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arxiv: 2605.21583 · v1 · pith:OYWDACEZnew · submitted 2026-05-20 · ✦ hep-ph · hep-ex

Echoes of Nucleon Decay from Long-Lived Particles

Patrick Adolf , Chandan Hati , Martin Hirsch , Volodymyr Takhistov This is my paper

Pith reviewed 2026-05-22 09:22 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords nucleon decaylong-lived particlesecho signaturesbaryon number violationSuper-KamiokandeHyper-KamiokandeJUNOvector particles
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0 comments X

The pith

Nucleon decay can produce long-lived particles that leave detectable echo signals with up to 80 percent acceptance in current detectors.

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

The paper proposes a new way to look for nucleon decay by focusing on long-lived particles that travel some distance before decaying. These create two decay points that are separated in space but happen close enough in time to be linked as echoes, something standard searches for prompt decays at one spot would miss. The authors build effective operators and sample ultraviolet models for vector long-lived particles, then calculate that Super-Kamiokande, Hyper-Kamiokande, and JUNO can geometrically accept nearly 80 percent of such events across many possible lifetimes. This approach could apply to any long-lived particle that decays into visible particles and would extend the reach for finding baryon-number violation.

Core claim

Nucleon decay searches provide uniquely sensitive probes of baryon number violation and physics beyond the Standard Model. We propose a new class of nucleon decay observables involving long-lived particles (LLPs), characterized by spatially separated but temporally correlated echo vertices not captured by conventional prompt searches. Focusing on vector LLPs, we construct effective operators and ultraviolet realizations, and show that Super-Kamiokande, Hyper-Kamiokande and JUNO can achieve geometric acceptances approaching 80% over a broad range of LLP decay lengths. Echo signatures could in principle arise from any visibly decaying LLP.

What carries the argument

Echo vertices: two decay locations from a long-lived particle produced in nucleon decay, spatially separated yet close enough in time to remain correlated within detector timing resolution.

If this is right

  • Super-Kamiokande, Hyper-Kamiokande and JUNO reach geometric acceptances approaching 80 percent for vector long-lived particles over a wide range of decay lengths.
  • Standard prompt nucleon decay searches miss these spatially separated yet time-correlated signals.
  • Echo signatures can appear from any visibly decaying long-lived particle, not just specific models.
  • Effective operators and ultraviolet realizations for vector long-lived particles supply concrete frameworks for further model building.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Existing data sets from these detectors could be reanalyzed with new echo-selection criteria to set additional limits on long-lived particle lifetimes.
  • The same time-linked but space-separated signature idea could be adapted to other rare-decay experiments or dark-sector searches.
  • Observation of echoes would favor models where long-lived particles are produced directly in nucleon decay rather than through intermediate states.

Load-bearing premise

Long-lived particles from nucleon decay have kinematics and lifetimes that keep their decay vertices spatially separated but temporally correlated inside the detector timing window without being rejected by prompt-search cuts.

What would settle it

A dedicated search in Super-Kamiokande data for pairs of decay-like vertices separated by meters yet occurring within the detector's timing resolution that finds no excess over background would test whether the proposed echo signals are observable.

Figures

Figures reproduced from arXiv: 2605.21583 by Chandan Hati, Martin Hirsch, Patrick Adolf, Volodymyr Takhistov.

Figure 1
Figure 1. Figure 1: FIG. 1: Illustration of nucleon decays with “echo” [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Geometric acceptance (Left) and partial lifetime sensitivity [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Illustration of the representative UV completion discussed in the text. (Left) Example tree-level [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Momentum distributions for free two-body and three-body nucleon decays into a vector boson [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Sensitivity to the effective energy scale [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Ratios of the geometric acceptance computed under different assumptions. (Left) The panel shows the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Summary of existing constraints as well as projected sensitivity reaches for dark photons in the kinetic [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Nucleon decay searches provide uniquely sensitive probes of baryon number violation and physics beyond the Standard Model. We propose a new class of nucleon decay observables involving long-lived particles (LLPs), characterized by spatially separated but temporally correlated "echo" vertices not captured by conventional prompt searches. Focusing on vector LLPs, we construct effective operators and ultraviolet realizations, and show that Super-Kamiokande, Hyper-Kamiokande and JUNO can achieve geometric acceptances approaching 80% over a broad range of LLP decay lengths. Echo signatures could in principle arise from any visibly decaying LLP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a new class of nucleon decay observables based on long-lived particles (LLPs) that produce spatially separated but temporally correlated 'echo' vertices. Focusing on vector LLPs, it constructs effective operators and UV completions, and claims that Super-Kamiokande, Hyper-Kamiokande, and JUNO can achieve geometric acceptances approaching 80% over a broad range of LLP decay lengths. Echo signatures are argued to be accessible in any visibly decaying LLP scenario.

Significance. If the acceptance results hold after accounting for detector-specific cuts and kinematics, the work could provide a complementary probe of baryon-number violation that is missed by conventional prompt searches. The emphasis on geometric acceptance in water Cherenkov and liquid-scintillator detectors offers a concrete technical contribution to LLP phenomenology in existing and near-future experiments.

major comments (2)
  1. [§4] §4 (Geometric Acceptance and Detector Response): The headline claim that geometric acceptances approach 80% for vector LLPs over a broad decay-length range is load-bearing for the central result, yet the text provides no explicit efficiency calculation after applying the published prompt nucleon-decay vetoes from Super-Kamiokande analyses. Without this, it remains unclear whether the echo events survive the timing and spatial cuts that define the prompt searches.
  2. [§3.2] §3.2 (Kinematics and Boost): The effective operators determine the LLP boost and any co-produced particles; the manuscript does not quantify how polarization or associated visible activity affects the fraction of events that remain inside the fiducial volume while satisfying the temporal-correlation window (few ns) without triggering prompt vetoes.
minor comments (2)
  1. The abstract states the 80% acceptance result without referencing the underlying assumptions on decay lengths or veto survival; a short qualifier would improve clarity.
  2. Figure captions for acceptance plots should explicitly state the LLP mass, boost distribution, and whether prompt cuts are applied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying these important points regarding detector response and kinematics. We address each major comment below and have revised the manuscript to add clarifications and discussions where feasible. Our responses focus on the substance of the comments.

read point-by-point responses

  1. Referee: [§4] §4 (Geometric Acceptance and Detector Response): The headline claim that geometric acceptances approach 80% for vector LLPs over a broad decay-length range is load-bearing for the central result, yet the text provides no explicit efficiency calculation after applying the published prompt nucleon-decay vetoes from Super-Kamiokande analyses. Without this, it remains unclear whether the echo events survive the timing and spatial cuts that define the prompt searches.

    Authors: We agree that a complete efficiency estimate incorporating the specific timing and spatial vetoes from existing Super-Kamiokande nucleon-decay analyses would strengthen the result. The geometric acceptance reported in Section 4 is computed as the fraction of LLP decays occurring inside the detector volume given a primary vertex inside the fiducial region, without applying analysis cuts. Because the echo vertex is delayed by the LLP proper lifetime (typically ns to μs), it falls outside the narrow prompt time window used in those analyses. In the revised manuscript we have added a paragraph in Section 4 that explains this separation and notes that the echo events are therefore not expected to be removed by the prompt vetoes. We acknowledge, however, that a full Monte-Carlo study folding in detector-specific reconstruction efficiencies and any residual overlap cuts lies beyond the scope of the present phenomenological work and is left for dedicated experimental follow-up. revision: partial

  2. Referee: [§3.2] §3.2 (Kinematics and Boost): The effective operators determine the LLP boost and any co-produced particles; the manuscript does not quantify how polarization or associated visible activity affects the fraction of events that remain inside the fiducial volume while satisfying the temporal-correlation window (few ns) without triggering prompt vetoes.

    Authors: The effective operators in Section 3.2 fix the two-body decay kinematics of the vector LLP but do not fully specify the production boost or polarization. We have added a short discussion in the revised Section 3.2 that examines the effect of moderate boosts on the lab-frame decay length and angular distribution. For the decay-length range where geometric acceptance exceeds 60 %, the acceptance remains above 50 % even after including a typical boost factor of a few. Polarization effects are estimated to change the acceptance by at most 10–15 % for the operators considered. Regarding co-produced visible activity, the minimal UV completions we examine produce the LLP with little additional prompt energy; we have clarified this assumption and noted that more elaborate completions could introduce extra activity that might interact with vetoes. A quantitative scan over all possible UV realizations is not performed here, but the geometric-acceptance curves already bracket the plausible range. revision: partial

Circularity Check

0 steps flagged

No circularity: geometric acceptance follows from detector geometry and decay-length integration without self-referential fitting or load-bearing self-citations.

full rationale

The paper constructs effective operators for vector LLPs from nucleon decay, then computes geometric acceptances for Super-Kamiokande, Hyper-Kamiokande and JUNO by integrating over possible decay vertices inside the fiducial volume for a range of decay lengths. This is a standard geometric or Monte-Carlo exercise using detector dimensions and the exponential decay law; the resulting ~80% figure is an output of that integration rather than an input that is redefined or fitted to itself. No equations reduce the acceptance to a prior fit or to a self-citation whose content is the acceptance result. The derivation remains self-contained against external detector specifications and does not invoke uniqueness theorems or ansatze from the authors' prior work to force the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into explicit parameters or axioms; the proposal implicitly relies on standard effective-field-theory assumptions for operator construction and on detector geometry models that are not detailed here.

axioms (1)
  • domain assumption Effective operators can be constructed for vector LLPs that mediate nucleon decay while allowing macroscopic decay lengths.
    Invoked when the authors state they construct effective operators and UV realizations for vector LLPs.

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