{"id":"a08160ad-3f35-4566-9ca8-14e4cb6c1251","arxiv_id":"2602.09421","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using 532 days of DarkSide-50 data, a multi-scatter analysis excludes nuclear ultra-heavy dark matter cross sections between the geometric and saturation limits for dark nucleon masses from 10 to 500 GeV/c².","lead":"The DarkSide-50 experiment searched for giant composite dark-matter particles that would repeatedly bump into argon atoms inside its detector. No such particles were found, so the team set new limits on how strongly these ultra-heavy dark-matter candidates can interact with ordinary matter.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (7) may normalize the UHDM flux with the dark-nucleon mass mχ instead of the composite mass Mχ, inflating predicted event rates by 10^5–10^12 and potentially shifting the quoted exclusion limits.","rationale":"The reader identifies the assumed dark-nucleus radius and form factor as the weakest assumption. That is a real model-dependence caveat, but the paper explicitly adopts it from ref. [15] and the limits would still be valid within that stated model. Eq. (7) is different: it should be internally correct under the paper's own definitions. The manuscript defines Mχ as the mass of the UHDM nucleus and mχ as the mass of its constituent dark nucleon. The number density of incident UHDM nuclei is therefore ρχ/Mχ. Using ρχ/mχ in Eq. (7) overcounts the flux of composite particles by Mχ/mχ, which ranges over five to twelve orders of magnitude in the plotted parameter space. Because the 90% CL contour is obtained by testing µ = 1 against the data, an inflated event rate makes weak-signal points appear excluded and can move the exposure-limited boundary substantially. This is a concrete, testable internal inconsistency rather than an unconstrained model parameter, so it is more load-bearing than the Rχ/Fχ uncertainty. The proposed check is a single numerical replacement and would settle whether the printed formula affects the central result. I therefore keep the verdict conditional: if the code follows Eq. (7) as written, the printed exclusion claim is not supported and should be corrected or rejected.","tokens_in":11602,"tokens_out":26008,"duration_ms":267722,"concrete_test":"Compute, for a benchmark point on the right-hand edge of Fig. 9 (e.g., mχ = 10 GeV/c², Mχ = 10¹² GeV/c², σχ,n = 10⁻²⁶ cm²), the 90% CL p-value using the printed Eq. (7) and using the corrected normalization N = T (ρχ/Mχ) ∫|v| f d³v dA, with all other inputs identical. If the point changes from excluded to not-excluded, or the contour shifts by more than ~0.5 dex in σχ,n or Mχ, Eq. (7) is load-bearing and the central claim requires revision. If unchanged, the printed formula is a typo and only a correction is needed.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Most load-bearing issue is not the assumed radius/form factor but the flux normalization in Eq. (7). It reads N = T (ρχ/mχ) ∫|v| f d³v dA, where mχ is the dark-nucleon mass. The incident UHDM objects are composite nuclei of mass Mχ; their number density is ρχ/Mχ, not ρχ/mχ. Across the scanned range Mχ/mχ ≈ 10^5–10^12, so the printed event rate is inflated by that factor. §II explicitly treats σχ,n as the whole UHDM-nucleus–nucleon cross section, bounded by σgeo = 4πRχ², so the flux must be of whole nuclei. If the analysis code implements Eq. (7) as written, the 90% CL p-values and the right-hand, exposure-limited edge of Fig. 9 are not the quoted limits; the excluded band can extend to regions with true expected events ≪2.44. If it is only a typographical error and Mχ was used in the computation, the paper must state so. This is an internal consistency issue, not simply a choice of dark-sector model.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports the first search for nuclear ultra-heavy dark matter (UHDM) in a dual-phase liquid argon TPC, using the 532-day low-radioactivity argon campaign of DarkSide-50. UHDM candidates are modeled as composite dark nuclei of total mass Mχ and constituent dark-nucleon mass mχ; the analysis includes overburden energy loss with the Verne package, a multi-scatter signal simulation with LAr response from ARIS measurements, and a profile-likelihood fit to radiogenic backgrounds. The central result is a set of 90% CL exclusion curves in the (Mχ, σχ,n) plane for mχ = 10, 50, 100, and 500 GeV/c² (Fig. 9).","tokens_in":11782,"tokens_out":7343,"duration_ms":79402,"significance":"If the numerical results are correct, this is the first direct UHDM constraint from a dual-phase LAr TPC and a useful complement to existing searches by DEAP-3600 and LZ. Strengths of the manuscript are the coherent use of an external theoretical signal model, the published DarkSide-50 background model with small nuisance pulls (all |pull| < 0.03), and the explicit treatment of multi-scatter event topologies. However, the central quantitative claim depends on the event-rate normalization in Eq. (7), which appears to be internally inconsistent with the composite-mass formalism used everywhere else in the paper. Because this issue directly affects the reported exclusion curves and p-values, the manuscript cannot be accepted in its present form.","major_comments":[{"comment":"The event-rate formula N = T(ρχ/mχ)∫|v|f d³v dA uses the constituent dark-nucleon mass mχ rather than the composite UHDM mass Mχ. The incident flux of composite dark-matter nuclei is nχ⟨v⟩ = ρχ⟨v⟩/Mχ, so the printed expression overestimates the event rate by Mχ/mχ, which is ≈10⁵–10¹² over the parameter range considered. Since the right-hand, exposure-limited edge of Fig. 9 and the p-value calculation for μ=1 depend directly on this normalization, the quoted exclusions are not justified from the formula as written. The authors must either state explicitly that the computation uses Mχ (correcting Eq. (7) as a typographical error) or recompute the limits with the correct density.","section":"§IV A, Eq. (7)"},{"comment":"The manuscript is internally inconsistent about which mass governs UHDM kinematics. Equation (1) and the surrounding text treat σχ,n as a whole-nucleus–nucleon cross section and use reduced masses μχ,N and μχ,n that should be evaluated with the composite mass Mχ, while Eq. (7) uses mχ for the flux normalization. If the reduced masses in Eq. (1) are instead evaluated with mχ, the A² coherence enhancement and the form-factor suppression shown in Fig. 5 would also be affected. Please define explicitly which mass enters each reduced mass, the number density, and the kinetic-energy-loss formalism, and confirm that the signal Monte Carlo uses the same convention.","section":"§II, Eqs. (1)–(3); §IV A, Eq. (7)"},{"comment":"The treatment of S1 for multi-scatter events is not fully specified. The text states that S1 is evaluated using the sum of all energy deposits in a TPC pass, but the LAr response parameterized by L_eff(E_R) is nonlinear; summing individual recoil energies before applying the quenching model differs from summing the S1 produced by each individual scatter. Because the ROI boundaries (100–8000 PE) and the acceptance map in Fig. 6 are derived from S1, the magnitude of this approximation should be quantified, or the simulation should be described more precisely.","section":"§IV A, detector response"}],"minor_comments":[{"comment":"Typographical error: “time projection champer” should be “time projection chamber.”","section":"§I"},{"comment":"The sentence “masses below ∼Mχ = 10¹⁰ GeV/cm²” mixes a mass with a dimension of inverse length; this should be GeV/c², and the phrasing should be clarified.","section":"§III"},{"comment":"The sentence “No events had more than one S1 pulse” appears to contradict the preceding statement that successive energy deposits are not expected to merge into a single S1 pulse. Please clarify whether the toy simulation tested full multi-scatter events or individual energy deposits.","section":"§IV A"},{"comment":"Reference [11] contains a malformed author entry (“Tailby.”); this should be corrected.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The Eq. (7) normalization issue is serious: if the simulation actually used mχ in the flux, the central limits shift by orders of magnitude; if it used Mχ, the manuscript needs a clear correction of the printed formula. I would ask the collaboration for a definitive statement of which quantity was used in the computation before publication. The remaining concerns are addressable with clarifications and modest numerical checks."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimate first UHDM search in a dual-phase argon TPC, with a coherent analysis pipeline and a result worth having — but there is a likely normalization error in Eq. (7) that, if it made it into the code, would inflate the event rate by a factor of Mχ/mχ and shift the quoted exclusions by orders of magnitude. That has to be resolved before this paper can be taken at face value.\n\nWhat's new and good: The DarkSide-50 532-day dataset is used to place 90% CL limits on nuclear UHDM for four dark nucleon masses. The signal model comes from published work (Hardy, Coskuner, Butcher), the overburden treatment uses Verne, the detector response uses ARIS measurements, and the background fit has all nuisance pulls under 0.03. The structure is sensible and the paper is readable.\n\nThe soft spots, in approximate order of severity:\n\n1. Eq. (7) writes N = T (ρχ/mχ) ∫|v| f d³v dA. The number density of composite UHDM nuclei is ρχ/Mχ, not ρχ/mχ. Over the scanned range Mχ/mχ ≈ 10^5–10^12, so the printed rate is off by that factor. The text even says \"the number of events ... is estimated by [10]\", and the cited DEAP paper presumably has the correct expression. If the analysis code implements Eq. (7) literally, the exclusion band on the right side of Fig. 9 is not a real limit. If it's a typo and Mχ was used, the authors need to say so explicitly. This is internal-consistency, not a model choice.\n\n2. Section IV.A first says S1 pulses are not expected to merge, then the toy simulation finds \"no events had more than one S1 pulse\" — i.e., the deposits merge into a single S1. The signal model then sums all energy deposits, which is the merged picture. The text should say that.\n\n3. The symbol σ_s is used for both saturated overburden scattering and the detector saturation cross section. Confusing, though not fatal.\n\n4. The abstract says \"selection criteria optimized for multi-scatter topologies,\" but the cuts are three simple thresholds. Overstatement.\n\n5. No direct comparison with the DEAP-3600 and LZ limits cited in the same paper. That would be useful context.\n\n6. Ref [11] is not a UHDM search; it's a projected WIMP sensitivity paper.\n\nThe bottom line: the analysis pipeline looks solid and the result would be a useful addition, but the flux normalization in Eq. (7) is a load-bearing issue. If it's a typo, the paper is in good shape after minor revisions. If not, the central claim is wrong. Either way it deserves a serious referee, but I'd ask the authors for a clear statement on that point before spending too much time on the rest.","headline":"First dual-phase argon UHDM search with a solid pipeline, but Eq. (7) uses the wrong mass in the flux normalization — if the code follows it, the exclusions are off by orders of magnitude.","tokens_in":13176,"tokens_out":4733,"would_cite":false,"duration_ms":40799,"reading_group":"maybe","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":"DarkSide-50's multi-scatter search excludes composite dark nuclei from 10^7 to 10^13 GeV/c^2","keywords":["ultra-heavy dark matter","composite dark matter","multi-scatter search","dark nucleosynthesis","liquid argon TPC","DarkSide-50","direct detection","exclusion limits"],"falsifier":"A single observed event in the multi-scatter channel with an S1 train of two or more pulses separated by microseconds and total energy in the 100–8000 PE window would directly contradict the null result. Alternatively, a dedicated calculation showing that the dark-nucleus radius is not set by Standard-Model-like forces would undermine the cross-section axis of the limits.","tokens_in":11369,"feed_emoji":"⚛️","tokens_out":4770,"duration_ms":39987,"temperature":0.7,"pith_summary":"This paper reports the first search for ultra-heavy dark matter (UHDM) in a liquid argon time projection chamber, using 532 days of DarkSide-50 data. Instead of looking for single low-energy recoils as in WIMP searches, it looks for a dark-matter nucleus that scatters many times while crossing the detector, leaving a track of multiple scintillation pulses. The authors present 90% confidence-level excluded regions in the UHDM mass–cross-section plane for dark-nucleon masses of 10, 50, 100, and 500 GeV/c². The exclusion band runs from the saturated-overburden cross section up to the geometric cross section, covering UHDM total masses of roughly 10⁷ to 10¹³ GeV/c². If correct, this demonstrates that multi-scatter searches in argon TPCs can constrain composite dark matter and begin to probe its internal structure.","feed_headline":"First argon-TPC search shrinks the room for ultra-heavy dark matter","feed_subtitle":"Multi-scatter tracks in DarkSide-50 exclude composite nuclei up to 10^13 GeV/c^2 for four dark-nucleon masses.","key_machinery":"The signal is a series of S1 scintillation pulses from successive elastic scatters of a UHDM nucleus as it crosses the TPC. The recoil spectrum is shaped by the dark-nucleus form factor Fχ = 3j₁(qRχ)/(qRχ), a spherical top-hat density, and by the geometric radius Rχ = (9πMχ/4mχ⁴)^{1/3} obtained by assuming dark-nucleon forces equivalent to Standard Model ones. Overburden energy loss is computed with a continuous-slowing-down approximation, valid because the UHDM mass vastly exceeds the target mass, and the search is bounded from below by the saturated-overburden cross section σs. The analysis uses only S1, since S2 drift times are comparable to the UHDM transit time.","core_discovery":"For the first time, a dual-phase liquid argon TPC has been used to search for nuclear ultra-heavy dark matter, composite objects made of many dark nucleons that form when the dark sector has no long-range force. Using the 532-day low-radioactivity argon run of DarkSide-50, the analysis applies quality cuts that select multi-scatter event topologies, accounts for energy loss in the Earth's overburden with a continuous slowing-down model, and derives exclusion limits on the UHDM-nucleon cross section for four dark-nucleon masses. The central result is a 90% C.L. excluded band in total-mass versus cross-section space, bounded below by the saturated-overburden cross section and above by the geom","pith_inferences":["If the dark binding force differs from the Standard Model strong force, the radius formula and hence the excluded band would shift by orders of magnitude; the paper's limits quantify a specific dark-sector model, not a universal bound.","The same multi-scatter analysis could be applied to other noble-liquid detectors, since the signature depends only on a track of energy deposits, not on argon's specific response.","A testable extension is to re-analyze the same dataset with alternative dark-nucleus form factors (e.g., Gaussian) to gauge model dependence.","The dark-nucleon mass mχ acts as an internal-structure parameter; future experiments could treat it as a continuous variable rather than sampling a few fixed values."],"forward_implications":["A liquid argon TPC can detect composite UHDM through the multi-scatter topology, where a single crossing produces many S1 pulses.","The excluded band spans UHDM masses from roughly 10⁷ to 10¹³ GeV/c² for all four dark-nucleon masses considered.","The limits apply only for the assumed dark-nucleus radius; changing mχ shifts the band, so future searches can map the internal structure of UHDM.","The S1-only multi-scatter analysis with overburden energy loss is directly applicable to larger argon TPCs.","Cross sections above the geometric limit are already ruled out by self-interaction constraints, so this search closes the remaining window."],"fun_headline_variants":["First argon TPC search sets limits on ultra-heavy dark matter","DarkSide-50: new constraints on multi-scatter dark matter","Argon detector narrows the hunt for nuclear ultra-heavy dark matter","Ultra-heavy dark matter faces first argon-based exclusion limits","Multi-scatter dark matter searched in argon for the first time"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The search assumes a dark nucleus has the same force structure as ordinary strong interactions, giving radius Rχ = (9πMχ/4mχ⁴)^{1/3} and a top-hat density; if the dark binding force differs, the entire exclusion band shifts in cross section and mass.","fun_headline_variants_meta":{"raw":{"variants":["First argon TPC search sets limits on ultra-heavy dark matter","DarkSide-50: new constraints on multi-scatter dark matter","Argon detector narrows the hunt for nuclear ultra-heavy dark matter","Ultra-heavy dark matter faces first argon-based exclusion limits","Multi-scatter dark matter searched in argon for the first time"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000286,"raw_usage":{"total_tokens":1491,"prompt_tokens":685,"completion_tokens":806,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":429,"completion_tokens_details":{"reasoning_tokens":733}},"tokens_in":429,"tokens_out":806,"duration_ms":8030,"temperature":1.0,"reasoning_tokens":733,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T02:50:17.926054+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A single observed event in the multi-scatter channel with an S1 train of two or more pulses separated by microseconds and total energy in the 100–8000 PE window would directly contradict the null result. Alternatively, a dedicated calculation showing that the dark-nucleus radius is not set by Standard-Model-like forces would undermine the cross-section axis of the limits.","supporting_citations":[],"review_version":1}