{"id":"94ef2fcb-6a8d-4989-b42d-cee41171bde1","arxiv_id":"2607.08039","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"Using 7.32 kg·yr of data from CaMoO4 cryogenic detectors, AMoRE sets a 90% CL lower limit of 1.7×10^22 years on the neutrinoless double electron capture half-life of 40Ca.","lead":"The AMoRE experiment searched for a rare radioactive decay in calcium-40 that would only occur if neutrinos are their own antiparticles. They found no evidence for this decay, setting a new lower limit on its half-life and demonstrating a new detector technology for such searches.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"No significant objection identified","rationale":"The reader correctly identified the r_γ assumption as the most visible modeling choice, and correctly noted it is conservative. I examined whether the 186 keV background peak proximity to the 193.5 keV ROI could bias signal extraction, but the shared-shape-parameter approach with Gaussian constraints from calibration is a standard and adequate treatment. The slight excess (Γ_best non-zero) producing a limit weaker than median sensitivity is statistically expected under background-only. The BPO/APO split due to the power outage is handled by treating the two periods as independent datasets. The detection efficiency calculation (Eq. 1) is straightforward and the conservative r_γ = 1 choice is explicitly justified. The result is a modest improvement over CRESST's 1.4×10^22 yr, consistent with the exposure and background levels reported. No load-bearing concern lands. The reader's ACCEPT verdict at HIGH confidence is appropriate.","tokens_in":10621,"tokens_out":2188,"duration_ms":61109,"concrete_test":"Re-run the combined likelihood fit excluding CMO 05 (the high-background outlier) and verify that the 90% CL limit shifts by less than ~10%. If it shifts significantly more, the result may be disproportionately driven by the background modeling of a single anomalous detector rather than the aggregate dataset.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a 90% CL lower limit on the 0ν2EC half-life of 40Ca: T > 1.7×10^22 yr. The analysis is a standard binned-extended likelihood fit of signal-plus-background in a ±12σ window around 193.5 keV, with conservative assumptions throughout. The reader's identified concern (r_γ = 1 in Eq. 1) is indeed the most prominent modeling assumption, but it is explicitly conservative: setting r_γ = 1 minimizes the containment efficiency (ε_cont ≈ 0.91–0.93), yielding a weaker limit than the true value. If r_γ were 0, ε_cont would rise to ~0.99, strengthening the limit by ~7%. This does not threaten the claimed bound. The background peak at 186 keV (from 226Ra/235U) sits close to the ROI, but the authors share Bukin shape parameters between signal and background peaks and apply Gaussian constraints from calibration data, which is a reasonable treatment. The best-fit Γ_best ≈ 1.2×10^-23 yr^-1 is non-zero but attributed to background fluctuations; the actual limit (1.7×10^22 yr) being slightly weaker than the median sensitivity (2.0×10^22 yr) is consistent with the background-only hypothesis. The CMO 05 detector's 10× higher background is flagged and contributes only ~6% of total exposure. No internally inconsistent or non-conservative step was identified that would undermine the stated limit.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This manuscript reports a search for neutrinoless double electron capture (0ν2EC) in 40Ca using 7.32 kg·yr of exposure from thirteen 40Ca100MoO4 crystals in the AMoRE-I experiment. No significant excess is observed in the region of interest near Q2EC = 193.5 keV, and a 90% CL lower limit on the half-life of T_{1/2}^{0ν} > 1.7 × 10^22 yr is obtained, slightly improving the previous CRESST limit. The analysis uses a binned-extended likelihood fit with a background model comprising a linear component and a peak near 186 keV, with Gaussian constraints on peak shape parameters derived from calibration data. A projection for the upcoming AMoRE-II experiment is also provided.","tokens_in":10902,"tokens_out":1022,"duration_ms":135571,"significance":"The result represents a modest but meaningful improvement over the existing CRESST limit (1.4 × 10^22 yr) and demonstrates the capability of CaMoO4 detectors to probe rare decay processes beyond the primary 100Mo 0νββ program. The analysis is methodologically sound, with conservative assumptions clearly stated—most notably the choice of r_γ = 1 in Eq. (1), which minimizes the containment efficiency and thus yields a deliberately conservative (weaker) limit. The falsifiable AMoRE-II sensitivity projection (~9 × 10^22 yr) provides a concrete benchmark for future experiments. The dual-readout cryogenic calorimeter technique and the treatment of multiple capture channels (KK, KL) with GEANT4-based efficiency evaluation are strengths of the experimental approach.","major_comments":[],"minor_comments":[{"comment":"Section 2, Eq. (1): The statement 'We assumed r_γ = 1 to conservatively determine half-life' is correct and conservative, but a brief quantitative statement of the impact would strengthen the paper. For instance, noting that setting r_γ = 0 would raise ε_cont to approximately 0.99 (a ~7% change) would make the conservatism transparent to the reader.","section":null},{"comment":"Table 1: The 'Total / Average' row lists ΔE_FWHM = 3.4 keV and b = 9.7 count/keV/kg/day, but it is unclear whether these are exposure-weighted averages or simple means. Given the wide variation in both resolution (2.5–6.5 keV) and background (5.3–54.7), specifying the averaging method would improve clarity.","section":null},{"comment":"Section 2, paragraph on data-quality cuts: The single-hit requirement within a 3 ms window is stated to achieve ~99.8% efficiency, and the muon coincidence cut reduces efficiency by less than 0.1%. It would be helpful to state whether these efficiencies were measured from data (e.g., using randomly triggered events or calibration source runs) or estimated from simulation.","section":null},{"comment":"Section 3, Eq. (3): The Gaussian constraint term uses θ′_i and Δθ′_i, but the text earlier refers to θ_i and Δθ_i. The relationship between the primed and unprimed parameter sets is not explicitly defined. A brief clarifying sentence would help.","section":null},{"comment":"Figure 3: The caption mentions a 'green curve' for the 90% CL limit, but the visual distinction between the best-fit (red) and limit curves may be difficult to discern in print. Consider adding a brief textual description of what the green curve represents (e.g., the signal amplitude corresponding to the 90% CL upper limit).","section":null},{"comment":"Section 4, sensitivity paragraph: The median exclusion sensitivity is quoted as T_{1/2}^{0ν} = 2.0^{+0.8}_{-0.6} × 10^22 yr. The observed limit (1.7 × 10^22 yr) is slightly weaker, which is consistent with the background-only hypothesis. A brief statement explicitly noting this consistency (e.g., 'The observed limit is consistent with the median sensitivity within 1σ') would be informative.","section":null},{"comment":"Reference [24] is cited as 'in preparation.' Since this reference contains important details on the signal analysis and calibration framework, its availability is relevant for reproducibility. If possible, a preliminary version or additional supplementary material should be made available to referees.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a straightforward null-result experimental paper with a conservative analysis. The improvement over CRESST is marginal (1.7 vs 1.4 × 10^22 yr), but the demonstration of CaMoO4 capability for this channel and the AMoRE-II projection add sufficient value for publication. The in-preparation reference [24] is a minor concern for full reproducibility but does not block acceptance, as the key analysis choices are described adequately in the manuscript text."},"author_rebuttal":null,"desk_editor":{"model":"glm-5.2","letter":"This is a straightforward null-result paper: AMoRE-I searched for 0ν2EC in 40Ca using 7.32 kg·yr of CaMoO4 data and set a 90% CL lower limit of T > 1.7×10^22 yr, a ~20% improvement over the previous CRESST limit of 1.4×10^22 yr. The improvement is marginal in absolute terms, but the paper's real value is demonstrating that CMO crystals can do this physics alongside the primary 100Mo 0νββ program, and establishing a baseline for AMoRE-II, where they project ~9×10^22 yr sensitivity.","headline":"Solid, modest null-result paper from AMoRE on 40Ca 0ν2EC","tokens_in":12014,"tokens_out":201,"would_cite":true,"duration_ms":48007,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["23.40.Hc","29.40.Vj"],"model":"glm-5.2","headline":"No sign of neutrinoless double electron capture in calcium-40","keywords":[],"falsifier":"A statistically significant excess of events at 193.5 keV above the modeled background in a dataset with comparable or greater exposure would indicate discovery of the process. Conversely, if the true KL photon-to-internal-conversion branching ratio differs substantially from the assumed value, the detection efficiency and hence the derived half-life limit would shift quantitatively.","tokens_in":10977,"feed_emoji":"🔬","tokens_out":1063,"duration_ms":156559,"temperature":0.7,"pith_summary":"The AMoRE Collaboration searched for neutrinoless double electron capture (0ν2EC) in calcium-40 using cryogenic crystal detectors operated deep underground. This hypothetical decay, in which two atomic electrons are absorbed by the nucleus simultaneously with no neutrinos emitted, would violate lepton-number conservation and would imply that neutrinos are their own antiparticles (Majorana particles). The experiment used thirteen calcium molybdate crystals with a total exposure of 7.32 kg·yr, looking for a monoenergetic signal peak at 193.5 keV corresponding to the decay energy. No excess above background was found, allowing the collaboration to set a lower limit on the half-life of this process at greater than 1.7 × 10^22 years at 90% confidence, slightly improving the previous world limit set by the CRESST experiment. The result also demonstrates that calcium molybdate detectors, originally deployed to search for neutrinoless double beta decay of molybdenum-100, can simultaneously probe rare decays of calcium-40. A projected sensitivity of roughly 9 × 10^22 years is estimated for the upcoming AMoRE-II phase.","feed_headline":"No sign of neutrinoless double electron capture in calcium-40","feed_subtitle":"Underground crystal detectors push the half-life limit past 1.7×10²² years, tightening constraints on whether neutrinos are their own antip","key_machinery":"The key experimental machinery is a set of thirteen CaMoO4 scintillating crystals operated at millikelvin temperatures with metallic magnetic calorimeters providing dual phonon-photon readout. The signal signature is a monoenergetic peak at 193.5 keV in the heat channel, produced by the combined energy deposition of atomic relaxation products (X-rays and Auger electrons) plus an internal conversion electron or photon. Background rejection relies on the dual-readout particle identification to suppress alpha events, anti-coincidence cuts to remove multi-site events, and a binned-extended likelihood fit that models the background as a linear component plus a small peak at 186 keV from radium-22","core_discovery":"The paper establishes that neutrinoless double electron capture in calcium-40 has a half-life exceeding 1.7 × 10^22 years at 90% confidence, based on 7.32 kg·yr of data from cryogenic calcium molybdate detectors. No signal excess was observed in the region of interest near 193.5 keV, and the limit slightly improves upon the previous best constraint of 1.4 × 10^22 years. The central mechanism carrying the experimental argument is the detection of a monoenergetic peak at the Q-value of the decay, arising from X-rays and Auger electrons emitted during atomic relaxation after two bound electrons are captured by the nucleus, combined with either an internal conversion electron or a real photon to","pith_inferences":[],"forward_implications":["If neutrinos are Majorana particles, 0ν2EC in calcium-40 must occur at some rate; pushing half-life limits eventually either discovers the process or constrains the Majorana neutrino mass scale and lepton-number-violating physics.","The demonstrated sensitivity of CaMoO4 crystals to calcium-40 rare decays means that experiments primarily designed for molybdenum-100 neutrinoless double beta decay can perform dual-isotope physics without additional detector hardware.","The projected fivefold improvement to ~9 × 10^22 yr sensitivity in AMoRE-II, driven primarily by background reduction rather than increased mass, underscores that background control at the 193.5 keV region of interest is the critical bottleneck for this search.","If the 2ν2K (two-neutrino double K-capture) process at 6.4 keV becomes accessible with improved low-energy thresholds in AMoRE-II, it would provide the first observation of a standard-model double electron capture process in calcium-40, calibrating the nuclear matrix elements relevant to the neutrinoless channel."],"fun_headline_variants":["AMoRE-I: calcium-40 neutrinoless double capture half-life exceeds 1.7×10²² years","Cryogenic CaMoO4 detectors tighten neutrinoless electron capture limit in calcium-40","No signal in 7.32 kg·yr: calcium-40 neutrinoless double capture half-life above 1.7×10²² y","AMoRE raises bar on lepton-number violation in calcium-40 electron capture","Calcium-40 neutrinoless double electron capture half-life floor raised to 1.7×10²² years"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The limit depends on the assumed branching ratio for real photon emission versus internal conversion in the KL capture channel. The authors conservatively assume all KL captures produce a photon, which has lower full-energy absorption efficiency than internal conversion, meaning the true detection efficiency could be higher and the true limit stronger. But the exact ratio is unknown, making this an unmeasured modeling input that directly affects the quantitative result.","fun_headline_variants_meta":{"raw":{"variants":["AMoRE-I: calcium-40 neutrinoless double capture half-life exceeds 1.7×10²² years","Cryogenic CaMoO4 detectors tighten neutrinoless electron capture limit in calcium-40","No signal in 7.32 kg·yr: calcium-40 neutrinoless double capture half-life above 1.7×10²² yr","AMoRE raises bar on lepton-number violation in calcium-40 electron capture","Calcium-40 neutrinoless double electron capture half-life floor raised to 1.7×10²² years","No excess at Q-value: AMoRE-I constrains Majorana neutrino physics via calcium-40","7.32 kg·yr of CaMoO4 data shows no neutrinoless double capture in calcium-40","Cryogenic crystals extend half-life bound for neutrinoless electron capture in calcium-40"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":1810,"prompt_tokens":549,"completion_tokens":1261,"prompt_tokens_details":null},"tokens_in":549,"tokens_out":1261,"duration_ms":19208,"temperature":1.0,"reasoning_tokens":947,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T01:11:26.987078+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"A statistically significant excess of events at 193.5 keV above the modeled background in a dataset with comparable or greater exposure would indicate discovery of the process. Conversely, if the true KL photon-to-internal-conversion branching ratio differs substantially from the assumed value, the detection efficiency and hence the derived half-life limit would shift quantitatively.","supporting_citations":[],"review_version":1}