{"id":"967d199e-0924-4fa5-8ae8-3bf1cd4696bb","arxiv_id":"2608.05601","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"GAGG scintillator shows a stronger nonproportional light-yield response to gamma rays than to beta rays from 50 to 2614 keV, and correcting for this improves PIKACHU background fits.","lead":"This paper measures how a GAGG scintillator's light output depends on the energy of beta and gamma radiation, and finds the two radiation types respond differently. The measurements are used to improve background modeling for the PIKACHU double-beta decay experiment and could improve energy calibration in other scintillator detectors.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Single-scatter assumption in the CCT analysis is not protected by diagonal-band selection; multiple Compton scattering inside the large GAGG crystal can bias the beta nPR curve.","rationale":"The reader's weakest assumption identifies multiple Compton scattering as a contamination source in the CCT, which is the same underlying vulnerability I see. I agree that this is the most load-bearing assumption. However, I sharpen the issue: a sum-energy cut, which the reader suggests, would not remove multi-scatter events because they still satisfy E_GAGG + E_Ge = E_gamma when the scattered photon is fully absorbed in the Ge detector. The needed check is a simulation-based estimate of the multi-Compton fraction or an explicit correction. The reader's verdict is CONDITIONAL, largely on missing systematics and unverified high-energy points; my concern is a specific systematic that should be added to that condition. Since the reader already reached CONDITIONAL and my concern is a more precise form of the same weakness, the verdict should remain UNCHANGED rather than moving to a stricter category. I am not raising the objection to reject the paper; the experimental design and comparison with previous GAGG data are credible, but the beta nPR curve needs this verification before the beta-gamma difference can be accepted as quantitative. Agreement is partial because the reader also mentions escaped scattered photons and a sum-energy cut, whereas the decisive variant is multiple scattering in GAGG with full Ge absorption, which survives the diagonal selection.","tokens_in":1179,"tokens_out":917,"duration_ms":56516,"concrete_test":"Run a GEANT4 simulation of the CCT setup with the same source positions, lead shielding, GAGG dimensions (65 mm diameter, 100 mm length), and Ge crystal, applying the same trigger and diagonal-band selection as in Sec. 3.1. For each dataset in Table 1, record the number of Compton interactions in the GAGG per selected event and compute the fraction of selected events with more than one Compton interaction. If that fraction is non-negligible, especially for the 208Tl 2614 keV theta = 120 degree dataset, recompute the beta nPR values after removing or correcting such events, and check whether the beta-gamma difference in Fig. 6 persists.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central beta-versus-gamma comparison rests on Eq. (2), which assumes each selected event is a single Compton scatter in the GAGG crystal followed by full absorption of the scattered photon in the Ge detector. The diagonal-band selection in Fig. 4 does not enforce this assumption. If the scattered photon undergoes a second Compton scatter in the 65 mm diameter, 100 mm long GAGG crystal before reaching the Ge detector and is then fully absorbed there, the relation E_GAGG + E_Ge = E_gamma still holds, so the event remains on the diagonal. For a fixed Ge-energy slice, such events contribute to the same nominal deposited energy E_gamma - E_Ge, but the GAGG energy is deposited by two electrons rather than one. Since nonproportional response depends on the electron track structure, the light yield for two lower-energy electrons can differ from that for a single electron of the summed energy, shifting the fitted E_GAGG peak. The 2614 keV datasets, especially the 2313 keV point, are particularly exposed because the probability of a second Compton interaction in a large crystal grows with incident energy. The paper slices the Ge energy, fits the GAGG spectra, and reports nPR values without estimating or subtracting this multi-scatter fraction. A bias here would directly affect the claimed difference between beta and gamma nonproportional response, so the beta nPR curve is the least secure load-bearing input.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports measurements of the nonproportional response (nPR) of a large GAGG scintillator used in the PIKACHU double-beta-decay experiment. The beta-ray response is measured with the Compton coincidence technique using a germanium detector with 22Na and 208Tl sources, and the gamma-ray response is obtained from photopeak measurements with several radioactive sources. The authors find a stronger nonproportional response for gamma rays than for beta rays over 50-2614 keV, parameterize both responses with double-exponential functions, and incorporate them into a GEANT4-based background model. They report that the updated model reproduces measured alpha- and beta(gamma)-ray background spectra better than a model without the nPR correction.","tokens_in":8267,"tokens_out":4817,"duration_ms":48319,"significance":"If the reported beta-vs-gamma difference is correct, the paper provides the first nPR data for GAGG above 1 MeV and demonstrates a particle-type dependence of the light yield that is relevant for energy calibration and background modeling in scintillator-based rare-event searches. The manuscript is careful in describing the CCT setup, reports slice-width checks, and compares low-energy results with prior publications, which strengthens confidence in the lower-energy part of the beta curve and in the gamma curve. However, the high-energy beta points and the lack of a multi-scatter correction leave the central beta-vs-gamma comparison less secure than the text suggests.","major_comments":[{"comment":"The diagonal-band event selection in Fig. 4 does not exclude multiple Compton scattering inside the large GAGG crystal (65 mm diameter, 100 mm length). For events where the scattered photon undergoes a second Compton scatter in the GAGG and is then fully absorbed in the Ge detector, the relation E_GAGG + E_Ge = E_gamma still holds, so these events remain on the diagonal. In a fixed Ge-energy slice, such events contribute at the same nominal deposited energy E_gamma - E_Ge, but the GAGG energy is deposited by two lower-energy electrons rather than one. Since nPR depends on the electron track structure, the fitted E_GAGG peak is biased. The 2614 keV datasets, and especially the 2313 keV point, are most exposed because the multi-scatter probability grows with incident energy. No sum-energy cut, multi-scatter fraction estimate, or simulation-based correction is provided, so the beta nPR curve in Fig. 6 is not robustly established.","section":"§3.2 (Eq. 2), Fig. 4"},{"comment":"The two highest-energy beta points (E_gamma - E_gamma' = 2016 and 2313 keV, from 208Tl) are based on only 0.7 h and 28.1 h of data at approximately 0.1 Hz coincidence rate, yielding sparse GAGG spectra in each Ge slice. The spectrum in Fig. 5(c) is fit with a double Gaussian whose background component is an empirical Gaussian attributed to accidental coincidences; the text states that nPR was 'confirmed to be insensitive' to this component, but no quantitative systematic uncertainty is provided. No systematic error budget is given for the background model choice, the Ge slice midpoint approximation, or the energy calibration. These two points drive the asymptotic nPR value of 1.07 for beta rays and the claimed difference from gamma nPR; without a systematic error estimate the central comparison is underdetermined.","section":"§4, Fig. 6, Fig. 5(c)"},{"comment":"The claim that the background model incorporating the measured nPR 'successfully reproduced' the alpha- and beta(gamma)-ray data is supported only by showing chi-square values in Fig. 7. Because the updated model adds the double-exponential nPR parameters, a reduction in chi-square is expected even without a genuine improvement, and the reader cannot evaluate whether the improvement is statistically significant. A quantitative comparison, such as delta chi-square with the number of added parameters or a likelihood-ratio test, is needed to support the abstract and conclusion.","section":"§4, Fig. 7"}],"minor_comments":[{"comment":"The phrase 'which was calculated using Eq. (1)' in the Table 1 caption is awkwardly placed; consider moving this information to the text.","section":"Sec. 3.2 / Table 1"},{"comment":"There is a typo in the sentence 'the model with correction of the nonproprotional response': 'nonproprotional' should be 'nonproportional'.","section":"Sec. 4"},{"comment":"The quoted Ge detector energy resolution (0.26% sigma at 662 keV) and nonlinearity (<0.17 keV) would be easier to assess if the set of calibration gamma lines used to determine them were specified.","section":"Sec. 2.2"},{"comment":"The figure caption does not explain the filled/open marker convention for the 22Na and 208Tl beta data; the explanation appears only in the body text and should be repeated in the caption.","section":"Fig. 6 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of physics.ins-det and addresses a real need for the PIKACHU background model. The main risk is the multi-scatter bias in the beta nPR curve, which is load-bearing for the beta-vs-gamma claim. The authors should be asked to provide a quantitative multi-scatter estimate or simulation, and to add a systematic uncertainty budget for the high-energy beta points, before the central conclusion can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a read if you care about scintillator energy calibration. The paper gives the first >1 MeV nonproportional response data for GAGG and compares beta and gamma in the same setup, and it uses the result to improve the PIKACHU background model. The CCT work is carefully described: time coincidence, Ge energy slices, fitting, slice-width checks. The low-energy agreement with Refs [5,6] after renormalization is a good sanity check. The background model showing reduced chi-square is a nice downstream validation, even if the improvement is not quantified beyond a chi-square number in the figure.\n\nSoft spots. The multi-scatter issue is real and not addressed. The diagonal band selects events where E_GAGG + E_Ge equals the incident energy, but that includes events where the GAGG deposition is two Compton scatters before the photon reaches the Ge detector. For a 65 mm x 100 mm crystal and 2614 keV, that fraction is not negligible, and two lower-energy electrons do not have the same light yield as one electron of the summed energy. The 2313 keV point is most exposed. The paper does not estimate this fraction or subtract it. That is the weakest link in the beta curve.\n\nSecond, the high-energy beta points are sparse: the 2016 keV point comes from 0.7 hours of data, and the 2313 keV point from 28 hours. The high-energy slice (800–850 keV) is fit with a double Gaussian where the background is an empirical Gaussian for accidentals, with no systematic uncertainty on that choice. The paper states the nPR was insensitive to including that background, but no numbers are shown. Overall there are no systematic uncertainties beyond the fit mean errors. That is a modest gap for a measurement paper.\n\nThird, the gamma nPR points are photopeak measurements at discrete energies, which is fine, but the comparison between beta and gamma rests on the beta curve being unbiased. If the multi-scatter bias pushes the beta points up, the claim that gamma is more nonproportional could partially wash out. I think the qualitative direction is likely right—the physical argument about photoelectric cascades is standard—but the quantitative difference should be treated with caution until the multi-scatter fraction is estimated.\n\nWho this is for: people modeling GAGG detectors, double-beta experiments using GAGG, and scintillator nonproportionality folks. It deserves a serious referee. The issues are fixable in revision—an estimate of the multi-scatter contamination, even a simple Geant4 simulation, plus systematic uncertainties. I would encourage you to engage with it; it is a solid incremental measurement with one load-bearing assumption that needs shoring up.","headline":"Useful new high-energy GAGG nonproportionality data, with a real but manageable multi-scatter contamination concern in the CCT beta points.","tokens_in":8919,"tokens_out":2395,"would_cite":true,"duration_ms":25298,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The GAGG scintillator's light yield responds more nonlinearly to gamma rays than to beta rays over 50–2614 keV, and separating the two response curves makes the PIKACHU background model fit better.","keywords":["GAGG scintillator","nonproportional response","Compton coincidence technique","beta-ray response","gamma-ray response","background model","PIKACHU","scintillator calibration"],"falsifier":"Re-run the analysis with a sum-energy requirement that the GAGG and germanium energies add up to the incoming gamma energy; if the reported nonproportionality values shift by more than the quoted uncertainties, multiple Compton scattering contaminated the diagonal-band selection and the beta-ray curve is biased. A small-crystal version of the same setup, where a second scatter is kinematically suppressed, would provide a clean cross-check.","tokens_in":7794,"feed_emoji":"⚛️","tokens_out":10331,"duration_ms":94950,"temperature":0.7,"pith_summary":"This paper, from the PIKACHU double-beta-decay program, measures how the light yield of a large GAGG scintillator crystal depends on whether energy is deposited by beta electrons or by gamma rays. The central result is that the two responses are not the same: gamma rays show a stronger nonproportional response than beta rays across 50–2614 keV, meaning a gamma-ray energy deposit produces less light at low energies than a beta electron depositing the same energy. The authors use a Compton coincidence technique with a germanium detector for beta rays and monoenergetic gamma sources for gamma rays, then feed the two measured curves into the PIKACHU background model as separate double-exponential functions. The corrected model reproduces the measured alpha and beta/gamma background spectra better than the previous model, which had assumed a proportional response below 80 keV. If the result is right, scintillator experiments that calibrate with gamma sources while detecting beta-like events need to correct for this particle-type dependence.","feed_headline":"Gamma rays distort GAGG light yield more than beta rays","feed_subtitle":"Separate beta and gamma response curves, measured from 50 to 2614 keV, improve the background model.","key_machinery":"The key object is the nonproportional-response ratio $\\mathrm{nPR}=E_{\\mathrm{GAGG}}/(E_\\gamma-E_{\\mathrm{Ge}})$, which is measured event-by-event using the Compton coincidence technique: a germanium detector tags the scattered gamma ray, and the Compton formula $E'_\\gamma=E_\\gamma/[1+(E_\\gamma/m_e c^2)(1-\\cos\\theta)]$ fixes the energy that the GAGG crystal absorbed. For gamma rays, photopeak centroids from monoenergetic sources supply the same ratio without a coincidence requirement. The two response curves are then represented as double-exponential functions of deposited energy and used as separate correction factors in the background model, replacing the previous single assumption of 70% light yield below 80 keV.","core_discovery":"On its own terms, this paper establishes that the GAGG scintillator's light yield per deposited energy is not the same for gamma-ray and $\\beta$-ray energy deposits. The $\\beta$-ray response, measured with the Compton coincidence technique, is quantified as $\\mathrm{nPR}=E_{\\mathrm{GAGG}}/(E_\\gamma-E_{\\mathrm{Ge}})$ and falls to about 0.90 at 76 keV while remaining near 1.0 at higher energies; the gamma-ray response, from photopeak centroids, drops to about 0.88 at 100 keV after renormalizing to 661.7 keV. The fitted double-exponential curves asymptote to 1.07 for $\\beta$ rays and 1.02 for gamma rays above 3000 keV. Inserting these two curves separately into the PIKACHU background model improves the fit to both $\\alpha$ and $\\beta$/gamma background spectra, with the 2.0 MeV discrepancy attributed to $^{234\\mathrm{m}}$Pa largely removed.","pith_inferences":["Because the light yield depends on particle type, a scintillator calibrated with gamma sources will systematically misestimate energies of beta-like events unless the same two-curve correction is applied; this extends beyond the PIKACHU background to any GAGG-based detector.","The attributed mechanism, inner-shell photoelectric absorption followed by X-ray and Auger cascades, predicts that the gamma-beta gap should grow as the photoelectric fraction of the gamma interaction increases, which could be tested by comparing high-Z and low-Z scintillator compositions.","The double-exponential fit is unconstrained below 50 keV, so the curves could diverge differently at very low energies; a conversion-electron or x-ray source calibration below 50 keV would be a direct test of the extrapolation."],"forward_implications":["The PIKACHU background model should use separate beta and gamma response functions; the paper reports that this correction lowers the chi-square of the fits to the measured alpha and beta/gamma background spectra.","The old assumption of a flat 70% light-yield factor below 80 keV is replaced by measured double-exponential curves, which shifts the modeled positions of sub-100 keV background peaks.","The dominant beta background, $^{234\\mathrm{m}}$Pa with a 2.269 MeV Q-value, is modeled with the beta curve, which removes the model-data mismatch around 2.0 MeV.","The Compton coincidence setup can be applied directly to future GAGG crystals so their nonproportional response is known before deployment in the double-beta decay search."],"supporting_citations":[{"why":"Provides the earlier GAGG gamma-ray nonproportional response (normalized to 661.7 keV) that this paper renormalizes and compares against at 100 keV.","marker":"[5]"},{"why":"Provides the earlier GAGG beta-ray nonproportional response at 435.4 keV that is used to check the present beta curve.","marker":"[6]"},{"why":"Describes the PIKACHU background model whose 70%-light-yield-below-80-keV assumption this study replaces with measured curves.","marker":"[7]"},{"why":"Reports the same beta-versus-gamma nonproportional difference in Ce:LaBr3 and Ce:LYSO, the precedent for the central comparison.","marker":"[11]"},{"why":"Documents the purified high-purity GAGG crystal used as the test detector in these measurements.","marker":"[4]"},{"why":"Supplies the separate beta/gamma nonproportional treatment used in a liquid-scintillator experiment, the modeling approach adopted here.","marker":"[12]"}],"fun_headline_variants":["GAGG light yield: gamma rays more nonproportional than beta","Beta vs gamma response: GAGG needs separate curves","Gamma rays skew GAGG energy response more than beta rays","Nonproportional GAGG: gamma differs from beta over 50-2614 keV","GAGG scintillator: distinct beta, gamma light-yield curves"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result assumes that each selected event is a single bounce of the gamma ray inside the GAGG crystal and that the germanium detector absorbs the outgoing gamma ray whole, so the energy deposited in the crystal is exactly the difference between the incoming and outgoing gamma-ray energies.","fun_headline_variants_meta":{"raw":{"variants":["GAGG light yield: gamma rays more nonproportional than beta","Beta vs gamma response: GAGG needs separate curves","Gamma rays skew GAGG energy response more than beta rays","Nonproportional GAGG: gamma differs from beta over 50-2614 keV","GAGG scintillator: distinct beta, gamma light-yield curves"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1554,"prompt_tokens":996,"completion_tokens":558,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":468}},"tokens_in":612,"tokens_out":558,"duration_ms":5264,"temperature":1.0,"reasoning_tokens":468,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T05:42:39.984494+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the analysis with a sum-energy requirement that the GAGG and germanium energies add up to the incoming gamma energy; if the reported nonproportionality values shift by more than the quoted uncertainties, multiple Compton scattering contaminated the diagonal-band selection and the beta-ray curve is biased. A small-crystal version of the same setup, where a second scatter is kinematically suppressed, would provide a clean cross-check.","supporting_citations":[{"cited_title":"Sibczy` nskiet al.,Nucl","cited_arxiv_id":null,"evidence_quote":"Provides the earlier GAGG gamma-ray nonproportional response (normalized to 661.7 keV) that this paper renormalizes and compares against at 100 keV."},{"cited_title":"Kaewkhaoet al.,Appl","cited_arxiv_id":null,"evidence_quote":"Provides the earlier GAGG beta-ray nonproportional response at 435.4 keV that is used to check the present beta curve."},{"cited_title":"Omoriet al.,Nucl","cited_arxiv_id":null,"evidence_quote":"Describes the PIKACHU background model whose 70%-light-yield-below-80-keV assumption this study replaces with measured curves."},{"cited_title":"Swiderskiet al.,IEEE Trans","cited_arxiv_id":null,"evidence_quote":"Reports the same beta-versus-gamma nonproportional difference in Ce:LaBr3 and Ce:LYSO, the precedent for the central comparison."},{"cited_title":"Search for Neutrinoless Double-Beta Decay in 136Xe after Intensive Background Reduction with KamLAND-Zen,","cited_arxiv_id":null,"evidence_quote":"Supplies the separate beta/gamma nonproportional treatment used in a liquid-scintillator experiment, the modeling approach adopted here."}],"review_version":1}