{"id":"9b69946b-86cf-46f5-b741-32462c7c10e6","arxiv_id":"2412.15641","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Decaying composite dark matter in the 1 to 10 GeV mass range is most strongly constrained by AMS-02 positron data, needing lifetimes above roughly 10^26 seconds.","lead":"This paper works out what decay signals a dark matter candidate made of dark quarks, with mass between 1 and 10 GeV, would send into space. The strongest limits come from positron measurements by AMS-02, which require the dark matter to live longer than about 10^26 seconds.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Footnote-5 assumption of two-body-only dark baryon decay is load-bearing: comparable three-body channels would smear the neutrino line and soften the e± spectrum, shifting the quoted lifetime limits.","rationale":"I agree with the reader that the weakest assumption is the two-body-only decay of the dark baryon, stated in footnote 5. This assumption is load-bearing because it shapes all of the computed spectra: the monoenergetic neutrino line that the Super-K analysis is built around, and the electron/positron and gamma-ray cascade spectra that drive the AMS-02 and Voyager bounds. The paper itself acknowledges the possibility of comparable three-body channels in GUT nucleon decay via final-state interactions, citing Ref. [110], but does not quantify their importance in the dark sector. If the three-body branching ratio is O(0.1-1), the neutrino line is broadened into a continuum and the e± spectrum is softened, which would weaken the headline lifetime constraints. The proposed check is a concrete calculation in the same chiral perturbation theory framework; it is feasible and would settle the question. I do not think this concern rises to the level of rejection, because the paper is internally consistent and transparent about the assumption; rather, it reinforces the reader's CONDITIONAL verdict. The equal reduced matrix elements in Appendix A and the lack of shipped code are secondary issues that would affect the precise values but not the overall structure of the argument.","tokens_in":31031,"tokens_out":7261,"duration_ms":69569,"concrete_test":"Compute the ratio R = Γ(n'→π'π'ν)/Γ(n'→π'ν) at the benchmark m_{π'}/m_{N'}=0.1, m_{A'}/m_{N'}=0.02 using the dark-sector analog of the Wise–Blankenbecler–Abbott calculation [110] for the operator in Eq. (3), including π'π' final-state rescattering (e.g., through a dark-sigma resonance or chiral loops). If R ≥ 0.1, recompute the neutrino spectrum in Section III without the two-body-only assumption (replacing the delta-function line at E = m_N'/2 by the full three-body distribution), redo the Super-K bound of Section IV.D, and redo the AMS-02/Voyager e± bounds of Section IV.C with the corrected injection spectrum. If the resulting τ_DM limits change by more than a factor of ~3, the headline claim as stated is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing unverified input is the stated assumption in Section III (footnote 5) that dark baryons decay only through two-body channels n' → π' + ν, with spin-one, multi-meson, and three-body channels negligible. The full spectral machinery of Eqs. (10)-(15), and the two-body vs three-body dark-meson cascade treatment in Section III.B, all suppose this initial two-body kinematics. Two consequences follow if the three-body channel n' → π'π'ν is even comparable to the two-body one, as the authors note can happen in GUT nucleon decay through final-state interactions (Ref. [110]). First, the 'monochromatic' neutrino signal used in the Super-K analysis of Section IV.D is actually a continuum spread from low energy up to roughly m_N'/2, so the line-search method (three bins of width 0.2 in log10 E centered on E0 = m_N'/2, with χ2 likelihood) loses its sharp peak; the derived τ_DM ≳ 2×10^23 s to 6×10^23 s would weaken, possibly substantially. Second, the electron/positron injection spectrum from the cascade is softened because each π' carries less energy and the pion multiplicity changes; since the headline AMS-02 e+ bound τ_DM ≳ 10^26 s is obtained by comparing the predicted e+ flux from this cascade to the data (Section IV.C), a comparable three-body baryon decay mode could lower that bound by an order of magnitude or more, depending on the actual branching ratio. The paper explicitly defers this check to future work ('it is worthwhile to investigate other decay channels'), so the quoted limits are conditional on an unverified ratio of hadronic matrix elements. This is not an internal inconsistency, but it is a physical input that determines the strength of the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies decaying composite asymmetric dark matter (ADM) in the 1-10 GeV mass range, in both vector-like and chiral realizations with a dark photon portal. It computes analytic cascade spectra for dark baryon decay into a dark meson plus antineutrino, followed by two- or three-body dark meson decays into dark photons and e±/γ, and uses these spectra to derive 95% C.L. lifetime lower limits from AMS-02 e±, Voyager e±, Fermi/EGRET/COMPTEL/SMM γ-ray data, and a dedicated three-bin line search against atmospheric neutrino backgrounds for Super-K, with projections for Hyper-K. The headline result is that AMS-02 positrons provide the most stringent limit, τ_DM ≳ 10^26 s, corresponding to a portal cutoff of about 10^8-10^9 GeV, and that Super-K yields constraints around 2×10^23 s at low masses and 6×10^23 s at 10 GeV.","tokens_in":31437,"tokens_out":8485,"duration_ms":84498,"significance":"The paper fills a genuine gap: existing decaying-DM constraints at 1-10 GeV are not directly applicable to this scenario because the e± spectrum is softened by the cascade and the atmospheric neutrino background is large. The authors provide explicit analytic spectra for both two-body and three-body dark meson decays, use four cosmic-ray propagation scenarios, cross-check against CMB constraints, and give a concrete Hyper-K projection. The methods are transparent: Section III and Appendices A-C contain the spectrum derivations, decay-rate relations via Clebsch-Gordan coefficients, and an equivalence-theorem check for the chiral model, while the propagation uses the public GALPROP code. The derived limits are robust across propagation models for the higher end of the mass range, and the neutrino analysis is appropriately framed as conservative. If the two-body dominance assumption for dark baryon decay holds, the constraints are an important and nontrivial input to composite ADM model building.","major_comments":[{"comment":"The assumption that dark baryon decay is dominated by two-body channels n' → π' + ν (and analogous modes), with spin-one, multi-meson, and three-body channels negligible, is load-bearing for the entire spectrum computation. The paper itself notes in footnote 5 that in GUT nucleon decay three-body final states can be comparable via pion final-state interactions (Ref. [110]), and it defers investigation of such channels to future work. Because the monochromatic neutrino line used in the Super-K analysis (Section IV.D) and the e± injection spectrum behind the AMS-02 bound (Section IV.C) both assume precisely these initial two-body kinematics, the quoted lifetime limits in Figs. 6 and 9 are conditional on an unquantified model assumption. I request either a chiral-perturbation/final-state-interaction estimate of the three-body branching fraction in this specific model, or at least a sensitivity study showing how the τ_DM limits shift for a non-negligible three-body branching fraction (e.g., 10% and 50%). Without one of these, the caveat is not merely cosmetic but directly affects the central numerical claims.","section":"Section III, footnote 5; Eqs. (10)-(15)"},{"comment":"The Super-K 'constraint' is not derived from observed event counts; it is a comparison of the predicted signal plus atmospheric background model to the HKKM model expectation, with the model used as pseudo-data. The text does state that this is intended as a conservative bound and encourages more sophisticated analyses with actual Super-K data, which is commendable. However, the abstract and figure captions present the result as a constraint from Super-K data, and the quantitative statements in the abstract ('Super-K neutrino data require...') are stronger than what the analysis actually supports. I recommend rewording the presentation to make explicit that these are expected limits from a Super-K-like background-model analysis, not limits extracted from the unbinned or event-level data set, and to state this qualification in the abstract and conclusions where the neutrino numbers are quoted.","section":"Section IV.D, Figs. 8-9"}],"minor_comments":[{"comment":"The expression for ξ1:min is missing parentheses; as printed, the denominator is ambiguous. It should read ξ1:min = [1 + ϵ1^2 − 2ξ2 + ξ2^2]/(1 − ξ2).","section":"Eq. (21)"},{"comment":"For m_DM below about 2.4 GeV, the PD and DC propagation models produce no AMS-02 limits because the modulated flux falls below the lowest data point, as noted in the text. The summary statement that e± yield τ_DM ≳ 10^26 s 'for all ADM models' should therefore be qualified by the mass range and propagation-model dependence.","section":"Section IV.C and summary"},{"comment":"The effective cutoff M_* in Eq. (5) is defined only collectively, and its relation to M and M' in Eq. (3) is not stated. A sentence or footnote explaining this connection would help readers follow the cutoff-scale interpretation of the main limit.","section":"Section II.A, Eqs. (3)-(5)"},{"comment":"The caption uses '2mA/mπ = 0.4'; this should be '2mA′/mπ′' for consistency with the rest of the paper.","section":"Fig. 4 caption"},{"comment":"The statement that both vector-like and chiral models lead to the same neutrino constraint is correct but should be explained at first use: the neutrino line flux is independent of the neutral-meson branching ratio because every dark baryon decay produces an antineutrino, whereas the e± and γ-ray fluxes do depend on that branching ratio.","section":"Section IV.D, Fig. 9 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically solid and well organized, and the main numerical results are likely to be useful to the composite ADM community. My recommendation rests on the unquantified two-body-dominance assumption for dark baryon decay, which the authors explicitly acknowledge and defer. A sensitivity estimate for three-body branching would resolve my main concern; without it, the headline limits should be presented as conditional on that assumption. The Super-K pseudo-data issue is secondary but should be corrected in the presentation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a careful, thorough paper. The new pieces are the off-shell dark photon three-body cascade spectra and a dedicated Super-K/Hyper-K neutrino line search in the 1–10 GeV window; neither is in the earlier literature. The authors also do a genuinely complete job with the astrophysical side: AMS-02 e±, Voyager, Fermi-LAT/EGRET/COMPTEL/SMM gamma rays, four propagation models, and an honest discussion of solar modulation and systematic uncertainties. The headline result, tau_DM > ~10^26 s from AMS-02 positrons for mDM > ~2 GeV, is clearly derived and the propagation-model spread is shown.\n\nThe main soft spot is the one the authors flag themselves in footnote 5: they assume dark baryon decay is dominated by two-body channels n' -> pi' + nu (and analogous modes), dropping spin-one, multi-meson and three-body final states. That assumption is load-bearing. The monochromatic neutrino line that drives the Super-K analysis is a line only because the initial decay is two-body. The e± spectrum that produces the AMS-02 bound has a distinctive hard edge for the same reason. If three-body channels are even comparable, as the GUT nucleon decay literature they cite suggests can happen, the neutrino line becomes a continuum and the e± spectrum softens; the quoted limits could weaken by an order of magnitude or more. The authors acknowledge this and defer it to future work, but they don't quantify the impact. That is a legitimate referee request, not a fatal flaw.\n\nOther, smaller issues: the benchmark mass ratios and equal reduced matrix elements in the chiral model are chosen by hand, and the Super-K analysis is a conservative line-search against a background model rather than a full fit to the actual data. No code or configuration is shipped, so the numerical pipeline would take some effort to reproduce, though the public data and codes are clearly identified.\n\nOverall: this is a solid, useful paper for anyone building composite ADM models or working on sub-GeV to 10 GeV decaying DM. It deserves a serious referee. I'd send it to review with the request that the authors address the two-body assumption — at minimum a parametric estimate of three-body branching and its effect on the limits.\n\nBest.","headline":"Solid multimessenger analysis of 1–10 GeV composite ADM; the headline lifetime bound is conditional on a stated but unquantified two-body decay assumption that could shift the limits by an order of magnitude.","tokens_in":32051,"tokens_out":4268,"would_cite":true,"duration_ms":39000,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["95.35.+d"],"model":"deepseek-v4-flash","headline":"Composite asymmetric dark matter in the 1-10 GeV mass range must be extremely long-lived: AMS-02 positrons require a lifetime above about 10^26 seconds, while Super-K neutrino data require at least 10^23 seconds.","keywords":["composite asymmetric dark matter","dark photon portal","dark QCD","decaying dark matter","cosmic-ray constraints","neutrino line","AMS-02 positrons","Super-Kamiokande"],"falsifier":"A dedicated search for a monoenergetic neutrino line at an energy near half the dark matter mass in the 1-10 GeV range would settle the claim: if Super-K, Hyper-K, or DUNE sees a line flux corresponding to a lifetime below the limits claimed here, the central conclusion would be wrong. Equally decisive would be a lattice or chiral-effective-theory calculation showing that the three-body dark-baryon decay rate is comparable to the two-body rate, since that would invalidate the assumed spectra and require all limits to be recomputed.","tokens_in":30813,"feed_emoji":"🌌","tokens_out":5892,"duration_ms":51023,"temperature":0.7,"pith_summary":"Composite asymmetric dark matter aims to explain why the dark matter and baryon densities of the Universe are so similar by making dark matter a dark-sector baryon whose asymmetry is shared with the Standard Model. This paper asks how long such dark baryons can survive if they decay through a dark photon portal, and it answers with existing multimessenger data. For dark matter masses of 1-10 GeV, the most restrictive probe is the AMS-02 positron flux, which forces the dark baryon lifetime above roughly $10^{26}$ seconds for masses above about 2 GeV, corresponding to a portal cutoff scale of about $10^{8}$-$10^{9}$ GeV. Neutrino telescopes give independent, more conservative limits: Super-Kamiokande data require lifetimes above about 2 x $10^{23}$ seconds at low masses and about 6 x $10^{23}$ seconds at 10 GeV. If correct, the composite ADM framework survives only in a narrow region with very long-lived dark baryons and a very weak portal interaction.","feed_headline":"AMS-02 positrons push dark matter lifetime past 10^26 seconds","feed_subtitle":"AMS-02 positron data squeeze composite asymmetric dark matter into a long-lived corner with a portal scale near 10^8-10^9 GeV.","key_machinery":"The engine of the calculation is the cascade-decay spectrum: the dark baryon n' decays through the portal operator into a neutral dark meson pi'0 plus an antineutrino; pi'0 then decays either into two on-shell dark photons when kinematically allowed, or into an off-shell dark photon plus an electron-positron pair, and each dark photon decays to e+e-(gamma) through kinetic mixing with the Standard Model photon. The primary spectra are built by boosting the rest-frame decay spectra using the final-state-radiation splitting function, with the branching fractions of dark baryons into neutral dark mesons fixed by Clebsch-Gordan coefficients, one-third in the minimal vector-like model. These spectra are then propagated with a standard cosmic-ray transport framework under four propagation scenarios, and the neutrino signal is analyzed with a three-bin chi-squared approach using Super-K effective areas and the atmospheric neutrino background.","core_discovery":"The paper claims that the decay of composite asymmetric dark matter in the 1-10 GeV mass window is already strongly bounded by existing cosmic-ray and neutrino observations, and that these bounds cannot be obtained by naive extrapolation from higher-mass dark matter searches. Modeling the full cascade chain, dark baryon to dark meson plus antineutrino, dark meson to dark photons (or to an off-shell dark photon plus electron-positron pair), and dark photon to e+e-(gamma), the authors compute the primary e±, gamma-ray, and neutrino spectra and compare them with positron, electron, gamma-ray, and neutrino data. The strongest limit comes from AMS-02 positrons at masses above about 2 GeV, requiring the dark matter lifetime to exceed about $10^{26}$ seconds, which translates into a portal cutoff scale of about $10^{8}$-$10^{9}$ GeV. The dedicated Super-K monoenergetic neutrino search yields tau_DM greater than about 2 x $10^{23}$ seconds at low masses and about 6 x $10^{23}$ seconds at 10 GeV. These results imply that in the viable parameter region the dark baryon must be very long-lived and the portal interaction that shares the asymmetry must be very weak.","pith_inferences":["If three-body dark-baryon decay channels are comparable to the two-body ones, as the paper notes can happen in GUT nucleon decay through final-state interactions, the monochromatic neutrino line would be smeared and the e± and gamma spectra softened, shifting the quoted lifetime limits; a dedicated calculation of the three-body branching fraction would settle how much.","The same cascade-spectrum machinery could be applied to other portal-decay dark matter scenarios with GeV-scale masses, and the steep mass scaling of the lifetime means the bounds tighten quickly toward 10 GeV and relax toward 1 GeV.","A full analysis of actual Super-K event data rather than the conservative effective-area and binning approach used here could strengthen the neutrino limits by a factor of a few."],"forward_implications":["AMS-02 positron data alone place the vector-like two-body model at tau_DM above about 3 x 10^27 seconds at 1 GeV and above about 10^26 seconds across most of the 2-10 GeV range, making positrons the current strongest probe.","The neutrino line at roughly half the dark matter mass is robust and nearly model-independent, and Super-K already excludes lifetimes below about 2 x 10^23 seconds at low masses and about 6 x 10^23 seconds at 10 GeV.","Hyper-Kamiokande will improve on Super-K only if the systematic uncertainty on the atmospheric neutrino background drops to roughly 10 percent or better energy resolution is achieved.","Chiral composite ADM models are less constrained than vector-like models because their branching fractions into neutral dark mesons differ."],"supporting_citations":[{"why":"Supplies the composite ADM framework with SU(3)_D x U(1)_D gauge dynamics and the dark photon portal that defines the decay channels.","marker":"[17]"},{"why":"Establishes that the portal interaction makes dark baryons decay into a dark meson and an antineutrino, the decay mode analyzed throughout the paper.","marker":"[19]"},{"why":"Provides the AMS-02 positron and electron flux measurements that yield the most stringent lifetime limits.","marker":"[27, 28]"},{"why":"Provides Voyager electron and positron measurements outside the solar modulation region, used to constrain low-mass dark matter.","marker":"[29, 30]"},{"why":"Supplies the Fermi-LAT isotropic diffuse gamma-ray background used for gamma-ray lifetime constraints.","marker":"[31]"},{"why":"Provides the four cosmic-ray propagation scenarios used to transport the injected e± spectra.","marker":"[124]"},{"why":"Supplies the Super-K detector response and observation information used for the neutrino event-rate calculation.","marker":"[21]"},{"why":"Provides the Super-K atmospheric neutrino background model used in the neutrino chi-squared analysis.","marker":"[131]"},{"why":"Provides the detailed atmospheric neutrino flux calculation used to estimate background events.","marker":"[132]"}],"fun_headline_variants":["AMS-02 positrons set toughest bound on composite dark matter","Composite dark matter must live >10^26 s from positron data","Positron data push DM lifetime to 10^26 s and beyond","Multimessenger probe: dark matter must outlive 10^26 s"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire spectral calculation rests on the assumption that dark baryons decay overwhelmingly through the two-body channels such as n' -> pi'0 + nu, with spin-one, multi-meson, and three-body final states negligible; the paper flags this in footnote 5, and if the neglected channels are comparable, the e±, gamma-ray, and neutrino spectra change and the derived lifetime limits shift.","fun_headline_variants_meta":{"raw":{"variants":["AMS-02 positrons set toughest bound on composite dark matter","Composite dark matter must live >10^26 s from positron data","Positron data push DM lifetime to 10^26 s and beyond","Multimessenger probe: dark matter must outlive 10^26 s"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001521,"raw_usage":{"total_tokens":6152,"prompt_tokens":1064,"completion_tokens":5088,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":680,"completion_tokens_details":{"reasoning_tokens":5008}},"tokens_in":680,"tokens_out":5088,"duration_ms":31041,"temperature":1.0,"reasoning_tokens":5008,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:14:31.696975+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A dedicated search for a monoenergetic neutrino line at an energy near half the dark matter mass in the 1-10 GeV range would settle the claim: if Super-K, Hyper-K, or DUNE sees a line flux corresponding to a lifetime below the limits claimed here, the central conclusion would be wrong. Equally decisive would be a lattice or chiral-effective-theory calculation showing that the three-body dark-baryon decay rate is comparable to the two-body rate, since that would invalidate the assumed spectra and require all limits to be recomputed.","supporting_citations":[],"review_version":1}