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Nucleon Decays into Light New Particles in Neutrino Detectors

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2506.08090 v2 pith:NGBHZVNM submitted 2025-06-09 hep-ph hep-ex

Julian Heeck , Ian M. Shoemaker This is my paper
classification hep-phhep-ex
keywords baryonnumberviolationnucleondecayprotonsterileneutrinosheavyneutralleptonsCherenkovthresholdneutrinodetectorsleptoquarkmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

The flux prediction in Eqs. (11)–(14) treats every proton in the Earth as an independent free emitter of the sterile neutrino $N$ with the free-nucleon decay rate, ignoring nuclear binding, Pauli blocking of the final state, form-factor suppression for $p\to K^+N$ in heavy nuclei, and reabsorption or scattering of $N$ in rock; if any of these suppresses production, the 'up to five events' estimate and the Fig. 5 contours are optimistic.

Editorial extensions

If this is right

  • 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 $N$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [A SIMPLE MODEL, Eqs. (13)-(15) and Fig. 5] 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.
  2. [A SIMPLE MODEL, text after Eq. (15)] 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.
  3. [A SIMPLE MODEL, Eq. (11)] 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.
  4. [A SIMPLE MODEL, definition of Nsig after Eq. (15)] 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.
minor comments (5)
  1. [A SIMPLE MODEL, Eq. (15)] 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.
  2. [LIGHT FERMIONS, Eq. (7)] The notation is inconsistent: the text writes n -> gamma chi while Eq. (7) gives the rate for n -> chi gamma. Please unify the ordering.
  3. [A SIMPLE MODEL, paragraph on displaced vertices] 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.
  4. [Fig. 5] 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.
  5. [Supplemental Material, Eq. (A.21)] There is a typo: 'assinged' should be 'assigned'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the event-rate estimates are direct integrals of assumed benchmark lifetimes, external densities, and quoted detector parameters, with no fitted parameter renamed as a prediction.

full rationale

The paper's central predictions are self-contained calculations rather than circular reductions. The Earth-flux event count in Eqs. (11)-(15) multiplies an assumed proton-decay rate (benchmark lifetimes such as tau_{p->N} = 6 x 10^33 yr, stated as 'the estimated current limit' for p -> K+N) by the PREM proton density n_p(r), the detector area/volume parameters (A_eff and Delta L), and the measurement time T. No quantity appearing in the predicted event rate is fitted to the SK/HK data that the contours are meant to probe. The N-decay branching ratios are taken from Ref. [38], an external computation, and the seesaw band is plotted using the standard relation m_nu ~ |U_lN|^2 m_N with m_nu from external atmospheric and KATRIN constraints; this band is not derived from the event rate. Existing laboratory constraints are overlaid as independent bounds. The self-citations present (e.g., Refs. [11] and [28] by one of the authors) supply operator conventions and Cherenkov-threshold kinematics, but they are not used as a uniqueness theorem, do not forbid alternative explanations, and are not the load-bearing step that makes the event count nontrivial. The skeptic's concern about atmospheric-neutrino backgrounds is a real experimental-reach issue, not a circularity issue, because it does not involve redefining an input as an output. Thus there is no circular step that reduces a prediction to its own input.

Assumptions & free parameters 5 free parameters · 5 assumptions · 4 invented entities

The central results are sensitivity estimates: masses, mixings, and benchmark lifetimes are scanned rather than fitted, so the circularity burden is low. The main ledger cost is the chain of domain assumptions: chiral matching, free-nucleon decay in Earth, N decay only through mixing, 100% geometric acceptance, and the seesaw prior. No fundamentally new entity is invented solely to fit a result; the new fields are inherited from the cited baryon-number-violation and heavy-neutral-lepton literature.

free parameters (5)
  • benchmark proton decay lifetime tau_p->N = 6 x 10^33 yr
    Chosen to match the estimated current bound on p->K+N; all Nsig contours and Eq. (15) scale linearly with this value.
  • active-sterile mixing |U_lN|^2 = scanned over about 10^-13 to 10^-4 in Fig. 5
    Controls the N decay length and event rate; the reach contours depend on the chosen window where detector size is smaller than the decay length but the decay length is smaller than the Earth radius.
  • sterile neutrino mass m_N = 0 to about 1 GeV
    Scanned; determines phase space, N decay channels, and whether the seesaw relation targets the plotted contour region.
  • light scalar and fermion masses m_phi, m_chi = 0.60 to 0.95 GeV
    Scanned; the Cherenkov-blind windows in Eqs. (4), (5), and Fig. 2 depend on these masses being near the nucleon mass.
  • effective operator scales Lambda_l, Lambda_1, Lambda_2 = constrained indirectly by lifetime limits
    Input operator scales; not fitted in this paper, but used to convert existing lifetime bounds into effective scale limits.
assumptions (5)
  • domain assumption Chiral perturbation theory gives the hadronic matrix elements for the operators in Eqs. (1) and (6), with beta approximately -0.013 GeV^3 and f_pi approximately 130 MeV.
    Used to convert quark-level baryon-number-violating operators into p ell phi and n chi pi couplings; the lattice input beta comes from Ref. [23].
  • domain assumption Nucleon decay inside Earth's nuclei proceeds at the free-nucleon rate with no nuclear suppression or Pauli blocking, and the emitted N travels through rock only with exponential decay attenuation.
    Eq. (11) integrates over proton density n_p(r) from PREM as if each proton is an independent free emitter; no nuclear form factors or reabsorption are included.
  • domain assumption The sterile neutrino N decays only through active-sterile mixing, with branching ratios taken from Ref. [38].
    Used for Nsig = BR(N to X) times (N_in decays plus N_out decays); other possible interactions of N are neglected.
  • domain assumption The seesaw relation m_nu approximately |U_lN|^2 m_N identifies the target parameter band.
    Used to mark the 'seesaw-motivated parameter space' in Fig. 5; it is a theoretical prior, not a derived consequence of the paper.
  • domain assumption Detector acceptance is A_eff times Delta L with 100% efficiency and zero background.
    Eqs. (13)-(15) estimate N_decays as flux times A_eff T times (1 - exp(-Delta L / ell_D)); no reconstruction efficiencies or background modeling are included.
invented entities (4)
  • Light scalar phi with B = L = 1 independent evidence
    purpose: Mediates two-body proton decays p -> ell+ phi and defines the Cherenkov-blind mass windows.
    Predicted p -> ell+ phi rates and mass windows are falsifiable in SK, JUNO, and DUNE; the UV completion in the Supplemental Material justifies the operator but gives no independent collider prediction.
  • Sterile baryonic fermion chi independent evidence
    purpose: Mediates n -> chi pi0, p -> chi pi+, and n -> gamma chi.
    The mass-dependent decay signatures in Fig. 2 are directly searchable, and SK data already bound the massless limit.
  • Sterile neutrino N, acting also as a sterile neutron independent evidence
    purpose: Carries the decay chain p -> K+ N, N -> pi+- l-+ or pi0 nu, producing a terrestrial flux.
    Predicts displaced vertices and a zenith-dependent Earth flux with order-five events at benchmark lifetimes; the contour maps give a falsifiable target for Super-K and Hyper-K.
  • Heavy scalars S1 and S1' in the UV completions
    purpose: Generate the effective baryon-number-violating operators by being integrated out at scales above about 10^9 GeV.
    No collider or precision observables are computed for these states; they serve only to justify the effective operators and are not directly probed by the paper's signatures.

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Pith. "Pith review of Nucleon Decays into Light New Particles in Neutrino Detectors." pith.science (2026). https://pith.science/paper/NGBHZVNM

@misc{pith2026250608090,
  author       = {Pith},
  title        = {Pith review of: Nucleon Decays into Light New Particles in Neutrino Detectors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NGBHZVNM}},
  note         = {Machine review of arXiv:2506.08090}
}
abstract

Proton and neutron decays into light new particles $X$ can drastically change the experimental signatures and benefit from the complementarity of large water-Cherenkov neutrino detectors such as Super/Hyper-Kamiokande and tracking detectors such as JUNO and DUNE. The proton decays $p\to \ell^+ X$ and $p\to \pi^+ X$ with $m_X$ near phase-space closure lead to charged particles below Cherenkov threshold, rendering them practically invisible in Super- and Hyper-Kamiokande but not in JUNO and DUNE, which are therefore uniquely positioned for these baryon-number-violating signatures despite their smaller size. As an additional signature, such nucleon decays in Earth can produce a sizable flux of $X$ particles in underground detectors. We present a simple model in which nucleons decay into sub-GeV sterile neutrinos that subsequently decay through active-sterile neutrino mixing, with a promisingly large number of events in Super-Kamiokande even in the seesaw-motivated parameter space.

Figures

Figures reproduced from arXiv: 2506.08090 by the authors.

Figure 1
Figure 1. FIG. 1: Free proton decay rates vs [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. N plays the dual role of sterile neutron and sterile neutrino, with well-studied decay channels parametrized by their mixing UℓN with SM neutrinos νℓ [36–38]. We assume N to be Majorana fermions here, so they give rise to seesaw neutrino masses [39–42], generically of or￾der mν ∼ |UℓN | 2mN . This also gives rise to ∆B = 2 [43] 1 The two channels can be decoupled in the parameter-space region β Λ2 1 + α Λ2 2 ≃ 0, wh… view at source ↗
Figure 4
Figure 4. FIG. 4: The zenith-angle [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5: Left: contours of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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