{"id":"890082e0-656e-4627-a5e5-840457078f7c","arxiv_id":"2607.08587","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Delayed neutron-capture energy in a Gd-loaded sampling calorimeter recovers invisible hadronic energy and improves 10 GeV proton resolution from 21.8% to 13.3% via event-by-event correction.","lead":"Geant4 simulations of a six-layer lead/gadolinium-loaded scintillator calorimeter show that delayed neutron-capture energy tracks invisible hadronic energy and can correct the prompt signal. A simple event-by-event correction improves 10 GeV proton energy resolution from 21.8% to 13.3% without discarding events.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Idealized Geant4 energy deposits (no optics, sensors or electronics) leave the 21.8%→13.3% gain unproven for a real detector.","rationale":"The reader correctly isolates the idealized energy-deposit assumption as the weakest link supporting the 21.8%→13.3% claim. No stronger internal inconsistency or circularity appears: the delayed-vs-multiplicity calibration is essentially perfect (R²=0.9998), the anti-correlation is physically expected, and the branch-wise correction is a transparent, non-over-fitted use of that correlation. The numerical tension between the quoted 907 MeV total deposit and the ~1.57 GeV delayed deposit implied by 197 captures × 7.97 MeV is almost certainly a drafting slip and does not affect the relative resolution figures. Because the paper is explicitly a first-principles MC feasibility study and already lists the missing detector-response steps as future work, the CONDITIONAL verdict and MODERATE confidence remain appropriate; the present stress-test does not move them.","tokens_in":13471,"tokens_out":597,"duration_ms":58171,"concrete_test":"Re-run the identical six-layer geometry with Geant4 optical physics (scintillation yield, absorption/scattering lengths of LAB-Gd, 20% APD coverage) plus a simple APD response model; regenerate the prompt/delayed observables, rebuild the branch-wise interpolation of Fig. 11b, and recompute the resolution. If the corrected resolution degrades beyond 16% (or the variance reduction falls below ~40%), the headline improvement does not survive realistic detector effects.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on event-by-event prompt vs. delayed deposited-energy correlations extracted from pure Geant4 energy deposits (§3.4.3–3.4.6, Figs. 11 & 14). The simulation (§2) scores only ionization and capture-γ energy; it omits optical-photon transport, light-collection non-uniformity, APD quantum efficiency/noise, scintillation quenching differences between prompt charged particles and delayed ~8 MeV γ cascades, and finite timing windows needed to separate the two signals. Because the delayed observable is used both to build the branch-wise correction curve and to apply it, any degradation of delayed-signal fidelity (partial γ containment fluctuations, photostatistics on the ~1.5 GeV delayed sum, residual prompt–delayed pile-up) directly weakens or destroys the reported variance reduction. The paper itself flags this gap in the Conclusions, yet the quantitative claim is presented without that uncertainty quantified. Within the idealized MC the arithmetic is consistent, but the mapping to a physical calorimeter is the least secure link.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript proposes a sampling hadronic calorimeter of alternating lead absorbers and Gd-loaded LAB liquid scintillator that records both a prompt ionization signal and a delayed signal from neutron moderation and capture on gadolinium. Using Geant4 (v11.2.2, HP/G4NDL) simulations of 10 GeV protons on a six-layer prototype (~3.66 λ_I), the authors show that delayed deposited energy is nearly perfectly linear with neutron-capture multiplicity (~8 MeV per capture), that prompt and delayed observables are correlated (with an anti-correlation at high multiplicity), and that a branch-wise nonlinear event-by-event correction based on the delayed energy improves the prompt-energy resolution from 21.8% to 13.3% without event rejection. Multiplicity-slice analyses are used to argue that neutron-production fluctuations are a major contribution to hadronic energy resolution.","tokens_in":13725,"tokens_out":1730,"duration_ms":42420,"significance":"If the reported correlation between delayed neutron-capture energy and invisible hadronic energy survives in a real detector, the concept would offer a practical route to recovering part of the invisible energy inside a sampling HCAL, complementary to dual-readout approaches. Strengths of the work include a clean demonstration that delayed energy calibrates capture multiplicity (R² ≈ 0.9998), a systematic fixed-multiplicity resolution study, and an explicit event-by-event correction that retains all events. The study is a simulation proof-of-principle only: optical transport, photosensor response, electronics, and multi-energy/particle validation are deferred. Within that scope the internal MC evidence is coherent and the idea is worth developing.","major_comments":[{"comment":"§3.3 states that the six-layer scintillator layers collect ~907 MeV per 10 GeV proton, yet Table 4 reports a mean prompt energy of 6226 MeV (with means ~6.1–6.5 GeV across multiplicity cuts) and §3.4.3–3.4.6 analyze resolution on that scale. The sampling fraction implied by 907 MeV cannot yield a ~6.2 GeV scintillator signal. Either a reconstruction weight, a total (Pb+scint) deposit, or a different observable is being used, but this is never defined. The absolute resolution numbers (21.8% → 13.3%) and the anti-correlation in Fig. 11 cannot be interpreted until the prompt-energy definition is stated consistently and the 907 vs 6226 discrepancy is resolved.","section":null},{"comment":"The prototype is only ~3.66 nuclear interaction lengths (§3.3). For 10 GeV protons, longitudinal leakage is large and is itself a major resolution driver. Neutron multiplicity is longitudinally correlated with shower development, so the prompt–delayed correlation and the 21.8%→13.3% gain may partly reflect leakage fluctuations rather than invisible energy inside a containing calorimeter. The paper should quantify leakage (energy and neutrons leaving the volume), show the correction performance versus depth or for a deeper geometry, and qualify the claim that neutron-production fluctuations dominate the resolution when containment is incomplete.","section":null},{"comment":"§2 and the Conclusions score only Geant4 ionization and capture-γ energy deposits. There is no optical-photon transport, light-collection non-uniformity, APD response/noise, scintillation quenching differences between prompt charged particles and delayed ~8 MeV γ cascades, or finite timing windows to separate prompt and delayed signals. The headline correction (§3.4.6, Fig. 14; Abstract) uses the delayed deposit both to build and to apply the branch-wise curve; any degradation of delayed-signal fidelity directly reduces the reported variance gain. A sensitivity study (e.g., photostatistics on the ~1.5 GeV delayed sum, partial γ containment, residual pile-up) or explicit caveats on the 13.3% figure are needed before the quantitative claim can stand for a physical detector.","section":null},{"comment":"§3.4.6 builds the branch-wise interpolation of average prompt energy versus delayed energy on the full 10⁴-event sample and applies it to the same sample. No hold-out, k-fold, or independent test sample is reported. For a reconstruction method this is a mild but load-bearing circularity: the quoted 13.3% may be optimistically biased. The authors should retrain on one subsample, evaluate on a disjoint subsample, and report the out-of-sample resolution (and stability of the two-branch shape).","section":null},{"comment":"All quantitative performance claims are for a single energy and species (10 GeV protons). The Abstract and Conclusions generalize to “hadronic energy reconstruction and energy resolution.” At minimum the paper should either (i) show the same correlation and correction at one additional energy and for charged pions, or (ii) clearly restrict the claim to this benchmark and treat multi-energy/particle performance as required future work rather than an implied result.","section":null}],"minor_comments":[{"comment":"FLUKA is cited as an independent benchmark (§2, Conclusions) but no comparison plots or quantitative metrics are shown. A short appendix or overlay for neutron yield, capture time, and delayed energy would strengthen confidence.","section":null},{"comment":"APDs and 5×5×5 cm³ cells with 20% coverage are motivated in the Introduction but never appear in the simulation. Either drop the hardware detail or state explicitly that the MC is volume-deposit only.","section":null},{"comment":"Table 1 vs Table 2: mean capture time 58.9 µs (0.5% Gd) vs median 8.90 µs is fine, but the text sometimes mixes mean and median without labeling; keep the distinction consistent in captions.","section":null},{"comment":"Figure 1 (n_TOF spectrum) and Figure 2 (capture cross sections) are illustrative background; ensure licenses/adaptations from Refs. [5,9] are correctly attributed and that they are not mistaken for results of this work.","section":null},{"comment":"Typographical/style: “discusion” (§3.4.2), “T able” spacing in several table titles, and “n TOF” / “n_TOF” inconsistency. Also “July 9, 2026” on the title page should match the intended submission date.","section":null},{"comment":"The dual-readout and neutron-tagging literature (e.g. DREAM/RD52 neutron results, Ref. [23]) is cited but not compared quantitatively to the present correction gain; a short paragraph placing 21.8%→13.3% in that context would help readers.","section":null}],"recommendation":"major_revision","confidential_remarks":"The core idea is publishable as a simulation methods/instrumentation paper after the energy-scale inconsistency and containment caveats are fixed. I would not reject on novelty grounds: integrating Gd-loaded scintillator as active sampling layers with an explicit delayed-energy correction is a useful incremental concept. The main risk is overselling a single-energy, non-containing, deposit-only MC result as a demonstrated calorimeter resolution improvement; the revision should force the Abstract and Conclusions to match the actual scope. Fit for a instrumentation journal (e.g. NIM A, JINST) is appropriate; less so for a results-focused HEP journal without detector-response studies."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The new piece is concrete: a six-layer Pb/LAB-Gd stack, 10 GeV protons, delayed capture energy used as a branch-wise event-by-event corrector that moves the prompt resolution from 21.8% to 13.3% while keeping every event. That number is not hand-waved; the delayed deposit is linear with capture multiplicity (R² ≈ 0.9998, slope ~8 MeV/n), the capture efficiency plateaus near 70%, and the multiplicity-slice analysis shows that fixed-neutron classes already sit at ~6%. So the physics correlation they are exploiting is real inside Geant4.\n\nWhat they do well is keep the story clean. Neutron production, moderation, and capture are tracked with HP/G4NDL, they show the timing collapse from hundreds of µs to a few µs once Gd is added, and they separate the detector’s own ~7% neutron-counting resolution from the shower fluctuations. The anti-correlation at high multiplicity is the right physical signature of invisible energy. Citations to dual-readout and earlier neutron-tagging work are honest; they are not claiming to have invented neutron sensitivity, only the integrated prompt+delayed sampling geometry and the nonlinear correction.\n\nSoft spots are exactly the ones the paper itself flags. Everything is pure energy deposits—no optical transport, no APD response, no quenching difference between charged particles and the ~8 MeV γ cascades, no finite timing window. The correction curve is built on the same sample it is applied to (mild circularity, common in MC reconstruction papers). Containment is only ~3.7 λI and they show only one energy. Those gaps mean the 13.3% figure is an upper-bound demonstration, not a hardware prediction. Still, the arithmetic inside the idealized MC is consistent and the stress-test concern does not invent a contradiction that is not already acknowledged.\n\nThis is for people who design or simulate hadronic calorimeters and care about invisible-energy recovery. It is not a paradigm shift, but it is a clean, quantitative step that a serious referee should see. I would send it out; the concept is worth the discussion and the authors already know what the next simulation must include.","headline":"Solid Geant4 study of Gd-loaded sampling layers that recovers ~40% of the resolution width via delayed neutron energy; the 21.8%→13.3% number is real inside the MC but still unproven for hardware.","tokens_in":14372,"tokens_out":572,"would_cite":true,"duration_ms":6290,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A gadolinium-loaded sampling calorimeter recovers invisible hadronic energy via delayed neutron capture, improving 10 GeV proton resolution from 21.8% to 13.3%.","keywords":["hadronic calorimeter","neutron capture","gadolinium-loaded scintillator","invisible energy","energy resolution","Geant4 simulation","sampling calorimeter","delayed neutron signal"],"falsifier":"Build a multi-layer Pb/LAB-Gd prototype, expose it to a mono-energetic hadron beam near 10 GeV, measure both the prompt scintillation and the delayed capture signals, apply the same nonlinear correction, and check whether the energy resolution improves by a comparable factor without event rejection.","tokens_in":14337,"feed_emoji":"⚛️","tokens_out":695,"duration_ms":6730,"temperature":0.7,"pith_summary":"Hadronic calorimeters lose resolution because a large share of shower energy goes into neutrons and nuclear breakup that never appears in the prompt signal. This paper proposes embedding gadolinium-loaded liquid scintillator layers between lead absorbers so the same cells that record the prompt ionization also record the delayed energy released when neutrons thermalize and capture on gadolinium. Geant4 simulations of a six-layer Pb/LAB-Gd stack hit by 10 GeV protons show that the delayed deposit is almost perfectly proportional to neutron multiplicity and is strongly correlated with the invisible energy that distorts the prompt measurement. A simple nonlinear correction that uses the delayed energy to predict and shift each event’s expected prompt response tightens the energy resolution from 21.8 % to 13.3 % without discarding events. Events that share similar neutron multiplicities already have much narrower prompt distributions, confirming that neutron-production fluctuations are a dominant source of the resolution limit.","feed_headline":"Neutron-capture readout cuts hadronic resolution from 21.8% to 13.3%","feed_subtitle":"Gd-loaded scintillator layers turn delayed captures into an event-by-event correction for invisible shower energy","key_machinery":"The delayed neutron-capture signal: after moderation in the hydrogenous scintillator, neutrons capture on gadolinium and release ~8 MeV gamma cascades that produce a delayed scintillation deposit almost perfectly proportional to neutron multiplicity, giving a direct, high-resolution estimator of the invisible energy that can be used for event-by-event correction of the prompt response.","core_discovery":"In a six-layer lead / Gd-loaded liquid-scintillator calorimeter, the delayed energy deposited by neutron-capture gamma cascades is nearly perfectly proportional to neutron multiplicity and carries substantial information about the invisible hadronic energy. Using that delayed observable for a branch-wise event-by-event correction improves the prompt-energy resolution for 10 GeV protons from 21.8 % to 13.3 % without rejecting any events.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Neutron-capture signal cuts hadronic resolution 21.8% to 13.3%","Delayed Gd-capture energy improves resolution to 13.3% without cuts","Event-by-event neutron correction trims resolution from 21.8% to 13.3%","Direct neutron readout recovers invisible energy, resolution 13.3%","Pb/Gd calorimeter uses delayed captures to reach 13.3% resolution"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The Geant4 simulation of neutron production, moderation, capture and energy deposition, without optical-photon transport or real photosensor and electronics response, is assumed accurate enough that the same correlation and resolution gain will appear in a physical detector.","fun_headline_variants_meta":{"raw":{"variants":["Neutron-capture signal cuts hadronic resolution 21.8% to 13.3%","Delayed Gd-capture energy improves resolution to 13.3% without cuts","Event-by-event neutron correction trims resolution from 21.8% to 13.3%","Direct neutron readout recovers invisible energy, resolution 13.3%","Pb/Gd calorimeter uses delayed captures to reach 13.3% resolution"]},"model":"grok-4.5","effort":"low","cost_usd":0.004282,"raw_usage":{"total_tokens":1289,"prompt_tokens":815,"num_sources_used":0,"completion_tokens":95,"cost_in_usd_ticks":42820000,"prompt_tokens_details":{"text_tokens":815,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":379,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":815,"tokens_out":95,"duration_ms":4842,"temperature":1.0,"reasoning_tokens":379,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T04:43:24.822484+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Build a multi-layer Pb/LAB-Gd prototype, expose it to a mono-energetic hadron beam near 10 GeV, measure both the prompt scintillation and the delayed capture signals, apply the same nonlinear correction, and check whether the energy resolution improves by a comparable factor without event rejection.","supporting_citations":[],"review_version":1}