give a projected Hyper-Kamiokande sensitivity. The headline result is a new excluded band for ma ~ 1-70 MeV and gap ~ 2e-5 to 2e-4, above the SN 1987A cooling bounds.","tokens_in":16241,"tokens_out":20961,"duration_ms":193262,"significance":"If the flux normalization is correct, this would be a genuinely new probe of the trapping regime of MeV ALPs, complementary to SN 1987A cooling limits, solar-axion searches, and SNO bounds. The paper is commendably explicit: the production and absorption formalism follows Refs. [27,28], the galactic-flux convolution is written out, the ALP-proton cross section is given in closed form, and the statistical treatment is relegated to an appendix with enough detail to reproduce the limit. I also checked the phase-space normalization of Eq. (14): the apparent absence of a Jacobian is not an error, because after the angular integral over the energy-conservation delta the E_gamma/E_f factors cancel with |d(E_a+m_p-E_f-E_gamma)/d cos(theta)|, leaving exactly |M|^2/(32*pi*|p_a|^2*m_p). The main risk to the central claim is therefore not the cross-section normalization but the normalization of the diffuse galactic flux itself, which rests on a single progenitor profile and on a marginal steady-flux approximation at the low-mass edge.","major_comments":[{"comment":"The exclusion contour is computed from a single 18 solar-mass proto-neutron-star profile, although the text acknowledges that most galactic progenitors are lighter and have temperatures and densities about 20% lower, while a minority are hotter. Since the ALP production rate and the absorption optical depth depend steeply on temperature and density (through Boltzmann-type factors), a 20% change in the profile can translate into an O(1) or larger change in the predicted photon counts. The quoted ~30% uncertainty from the galactic supernova rate does not cover this systematic. Because the limit sets the coupling where the predicted signal crosses the Super-Kamiokande background, the boundary of the pink band in Fig. 4 will move with this normalization. I request a bracketing estimate: recompute the flux, and if possible the contour, using a lower-mass profile from the same simulation set, or state explicitly how the contour shifts under a factor-of-two flux rescaling. Without this, the claimed one-order-of-magnitude exclusion is not quantitatively robust.","section":"Section III, 'For simplicity...' and Fig. 4"},{"comment":"At ma ~ 1 MeV the arrival-time spread is only about 500 years, and with a galactic supernova rate of roughly 2 per century the expected number of overlapping bursts is only about eight to ten. The diffuse flux is then a Poisson sum with fluctuations of order 30%, not a steady background. The analysis nevertheless includes ma = 1 MeV in the excluded range and in Fig. 4. Either the claimed mass range should start where the overlap is clearly sufficient, or the Poisson variance from the finite number of contributing supernovae should be propagated into the limit. This directly affects the low-mass edge of the abstract's central claim.","section":"Section III, 'It is important to remark...' and Fig. 4"}],"minor_comments":[{"comment":"To help readers and to preempt the Jacobian question, add one sentence after Eq. (14) showing that the displayed form follows from the two-body phase space after the photon-angle integration: the E_gamma/E_f factor from the phase space cancels the Jacobian |d(E_a+m_p-E_f-E_gamma)/d cos(theta)| = q E_gamma/E_f. The formula is correct, but a brief derivation would make this transparent.","section":"Eq. (14) and surrounding text"},{"comment":"The notation alternates between ga and gap in a confusing way; for example, the text says 'we fixed the ALP-proton coupling to ga = 10^-5' even though ga = m_N/f_a and gap = ga Cap with Cap = -0.47. Please define both quantities consistently and use the same symbol for the constrained coupling shown on the vertical axis of Fig. 4.","section":"Section III and Fig. 1"},{"comment":"The likelihood treatment fixes the background to the Horiuchi+09 DSNB model without profiling over background normalization or energy-scale nuisance parameters. This is probably acceptable for a first constraint, but it should be stated as a limitation, since the Super-Kamiokande observed spectrum has its own uncertainties.","section":"Appendix B"}],"recommendation":"major_revision","confidential_remarks":"To the editor: I checked the stress-test objection to Eq. (14) carefully. It does not survive a standard phase-space derivation: after angular integration of the energy-conservation delta, the cross section is exactly |M|^2/(32*pi*|p_a|^2*m_p), so the event-rate normalization is not flawed on that account. The more serious issue is the single-progenitor normalization of the diffuse galactic ALP flux; I have asked for a bracketing quantification in the major comments. The manuscript is otherwise within the journal's scope and the proposed bound is interesting, but I would not accept before the flux-normalization robustness is addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper has a solid, interesting idea — a diffuse galactic flux of semi-relativistic MeV ALPs from core-collapse SNe, observable via a p → p γ in water Cherenkov detectors — and the authors use it to claim a new exclusion region above SN 1987A cooling bounds. But the quantitative claim is not secure because the detection cross section in Eq. (14) is missing a Jacobian. The stress-test note lands. Eq. (14) gives dσ/dEγ as an integral over dcosθ of δ(cosθ − cosθ0) without the factor |dcosθ0/dEγ|. From their own Eq. (16) the correct factor is (2m_p E_a + m_a^2)/(2Eγ^2 sqrt(E_a^2 − m_a^2)). It is not a constant; it changes the energy shape of the predicted photon spectrum in Eq. (13), and therefore the exclusion contours in Fig. 4. The same issue appears in Appendix A, though the photoproduction channel is negligible there.\n\nWhat the paper does well: the trapping-regime treatment, including ALP reabsorption and gravitational redshift, follows the established literature, and the statistical analysis with the four SK phases is standard. The diffuse-flux argument is a good adaptation of the dark-matter work in Ref. [48]. The authors are transparent about the single 18-solar-mass progenitor profile and the marginal steady-flux approximation at ma ~ 1 MeV. Those are genuine soft spots, but they are disclosed and the reader's conditional verdict is reasonable.\n\nMy main concern is the Jacobian, which the reader's summary did not flag. The effect is not tiny: over the energy range of interest the Jacobian varies from ~2 to ~0.5, so both the event-rate normalization and the spectral shape change. If the true cross section is larger, the bound strengthens; if smaller, the claimed region could shrink. Either way, the abstract's number is not reliable until Eq. (14) is rederived.\n\nThis paper deserves a serious referee, but it needs revision that fixes the cross-section formula and re-derives the exclusion region. I would not cite the current numbers, and I would not accept as is. For a reading group it is a good example of how easy it is to drop a phase-space factor in a 2→2 calculation.\n\nBest,\n[You]","headline":"Good idea with a new exclusion claim, but a missing Jacobian in Eq. (14) makes the bound unreliable until the cross section is corrected.","tokens_in":16885,"tokens_out":11460,"would_cite":false,"duration_ms":99388,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"MeV-mass axion-like particles from galactic supernovae form a diffuse flux detectable by water Cherenkov detectors, and Super-Kamiokande data exclude proton couplings of roughly $2\\times10^{-5}$ to $2\\times10^{-4}$ for masses of 1–70 MeV.","keywords":["axion-like particles","MeV ALPs","core-collapse supernovae","diffuse galactic flux","water Cherenkov detectors","ALP-proton coupling","trapping regime","Super-Kamiokande"],"falsifier":"Recompute the diffuse ALP flux using a mass-weighted distribution of supernova progenitor profiles rather than the single 18-solar-mass profile; if the resulting flux at Earth is lower by more than about a factor of 2.5, the claimed Super-Kamiokande exclusion no longer reaches the stated couplings.","tokens_in":15694,"feed_emoji":"🔭","tokens_out":9211,"duration_ms":85400,"temperature":0.7,"pith_summary":"MeV-mass axion-like particles produced in core-collapse supernovae would not arrive as a single burst: because they leave the proto-neutron star with a spread of semi-relativistic speeds, their arrival times stretch over hundreds to thousands of years, so the roughly two supernovae per century in the Milky Way produce a near-steady diffuse galactic flux. The paper shows that this flux can be detected in neutrino water Cherenkov detectors through $a p \\to p \\gamma$ scattering on free protons, yielding photons in the tens-of-MeV range where backgrounds are small. Using the first four phases of Super-Kamiokande data, the authors exclude ALP-proton couplings between about $2\\times10^{-5}$ and $2\\times10^{-4}$ for ALP masses of 1–70 MeV, a band one order of magnitude above the SN 1987A cooling bounds. This would be the first direct probe of the trapping regime of MeV ALPs through a diffuse galactic supernova flux, and the projected Hyper-Kamiokande sensitivity would extend the reach down to couplings near $\\sim 10^{-5}$.","feed_headline":"Super-K data excludes MeV axions from galactic supernovae","feed_subtitle":"MeV axions from supernovae would form a diffuse galactic flux; Super-K cuts a decade of couplings, Hyper-K goes deeper.","key_machinery":"The load-bearing mechanism is the arrival-time spread: ALPs with $m_a \\gtrsim 1$ MeV leave the proto-NS with an order-one velocity spread, giving arrival-time differences $\\Delta t \\simeq d/\\bar v\\,\\delta v \\sim 5\\times10^2$–$5\\times10^3$ years for Galactic Center distances, so the Milky Way supernova rate of about two per century makes the flux from roughly ten to one hundred supernovae overlap into a steady diffuse galactic component. The detection mechanism is the inverse photo-production process $a p \\to p \\gamma$, whose photon energy is fixed by two-body kinematics and falls near the ALP energy, in the tens-of-MeV range; in water Cherenkov detectors a photon is reconstructed almost like a positron, so the same signal region used for the diffuse supernova neutrino background applies. Production is computed from nucleon-nucleon bremsstrahlung and pion conversion, with reabsorption through $NN a \\to NN$ and $N a \\to N\\pi$ and gravitational redshift included.","core_discovery":"The authors' central claim is that ALPs coupled to protons, with masses in the 1–70 MeV range, are produced in proto-neutron star interiors by nucleon-nucleon bremsstrahlung and pion conversion, and that enough of them escape even in the trapping regime to make a detectable diffuse galactic flux. The flux is anisotropic and peaked toward the Galactic Center. Comparing the expected photon events from $a p \\to p \\gamma$ with the observed Super-Kamiokande event rates in the reconstructed-energy window 16–80 MeV, they find that the measured data are consistent with background, so the ALP signal is excluded for couplings of roughly $2\\times10^{-5}$ to $2\\times10^{-4}$ across 1–70 MeV. They project that Hyper-Kamiokande, with a $187\\times10$ kton-year exposure, would improve that bound by up to a factor of 2.5.","pith_inferences":["Beyond the paper, the same arrival-time argument should apply to any long-lived MeV-scale particle with nucleon couplings, so water Cherenkov detectors become a generic telescope for semi-relativistic dark-sector fluxes from galactic supernovae.","Because the diffuse flux is anisotropic and peaked toward the Galactic Center, a directional or angular-template analysis could separate it from the isotropic diffuse supernova neutrino background and strengthen the limit.","The paper notes that oxygen de-excitation photons from ALP scattering would outnumber the $a p \\to p \\gamma$ signal by two orders of magnitude; a dedicated low-energy analysis near the detector threshold could therefore probe lower couplings if the spallation background can be controlled.","A single nearby galactic supernova during the Hyper-Kamiokande era would break the steady-flux assumption on human timescales and provide a time-resolved check of the production spectrum used here."],"forward_implications":["The SN 1987A cooling bounds, which lose sensitivity above couplings of roughly $10^{-6}$, are now supplemented by a flux-based exclusion that covers the trapping regime for $m_a=1$–70 MeV.","Hyper-Kamiokande should exclude couplings down to about $10^{-5}$ for $m_a=1$–50 MeV, cutting the allowed region above the upper cooling bound by up to a factor of 2.5.","The constraints degrade sharply outside $m_a=1$–70 MeV: below 1 MeV the steady-flux assumption fails, and above 70 MeV the SK energy window and the production suppression kill the signal.","The four Super-K phases combined give limits only slightly stronger than SK-IV alone, so the result is driven by the SK-IV exposure."],"supporting_citations":[{"why":"It supplies the 18 solar-mass proto-neutron star temperature, density, and lepton-fraction profiles used for the ALP production and absorption calculation.","marker":"[24]"},{"why":"It provides the supernova axion emission and absorption treatment and the SN 1987A cooling bounds that the new exclusion is compared against.","marker":"[27]"},{"why":"It gives the expressions for ALP production spectra from nucleon-nucleon bremsstrahlung and pion conversion, and the absorption mean free paths.","marker":"[28]"},{"why":"It supplies the observed event rates and expected backgrounds in Super-Kamiokande phases I–IV that the signal is tested against.","marker":"[31]"},{"why":"It provides the Hyper-Kamiokande design exposure and expected background used for the projected constraint.","marker":"[34]"},{"why":"It establishes the arrival-time spread argument for semi-relativistic particles from supernovae that motivates the diffuse flux.","marker":"[48]"},{"why":"It provides the galactic supernova rate and spatial distribution used to normalize the diffuse ALP flux.","marker":"[50]"},{"why":"It gives the oxygen de-excitation detection channel that the paper compares with the $a p \\to p \\gamma$ signal.","marker":"[64]"}],"fun_headline_variants":["Diffuse supernova axions excluded by Super-K data","MeV axions from supernovae fail to show in Super-K","Hyper-K to probe smaller axion-proton couplings after Super-K","Super-K data narrows axion-proton coupling from supernova flux"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes every galactic core-collapse supernova emits ALPs like the same 18-solar-mass proto-neutron star profile evaluated one second after bounce; if the population-averaged flux is lower, the excluded coupling region shrinks.","fun_headline_variants_meta":{"raw":{"variants":["Diffuse supernova axions excluded by Super-K data","MeV axions from supernovae fail to show in Super-K","Hyper-K to probe smaller axion-proton couplings after Super-K","Super-K data narrows axion-proton coupling from supernova flux"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001049,"raw_usage":{"total_tokens":4389,"prompt_tokens":910,"completion_tokens":3479,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":3404}},"tokens_in":526,"tokens_out":3479,"duration_ms":26399,"temperature":1.0,"reasoning_tokens":3404,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:53:43.135244+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the diffuse ALP flux using a mass-weighted distribution of supernova progenitor profiles rather than the single 18-solar-mass profile; if the resulting flux at Earth is lower by more than about a factor of 2.5, the claimed Super-Kamiokande exclusion no longer reaches the stated couplings.","supporting_citations":[],"review_version":1}