{"id":"3389bb35-8203-44b2-95e5-aeb4b0fc4ca0","arxiv_id":"2412.16047","paper_version":4,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"With the full Majorana Demonstrator data set, new 90% confidence partial lifetime limits are set for tri-nucleon and dinucleon decays in germanium isotopes, with the strongest limits of 1.83 x 10^26 years for two specific channels.","lead":"The Majorana Demonstrator experiment used 64.5 kg years of enriched germanium data to search for ultra-rare decays in which three protons or neutrons vanish from a nucleus. It sets new lower limits, up to 1.83 x 10^26 years, on these baryon-number-violating processes, tightening constraints on physics beyond the Standard Model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified: headline limits are robust to the identified MC-efficiency and daughter-emission caveats.","rationale":"The reader's ACCEPT verdict is well-founded. I read the full text and the central claim is an experimental lower limit on partial lifetimes from zero observed candidates in the two headline channels. The limiting assumptions are (1) Monte Carlo efficiencies and (2) the interpretation of the 73Cu/73Zn final state, which the paper explicitly flags for daughter-nucleon emission. Neither is load-bearing. The total efficiency for the semi-inclusive channels is near unity and dominated by directly measured live-time fractions; a large efficiency error would have to be implausible to change the order of magnitude. The candidate in the semi-inclusive search affects only channels with 1 count and is included conservatively. The fully inclusive limits are more model-dependent but are secondary and transparently compared to GERDA. The only concrete technical simplification I noticed is the use of a single, detector-type-independent ϵ0 and ϵEi in Eqs. (3)-(4), despite the different active masses of PPC, ICPC, and BEGe (0.6–2.1 kg). For the headline 76Ge channels this is negligible because BEGe contributes only a few percent of the enriched 76Ge exposure; for BEGe-dominated channels (e.g., 70Ge nnn) it could bias the limit at the few-percent level, not enough to affect the paper's conclusions. Thus no change to the ACCEPT verdict is required.","tokens_in":11338,"tokens_out":40034,"duration_ms":322307,"concrete_test":"Run the MaGe simulation of the saturated-trigger efficiency separately for PPC, ICPC, and 0.6-kg BEGe geometries for the 76Ge(ppp) and 70Ge(nnn) channels; if the BEGe ϵ0 differs from the table's single value by more than 2% (or if the exposure-weighted total NTϵTot shifts by more than 2%), recompute the limits with detector-type-dependent ϵ0.","verdict_should_be":"UNCHANGED","load_bearing_attack":"No load-bearing flaw found. The headline limits for 76Ge(ppp)→73Cu e+π+π+ and 76Ge(ppn)→73Zn e+π+ rest on zero observed candidates, and the total efficiency product for these semi-inclusive channels is ~0.96, dominated by near-unity factors (ϵ0≈0.998, ϵE1≈0.996, ϵDC≈0.999, ϵτ1≈0.969 from live time). Even a 10–20% error in Monte Carlo efficiencies would shift limits proportionally but would not change the qualitative claim of new ~1.8×10^26 yr bounds. The fully inclusive mode has larger spectral-shape sensitivity (ϵE1=0.445, ϵE2=0.350), but it is explicitly disclosed as less competitive than GERDA and is not the central claim. The self-acknowledged caveat that 73Cu production does not uniquely imply ΔB=3 is valid, but it only makes the quoted ppp/ppn limits conservative upper bounds on those modes, not invalid. The single 70Ge(nnn) candidate in a BEGe detector is conservatively included. The remaining soft spot is the single-valued ϵ0 applied across detector types in Eq. (3); a concrete check is proposed below.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The Majorana Demonstrator reports limits on multi-nucleon decays in germanium isotopes using its full data set (64.5 kg yr enriched, 27.4 kg yr natural). For the two headline semi-inclusive visible channels, 76Ge(ppp)→73Cu e+π+π+ and 76Ge(ppn)→73Zn e+π+, zero candidate events are observed, leading to 90% confidence level partial-lifetime limits of 1.83×10^26 yr each. The fully inclusive tri-proton decay of 76Ge is bounded at 2.1×10^25 yr, and additional ΔB=2 and ΔB=3 channels are tabulated. The analysis uses a saturated-event trigger followed by a daughter-decay search, with efficiencies from MaGe simulations and calibration data. One candidate event in semi-inclusive channels is conservatively treated as a potential signal in each possible channel.","tokens_in":11535,"tokens_out":36072,"duration_ms":256398,"significance":"The paper presents the most stringent existing limits on the two specific semi-inclusive tri-nucleon decay modes of 76Ge, improving on the previous Demonstrator result with the full exposure. The analysis is straightforward and internally consistent: the limits follow from zero observed candidates, near-unity total efficiencies (~0.96) for the headline modes, and Feldman-Cousins statistics. The single observed candidate is handled conservatively, and the systematic uncertainties are itemized. The paper is also notable for its explicit disclosure of limitations, including the non-uniqueness of 73Cu production for ΔB=3 and the reduced sensitivity in the fully inclusive channel due to cosmogenic 73mGe backgrounds. The result is a solid experimental constraint that will be useful for baryon-number-violation studies.","major_comments":[],"minor_comments":[{"comment":"The saturated-trigger efficiency ϵ0 is quoted as a single value (0.998 or 0.999) across all three detector types (PPC, ICPC, BEGe). Since the saturation response may depend on detector geometry and electronics, the authors should either provide per-detector ϵ0 values or justify the uniformity with calibration data.","section":"Eq. (3) and Table I"},{"comment":"The systematic uncertainties (exposure <2%, DC <0.1%, PSD <5%, simulation 2%, statistical <1%) are listed but not propagated into the quoted limits; the authors state they are ignored because the limit is statistically limited. A sentence quantifying the combined systematic (e.g., <6%) and its negligible impact on the 90% CL limit would make the treatment explicit.","section":"Systematic uncertainties paragraph"},{"comment":"The paper does not provide a quantitative background estimate for the fully inclusive sequential beta-decay search; the one observed sequence is attributed to 208Tl, but a background-rate estimate for this search would strengthen the presentation.","section":"Fully inclusive mode description"},{"comment":"The symbol τ is defined as the partial lifetime limit in Eq. (1), but the text does not explicitly state the relation to the half-life (T1/2 = τ ln 2). A brief clarification would avoid ambiguity for readers comparing with half-life limits in other experiments.","section":"Eq. (1) and abstract"}],"recommendation":"minor_revision","confidential_remarks":"The central claim is sound and the paper is well within the scope of the journal. The only issues are local and do not affect the headline limits; I would encourage the authors to address the per-detector efficiency and systematic-propagation comments before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know: the paper delivers new world-best partial lifetime limits for 76Ge(ppp) and 76Ge(ppn) decays at 1.83e26 yr, and it does so with a clean, conservative analysis that holds up on inspection. It's not a new technique — it's the Demonstrator's existing search strategy applied to the full dataset with extra pulse-shape cuts — but the results are new and the details are handled properly.\n\nThe core analysis: zero candidates in the two headline semi-inclusive channels, Feldman-Cousins limits using the full 64.5 kg yr enriched exposure, and MC-derived efficiencies that are all near unity (the product for 76Ge(ppp) is ~0.96). The one candidate in the other semi-inclusive channels is included as an observed count, which is the conservative choice. The fully inclusive mode is less competitive (2.1e25 yr) because of the 73mGe cosmogenic background, and the paper says so plainly. The systematic errors (exposure <2%, PSD <5%, simulation 2%, MC statistics <1%) are genuinely small next to the zero-candidate statistics. Data are released. Good.\n\nSoft spots, in proportion. The efficiency model is the weakest link, but it's not broken. The single-valued epsilon0 across detector types is a simplification; given epsilon0 > 0.99, the effect of detector-to-detector variation is probably negligible, but the paper doesn't show a validation plot for it. The fully inclusive efficiencies are more spectral-shape sensitive (epsilon_E1 = 0.445, epsilon_E2 = 0.350), but the paper discloses this and the fully inclusive result is not the headline. The daughter-nucleon-emission caveat is real — detection of 73Cu doesn't uniquely imply ΔB=3 because a ΔB=2 decay could feed 74Zn* which then proton-emits to 73Cu — but the paper acknowledges it. That makes the quoted limits conservative upper bounds on those specific modes, not invalid.\n\nThe citation pattern looks appropriate: prior Demonstrator result, GERDA, Babu et al. theory, ENSDF. No circular fitting. The paper is what it claims: an incremental but decisive update to the best limits for these channels.\n\nWho should read it: anyone working on baryon number violation in rare decays, and the LEGEND-1000 collaboration will want it on file. It deserves a serious referee, and it should pass with minor revisions — I'd ask for a validation plot for epsilon0 and a sentence separating the ΔB=3 interpretation caveat from the channel-specific limits.\n\nVerdict: accept.","headline":"Solid, conservative limits on rare multi-nucleon decays from the full Majorana dataset; the results are new and the analysis holds up, though the technique is incremental.","tokens_in":12327,"tokens_out":2561,"would_cite":true,"duration_ms":21118,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["23.40-s","23.40.Bw","14.60.Pq","27.50.+j"],"model":"deepseek-v4-flash","headline":"Using the full Majorana Demonstrator dataset, this paper sets the most stringent partial-lifetime limits to date for tri-nucleon decays in germanium, with 1.83 x 10^26 years for the ppp and ppn visible modes.","keywords":["tri-nucleon decay","baryon number violation","Majorana Demonstrator","germanium-76","double-beta decay","pulse-shape discrimination","partial lifetime limit","rare nuclear decays"],"falsifier":"Measure the saturated-event efficiency with tagged high-energy events in the actual detector; if it falls below the assumed >99%, the limits must be reduced proportionally. In a larger dataset, test whether candidate events' time differences follow the daughter half-lives (e.g., 4.2 s for $^{73}$Cu) or stay flat in time; a flat time distribution would confirm the one candidate here is background.","tokens_in":11147,"feed_emoji":"⏳","tokens_out":9998,"duration_ms":77460,"temperature":0.7,"pith_summary":"The paper searches for baryon-number-violating decays in germanium isotopes using the complete dataset of the Majorana Demonstrator, an ultra-low-background experiment originally built for neutrinoless double-$\\beta$ decay. It sets new lower limits on partial lifetimes for three-nucleon (ΔB=3) and two-nucleon (ΔB=2) decays, the most stringent being $1.83 \\times 10^{26}$ years for $^{76}$Ge(ppp)$\\rightarrow^{73}$Cu e$^+\\pi^+\\pi^+$ and $^{76}$Ge(ppn)$\\rightarrow^{73}$Zn e$^+\\pi^+$. These numbers matter because baryon-number violation is one of the Sakharov conditions for the matter-antimatter asymmetry; tri-nucleon decay is a specific Standard Model-allowed ΔB=3 process. The limits are derived from a two-step signature: a high-energy saturated event from the decay, followed by the $\\beta$ decay of the unstable daughter isotope. No candidate events beyond expected background were found, so the results are lower bounds on the decay lifetimes.","feed_headline":"New best limits on rare tri-nucleon decays: 1.83e26 yr","feed_subtitle":"Full Majorana Demonstrator data push three-nucleon decay lifetimes beyond 10^26 years.","key_machinery":"The search uses a two-step 'saturated event + daughter $\\beta$ decay' signature. For semi-inclusive visible modes, the first event is a saturated energy deposit (above the ~10 MeV dynamic range) from the positron and pions produced in the multi-nucleon decay, which occurs inside a germanium crystal and is not tagged by the muon veto; the second is the $\\beta$ decay of the unstable daughter within 5 half-lives and with energy between 100 keV and the Q value. For fully inclusive modes, both steps are $\\beta$ decays of the daughter and granddaughter (e.g., $^{73}$Cu$\\rightarrow^{73}$Zn$\\rightarrow^{73}$Ga) with energies above 2 MeV, and pulse-shape discrimination (AvsE, DCR, LQ) is applied to suppress $\\gamma$, $\\alpha$, and surface backgrounds. Each step's efficiency ($\\epsilon_0$, $\\epsilon_\\tau$, $\\epsilon_{E1}$, $\\epsilon_{E2}$, $\\epsilon_{PSD}$) is computed from Monte Carlo simulation and calibration data, and combined with the isotope exposure $NT$ to obtain the effective exposure $NT\\epsilon_{\\mathrm{Tot}}$; the partial-lifetime limit is $\\tau > NT\\epsilon_{\\mathrm{Tot}}/S$, with $S$ the Feldman-Cousins 90% upper limit on the observed signal count.","core_discovery":"Using the full 64.5 kg yr enriched and 27.4 kg yr natural germanium exposure of the Majorana Demonstrator, the collaboration establishes the most stringent partial-lifetime limits to date for tri-nucleon decays in $^{76}$Ge with visible products: $\\tau > 1.83 \\times 10^{26}$ yr (90% CL) for $^{76}$Ge(ppp)$\\rightarrow^{73}$Cu e$^+\\pi^+\\pi^+$ and $^{76}$Ge(ppn)$\\rightarrow^{73}$Zn e$^+\\pi^+$. For the fully inclusive tri-proton channel $^{76}$Ge(ppp)$\\rightarrow^{73}$Cu+X the limit is $\\tau > 2.1 \\times 10^{25}$ yr. The analysis updates the earlier Demonstrator search by applying additional pulse-shape discrimination cuts (AvsE and LQ), which removed the two previously reported candidate sequences. One new candidate sequence in the semi-inclusive search is consistent with the expected random-coincidence background of about 0.017 counts. The paper also reports updated limits for other ΔB=2 and ΔB=3 modes across $^{74}$Ge, $^{73}$Ge, $^{72}$Ge, and $^{70}$Ge.","pith_inferences":["If the new limits are correct, they begin to probe the effective scale of the dimension-15 operator responsible for ΔB=3 transitions; a rough estimate would place that scale far above the TeV, implying that any observable signal in near-future experiments would require a specific UV completion rather than generic new physics.","The saturated-event trigger technique is transferable: any large-volume, low-background detector with a dynamic energy range can search for multi-nucleon decays by looking for a high-energy deposit followed by a characteristic beta-decay chain, so similar searches could be performed with other isotopes in existing double-beta experiments.","The fact that the fully inclusive channel is background-limited by cosmogenic $^{73m}$Ge in the Demonstrator suggests that next-generation germanium detectors should minimize surface exposure during fabrication or add a tag for the $^{73m}$Ge two-step waveform to recover sensitivity in that channel.","A testable prediction: if the one semi-inclusive candidate were signal, its time difference would need to match a daughter half-life (e.g., ~487 s for $^{74}$Ga); the observed 1712 s makes the signal hypothesis unlikely, and additional events in the LEGEND dataset should show a flat time distribution if the background interpretation is correct."],"forward_implications":["The new limits for $^{76}$Ge(ppp) and $^{76}$Ge(ppn) visible tri-nucleon decays are the most stringent for these channels, improving on the previous Demonstrator result.","The fully inclusive tri-proton limit of $2.1 \\times 10^{25}$ yr is weaker than GERDA's $1.2 \\times 10^{26}$ yr because the Demonstrator sees background events from cosmogenic $^{73m}$Ge decays, which reduces sensitivity to that mode.","With no signal candidates, the observation is consistent with background; the single candidate in the semi-inclusive search is likely a random coincidence (expected 0.017 counts).","The limits constrain ΔB=3 baryon-number-violating processes in germanium, complementing proton-decay and dinucleon-decay bounds from other experiments.","Future experiments like LEGEND-1000 with ~$10^4$ kg yr exposure are expected to improve these limits by two orders of magnitude, reaching ~$10^{28}$ yr."],"supporting_citations":[{"why":"Supplies the previous Demonstrator tri-nucleon search and the detection procedure and efficiencies being updated.","marker":"[14]"},{"why":"Provides the final exposure values, data-cleaning efficiencies, and pulse-shape discrimination efficiencies used in the limits.","marker":"[35]"},{"why":"The GERDA inclusive tri-nucleon limit used as a comparison for the fully inclusive channel.","marker":"[15]"},{"why":"Gives the ΔB=3 decay modes and the Z6 symmetry motivation that defines the searched signatures.","marker":"[8]"},{"why":"Defines the Feldman-Cousins 90% confidence interval used to convert observed candidates into signal upper limits.","marker":"[38]"},{"why":"Supplies the half-lives and Q values of daughter isotopes used to set time windows and energy cuts.","marker":"[39]"},{"why":"Describes the Monte Carlo simulation framework used to compute detection efficiencies.","marker":"[40]"}],"fun_headline_variants":["Record tri-nucleon decay limit: 1.83e26 yr","Majorana sets best limit on rare triple-nucleon decay","Full data push tri-nucleon decay bounds past 10^26 yr","New stringent limits on tri-nucleon decays from Majorana","Tri-nucleon decay search yields 10^26-year lower bound"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quoted limits scale linearly with Monte Carlo-derived detection efficiencies, especially the saturated-event efficiency assumed to be above 99%, so a simulation error in those efficiencies changes all quoted lifetimes by the same factor.","fun_headline_variants_meta":{"raw":{"variants":["Record tri-nucleon decay limit: 1.83e26 yr","Majorana sets best limit on rare triple-nucleon decay","Full data push tri-nucleon decay bounds past 10^26 yr","New stringent limits on tri-nucleon decays from Majorana","Tri-nucleon decay search yields 10^26-year lower bound"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000804,"raw_usage":{"total_tokens":3597,"prompt_tokens":1072,"completion_tokens":2525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":688,"completion_tokens_details":{"reasoning_tokens":2431}},"tokens_in":688,"tokens_out":2525,"duration_ms":15906,"temperature":1.0,"reasoning_tokens":2431,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:51:34.091957+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the saturated-event efficiency with tagged high-energy events in the actual detector; if it falls below the assumed >99%, the limits must be reduced proportionally. In a larger dataset, test whether candidate events' time differences follow the daughter half-lives (e.g., 4.2 s for $^{73}$Cu) or stay flat in time; a flat time distribution would confirm the one candidate here is background.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the previous Demonstrator tri-nucleon search and the detection procedure and efficiencies being updated."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the final exposure values, data-cleaning efficiencies, and pulse-shape discrimination efficiencies used in the limits."},{"cited_title":"Agostini et al","cited_arxiv_id":null,"evidence_quote":"The GERDA inclusive tri-nucleon limit used as a comparison for the fully inclusive channel."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the ΔB=3 decay modes and the Z6 symmetry motivation that defines the searched signatures."},{"cited_title":"Feldman and Robert D","cited_arxiv_id":null,"evidence_quote":"Defines the Feldman-Cousins 90% confidence interval used to convert observed candidates into signal upper limits."},{"cited_title":"nndc.bnl.gov, 2023, accessed on October 27, 2023","cited_arxiv_id":null,"evidence_quote":"Supplies the half-lives and Q values of daughter isotopes used to set time windows and energy cuts."},{"cited_title":", MaGe-a Geant4-based Monte Carlo Application Framework for Low-background Ger- manium Experiments","cited_arxiv_id":null,"evidence_quote":"Describes the Monte Carlo simulation framework used to compute detection efficiencies."}],"review_version":1}