{"id":"244d803a-1a61-4683-9d1c-2c02821c5fa5","arxiv_id":"2506.08090","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Nucleon decays into light new particles can hide from water-Cherenkov detectors when the charged partner is slow, while Earth-born fluxes of the decay products could be visible in existing underground detectors.","lead":"Proton and neutron decays into light new particles would be easiest to spot in the smaller detectors JUNO and DUNE, because the charged partners of the new particles can be too slow to make light in the giant water tanks Super-K and Hyper-K. The paper also estimates that decays of protons inside Earth could send a detectable flux of sterile neutrinos through Super-K, even for long proton lifetimes.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline event count in Eqs. (13)-(15) and Fig. 5 counts raw N decays in the detector volume, not signal above background; without an atmospheric-background estimate, the claim that SK can probe the seesaw-motivated parameter space is not yet supported.","rationale":"The paper is a genuine phenomenology study with a useful detector-complementarity argument, and the free-proton flux treatment is a reasonable first approximation for an order-of-magnitude estimate. The authors are appropriately cautious in calling for experimental sensitivity studies, and the conditional verdict is appropriate. The reader's weakest-assumption identification of nuclear suppression is a real issue, but it is not the single most load-bearing one: sterile N is not subject to Pauli blocking, binding affects only a narrow mass window near phase-space closure, and any in-medium suppression is likely a factor of order unity. The larger gap is that the 'promisingly large number of events' is a raw decay count, with no estimate of the atmospheric neutrino background for the same final state. At Super-K, the analogous sub-GeV atmospheric background is expected to be orders of magnitude above 5 events, so the central 'probe the seesaw-motivated parameter space' claim is not yet established. The concrete test of simulating the background for the N->pi l topology would settle whether the proposed search is viable or whether the paper should be read only as a call for dedicated experimental work.","tokens_in":11581,"tokens_out":40351,"duration_ms":509114,"concrete_test":"Compute the expected Super-K atmospheric-neutrino background for the N->pi+-l-+ topology: fully contained events with one pion and one charged lepton, no visible entering track, vertex inside the 22.5 kt fiducial volume, and total visible energy in the 0.2-1.0 GeV range, using published SK sub-GeV atmospheric event rates or a GEANT-based simulation. If the expected background in 20 years exceeds about one event, then the N_sig = 5 contours in Fig. 5 do not represent a searchable signal, and the abstract's 'promisingly large number of events' should be rephrased as raw decay counts pending a dedicated sensitivity study.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing condition for the Earth-flux signature is not the free-proton approximation but the implicit identification of N_decays with detectable events. Equations (13)-(15) count N->pi+-l-+ decays inside the Super-K fiducial volume. The text states these searches 'will face the atmospheric neutrino background', but no background rate is estimated. Over 20 years, Super-K records thousands of fully contained sub-GeV atmospheric neutrino events, and the N decay final state (one pion plus one lepton, no visible entering track, visible energy roughly 0.2-1.0 GeV) closely resembles charged-current atmospheric neutrino interactions with associated pion production. A handful of raw decays is therefore not a probe of baryon-number violation or the seesaw band unless strong kinematic discriminants exist and are demonstrated. The reader's nuclear-suppression concern is less likely to be decisive: the emitted N is a sterile state, so Pauli blocking of ordinary neutrons does not apply; kaon reabsorption can alter the visible kaon but does not remove N production at leading order; and nuclear binding shifts the phase-space boundary by only the ~8 MeV separation energy, affecting a narrow slice of the m_N range. These effects change the expected rate by an O(1) factor, not by the large factor needed to overcome the atmospheric background gap.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies baryon-number-violating nucleon decays into light new particles and their observability in current and near-future neutrino detectors. The first part shows that for scalar or fermionic decay products with masses near phase-space closure, the accompanying charged lepton or pion falls below Cherenkov threshold in water, making Super-K and Hyper-K effectively blind and giving JUNO and DUNE a comparative advantage. The second part constructs a simple leptoquark-plus-right-handed-neutrino model in which nucleons decay into sub-GeV sterile neutrinos N, which then decay through active-sterile mixing. The authors integrate the terrestrial production rate over the PREM proton density and claim that Super-K could see up to about five N decays even for a proton lifetime of 10^35 yr, with the seesaw-motivated parameter region potentially accessible. The paper is exploratory and explicitly encourages dedicated experimental sensitivity studies.","tokens_in":11941,"tokens_out":8498,"duration_ms":115307,"significance":"If the claimed signatures are real, the paper identifies a concrete blind spot in existing nucleon-decay searches and a useful complementarity between Cherenkov and tracking detectors. The Earth-flux idea is interesting and the analytic treatment of the uniform-Earth integral in Eqs. (11)-(15) is a useful contribution. The paper is largely self-contained: no quantity is fitted to data to produce the central prediction; masses and mixings are scanned, the benchmark lifetime is taken from existing limits, and branching ratios are imported from the literature. The main value is in framing new searches and in giving experimentalists a target region. However, the quantitative reach claims, especially the 'up to 5 events' statement and the contours in Fig. 5, need additional work before they can be considered established.","major_comments":[{"comment":"The central Earth-flux claim counts raw N decays inside the detector volume, not signal events above background. The text admits that these searches will face the atmospheric neutrino background, but no background rate is estimated and no kinematic discriminants are demonstrated. Over twenty years, Super-K contains thousands of sub-GeV atmospheric neutrino events, and the N -> pi + lepton final state with no entering track resembles charged-current atmospheric neutrino interactions with associated pion production. A raw count of five (or even tens of) decays is therefore not by itself evidence that the seesaw-motivated parameter space is testable. Please provide a rough background estimate for the specific final states and detector, or reframe the claim as a raw-event-count estimate that requires dedicated experimental study.","section":"A SIMPLE MODEL, Eqs. (13)-(15) and Fig. 5"},{"comment":"The statement that Super-K could have up to five N decays even for a proton lifetime of 10^35 yr is inconsistent with Eq. (15). Using the paper's values Aeff = 707 m^2, Delta L = 32 m, and T = 20 yr gives Aeff Delta L T = 4.52 x 10^5 m^3 yr, about 45 times the benchmark denominator in Eq. (15). At tau = 10^35 yr, Eq. (15) gives about 2.3 decays for Super-K and about 23 for Hyper-K, not five for Super-K. This numerical inconsistency should be corrected, and the abstract and conclusions should be adjusted accordingly.","section":"A SIMPLE MODEL, text after Eq. (15)"},{"comment":"The Earth-flux calculation treats every proton in the Earth as a free emitter with the free-nucleon decay rate and the free-proton density n_p(r). Nuclear binding shifts the phase-space boundary for p -> K + N and p -> pi + N inside oxygen, silicon, and iron nuclei, while final-state kaon reabsorption can deplete the K+N channel. These effects are probably O(1) rather than order-of-magnitude, and Pauli blocking does not apply directly to the sterile N, but they should be quantified or at least discussed in the text. This is particularly relevant near the thresholds used in Fig. 5, where a few MeV shift can change the allowed mass range.","section":"A SIMPLE MODEL, Eq. (11)"},{"comment":"The quantity Nsig is introduced as the number of N decays into a given final state X, but it is then used to draw contours labeled as if they represent detectable signals. No detector efficiency, reconstruction efficiency, or containment efficiency is folded in. For sub-GeV pions and leptons, Super-K's reconstruction efficiency is not 100%, and the pion from N -> pi + lepton may be near threshold in part of the mass range. Please clarify whether Nsig is a raw decay count or an expected detected event count, and if the latter, state the assumed efficiencies.","section":"A SIMPLE MODEL, definition of Nsig after Eq. (15)"}],"minor_comments":[{"comment":"Please state explicitly that the benchmark value of 5 in Eq. (15) corresponds to tau = 10^33 yr and the reference detector volume of (10 m)^3 accumulating 10 yr of data.","section":"A SIMPLE MODEL, Eq. (15)"},{"comment":"The notation is inconsistent: the text writes n -> gamma chi while Eq. (7) gives the rate for n -> chi gamma. Please unify the ordering.","section":"LIGHT FERMIONS, Eq. (7)"},{"comment":"The sentence stating that the actual decay time always exceeds 10^-5 s (10^-4 s for U_eN) should specify whether this is the lab-frame or rest-frame time and for which mass range it is claimed.","section":"A SIMPLE MODEL, paragraph on displaced vertices"},{"comment":"The three panels are not labeled inside the figure; the reader must infer from the caption which mixing scenario and final state each panel shows. Adding (a), (b), (c) labels would improve readability.","section":"Fig. 5"},{"comment":"There is a typo: 'assinged' should be 'assigned'.","section":"Supplemental Material, Eq. (A.21)"}],"recommendation":"major_revision","confidential_remarks":"This is a reasonable exploratory phenomenology paper with a useful central idea, but the quantitative claims in the Earth-flux section need to be tightened. The background issue is the most serious: without a background estimate, the abstract's 'promisingly large number of events' is not supported. The numerical inconsistency in the 10^35 yr statement should also be fixed. The nuclear-medium corrections are less likely to be decisive, but they should be addressed for completeness."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid phenomenology paper that does two genuinely useful things—it maps the mass windows where Super-K and Hyper-K lose Cherenkov sensitivity for p→ℓ+φ and p→π+χ, and it computes the terrestrial sterile-neutrino flux from nucleon decay. The rate formulas are internally consistent, the PREM integration is straightforward and correct as far as I can tell, and the authors are honest that the p→K+N displaced-vertex idea comes from Ref. [16]. The complementarity point—JUNO and DUNE can beat the big water tanks in the slow-lepton/pion windows—is worth having on record.\n\nThe soft spot is the one the stress-test flags. Equations (13)–(15) count N decays inside the detector volume, not events above background. The final state N→π±ℓ∓, with no visible entering track and visible energy around a few hundred MeV, resembles an atmospheric charged-current interaction with associated pion production. Super-K has thousands of those over 20 years. The paper says these searches 'will face the atmospheric neutrino background' and then moves on. Without a background estimate or at least a demonstrated kinematic discriminator, the 'up to 5 events at 10^35 yr' line is a raw rate, not a projected sensitivity. The authors do explicitly encourage dedicated searches, so it is an invitation rather than an overclaim, but the abstract's 'promisingly large number of events' is stronger than the evidence supports.\n\nThe reader's worry about nuclear suppression inside the Earth is, I think, over-stated. The emitted N is a sterile state, so Pauli blocking of the final neutron is not obviously relevant; kaon reabsorption changes the visible kaon but not the N production at leading order; binding-energy shifts change the phase-space boundary by an O(1) amount. That concern is minor. The background gap is the real issue.\n\nVerdict: this deserves a serious referee. The central physics arguments hold up; the paper just needs a dose of realism about backgrounds and efficiencies, which the authors partly acknowledge. For a phenomenology paper proposing new search channels, that is the right balance. I would cite it for the Cherenkov-blind windows and the Earth-flux formula, and I would bring it to a reading group focused on baryon-number violation or sub-GeV sterile neutrinos. It is not a discovery paper, and it should not be read as one.","headline":"A useful phenomenology map of Cherenkov-blind nucleon decay windows and a new Earth-flux calculation, but the headline event rate is raw decays, not a background-subtracted signal.","tokens_in":12473,"tokens_out":2057,"would_cite":true,"duration_ms":25010,"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":"Nucleon decays into light new particles can hide from the largest water-Cherenkov detectors while remaining visible to tracking detectors, and the Earth itself may produce a sterile-neutrino flux that Super-Kamiokande can catch.","keywords":["baryon number violation","nucleon decay","proton decay","sterile neutrinos","heavy neutral leptons","Cherenkov threshold","neutrino detectors","leptoquark model"],"falsifier":"Search 20 years of Super-Kamiokande data for the predicted $N\\to\\pi^\\pm\\ell^\\mp$ decays: mono-energetic, back-to-back charged pions and leptons with summed energy $m_p-m_K-m_N$ and the zenith-angle distribution of Fig. 4, which peaks toward the opposite side of the Earth when the decay length $\\ell_D$ is near the Earth's radius. Finding zero events above the atmospheric-neutrino background would exclude the benchmark production lifetime $\\tau_{p\\to N}=6\\times10^{33}$ yr in the seesaw-motivated mixing region of Fig. 5, contradicting the claim of up to five detectable decays.","tokens_in":11380,"feed_emoji":"⚛️","tokens_out":17371,"duration_ms":175454,"temperature":0.7,"pith_summary":"This paper argues that two previously ignored nucleon-decay signatures could make baryon-number violation visible in existing and near-future neutrino detectors in parameter regions thought to be out of reach. First, proton decays into a light neutral particle $X$ with $X$ mass near the maximum allowed value produce a charged lepton or pion so slow that it emits no Cherenkov light, leaving Super-Kamiokande and Hyper-Kamiokande effectively blind while JUNO and DUNE, being tracking detectors, could see the mono-energetic charged particle. Second, the authors propose a simple leptoquark model in which nucleons decay into sub-GeV sterile neutrinos, and they show that proton decays inside the Earth would generate a flux of sterile neutrinos whose decays in Super-Kamiokande could yield up to about five events even for a proton lifetime of $10^{35}$ years, within the range motivated by the seesaw mechanism.","feed_headline":"Earth's protons could beam sterile neutrinos into Super-K","feed_subtitle":"Nucleon decays in the planet's interior may give up to 5 visible events even at a 10^35-year proton lifetime.","key_machinery":"The analysis is carried by three objects. The first is the chiral-Lagrangian translation of the quark-level operators: the operator $\\bar u^c d\\,\\bar u^c \\ell \\phi^*/\\Lambda_\\ell^3$ leads to $p\\to\\ell^+\\phi$ with rate (2) and final-state momentum (3), and the mass-mixing operator between the neutron and a sterile fermion $\\chi$ gives $n\\to\\chi\\pi^0$, $p\\to\\chi\\pi^+$, and $n\\to\\chi\\gamma$ with the rates of Eqs. (7)–(8). The second is the Cherenkov threshold in water—a charged particle with momentum below $1.14$ times its mass emits no Cherenkov light—which defines the mass windows in which Super-K and Hyper-K are blind. The third is the Earth-flux integral of Eq. (11), which sums proton-decay sources $n_p(r)\\,d^3r$ over the PREM density profile with attenuation $e^{-|R_\\oplus-r|/\\ell_D}$; its uniform-density maximum, Eq. (14), gives the benchmark of up to five detectable sterile-neutrino decays in Super-Kamiokande for a proton lifetime as long as $10^{35}$ yr.","core_discovery":"The central discovery claim is that light new particles $X$ opened up by nucleon decay change the experimental landscape in two complementary ways. For scalars $\\phi$ with baryon and lepton number one, the decay $p\\to\\ell^+\\phi$ ($\\ell=e,\\mu$) has a charged-lepton momentum set by two-body phase space, and when $m_\\phi$ lies in the windows $937.5$–$937.8$ MeV (for $e^+$) or $768.2$–$832.6$ MeV (for $\\mu^+$) that momentum falls below the Cherenkov threshold in water, so the decay is practically invisible to Super-Kamiokande and Hyper-Kamiokande; the same happens for $p\\to\\pi^+\\chi$ with a sterile fermion $\\chi$ heavier than about $0.71$ GeV. JUNO and DUNE, with their tracking capabilities and lower energy thresholds, are therefore the detectors best placed to search for these Cherenkov-blind baryon-number-violating decays despite being smaller. In the same framework, nucleon decays inside the Earth—in particular $p\\to K^+N$ via a scalar leptoquark, with $N$ a sub-GeV sterile neutrino—produce a quasi-mono-energetic flux of $N$ at a detector; the number of $N$ decays inside Super-Kamiokande is maximal for decay lengths between the detector size and the Earth's radius, and reaches about five events for a proton lifetime of $10^{35}$ years, with the seesaw-motivated mixing region overlapping the sensitivity contours of Fig. 5.","pith_inferences":["Extension: the Cherenkov-blindness mechanism is generic—any two-body nucleon decay into a light neutral particle near phase-space closure will hide the charged daughter from water-Cherenkov detectors, so the JUNO/DUNE advantage plausibly extends to axion-like particles, dark photons, and other light states beyond the scalar and fermion examples treated here.","Extension: the Earth-flux estimate treats protons as free emitters; including nuclear binding, Pauli blocking, form-factor suppression for $p\\to K^+N$ inside mantle nuclei, and reabsorption of $N$ in rock would shift the event-rate contours, likely downward, and a full nuclear calculation is a natural next step.","Extension: the same flux mechanism could produce signals in other detectors—DUNE's near detector and satellite-based searches for $N\\to e^+e^-\\nu$ in interplanetary space, which the paper mentions but does not quantify.","Extension: if the flux is observed, the zenith-angle distribution of Fig. 4 would directly measure the decay length $\\ell_D$ and hence the active-sterile mixing, and the kink in the distribution would simultaneously probe the sharp density change at the Earth's core."],"forward_implications":["Super-Kamiokande and Hyper-Kamiokande cannot tag $p\\to\\ell^+\\phi$ in the mass windows of Eqs. (4)–(5); the best limits for those channels will come from JUNO and DUNE, which should reach lifetimes of $10^{31}$ yr or more.","For the sterile-fermion case, $p\\to\\pi^+\\chi$ becomes Cherenkov-invisible above $m_\\chi\\simeq0.71$ GeV, while the isospin-related mode $n\\to\\chi\\pi^0$ stays visible through its $\\pi^0\\to\\gamma\\gamma$ photons, so SK's limits on the latter already approach $10^{33}$ yr across the mass range.","Nucleon decays anywhere in the Earth generate a sterile-neutrino flux whose direction encodes the decay length: for $\\ell_D\\simeq R_\\oplus$ the flux comes mostly from the opposite side of the planet, and for $\\ell_D\\lesssim$ km it becomes isotropic.","Super-Kamiokande could see up to five $N\\to\\pi^\\pm\\ell^\\mp$ events in 20 years even for a proton lifetime of $10^{35}$ yr, reaching into the seesaw-motivated mixing region $|U_{\\ell N}|^2\\sim m_\\nu/m_N$ shown in Fig. 5.","Dedicated searches for the short-decay-length regime $\\ell_D\\lesssim\\Delta L$—displaced vertices—complement the flux search and are needed to cover the $U_{\\tau N}$ case where no fully visible decay exists for sub-GeV $N$."],"supporting_citations":[{"why":"This reference introduced the scalar $\\phi$ carrying baryon and lepton number and derived the $p\\to\\ell^+\\phi$ decay rate used in Eq. (2).","marker":"[11]"},{"why":"SK's search for nucleon decays with an invisible particle and a charged lepton provides the $m_\\phi=0$ lifetime limits and the momentum-binned data that the paper uses to extend limits toward the Cherenkov window.","marker":"[27]"},{"why":"The reference on nucleon decay into a dark sector supplies the $n\\to\\chi\\gamma$ channel and the effective treatment of light sterile fermions.","marker":"[8]"},{"why":"This work established $p\\to\\chi\\pi^+$ as the dominant sterile-fermion decay, its isospin relation to $n\\to\\chi\\pi^0$, and the model constraints for light masses.","marker":"[9]"},{"why":"SK's $n\\to\\bar\\nu\\pi^0$ and $p\\to\\bar\\nu\\pi^+$ search gives the $m_\\chi\\to0$ limits on $p\\to\\chi\\pi^+$ that anchor the sterile-fermion constraints.","marker":"[35]"},{"why":"SK's search for $p\\to\\nu K^+$ provides the $5.9\\times10^{33}$ yr limit that, the paper argues, applies to $p\\to K^+N$ for all $m_N