arxiv: 2507.01675 · v3 · submitted 2025-07-02 · ✦ hep-ph · hep-ex

Recognition: 2 theorem links

· Lean Theorem

Extending the sensitivity of heavy sterile neutrino searches with solar neutrino experiments

Yutao Zhu , Haoyang Fu , Wentai Luo , Shaomin Chen , Litao Yang , Zhicai Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-06 17:29 UTC · model claude-opus-4-7

classification ✦ hep-ph hep-ex PACS 14.60.St26.65.+t13.15.+g

keywords heavy sterile neutrinosolar neutrinos8B decayactive-sterile mixingCherenkov scintillation detectordirectional reconstructionBorexinoJinping Neutrino Experiment

0 comments

The pith

Combining in-detector e+e- pairs with off-axis ν_e from in-flight decay lets a 500-ton solar neutrino experiment cover most of the MeV heavy-sterile-neutrino parameter space in a year.

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

Heavy sterile neutrinos in the MeV range can be produced in 8B beta decay in the Sun whenever they mix with the electron neutrino, and if heavier than 2m_e they decay to ν_e e+ e-. The paper points out that whether such a ν_H decays inside or outside an Earth-based detector depends on its lifetime, and that the two regimes call for different signatures: an e+e- pair in the detector for intermediate lifetimes, and a soft ν_e arriving from off the Sun-Earth line for short lifetimes. The authors compute both signal yields and the dominant 8B elastic-scattering background across the full (m_νH, |U_eH|²) plane, propose the e+e- opening angle and the ν_e solar angle as the key discriminators, and translate everything into 90% C.L. exclusion contours via a profile-likelihood Asimov fit. Combined, the two channels cover most of 10⁻⁶ < |U_eH|² < 1 from 2 to ~14 MeV with one year on a 500-ton detector, and notably extend reach into the short-lifetime corner Borexino's e+e- search could not see.

Core claim

The paper argues that solar neutrino detectors can search for MeV-scale heavy sterile neutrinos produced in 8B decay through two complementary channels: detecting the e+e- pair when ν_H decays inside the detector (sensitive to intermediate lifetimes) and detecting the daughter ν_e via elastic scattering when ν_H decays outside the detector (sensitive to short lifetimes). The two channels cover opposite corners of the (m_νH, |U_eH|²) plane, and together they reach at least a few signal events across most of 10⁻⁶ < |U_eH|² < 1 and 2-14 MeV with a 500-ton detector and one year of running. The decay-in-flight ν_e channel, distinguishable by a softer energy spectrum and a non-zero solar angle tai

What carries the argument

A two-channel sensitivity calculation built on the ν_H lifetime contour: ν_H produced in 8B decay with rate ∝ |U_eH|² has a proper lifetime τ ∝ 1/(G_F² m_νH⁵ |U_eH|²), so the decay rate inside an Earth-based detector peaks along the τ ≈ 500 s ridge in the (m_νH, |U_eH|²) plane. The e+e- channel uses the differential decay distribution from Shrock to predict the lab-frame energy spectrum and opening angle; the ν_e channel reduces the 3D integration over decay vertices to a 1D integration along the Sun-Earth axis using spherical symmetry, yielding an analytic prediction for the ν_e energy and solar-angle distributions on Earth. A binned-Poisson profile likelihood with Asimov data sets the 90%

If this is right

A 500-ton detector running one year can yield ≥ a few signal events across most of 10⁻⁶ < |U_eH|² < 1 and 2-14 MeV by combining the two channels.
The previously unused ν_e-from-decay channel extends sensitivity into the short-lifetime (large mixing, large mass) corner that the e+e- search cannot reach.
Directional sensitivity at ~25° is the key handle: it lets the e+e- pair be separated from single-electron 8B events via opening angle, and lets the decay-in-flight ν_e be tagged by a non-zero solar angle tail.
Projected 90% C.L. exclusion contours improve on the published Borexino limits, with the e+e- opening-angle cut and the ν_e channel each contributing distinct new regions.
An energy threshold of E_ee > 4.8 MeV is sufficient to render 208Tl and 11C cosmogenic backgrounds subdominant for the e+e- analysis.

Where Pith is reading between the lines

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

The decay-in-flight ν_e channel is in principle reusable on existing solar neutrino data sets (Borexino, SNO+, Super-K) by re-binning in solar angle, since the signature is a soft excess with a tail away from cosθ_Sun = 1; a reanalysis could already set limits without waiting for a new detector.
The 'τ ≈ 500 s ridge' framing makes explicit that sensitivity to |U_eH|² scales roughly as 1/m_νH⁵ along the optimal contour, which suggests that pushing to lower m_νH (where the seesaw target sits closer) is mass-bounded by the detector size, not by the analysis strategy.
The opening-angle handle assumes scintillation+Cherenkov directional reconstruction at ~25° is achieved in practice; if real detectors hit ~40° instead, the cyan e+e- contour collapses back toward the energy-only blue contour, but the ν_e channel is largely unaffected because its angular tail extends to much larger solar angles.
Charged-current ν_e detection on isotopes like Cl, Te, or Li (mentioned in passing) would convert the soft ν_e spectrum into a directly measured neutrino energy, potentially tightening the ν_e channel substantially over elastic scattering.

Load-bearing premise

The projected sensitivity assumes a 500-ton detector with Borexino-class radiopurity, ~5%/√E energy resolution, and ~25° directional resolution, with 8B elastic scattering as effectively the only relevant background above 4.8 MeV — none of which has been demonstrated for a real operating detector at this scale.

What would settle it

A 500-ton-class solar neutrino detector with ~5%/√E energy resolution and ~25° angular resolution, after one year of exposure, should either see the predicted handful of e+e- pair events above 4.8 MeV (with characteristic large opening angle) or an excess of low-energy electron-scattering events with a tail at cosθ_Sun < 0.9; absence of both, with backgrounds at the assumed 8B-dominated level, would rule out the projected reach.

read the original abstract

A sensitivity study of the search for heavy sterile neutrinos ($\nu_H$) in the MeV mass range using solar neutrino experiments is presented. $\nu_H$, with masses ranging from a few MeV up to around 15 MeV, can be produced in the Sun through $^8$B decay and subsequently decay into $\nu_e e^+ e^-$. Its flux and lifetime strongly depend on the mixing parameter $|U_{eH}|^2$ and mass $m_{\nu_H}$. The $\nu_H$ signal can be detected via its decay products, either the $e^+e^-$ pair or $\nu_e$, depending on whether $\nu_H$ decays inside or outside the detector. Expected signal yields for both detection methods (detecting $e^+e^-$ or $\nu_e$ signal) are presented across the full $|U_{eH}|^2$ and $m_{\nu_H}$ parameter space. These two methods are found to be complementary in different regions of the $|U_{eH}|^2$ and $m_{\nu_H}$ phase space. By combining both approaches, we anticipate observing at least a handful of signal events across most of the parameter space of $10^{-6} < |U_{eH}|^2 < 1$ and 2 MeV $< m_{\nu_H} < $ 14 MeV, assuming a 500-ton solar neutrino experiment operating for one year. Key variables, such as the energy spectra and opening angle of $\nu_e$ or $e^+e^-$ and the solar angle of $\nu_e$ and its scattered electron, are also discussed to help distinguish signal from major backgrounds, such as solar neutrino events.

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.

Desk Editor's Note private letter to a colleague

Clean phenomenology paper with a genuinely new channel idea, but the Method-2 background model is too thin to support the headline contour.

read the letter

Quick take: this is a competent, well-organized sensitivity study of heavy sterile neutrinos from 8B decay in solar detectors. The phenomenology is standard (Shrock differential width, Gorbunov–Shaposhnikov for the e+e-νe partial width, the usual flux suppression by |U_eH|² and phase space), and the authors lay out clearly why the in-detector e+e- channel and the external-decay → νe channel cover complementary regions of the (m_νH, |U_eH|²) plane. The crest-shaped signal-rate contour aligned with the τ ~ 500 s lifetime line is a nice, intuitive way to organize the parameter space.

What's actually new is Method 2: using νe from νH decays that happen outside the detector, with the solar angle of the recoil electron as the discriminant. To my knowledge nobody has explicitly proposed this for the short-lifetime/large-mixing corner that Borexino and PIENU don't cleanly cover. The 1D-along-the-Sun-line trick for collapsing the 3D decay-vertex integral is neat and correct.

The soft spot is real and the stress-test note has it right. The Method-2 likelihood in §V uses only 8B elastic scattering as background. But Fig. 8 shows the signal νe spectrum peaks below 5 MeV, and Fig. 11 makes it explicit that the directional handle (cos θ_Sun < 0.9) only buys you anything below ~2 MeV recoil. That is exactly the energy window where 11C, 210Bi, 208Tl, external γ, and pep/CNO ES dominate in any real liquid scintillator — Borexino's own 8B analysis [16] had to model all of these, and the 4.8 MeV threshold the authors apply in Method 1 is precisely an admission of this. No analogous threshold or background component appears in Method 2. So the orange contour in Fig. 12 is best read as "what you'd get if every non-8B background were negligible," not as a realistic projection. The authors should either propagate a Borexino-like background budget or label the contour as an idealized benchmark.

The Method-1 contours, including the cos θ_e+e- < 0.9 variant, look defensible given a JNE-class directional detector.

Recommendation: send to peer review. The core idea is worth publishing, but referees should push hard on the Method-2 background model and on labeling the projections as detector benchmarks rather than experiment-specific forecasts. Worth a reading-group slot if anyone in the group works on HNL searches; otherwise skip. I would not cite it in the next year unless I'm writing about HNL solar searches specifically.

Referee Report

5 major / 8 minor

Summary. The paper presents a sensitivity study for heavy sterile neutrinos ν_H in the MeV mass range, produced via |U_eH|² mixing in 8B solar β+ decays and detected through ν_H → ν_e e+e−. Two complementary detection methods are studied for a benchmark 500-ton solar neutrino detector with one year of exposure: (Method 1) the e+e− pair from ν_H decays inside the detector, distinguished from 8B-ES backgrounds via energy spectrum and e+e− opening angle; and (Method 2) the ν_e from ν_H decays outside the detector, detected via ν_e–electron elastic scattering, distinguished using recoil energy and solar angle cos θ_Sun. Signal rates are tabulated/mapped across the (m_νH, |U_eH|²) plane, and 90% C.L. exclusion contours from a profile-likelihood asimov analysis are derived for both methods, showing that Method 2 covers the short-lifetime/large-mixing corner inaccessible to in-detector e+e− searches and extending the Borexino [16] limit.

Significance. The conceptual contribution that is genuinely new is Method 2 — using the ν_e from ν_H decays occurring outside the detector to probe the short-lifetime regime, exploiting the soft ν_e spectrum and the non-trivial solar-angle distribution arising from off-Sun decay vertices. The geometric reduction of the 3D integration to a 1D integration along a Sun-radial line (§IV) is a clean and useful observation. The signal-rate maps in Fig. 5 (top), Fig. 10, and Table I, together with the cos θ_Sun distributions in Fig. 9, provide a clear road map for which (m_νH, |U_eH|²) regions reward which strategy. If the projected sensitivities hold under realistic background conditions, Method 2 would meaningfully extend the heavy-neutral-lepton phase-space coverage of next-generation solar-neutrino detectors with directional sensitivity (e.g., Jinping). The MadGraph-based generation of decay kinematics and the explicit treatment of the polarization term in Eq. (7) are appropriate.

major comments (5)

[§V (Sensitivities), Method 2 background model] The likelihood for Method 2 takes the only background to be 8B–electron elastic scattering. This is not defensible in the kinematic region that drives the Method 2 sensitivity. Fig. 8 shows the signal ν_e spectrum peaks below 5 MeV, so recoil electrons populate ~1–4 MeV; Fig. 11 confirms that the directionally separable subsample (cos θ_Sun < 0.9) sits below ~2 MeV. In any real liquid-scintillator or water-based scintillator detector this regime is dominated not by 8B-ES but by cosmogenic 11C (the very background that motivated the E_ee > 4.8 MeV cut applied to Method 1), 210Bi, 208Tl from the 232Th chain, external γ from PMTs/vessel, 14C pile-up, 85Kr, and pep/CNO solar-ν ES (which leak into the cos θ_Sun ≈ 1 sideband). The orange contour in Fig. 12 is therefore a best-case projection that omits the dominant backgrounds. At minimum, the authors should include Borexino-class radiopurity
[§V, asymmetric analysis thresholds] Method 1 imposes E_ee > 4.8 MeV explicitly to suppress 208Tl/11C, but Method 2 applies no analogous threshold even though its signal lies in exactly the energy region where those backgrounds are most severe. This asymmetry is not justified in the text. Either Method 2 should adopt a comparable threshold (in which case much of the directionally-separable sample is removed and the orange contour will recede), or it must be argued why such backgrounds are absent for the Method 2 fit window. The 2D (E_e, cos θ_Sun) template fit can in principle exploit directional discrimination against isotropic backgrounds, but this requires those backgrounds to be in the model.
[§V, statistical model and nuisance parameters] The likelihood in Eq. (8) introduces a single unconstrained nuisance β scaling the 8B background. In a realistic search, the systematic budget includes (i) the ν_H survival probability through MSW propagation in the Sun (the conversion of the parent ν_e to ν_H is a process inside matter and the spectrum in Eq. 2 is taken directly from the 8B ν_e spectrum at Earth without explicit treatment of in-medium effects on the sterile production), (ii) energy-scale and resolution uncertainties, (iii) directional resolution uncertainty (the assumed 25° is aspirational for slow-scintillator detectors and not yet demonstrated at 500-ton scale), and (iv) flux uncertainty on subdominant solar components. The exclusion contours would benefit from at least a sensitivity check against these systematics, or an explicit statement that they are neglected.
[§II, Eqs. (1)–(2) and ν_H production] The production rate is written as |U_eH|² times the standard 8B ν_e flux times a phase-space factor. This implicitly assumes that the parent neutrino in the 8B decay is produced as a pure flavor eigenstate ν_e and then projected onto the sterile component, ignoring matter effects in the Sun on the active–sterile mixing. For m_νH in the few-MeV range the ν_H is kinematically distinct and decoheres rapidly from the active states, so the approximation is likely fine, but the manuscript should state this assumption explicitly and, ideally, cite or estimate the size of any in-medium correction to Eq. (2). This is load-bearing for the absolute normalization of every signal rate quoted in Fig. 5, Fig. 10, and Table I.
[Fig. 12 / comparison to existing limits] The comparison to Borexino [16] is shown, but the much stronger PIENU [22] limit is mentioned only in the text and not drawn on Fig. 12. Since PIENU is stated to be tighter than Borexino at lower |U_eH|² and at m_νH > 12 MeV, the reader cannot assess from the figure where the projected 500-ton sensitivity is genuinely new versus where it merely re-covers PIENU-excluded territory. Please overlay PIENU (and any other relevant peak-search/beam-dump constraints in the few-to-tens-of-MeV |U_eH|² range) on Fig. 12.

minor comments (8)

[Abstract vs. §VI] The abstract states sensitivity 'across most of the parameter space of 10⁻⁶ < |U_eH|² < 1 and 2 MeV < m_νH < 14 MeV', while §VI gives '< 15 MeV'. Please reconcile.
[Fig. 1 caption] The y-axis label and units appear garbled ('Neutrino Flux (MeV⁻¹ cm⁻² s⁻¹ 10)'). Please clean up the axis label and the legend ('|U|² = 1, m_νH = ...') in the final figure.
[Eq. (3)] The standard expression for Γ(ν_H → 3ν) for a Majorana N includes a symmetry/identical-particles factor; please state explicitly whether Eq. (3) is for Dirac or Majorana ν_H, since the lifetime in Fig. 3 (and hence all decay-in-flight rates) depends on this choice by an O(1) factor.
[§III, opening-angle discussion] Fig. 6 shows cos θ_{e+e−} distributions, but the text claims 'the majority of events' have a sufficiently large opening angle. Please quantify (e.g., the fraction with cos θ_{e+e−} < 0.9 versus m_νH) so readers can reproduce the cyan contour in Fig. 12.
[§IV, Fig. 7] The geometric construction (decay vertices on a single Sun-radial line, intersection with the Earth-orbit sphere S) is correct but terse. A short equation showing the 1D integral over the decay-vertex distance, with the Jacobian to the Earth-frame ν_e energy and θ_Sun, would make the calculation reproducible.
[Fig. 5 (top), Fig. 10 axis labels] Several plots have axis tick labels that read e.g. '−10²' where '10⁻²' is intended; the LaTeX rendering of the exponents is broken in the version supplied. Please fix before publication.
[References] Recent global compilations of HNL constraints in the MeV–GeV range (e.g., post-2020 reviews) and complementary searches with reactor experiments and Super-Kamiokande/SNO solar data could be cited for completeness.
[§V, energy resolution] The 5%/√E[MeV] resolution should be motivated; it is on the optimistic side for a slow-scintillator concept and worse than Borexino's intrinsic scintillator resolution. A short sentence justifying the choice (or showing the contour for a degraded resolution) would help.

Simulated Author's Rebuttal

5 responses · 2 unresolved

We thank the referee for a careful and constructive report. The five major comments identify real weaknesses in the manuscript, and we agree with the substance of all of them. The most consequential is the under-modelling of low-energy backgrounds in Method 2 (11C, 210Bi, 208Tl, external γ, 14C pile-up, 85Kr, pep/CNO), which we will remedy by adopting a Borexino-class radiopurity model and re-deriving the Method 2 exclusion contour with the full 2D (E_e, cos θ_Sun) template fit. We will also (i) treat the analysis-threshold asymmetry between Methods 1 and 2 transparently and show contour dependence on the Method 2 threshold, (ii) expand the systematics budget to include energy scale/resolution, directional resolution (varied 25°–35°, with the 25° value flagged as aspirational), and subdominant solar flux normalizations as constrained nuisances, (iii) state explicitly that Eq. (2) neglects in-medium corrections to sterile production and provide the numerical justification (V_CC·E / Δm²_H ~ 10^{-11}), and (iv) overlay the PIENU limit and other relevant laboratory constraints on Fig. 12 so the genuinely new portion of the projected sensitivity is unambiguous. We expect the revised Method 2 reach to recede in the softest-signal corner of parameter space; the complementary structure of the two methods, and the new reach of Method 1 at intermediate lifetimes, will be preserved. Two items — the achievable directional resolution at 500-ton scale and the absolute radiopurity level of

read point-by-point responses

Referee: Method 2 background model omits dominant low-energy backgrounds (11C, 210Bi, 208Tl, external γ, 14C pile-up, 85Kr, pep/CNO ES). The orange contour in Fig. 12 is a best-case projection.

Authors: The referee is correct. Our Method 2 likelihood used 8B-ES as the only background, which is appropriate at higher recoil energies but is clearly inadequate in the 1–4 MeV region that drives Method 2 sensitivity, exactly where 11C, 210Bi, 208Tl, external γ from PMTs/vessel, 14C pile-up, 85Kr, and pep/CNO ES dominate in any realistic liquid-scintillator or WbLS detector. In the revised manuscript we will: (i) add a low-energy background model based on Borexino Phase-II radiopurity assumptions (210Bi, 85Kr, 11C, 14C, 208Tl, pep, CNO) plus an external γ component scaled from published JNE/Borexino estimates; (ii) include them as constrained components in the 2D (E_e, cos θ_Sun) template fit, exploiting the fact that radiogenic backgrounds are isotropic in cos θ_Sun while pep/CNO peak at cos θ_Sun ≈ 1; and (iii) re-derive the orange exclusion contour. We expect the contour to recede at low |U_eH|² where the signal is softest, but to remain meaningful at large |U_eH|² and intermediate m_νH where the signal ν_e energies are higher. We will explicitly label the new contour as radiopurity-dependent and show a band reflecting Borexino-level vs. JNE-aspirational radiopurity. revision: yes
Referee: Asymmetric analysis thresholds: Method 1 uses E_ee > 4.8 MeV against 208Tl/11C, but Method 2 applies no analogous threshold despite its signal sitting in the same problematic region.

Authors: We agree this asymmetry was not justified. The 4.8 MeV cut in Method 1 was applied because the e+e− signal from ν_H decay typically deposits well above this threshold (Fig. 5, bottom), so the cut is nearly free for signal. For Method 2 the same cut would remove most of the signal, which is precisely why we did not apply it — but the proper response is to model the relevant backgrounds rather than ignore them. In the revision we will (a) explicitly state the rationale for the Method 1 cut, (b) for Method 2 perform the 2D template fit down to a realistic analysis threshold (we propose 1.0 MeV, comparable to Borexino's pep/CNO analyses) with the full background model described in our reply to the previous comment, and (c) show the exclusion contour as a function of analysis threshold so the reader can see how much of the directionally-separable sample survives at each threshold choice. We will be transparent that the fully background-loaded Method 2 contour is weaker than the curve currently shown. revision: yes
Referee: Statistical model uses a single unconstrained nuisance β; missing systematics include MSW/in-medium effects on sterile production, energy scale/resolution, directional resolution (25° is aspirational at 500-ton scale), and subdominant solar flux uncertainties.

Authors: We will expand the systematics treatment. Concretely: (i) Energy scale (±1%) and resolution (±10% on the 5%/√E coefficient) will be added as Gaussian-constrained nuisance parameters. (ii) Directional resolution will be varied between 25° (aspirational, JNE target) and 35° (more conservative slow-scintillator estimate) and the impact on Method 2 shown explicitly; we agree the 25° value is not yet demonstrated at 500-ton scale and will say so. (iii) Subdominant solar flux normalizations (pep, CNO, hep) will be included with the standard SSM uncertainties as constrained nuisances. (iv) On in-medium effects: as we note in our reply to the next comment, for m_νH in the few-MeV range the active–sterile mass splitting is enormous compared to the MSW potential (V_CC ~ 10^{-12} eV in the solar core), so matter-induced corrections to the production amplitude are of order (V_CC·E/Δm²)² ≪ 1 and are negligible. We will state this explicitly and add a sentence in §V acknowledging that this is the basis for omitting an MSW nuisance. revision: yes
Referee: Eq. (2) treats the parent as a pure ν_e flavor eigenstate and ignores matter effects in the Sun on active–sterile mixing. This assumption is load-bearing for all signal-rate normalizations.

Authors: The referee is right that the assumption was implicit and should be stated. The justification is the following: for m_νH ≳ 2 MeV the active–sterile mass-squared splitting Δm²_H ~ m_νH² is at least ~4×10^{12} eV² in the few-MeV range, while the charged-current matter potential in the solar core is V_CC ~ 7.6×10^{-12} eV. The in-medium correction to the effective mixing is therefore suppressed by (2EV_CC / Δm²_H)² ≲ 10^{-22} for E ~ 10 MeV, so matter effects on the production amplitude are completely negligible compared to the |U_eH|² values we probe. The ν_H is kinematically distinct from the active states, decoheres on a length scale far shorter than a mean free path in the Sun, and propagates as a free mass eigenstate. We will add a short paragraph after Eq. (2) stating this assumption, providing the numerical estimate above, and noting that no MSW correction to the sterile production rate is included. The same paragraph will clarify that the standard 8B ν_e spectrum used as input is the production spectrum (before active-flavor MSW conversion), so no double-counting occurs. revision: yes
Referee: PIENU [22] limit is stronger than Borexino in part of the relevant range but is not drawn on Fig. 12; the reader cannot tell which projected sensitivity is genuinely new.

Authors: We agree and will overlay the PIENU [22] exclusion on Fig. 12 across the range where it applies (m_νH up to ~m_π − m_e and the corresponding |U_eH|² reach). We will additionally include relevant peak-search and beam-dump constraints in the few-to-tens-of-MeV range where they bound |U_eH|², specifically: the π → eν peak searches reanalyzed in Bolton et al. [10], TRIUMF/KEK older π+ → e+ν, and the recent compilations from heavy-neutral-lepton global fits. The revised Fig. 12 will clearly distinguish (a) regions where our 500-ton projection genuinely extends beyond all existing laboratory limits — primarily the lower-|U_eH|², m_νH < 12 MeV corner accessed by Method 1's e+e− search — from (b) regions where it merely re-covers PIENU-excluded territory. The text in §V and the summary will be updated accordingly so the new-physics reach is not overstated. revision: yes

standing simulated objections not resolved

The achievable directional resolution at 500-ton scale in slow-scintillator or WbLS technology is not yet experimentally demonstrated. We will quote a range (25°–35°) and show the sensitivity dependence, but we cannot at present defend the 25° value as established; this is a forward-looking projection that depends on ongoing R&D (e.g., JNE).
Absolute radiopurity levels for a hypothetical 500-ton next-generation solar-neutrino detector are not known. Our revised low-energy background model will adopt Borexino Phase-II values as a benchmark, but the resulting Method 2 contour is necessarily contingent on this assumption and we will present it as a band rather than a single curve.

Circularity Check

0 steps flagged

No significant circularity: the sensitivity chain runs from external inputs (8B spectrum, seesaw mixing, standard νH decay widths) to event yields without renaming fits as predictions.

full rationale

The paper's derivation chain is straightforward and self-contained against external inputs. The νH flux (Eq. 2) is the 8B solar neutrino flux from Bahcall et al. [11] multiplied by |U_eH|² and a kinematic phase-space factor. The decay widths Γ_{3νe} (Eq. 3) and Γ_{e+e-νe} (Eq. 4) are standard expressions referenced to Gorbunov & Shaposhnikov [12] and Shrock [15]. The signal rate (Eq. 5) is a textbook decay-in-flight formula. None of these are fit to data and then re-presented as predictions; they are propagated forward to event counts (Table I, Figs. 5, 10) and to a profile-likelihood exclusion contour (Eqs. 8–9, Fig. 12) using the standard Cowan et al. [21] asymptotic formulae. Self-citations exist — JNE [14, 17] for the assumed 25° angular resolution, and the Cherenkov-scintillator reconstruction paper [14] — but they enter as detector-performance assumptions rather than as load-bearing physics premises; the sensitivity contours can be re-evaluated for any other resolution. The headline claim that Method 1 (e+e-) and Method 2 (νe ES) are complementary in (m_νH, |U_eH|²) space is a direct consequence of how the lifetime distribution interacts with the Sun-Earth distance, not a tautology. The genuine weaknesses flagged by the skeptic — namely, that the Method 2 likelihood treats only 8B-ES as background while the signal peaks at sub-5-MeV recoils where 11C, 208Tl, pep/CNO and external γ dominate, and that the 4.8 MeV threshold applied in Method 1 is not applied in Method 2 — are background-modeling/optimism issues that affect correctness and realism of the projected exclusion, not circularity. They do not show that any "prediction" is equivalent to its input by construction. There is no self-definitional loop, no fitted-input-renamed-as-prediction, and no uniqueness theorem imported from the authors' own prior work to forbid alternatives. Accordingly the circularity score is 1 (a minor self-citation footprint for assumed detector capabilities, with no central claim reducing to its inputs).

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Model omitted the axiom ledger; defaulted for pipeline continuity.

pith-pipeline@v0.9.0 · 9795 in / 6644 out tokens · 98926 ms · 2026-05-06T17:29:05.325017+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Foundation.PhiForcing phi_forcing_principle unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The flux of νH from such decay chain is proportional to the 8B solar neutrino flux and the mixing parameter |UαH|², scaled by a mass-dependent phase-space factor
Unification.YangMillsMassGap fibonacci_mass_recursion unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Γ_3νe = G_F²/(192π³) m_νH⁵ |U_eH|² ... we anticipate observing at least a handful of signal events across most of the parameter space of 10⁻⁶ < |U_eH|² < 1 and 2 MeV < m_νH < 15 MeV

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.