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Probing Solar Heavy Neutrinos with Heliospheric Electrons

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The Sun's $^8$B neutrino flux would produce MeV heavy neutral leptons that decay to $e^+e^-$ pairs, and a comparison of the predicted heliospheric electron flux with Ulysses and SOHO data yields the strongest direct upper bound on…

desk verdict A clever new heliospheric detection channel for solar-produced heavy neutrinos, but the claimed factor-of-three edge over Borexino sits inside an unquantified transport-model uncertainty. read the letter →

arxiv 2412.14752 v2 pith:QO5FNGBG submitted 2024-12-19 astro-ph.HE astro-ph.SRhep-phnucl-ex

Marco Drewes , Jan Heisig , Valentin Weber This is my paper · ORCID
classification astro-ph.HEastro-ph.SRhep-phnucl-ex
keywords heavyneutralleptonssterileneutrinossolarneutrinomixingheliosphericelectronpropagationJovianelectronsUlyssesSOHO
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

The paper asks whether heavy neutral leptons (HNLs) with masses in the MeV range and a small mixing $U_e^2$ with electron neutrinos could be produced in nuclear reactions in the Sun and then decay into electron-positron pairs inside the heliosphere. It computes the resulting electron and positron flux at 1 AU using a steady-state diffusion model and compares it with MeV electron spectra recorded by the Ulysses and SOHO satellites during quiet solar periods. The absence of an excess in the measured fluxes yields an upper limit that reaches $U_e^2 \simeq 10^{-6}$ at $M_N = 10$ MeV, which the authors state is the strongest direct upper bound on $U_e^2$ in the HNL mass range $(2\text{--}12)$ MeV, surpassing Borexino and PIENU. A side result is a $3\sigma$ preference in the fit for a small signal at $M_N \simeq 8.2$ MeV, $U_e^2 \simeq 7.9 \times 10^{-7}$, which the authors ascribe to incomplete background modeling rather than evidence for HNLs. The result matters because laboratory limits are weak in this mass window and cosmological bounds depend on assumptions about the early universe.

What carries the argument

The load-bearing object is the steady-state solution of the spherically symmetric diffusion equation for the electron phase-space density $\psi(R,E_e)$, Eq. (11): with a constant diffusion coefficient $D$, a factorized source term, and no convection or energy losses, the predicted flux follows as $\psi(R,E_e) = \xi(E_e)/(DR)\left(1-e^{-R/R_0} - (R/R_0)\operatorname{Ei}(-R/R_0)\right)$. This solution converts the solar HNL production flux, Eq. (5), into the electron/positron flux at 1 AU that is compared with data. The diffusion coefficient $D = 2 \times 10^{22}\,{\rm cm}^2/{\rm s}$ is taken from Jovian-electron transport analyses, and the background is modeled with the same transport framework, so the same machinery sets both the signal prediction and the dominant background.

What would settle it

A positron-sensitive MeV detector near 1 AU could settle the claim directly: positrons from HNL decays would appear as an excess over a background that is up to three orders of magnitude smaller than the electron background, so a null result after profiling the Jovian background would confirm the exclusion, while an excess matching $M_N \simeq 8.2$ MeV with $U_e^2 \simeq 7.9 \times 10^{-7}$ would confirm the tentative signal. In parallel, multi-spacecraft tracking of Jovian electrons during magnetic connection events could fix $D$ and the parallel mean free path, converting the current half-order-of-magnitude propagation uncertainty into a definite prediction for the 1 AU flux and shifting the limit as the square root of the flux.

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Extended reading notes

Core claim

The paper's central claim is that, for a Majorana HNL that mixes only with the electron flavor and has a mass between roughly 1 and 16 MeV, the MeV electron and positron data from Ulysses and SOHO exclude mixing strengths above $U_e^2 \simeq 10^{-6}$ at $M_N = 10$ MeV at 90% CL. The exclusion is obtained from a $\Delta\chi^2$ analysis that fits the signal and a Jovian-electron background model, profiling the parallel mean free path $\lambda_\parallel$ as a nuisance parameter, to the two datasets. In the mass range $(2\text{--}12)$ MeV this is claimed to be the strongest direct bound on $U_e^2$, stronger than the Borexino bound by roughly a factor of three and also excluding a region at larger $M_N$ that Borexino cannot reach. The same data prefer a signal at the $3\sigma$ level with $M_N \simeq 8.2$ MeV and $U_e^2 \simeq 7.9 \times 10^{-7}$, but the authors interpret this as a likely artifact of astrophysical background uncertainties.

Load-bearing premise

The bound rests on a simplified one-dimensional diffusion model for MeV electrons in the inner heliosphere, with a single constant diffusion coefficient, no convection or energy losses, and a Jovian-electron background model whose fitted normalization can absorb part of a real signal; if the true electron transport or the background differs substantially, the predicted flux, and therefore the excluded mixing which scales as the square root of the flux, shifts correspondingly.

Editorial extensions

If this is right

  • Solar $^8$B reactions do not produce an observable electron-positron excess from $N \to e^+e^-\nu$ decays for electron mixing $U_e^2$ above the reported line in the $(2\text{--}12)$ MeV mass window, and the previous direct bounds from Borexino and PIENU are superseded there.
  • Heavy neutral leptons in this mass range remain viable only if their electron mixing lies below roughly $10^{-6}$, or if they mix predominantly with muon or tau flavor, since the reported bound applies to electron-flavor coupling.
  • A detector that can separate positrons from electrons near 1 AU, or an ab initio model of the heliospheric electron background, would improve the sensitivity and could test whether the $3\sigma$ feature at $8.2$ MeV is real.
  • Because the limit scales as the square root of the predicted flux, each factor-two improvement in the diffusion-modeling uncertainty translates into a factor $\sqrt{2}$ improvement in the reach in $U_e^2$.

Reading between the lines

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

  • The same diffusion-based signal pipeline could be reused for any long-lived particle produced in the Sun that decays into electrons or positrons, since the inputs are just the solar production spectrum and the decay kinematics; the constraints would then apply with rescaled couplings.
  • The tentative $3\sigma$ excess is a concrete target: a positron-sensitive measurement with exposure similar to Ulysses or SOHO would either confirm the $8.2$ MeV peak or rule it out, because the positron background is expected to be negligible.
  • If future heliospheric transport modeling pins down the radial dependence of $D$ and the role of convection, the same datasets could yield a bound several times stronger without any new detector, since the current limit is set by propagation and background uncertainties rather than by counting statistics.
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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

3 major / 5 minor

Summary. The paper searches for MeV-scale heavy neutral leptons (HNLs) produced by solar nuclear reactions and decaying into e+e-ν, using archival MeV electron/positron spectra from the Ulysses KET and SOHO EPHIN instruments at 1 AU. The signal is computed from standard HNL production and decay rates, propagated to Earth with a simplified one-dimensional steady-state diffusion model, and compared to a Jovian-electron background with a profiled mean free path. The authors report a 90% CL upper limit reaching Ue^2 ~ 1e-6 at MN ~ 10 MeV and claim that this is the strongest direct bound in the 2-12 MeV mass range, about a factor of 3 stronger than the Borexino limit, with a tentative ~3 sigma preference for a signal at MN ~ 8.2 MeV.

Significance. If the propagation-model uncertainties were under control, the paper would provide a genuinely new direct probe of MeV HNL parameter space using existing heliospheric data, with a clean particle-physics input, careful decay kinematics, and a sensible comparison to Borexino and PIENU. The treatment of the Jovian background as a fitted nuisance is a reasonable first step, and the use of two independent datasets is a strength. However, the headline claim inherits an unquantified normalization uncertainty from the transport model, so the significance of the result is at present conditional rather than established.

major comments (3)
  1. [Sec. V B, Eq. (11)] The central claim of Sec. VI, that the result is the strongest direct upper bound in the 2-12 MeV range, is not supported at the required precision by the signal-flux normalization. The 1 AU flux is computed from the one-dimensional diffusion solution Eq. (11) with a constant D = 2e22 cm^2/s, while Sec. V B itself states that R-dependent diffusion and convection change fluxes by up to half an order of magnitude and that anisotropic perpendicular transport, with mean free path up to two orders of magnitude smaller, can give similar or larger corrections. In the small-mixing regime the electron flux scales as Ue^4, so the 90% limit on Ue^2 scales as the inverse square root of the flux normalization; a flux overestimate by a factor ~9, well within the range of corrections named in Sec. V B, would shift the limit up by a factor ~3 and erase the claimed factor-3 improvement over Borexino. Because these systematic uncertainties are not propagated into Fig. 3 or into the quoted value Ue^2 ~ 1e-6, the paper should present the limit as a band over the allowed transport-model choices, adopt an explicitly conservative flux normalization that accounts for perpendicular transport and convection, or weaken the 'strongest direct limit' claim to be conditional on the transport model.
  2. [Sec. III C, Eqs. (9)-(11)] The analytic solution Eq. (11) and the source factorization Eq. (9) are asserted rather than derived or validated. Since Eq. (11) is the only bridge between the standard HNL decay calculation and the observed electron flux, the paper should provide the derivation in an appendix and compare Eq. (11) with a numerical solution of Eq. (6) under the stated assumptions, including the finite-volume boundary conditions described in Footnote 4. Without such a validation the reader cannot distinguish a genuine solution from an approximation error that could be comparable to the propagation uncertainties already discussed in Sec. V B.
  3. [Sec. V A, Footnote 6, Eq. (13)] The background model is not fully independent of the signal hypothesis: Footnote 6 acknowledges that the Jovian-electron modeling was calibrated to data that could include HNL decays, and the analysis then profiles over lambda_parallel for each dataset. This procedure is likely conservative for an exclusion, but the paper should quantify the degeneracy between the signal normalization and lambda_parallel, for example by reporting the fitted lambda_hat_parallel as a function of Ue^2 and comparing with the limit obtained when lambda_parallel is fixed to the value from Ref. [97]. If a signal of similar spectral shape can be partially absorbed by the background normalization, the claimed sensitivity relies on spectral-shape differences that should be demonstrated explicitly.
minor comments (5)
  1. [Footnote 4] The phrase 'vanishing density at R -> infinity and R0 -> infinity' is unclear, because R0 is a parameter of the source model and not a spatial boundary; the two integration constants and their boundary conditions should be stated explicitly for the physical coordinate R and for the finite-volume radius RV.
  2. [Eq. (7)] The notation d(phi_N)/(dR dE_N) is confusing because phi_N in Eq. (5) is already a flux at fixed R, not a cumulative distribution; please define the derivative with respect to R explicitly.
  3. [Sec. IV A] The text 'Ionisation Energy Losstechnique' appears to be a typographical error for 'Ionisation Energy Loss technique'.
  4. [Sec. V B and Fig. 4] The right panel of Fig. 4 and the accompanying text describe a ~3 sigma preference for a signal at MN ~ 8.2 MeV; the caption or text should state explicitly that this preference is not claimed as a discovery and that no trials factor has been applied, so that readers do not over-interpret the simultaneous presentation of an exclusion limit and a best-fit excess.
  5. [Eq. (13)] The definition sigma_bd = f_d * D_bd uses the observed data rather than the predicted flux as the error template; because this can bias the chi-squared in low-count bins, a brief justification or a cross-check with an error based on the model prediction would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the limit is derived from external solar-neutrino spectra, SM decay kinematics, and independent Ulysses/SOHO data, with acknowledged transport and background uncertainties that are not input-output identities.

full rationale

I walked the claimed derivation chain. HNL production is computed from the measured solar neutrino flux (Ref. [80]) through Eq. (5); the decay signal is fixed by standard weak-interaction rates (Eqs. (2)-(3) and Appendix A); the electron/positron flux at 1 AU is obtained from an explicitly stated 1D diffusion model (Eqs. (6)-(11)) with the diffusion coefficient D taken from external Jovian-electron transport analyses; the dominant Jovian background is modeled with a published parametrization whose normalization λ∥ is profiled as a nuisance parameter; and the result is a χ2 comparison to Ulysses and SOHO spectra. None of these steps equates the prediction to a fitted input: the signal normalization U_e^2 is not calibrated to the same observed spectra before being 'predicted', and λ∥ is a fitted background parameter, not relabeled as a prediction. The paper explicitly flags the genuine limitations in Sec. V B (R-dependent diffusion, convection, and anisotropic perpendicular transport can shift fluxes by up to half an order of magnitude) and in footnote 6 (the Jovian background model was calibrated on data that could contain a signal, which is handled by simultaneous fitting). These are systematic uncertainties that could shift the quoted bound, but they do not make the derivation circular. The many self-citations appear in motivational or review contexts and do not carry the load-bearing argument. Thus there is no step where the central claim reduces by construction to its own input.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The central claim rests on standard particle-physics input (solar neutrino spectrum, HNL decay rates), one dominant modeling layer (the analytic diffusion solution with its simplifications), and one semi-empirical background (Jovian electrons calibrated on data that would contain the signal). The free parameters are the fitted Jovian mean free path per dataset, the adopted diffusion coefficient, and the benchmark systematic-error scales. No new entity is introduced; the heavy neutral lepton is a pre-existing search target, not an entity invented by this paper.

free parameters (4)
  • Jovian electron mean free path lambda_parallel = 0.15 (Ulysses), 0.11 (SOHO) at the background-only best fit
    Nuisance parameter of the Jovian electron background model, profiled over in the Delta-chi^2 fit (Eq. 13). Its freedom lets the background normalization absorb part of any excess, so the limit rests on spectral shape residuals.
  • Effective diffusion coefficient D = 2 x 10^22 cm^2/s
    Chosen, not fitted, from Jovian electron transport literature (Refs. 82, 100). Normalizes the signal flux (Eq. 11, psi proportional to 1/D). The paper notes perpendicular transport would imply smaller effective D and larger flux, while R-dependent D and convection would lower the 1 AU flux; the net uncertainty is unquantified.
  • Relative systematic error f_d per dataset = 10-20% (Ulysses), 20-30% (SOHO)
    Benchmark values (optimistic and pessimistic) from personal communication [99], setting the sigma_bd scale in Eq. (13) and hence the absolute chi^2 and the limit. Similar limits are reported for both benchmarks.
  • Jovian source spectrum normalization and shape = Fixed to the prior analysis (Vogt et al. 2018)
    Adopted from Vogt et al. 2018 (30 years of measurements). Calibrated on heliospheric electron data that would include any HNL-decay contribution; the spectral shape is not re-fitted here, which matters because the limit derives from shape residuals.
assumptions (8)
  • domain assumption HNL effective Lagrangian (Eq. 1): coupling to SM weak currents suppressed by U_e, with theta_mu = theta_tau = 0
    Standard benchmark model for HNL searches (Refs. 74, 75); a single Majorana HNL mixing only with electron flavor is not a fully consistent neutrino-mass model but is the declared benchmark.
  • domain assumption Solar neutrino flux spectrum from Ref. [80] used as the HNL production spectrum
    Relies on the measured and standard-solar-model 8B flux; external input, well established.
  • ad hoc to paper Diffusion equation with spherical symmetry, R-independent D, no convection, steady state, factorized source (Eqs. 6-11)
    The central simplification. The paper acknowledges numerical solutions with R-dependent D and convection differ by up to half an order of magnitude, and anisotropic diffusion could change results further.
  • domain assumption Negligible energy losses for MeV electrons (max ~10%), and negligible positron background
    Cited to Ref. [82] for Jovian electrons and Ref. [98] for positrons.
  • standard math Wilks theorem for one-sided 90% CL from Delta-chi^2 (Eq. 14)
    Standard asymptotic chi^2 statistics; appropriate for a one-parameter exclusion near a physical boundary, though the ~3 sigma best-fit preference complicates the null-hypothesis picture.
  • domain assumption Jovian electron background model (Refs. 82, 97) valid for the selected quiet and connected periods
    The background model and the data selection are mutually dependent; selection criteria are described qualitatively.
  • domain assumption Kinematic mass window: MN > 2 m_e and MN below the maximal solar neutrino energy (~16 MeV)
    Lower bound from the N -> e+e- nu threshold, upper bound from the solar neutrino endpoint; both are standard kinematics.
  • domain assumption Gravitationally captured HNLs (v_N < v_esc) are neglected
    Footnote 3 estimates this contribution as sub-leading and leaves a refined analysis to future work. If the estimate is wrong, the low-energy signal flux could be larger than modeled.

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Cite this review

Pith. "Pith review of Probing Solar Heavy Neutrinos with Heliospheric Electrons." pith.science (2026). https://pith.science/paper/QO5FNGBG

@misc{pith2026241214752,
  author       = {Pith},
  title        = {Pith review of: Probing Solar Heavy Neutrinos with Heliospheric Electrons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QO5FNGBG}},
  note         = {Machine review of arXiv:2412.14752}
}
abstract

We search for an excess of electrons and positrons in the interplanetary space from the decays of heavy neutrinos produced in nuclear reactions in the Sun. Using measurements of the electron spectra in the MeV range from the Ulysses and SOHO satellites, we report the strongest direct upper bound to date on the mixing between heavy neutral leptons with MeV masses and electron neutrinos, reaching $U_e^2\simeq 10^{-6}$ at $M_N=10\,$MeV. Our sensitivity is predominantly constrained by the uncertainties in the propagation of electrons and positrons, particularly the diffusion coefficient in the inner Solar System, as well as the uncertainties in the astrophysical background. Enhancing our understanding of either of these factors could lead to a significant improvement in sensitivity.

Figures

Figures reproduced from arXiv: 2412.14752 by the authors.

Figure 1
Figure 1. FIG. 1. Relevant 3-body decays of the HNL. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. HNL flux [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Constraints on the HNL parameter space in terms of the HNL mass and mixing parameter for a Majorana (left panel) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Flux of electrons and positrons measured by SOHO (blue data points) and Ulysses (red data points) at [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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