{"id":"ea33b5e2-baba-4334-90fc-58b31d7944c0","arxiv_id":"2506.04099","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A new differential decay width including neutral and charged current interference is used to show that future detectors could probe HNL mixing angles over two orders of magnitude below current bounds.","lead":"This paper calculates how often heavy neutral leptons born from the Sun's boron-8 neutrinos decay into electron-positron pairs inside detectors on Earth. It projects that future liquid noble gas and scintillator detectors could improve the sensitivity to the HNL-electron mixing angle by more than two orders of magnitude.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Rate normalization double-counts |UeN|^2, so the projected sensitivities cannot be reproduced from Eqs. (4), (5), and (9) as written.","rationale":"Good-faith reading: the paper aims to provide a new interference-corrected differential width and to project HNL decay searches at Borexino, DUNE, XLZD/Argo, and LiquidO. For that central claim to hold, the rate formulas must have consistent mixing-power counting. They do not: Eq. (5) already defines the HNL flux as proportional to |UeN|^2, and Eqs. (4) and (9) multiply by another |UeN|^2, while Gamma_e itself also carries |UeN|^2. The result is an internal inconsistency that changes the absolute normalization and the scaling of every limit and sensitivity curve. The detector-background concern in the reader's formal weakest_assumption is legitimate, but it is secondary here: even a perfect background-free detector cannot validate a projection whose rate normalization is wrong by a power of |UeN|^2. I also note the spin-handling ambiguity: the main text states that initial spins are averaged, while the appendix keeps the polarization-dependent term |s| cos(theta); because solar HNL production polarization is not specified, the differential distribution used for tracking projections is underdetermined. These are reproducibility failures, not disagreements with external consensus, so they support the reader's reject verdict. A corrected version with consistent normalization, a stated spin treatment, and a released implementation could be reconsidered, but the current preprint's central claim is not supported by its own equations.","tokens_in":11214,"tokens_out":10243,"duration_ms":104195,"concrete_test":"Implement Eq. (9) for a single HNL mass (e.g. 5 MeV) and a fixed solar-neutrino energy, then apply a scaling test: multiply |UeN|^2 by a factor of 4 while holding all other inputs fixed. The e+e- signal should increase by a factor of 16 if the normalization is the physical |UeN|^4 scaling, but by 64 if the written |UeN|^6 form is used. Then remove the redundant factor in Eq. (9) so that dePhi_odot already contains the production factor, and recompute the Borexino 90% limit and the 1 kt-yr tracking curve in Fig. 2. If either curve moves by more than roughly 30% in |UeN|^2, the central sensitivity claim is not supported by the equations as written.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim rests on the event-rate formulas. Eq. (5) defines the solar HNL flux as dePhi_odot/dE_N = |UeN|^2 (p_N/E_N) dPhi_odot/dE_nu, which already contains one power of |UeN|^2 from production. Eq. (9) then multiplies this flux by another explicit |UeH|^2, and Eq. (4) likewise contains Gamma_e |UeN|^2 / Gamma_tot even though Gamma_e, the partial width for N -> nu_e e+ e-, is itself proportional to |UeN|^2. The predicted rate therefore scales as |UeN|^6 instead of the physically required |UeN|^4 (production times decay). This internal inconsistency changes every derived limit and sensitivity curve. Because the paper provides no numerical implementation, the reader cannot tell whether Fig. 2 used the |U|^6 form or the |U|^4 form; the 'somewhat weaker' Borexino result in Fig. 1 does not disambiguate the two normalizations. A secondary but independent issue is that the spin term proportional to |s| cos(theta) in Eq. (3) requires a specified production polarization; the main text says initial spins are averaged while the appendix retains the polarization term, and no solar-production polarization is given.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes using the solar boron-8 neutrino flux as a source of heavy neutral leptons (HNLs) and searches for their decay N -> nu_e e+ e- in large detectors. It derives a fully differential decay width including charged- and neutral-current interference, reanalyzes the Borexino bound, and projects 90% C.L. sensitivities for DUNE, XLZD, Argo, and LiquidO. The headline quantitative claim is that future detectors can improve the |U_eN|^2 reach by one to two orders of magnitude relative to existing bounds.","tokens_in":11370,"tokens_out":20606,"duration_ms":200261,"significance":"The analytic expression for the NC/CC interference in the differential width is a potentially useful contribution, and the idea of using the solar 8B flux as an HNL source is interesting. If the rates were correct, the paper would provide new, falsifiable search channels for MeV-scale HNLs. However, as written, the event-rate normalization is not reproducible, the treatment of the initial HNL spin is internally inconsistent, and the tracking-based projections rest on an unquantified background-free assumption. These issues block acceptance of the numerical results.","major_comments":[{"comment":"Equation (4) has the wrong normalization for the number of decays and is dimensionally inconsistent. In natural units, V T times the integrated flux leaves a negative mass dimension, and the factor (m_N/p_N)[Gamma_e |U_eN|^2/Gamma_tot] does not supply the required factor of an actual decay width. A dimensionally correct expression must contain Gamma_tot through the inverse decay length, or equivalently Gamma_e^{actual}. If Gamma_e and Gamma_tot are the actual partial and total widths, then Gamma_e/Gamma_tot is the branching ratio and the explicit |U_eN|^2 in Eq. (4) is spurious. If they are reduced widths with the mixing angle removed, the text after Eq. (4) and the branching-ratio interpretation must be changed. Equation (9) repeats the same structure, and because no numerical implementation is provided, the limits in Figs. 1 and 2 cannot be checked against the formulas. I do not find the |U_eN|^6 power counting to be the cleanest statement of the problem (once Gamma_tot is also proportional to |U_eN|^2, the ratio Gamma_e/Gamma_tot is mixing-independent), but the normalization defect is real and load-bearing. The authors must correct the rate formula and regenerate all limits and sensitivity curves.","section":"Integrated Decay Rates, Eqs. (4), (5), (9)"},{"comment":"The treatment of the HNL spin is contradictory. The main text says that the differential width is obtained by summing over final-state spins and averaging over the two possible spin states of N, which would set |s_vec|=0 and remove the |s_vec| cos(theta) terms in Eq. (3). The appendix, however, retains those terms and says that because the calculation is interested in the polarization of the initial state, only the final-state spins are summed. If the polarization terms are physical, the solar HNL production mechanism must provide the polarization vector s_vec as a function of energy; no such distribution is given. If the terms are to vanish, Eq. (3), Eq. (23), and the surrounding discussion must be revised consistently. Since Eq. (9) is built from this differential distribution, the inconsistency directly affects the predicted event spectra.","section":"SM Decays of HNL and Appendix, Eq. (3)"},{"comment":"The tracking-based projections assume that e+e- pairs can be tagged with zero background and high efficiency. The text itself states that a detailed detector study is required for argon-39 and that the LiquidO projection is based on an assumed background-free tagging capability. Because the headline improvement of more than two orders of magnitude is carried by these curves, especially the 25 kton-yr LiquidO line, the paper should either provide a quantitative background model and an efficiency estimate (external gamma pair conversion, Compton pile-up, annihilation-gamma misidentification) or explicitly label those curves as idealized ceilings rather than sensitivities.","section":"Future Sensitivities and Fig. 2"},{"comment":"The Borexino reanalysis is not reproducible. The authors say that they digitize the electron recoil data from Fig. 4 of Ref. [1] and perform a binned likelihood fit with that data as background, but they do not specify the binning, the elastic-scattering background normalization and its uncertainty, the treatment of systematic errors, the signal efficiency, or the method used to derive the 90% C.L. contour. This matters because the comparison in Fig. 1 is used to demonstrate that the NC/CC interference is non-negligible.","section":"Existing Constraints"}],"minor_comments":[{"comment":"There are many typographical errors and inconsistent notations, for example 'predicitions', 'sensivity', and |U_eH|^2 where |U_eN|^2 is clearly intended; the manuscript needs a careful proofread.","section":"Throughout"},{"comment":"The variables in Eq. (3) are not fully defined: Q is introduced as a momentum transfer but appears in dimensionless ratios without an explicit scaling by m_N, and the definitions of g_V and g_A and their relation to the Standard Model couplings should be stated explicitly.","section":"Eq. (3)"},{"comment":"Figure 2 is very dense; the constraint labels and sensitivity curves should be enlarged or placed in a readable legend so that each curve can be identified without close scrutiny.","section":"Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The paper would be substantially stronger with a public code or a numerical table for the sensitivity curves, because as written the figures cannot be reproduced from the equations. There is no circularity issue: the decay width, solar flux, and statistical threshold are independent inputs. The topic is within the journal's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this is a promising HNL-search projection with a genuinely new piece of analytic work, but the central rate formulas do not close. Equation (5) already puts one power of |UeN|^2 into the solar HNL flux from production. Equation (9) then multiplies by another explicit |UeN|^2, and Eq. (4) carries a further Gamma_e |UeN|^2 where Gamma_e is the physical partial width for N -> nu_e e+ e- and already contains that factor. The two rate expressions imply different |U|^2 scalings, and the appendix makes clear that the physical width carries |Us1|^2; so both equations cannot be right. Without code or data, I cannot tell which normalization was actually used in Figs. 1 and 2. That is a load-bearing problem for every quantitative claim.\n\nWhat is good: the closed-form double-differential width including NC/CC interference does go beyond Shrock's charged-current result and may well be new to the literature. The opening-angle argument for a two-track e+e- signature is a real idea, and the detector concepts (XLZD, Argo, low-energy DUNE, LiquidO) are concrete. To the authors' credit, the optimistic assumptions behind the tracking sensitivities are mostly stated honestly, including the background-free tagging assumption.\n\nSoft spots beyond the normalization: the polarization of the solar HNL flux is never pinned down. The main text says initial spins are averaged, which would zero the |s| cos(theta) term in Eq. (3), but the appendix keeps polarization alive and no production polarization is given. That needs one sentence, not a rewrite. The tracking projections assume no backgrounds from pair conversion or Compton scatters, no efficiency, and no detector simulation; acceptable as an idealized upper reach if labeled that way, but the abstract should not present it as a firm sensitivity. The Borexino reanalysis is described in two sentences, with no binning or systematics, so the \"somewhat weaker\" conclusion cannot be checked.\n\nI would not cite the numbers in this version, and the paper should not be accepted as is. But the idea and the analytic result are worth a serious referee. Send it out; a competent referee will ask for a corrected and self-consistent normalization, a clear statement on polarization, and a numerical appendix detailed enough to reproduce the integrals.","headline":"Genuinely new differential width and interesting detector projections, but the central rate formula is internally inconsistent in its |UeN|^2 scaling and no code is provided, so the numbers cannot be trusted as written.","tokens_in":12001,"tokens_out":10547,"would_cite":false,"duration_ms":99583,"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":"Solar boron-8 neutrinos could probe heavy neutral lepton mixing far below current bounds.","keywords":["heavy neutral leptons","sterile neutrinos","solar neutrinos","boron-8 flux","electron-positron pair decay","neutral-current charged-current interference","liquid noble gas detectors","LiquidO"],"falsifier":"A detector-level simulation of the gamma-ray background in a 400-ton argon or 50-ton xenon detector that finds even a handful of $e^+e^-$-like coincidence events in the design exposure would invalidate the quoted 2.3-event sensitivity, and would directly test the tracking projections.","tokens_in":10887,"feed_emoji":"☀️","tokens_out":17585,"duration_ms":157696,"temperature":0.7,"pith_summary":"This paper argues that the Sun's boron-8 neutrino flux can act as a production source for heavy neutral leptons (HNLs), and that their Standard Model decay into an electron-positron pair plus a neutrino gives a searchable signal in large detectors. The authors derive a new fully differential decay width for $N \\to \\nu_e e^+ e^-$ that includes the interference between neutral- and charged-current amplitudes, and they show that this interference changes the expected rates; they use the width in both a calorimetric analysis (summed energy of the pair plus annihilation gammas) and a tracking analysis (two resolved tracks plus the two 0.511 MeV gammas). Reanalyzing the Borexino data with this width, they find the published mixing-angle limit is somewhat weaker than originally claimed. They then project that future detectors—a low-energy upgraded DUNE, the liquid noble gas detectors XLZD and Argo, and a kiloton-scale LiquidO detector—could improve the mixing-angle reach by factors from about 30 to more than two orders of magnitude. The practical interest is that these detectors will be built for other physics, so the HNL search costs little extra while probing a mass-mixing region tied to neutrino mass models and leptogenesis.","feed_headline":"Boron-8 solar neutrinos could expose heavy neutrinos 100x deeper","feed_subtitle":"New decay calculation with interference terms strengthens the case for next-generation detectors.","key_machinery":"The load-bearing object is the fully differential decay width $d^2\\Gamma/(dl_0\\,d\\cos\\theta)$ for $N \\to \\nu_e e^+ e^-$, including neutral-current/charged-current interference. The coefficients $X = [(g_V+1)^2 + (g_A+1)^2]$ and $Z = [(g_V+1)^2 - (g_A+1)^2]$ appear in the width; $X$ multiplies the structure already present in the charged-current-only result, while $Z$ multiplies new interference terms proportional to $m_e^2$. This width feeds the event-rate formula that includes the solar HNL flux, the survival factor from the Sun to Earth, and the decay-in-detector probability, and it is complemented by a kinematic calculation showing that the $e^+e^-$ opening angle stays above about 50 degrees for HNL energies from 2 to 16 MeV.","core_discovery":"The central claim is that the decay $N \\to \\nu_e e^+ e^-$, fed by solar boron-8 neutrinos, is a viable and potentially background-free channel for searching heavy neutral leptons with masses between the electron-positron threshold and about 16 MeV. The paper's new closed-form differential decay width reproduces the earlier charged-current result and adds the neutral-current and interference terms, organized through the coefficients $X = (g_V+1)^2 + (g_A+1)^2$ and $Z = (g_V+1)^2 - (g_A+1)^2$. With this width, the Borexino 0.122 kt-yr exposure gives a 90% confidence limit that is somewhat weaker than the collaboration's published limit, demonstrating that the interference is non-negligible. The paper also finds that a 100 kt-yr low-energy DUNE could improve the limit by about a factor of 30 using a calorimetric analysis, while track-resolving detectors XLZD and Argo could improve it by 30–80 for 1–5 kt-yr exposures, and a background-free kiloton-scale LiquidO detector could reach more than two orders of magnitude better. The lab-frame opening angle between the $e^+$ and $e^-$ is always at least about 50 degrees across the parameter space, which is what makes the two-track tagging signature resolvable.","pith_inferences":["The tracking projections rest on the assumption that kiloton-scale detectors can tag $e^+e^-$ pairs with zero background; if argon-39 beta decays or external gamma pair conversion cannot be fully rejected, the realistic sensitivity likely falls back toward the calorimetric DUNE level, and a detector simulation is the missing test.","The same $e^+e^-$ final state and tracking signature could be applied to other high-energy neutrino sources, such as diffuse supernova neutrinos, to extend HNL searches beyond the 16 MeV reach of solar boron-8 neutrinos.","Because the interference term changes both the rate and the spectral shape of the $e^+e^-$ energy distribution, a shape-based fit to existing or future solar-neutrino data could independently validate the new decay width."],"forward_implications":["A low-energy upgraded DUNE with 100 kton-year exposure could reach a mixing-angle limit about 30 times stronger than Borexino through a calorimetric analysis of the $e^+e^-$ pair plus annihilation gammas.","Tracking detectors XLZD (50 tons of xenon) and Argo (400 tons of argon) could improve the limit by factors of 30–80 with 1–5 kton-year exposures, using the two tracks and the two back-to-back 0.511 MeV gammas as the signature.","If LiquidO can tag $e^+e^-$ pairs with zero background in kiloton-scale detectors, a 25 kton-year exposure would push the mixing-angle reach more than two orders of magnitude beyond current bounds.","Because the $e^+e^-$ opening angle never drops below about 50 degrees, the two-track signature should be resolvable throughout the entire 2–16 MeV HNL mass range.","The published Borexino limit is somewhat weaker once the NC/CC interference is included, so future solar-neutrino analyses should use the new width rather than the charged-current-only result."],"supporting_citations":[{"why":"Supplies the Borexino dataset and published 90% confidence limit that the paper reanalyzes with the new decay width.","marker":"[1]"},{"why":"Provides the earlier charged-current decay width calculation that the new fully differential result confirms and extends.","marker":"[7]"},{"why":"Makes the case for a low-energy upgrade to DUNE that the calorimetric sensitivity projection assumes.","marker":"[2]"},{"why":"Defines the XLZD xenon detector concept used for the tracking-based sensitivity projection.","marker":"[3]"},{"why":"Defines the Argo argon detector concept used for the tracking-based sensitivity projection.","marker":"[4]"},{"why":"Introduces the LiquidO technology whose advertised tagging capabilities motivate the kiloton-scale projection.","marker":"[5]"},{"why":"Gives the invisible and radiative HNL decay widths used to justify neglecting those modes and to compute the branching ratio.","marker":"[6]"},{"why":"Provides the dominant existing reactor constraint in the 1–10 MeV mass range against which the new sensitivities are compared.","marker":"[9]"}],"fun_headline_variants":["Solar neutrinos could unmask heavy neutrinos 100x deeper","New cross section sharpens heavy neutrino searches by 100x","Interference terms boost solar neutrino sensitivity to heavy leptons","LiquidO could beat current heavy neutrino limits by 100x","Boron-8 neutrinos: clean channel to hunt heavy neutrinos"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The projected multi-order-of-magnitude improvements assume that kiloton-scale detectors can tag electron-positron pairs with high efficiency and zero background using position and timing cuts alone, a claim not yet backed by a detector simulation.","fun_headline_variants_meta":{"raw":{"variants":["Solar neutrinos could unmask heavy neutrinos 100x deeper","New cross section sharpens heavy neutrino searches by 100x","Interference terms boost solar neutrino sensitivity to heavy leptons","LiquidO could beat current heavy neutrino limits by 100x","Boron-8 neutrinos: clean channel to hunt heavy neutrinos"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001108,"raw_usage":{"total_tokens":4609,"prompt_tokens":927,"completion_tokens":3682,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":3593}},"tokens_in":543,"tokens_out":3682,"duration_ms":27355,"temperature":1.0,"reasoning_tokens":3593,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:48:45.103243+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A detector-level simulation of the gamma-ray background in a 400-ton argon or 50-ton xenon detector that finds even a handful of $e^+e^-$-like coincidence events in the design exposure would invalidate the quoted 2.3-event sensitivity, and would directly test the tracking projections.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the earlier charged-current decay width calculation that the new fully differential result confirms and extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Argo argon detector concept used for the tracking-based sensitivity projection."},{"cited_title":"Hagner, M","cited_arxiv_id":null,"evidence_quote":"Provides the dominant existing reactor constraint in the 1–10 MeV mass range against which the new sensitivities are compared."}],"review_version":1}