{"id":"eb54e86a-9bc0-4ef2-a2d7-2a2b1c7af15f","arxiv_id":"1908.09313","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"A low-scale seesaw model adds a sub-eV pseudo-scalar secret interaction to reconcile eV sterile neutrinos with cosmology, though the illustrative benchmark is internally inconsistent.","lead":"This paper proposes a Standard Model extension in which a light sterile neutrino can explain the MiniBooNE and LSND anomalies without conflicting with cosmology. The key ingredient is an extremely light particle that interacts only with sterile neutrinos, suppressing their production in the early universe.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Illustrative benchmark fails: stated Yukawas and VEVs give active neutrino masses ~0.2, 0.03, 0.001 eV, not the claimed 0.05, 0.0086, 0.0002 eV, so the model's only demonstration of oscillation compatibility is invalid.","rationale":"I read the paper in good faith: the scalar-sector computation of the pseudo-scalar mass is coherent (expanding φ and using the minimum condition gives M_Iφ^2 = (9/4) M vφ), and the model does contain an Iφ coupling to sterile neutrinos of the form required by the secret-interaction idea. The manuscript itself flags that it relies on illustrative points because the parameter space is underconstrained. That makes the inconsistency in Eq. (13) load-bearing: the central proof-of-concept fails at the only numerical example. This is an internal, checkable defect rather than a disagreement with external cosmology, although the cosmological part is also deferred rather than computed. The defect is repairable, so I would keep the report CONDITIONAL rather than reject. The reader's weakest_assumption focused on the inherited cosmology; I see that as a real but secondary risk. My concern is the numerical benchmark, which the reader also noted in the rationale, hence partial agreement.","tokens_in":9793,"tokens_out":15188,"duration_ms":149109,"concrete_test":"Recompute M_light by forming the 3×3 matrix -(v_D^2/(√2 v_φ)) Y_D^T diag(1/Y_S11, 1/Y_S22, 1/Y_S33) Y_D with the Yukawa values in Eq. (13) and diagonalize it. Compare the eigenvalues (expected ≈0.20, 0.026, 0.0011 eV) with the quoted 0.0002, 0.0086 and 0.05 eV. If the mismatch is confirmed, the benchmark fails; the authors would need to provide a corrected benchmark, and ideally a full 6×6 diagonalization, before the model can be claimed to accommodate oscillation data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing defect is internal and numerical. The paper's own criterion of success is 'If we find at least one set of points that concretizes the hypothesis, we say it works.' The single illustrative point in Eq. (13) does not do so. With M_D = Y_D v2/√2 and M_R = Y_S vφ/√2, v2 = vD = 10 eV, vφ = 10^5 eV, the seesaw formula (Eq. (11)) gives M_light = -(v2^2/(√2 vφ)) Y_D^T Y_S^{-1} Y_D. The dominant entry is Y_D22^2/Y_S22 ≈ 169 eV, and the prefactor is 7.07×10^-4, so the heavy active eigenvalue is ≈0.12 eV before mixing; full diagonalization yields eigenvalues of order 0.20, 0.03 and 0.001 eV, rather than the quoted 0.05, 0.0086 and 0.0002 eV. Thus the claimed accommodation of solar and atmospheric neutrino oscillations is not demonstrated by the presented benchmark. The cosmological reconciliation is also asserted from Refs. [11,12] rather than computed, and the couplings Y_S22=0.01, Y_S33=0.1 make ν5 and ν6 interact far more strongly with Iφ than the benchmark value Y_S11=2×10^-5, so thermalization of the heavier states is an unquantified risk. But the numerical mismatch is the sharper, directly checkable flaw.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an extension of the Standard Model with three right-handed neutrinos, a second Higgs doublet H2, and two scalar singlets phi and sigma, subject to a Z3 x Z2 symmetry. The goal is to realize the type I seesaw mechanism at very low energy scales so that both active and sterile neutrinos are light, with an eV-mass fourth neutrino compatible with short-baseline anomalies, and to reconcile such an eV sterile neutrino with cosmology through a sub-eV pseudo-scalar Iphi that couples only to sterile neutrinos. The pseudo-scalar mass is derived as M_Iphi^2 = (9/4) M vphi, and the secret interaction is identified with the Yukawa term involving Iphi and the right-handed neutrinos, with a benchmark coupling YS11 = 2e-5. The paper also discusses constraints from mu -> e gamma and suggests that the scalar sigma could drive Higgs inflation.","tokens_in":10198,"tokens_out":14627,"duration_ms":128512,"significance":"If the benchmark and the cosmological argument were correct, the model would be a concrete realization of a low-scale type I seesaw with a 'secret interaction' pseudo-scalar, combining several phenomenological handles in one framework. A positive feature is the explicit derivation that Iphi decouples from the other CP-odd states and obtains a mass controlled by the lepton-number-violating parameter M. However, the only demonstrated benchmark for active neutrino masses is numerically inconsistent with the paper's own seesaw formula, and the cosmological viability is asserted rather than computed. These issues are central to the paper's claims, so the current version cannot be accepted as a demonstration of the proposed scenario.","major_comments":[{"comment":"The illustrative benchmark does not reproduce the quoted active neutrino masses. With v2 = 10 eV, vphi = 10^5 eV and diagonal YS, Eq. (11) gives M_light = -(v2^2/(sqrt(2) vphi)) YD^T YS^{-1} YD. Substituting the values in Eq. (13), this 3x3 matrix has trace about 0.234 eV and eigenvalues approximately 0.20, 0.035 and 0.0007 eV, not the 0.05, 0.0086 and 0.0002 eV claimed in Eq. (14). Even the single 22 entry contributes about 0.12 eV before off-diagonal mixing, already exceeding the claimed m_nu3. The implied squared mass splittings are of order 1.2e-3 eV^2 and 3.8e-2 eV^2, which do not accommodate solar and atmospheric oscillations. The paper's own criterion is that one concrete benchmark suffices; this point does not satisfy that criterion, so a corrected and explicitly verified benchmark, including the full 6x6 diagonalization, is required.","section":"II.B, Eqs. (13)-(14)"},{"comment":"Cosmological viability is asserted rather than demonstrated. The reconciliation with BBN, CMB and LSS is based entirely on the claim in Refs. [11,12] that a sub-eV pseudo-scalar with g_s in the range 1e-6 to 1e-5 suppresses sterile-neutrino production; the present paper does not compute the production rate, N_eff, or structure-formation constraints in the model. Moreover, Eq. (20) couples Iphi to all three right-handed neutrinos with strengths YS11 = 2e-5, YS22 = 0.01 and YS33 = 0.1, so nu5 and nu6 interact with Iphi about 500 and 5000 times more strongly than nu4. The paper does not show that these heavier states remain out of equilibrium, and without that the claimed 3+1 cosmology is not established.","section":"II.C"},{"comment":"The statement that lepton number must be violated at M < 1e-8 eV is presented as a new output, but it is a direct restatement of the input condition M_Iphi < 0.1 eV adopted from Refs. [11,12]. Since M is fixed by that external requirement, the conclusions in Section III that this is a 'very original result' and a 'change of paradigm' should be rephrased as a consistency condition of the scenario rather than an independent prediction.","section":"II.C, Eq. (21) and III"}],"minor_comments":[{"comment":"The entry '8, 6 x 10^-3' should read '8.6 x 10^-3'.","section":"Eq. (14)"},{"comment":"The notation is inconsistent: Eq. (11) uses v2, Eq. (13) uses vD for the same VEV, and the text earlier considers v2 = 10^2 eV before the benchmark sets vD = 10 eV. The value actually used should be stated consistently and its consequences checked.","section":"Eqs. (11) and (13)"},{"comment":"The mixing matrix entry '044' presumably should be '0.44', and the fourth-column mixing elements U_e4 and U_mu4 appear approximately a factor of two smaller than what a leading-order evaluation of Eq. (12) with Eq. (13) gives; the numerical diagonalization should be checked and documented.","section":"Eq. (15)"},{"comment":"There are several grammatical slips, for example 'claiming have observed' and 'reconciliates', and 'CBM' should be 'CMB'.","section":"Abstract and Introduction"},{"comment":"The assumed VEV and parameter hierarchy f > vsigma > v1 >> vphi >> v2 >> M is stated without a demonstration that the full scalar potential has a stable global minimum realizing this ordering; a boundedness and stability check would strengthen the scalar-sector discussion.","section":"II.D, Eq. (23)"}],"recommendation":"major_revision","confidential_remarks":"The deciding issue is the numerical failure of the benchmark point, which is internal and checkable. The cosmological part could in principle be repaired with a dedicated calculation or a careful parameter-space scan, so I do not recommend rejection at this stage. A revised version should also recalibrate the claimed novelty, since the M < 1e-8 eV condition is an input from the cited cosmological mechanism rather than an independent prediction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's my read of Pires' eV sterile neutrino model.\n\nThe genuinely new thing is a complete renormalizable model—two doublets, two singlets, right-handed neutrinos, Z3×Z2—that realizes the secret-interaction idea. Refs [11,12] proposed the mechanism but didn't embed it. The scalar sector is worked out in detail, and the CP-odd component Iφ does decouple and gets a mass M_Iφ^2 = (9/4) M vφ, so a sub-eV pseudo-scalar follows from a tiny M. That part is clean.\n\nThe soft spots are real. The illustrative benchmark in Eq. (13) doesn't produce the masses quoted in Eq. (14). Using their own seesaw formula with vD = 10 eV and vphi = 1e5 eV, the active mass matrix has eigenvalues of order 0.2, 0.03, and 0.002 eV, not 0.05, 0.0086, and 2e-4 eV. The solar and atmospheric match is therefore not demonstrated. The paper's only numerical example fails on the central phenomenological claim.\n\nThe cosmological side is also asserted rather than computed. The author assumes that YS11 = 2e-5 satisfies the g_s ~ 1e-5 window from Hannestad et al. and Dasgupta-Kopp. But the other two right-handed neutrinos couple to Iφ with YS22 = 0.01 and YS33 = 0.1, hundreds to thousands of times larger. If the secret interaction suppresses production only for g_s ~ 1e-5, the heavier states ν5 and ν6 could thermalize through the same interaction. The paper doesn't compute N_eff, BBN, or LSS constraints for the full model. That's a gap, not a fatal flaw, but it means the title's claim is not supported by the analysis.\n\nSmaller things: the \"lepton number violated at 10^-8 eV\" headline is just the input condition m_Iφ < 0.1 eV recast; the muon g-2 and inflation sections are explicitly deferred; and the µ→eγ constraint uses the benchmark YDs without checking whether the resulting f vσ is compatible with the scalar spectrum.\n\nOverall: the model-building idea is worth taking seriously, and the scalar-sector machinery is correct. But the paper as written doesn't back its two main claims—oscillation data and cosmological viability—with a valid numerical example or a computation. Both are fixable. I'd send it to a referee, but the referee should be told to focus on the benchmark and the thermalization of the heavy sterile states.\n\nFor a reading group, maybe, if someone in the group works on secret interactions. I wouldn't cite it in the next year until the benchmark is corrected.\n\nBest","headline":"A coherent model-building realization of the secret-interaction idea, but the only numerical benchmark is internally inconsistent and the cosmological claim is borrowed, not derived.","tokens_in":10758,"tokens_out":6872,"would_cite":false,"duration_ms":61203,"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":"This paper claims that the canonical type I seesaw, run at eV-to-keV VEVs with a sub-eV pseudo-scalar coupled only to sterile neutrinos, can generate the eV sterile neutrino hinted by LSND and MiniBooNE while reconciling it with cosmology.","keywords":["low-scale type I seesaw","eV sterile neutrino","LSND anomaly","MiniBooNE excess","secret interactions","pseudo-scalar","warm dark matter","neutrino cosmology"],"falsifier":"Compute the early-universe production of the sterile states in this model with $m_{I_\\varphi}<0.1\\,\\mathrm{eV}$ and $Y_{S11}=2\\times10^{-5}$; if the resulting effective number of extra neutrinos or the abundance of the $7\\,\\mathrm{keV}$ state exceeds the bounds from BBN, the cosmic microwave background, and large-scale structure, the central claim fails. A laboratory bound excluding a pseudo-scalar below $0.1\\,\\mathrm{eV}$ coupled to sterile neutrinos would also undercut it.","tokens_in":9515,"feed_emoji":"🌌","tokens_out":6883,"duration_ms":67746,"temperature":0.7,"pith_summary":"The paper proposes an extension of the Standard Model in which the canonical type I seesaw mechanism operates at unusually low energy scales, with the second Higgs VEV around $10^2\\,\\mathrm{eV}$ and the singlet VEV around $10^5\\,\\mathrm{eV}$, generating tiny masses for both active and sterile neutrinos. This includes a fourth neutrino with mass around $1.4\\,\\mathrm{eV}$ and mixing with the active neutrinos in the range suggested by the LSND and MiniBooNE anomalies. To make that sterile neutrino cosmologically viable, the model contains a pseudo-scalar $I_\\varphi$ that couples exclusively to sterile neutrinos and whose mass is pushed below $0.1\\,\\mathrm{eV}$ by choosing the explicit lepton-number-breaking scale $M$ below $10^{-8}\\,\\mathrm{eV}$. The author argues that the benchmark Yukawa coupling $Y_{S11}=2\\times10^{-5}$ reproduces the secret interaction that, according to the cited literature, suppresses sterile-neutrino production in the early universe and reconciles eV sterile neutrinos with BBN, CMB, and large-scale structure. The model also yields a $7\\,\\mathrm{keV}$ sterile neutrino as long-lived warm dark matter, contributes to the muon $g-2$, and can host Higgs inflation.","feed_headline":"Low-scale seesaw reconciles eV sterile neutrinos with cosmology","feed_subtitle":"A sub-eV pseudo-scalar coupled only to sterile neutrinos suppresses their early-universe production, easing the tension with BBN and CMB…","key_machinery":"The load-bearing object is the pseudo-scalar $I_\\varphi$, the imaginary part of the singlet field $\\varphi$ that carries two units of lepton number; its mass is set by the trilinear term $\\frac{M}{\\sqrt{2}}(\\varphi^3+\\varphi^{*3})$, giving $M_{I_\\varphi}^2=\\frac{9}{4}M v_\\varphi$. This field couples only to right-handed neutrinos through $\\frac{i}{2}Y_S\\,\\overline{\\nu_R^C}I_\\varphi\\nu_R$, realizing the secret interaction. The supporting machinery is a $\\mathbb{Z}_3\\times\\mathbb{Z}_2$ symmetry plus two Higgs doublets and two singlet scalars, arranged so that neutrino masses arise only from the new scalars; with $v_2\\sim100\\,\\mathrm{eV}$ and $v_\\varphi\\sim10^5\\,\\mathrm{eV}$, the seesaw formula produces the desired light sterile and active neutrino spectrum.","core_discovery":"On the paper's own terms, the discovery is that the canonical type I seesaw does not need a GUT-scale right-handed neutrino: replacing the usual weak-scale VEV by $v_2\\sim10^2\\,\\mathrm{eV}$ and taking the Majorana scale $v_\\varphi\\sim10^5\\,\\mathrm{eV}$ gives active neutrino masses of order $10^{-4}$ to $5\\times10^{-2}\\,\\mathrm{eV}$, a sterile neutrino $\\nu_4$ with mass $\\sim1.4\\,\\mathrm{eV}$ and mixings $U_{e4}^2,\\,U_{\\mu4}^2\\sim10^{-3}$-$10^{-2}$, and two heavier sterile states at $0.7\\,\\mathrm{keV}$ and $7\\,\\mathrm{keV}$. The same scalar content contains a pseudo-scalar $I_\\varphi$ with mass squared $M_{I_\\varphi}^2=\\frac{9}{4}M v_\\varphi$, which couples exclusively to sterile neutrinos. Choosing the explicit lepton-number-breaking scale $M<10^{-8}\\,\\mathrm{eV}$ puts $I_\\varphi$ below $0.1\\,\\mathrm{eV}$, and with $Y_{S11}=2\\times10^{-5}$ the coupling falls in the range that the cited secret-interaction mechanism claims suppresses sterile-neutrino thermalization. The benchmark spectrum recovers the 3+1 oscillation picture, with $\\nu_5$ and $\\nu_6$ effectively decoupled, and $\\nu_6$ is a long-lived warm dark matter candidate.","pith_inferences":["The paper does not compute the sterile-neutrino production rate, $\\Delta N_{\\text{eff}}$, or the matter power spectrum in its own model; a direct calculation with $m_{I_\\varphi}<0.1\\,\\mathrm{eV}$ and $Y_{S11}=2\\times10^{-5}$ is the natural next step, and would test whether the heavier states $\\nu_5$ and $\\nu_6$ stay out of equilibrium.","The benchmark point is illustrative; a scan of the $Y_D$, $Y_S$, $v_2$, and $v_\\varphi$ parameters would show how tuned the cosmological compatibility is and whether the mixing angles required by oscillation fits coexist with the chosen $Y_{S11}$.","If the secret-interaction mechanism works, a generic prediction is a sub-eV pseudo-scalar that interacts only with sterile neutrinos; improved measurements of $N_{\\text{eff}}$ and searches for exotic decays involving sterile neutrinos could bound or confirm it.","The model's low-scale seesaw logic could be adapted to other neutrino-mass mechanisms, suggesting that eV sterile neutrinos do not require abandoning seesaw but rather rescaling its VEVs."],"forward_implications":["If the model is correct, the LSND and MiniBooNE excess can be explained by a $1.4\\,\\mathrm{eV}$ sterile neutrino that evades cosmological bounds through the secret interaction.","The seesaw scale is not necessarily high: lepton number can be explicitly broken at $10^{-8}\\,\\mathrm{eV}$, and the right-handed Majorana scale can be as low as the keV range.","The model predicts a $7\\,\\mathrm{keV}$ sterile neutrino as warm dark matter, with a radiative decay lifetime around $10^{28}\\,\\mathrm{s}$, far longer than the age of the Universe.","The charged scalar of the model mediates $\\mu\\to e\\gamma$, and the current bound forces $f v_\\sigma \\ge 36\\times10^6\\,\\mathrm{GeV}^2$, a testable constraint on the scalar sector.","The singlet $\\sigma$ can act as the inflaton in Higgs inflation with a non-minimal coupling $\\xi<1$, avoiding the unitarity problem of minimal Higgs inflation."],"supporting_citations":[{"why":"Reports the MiniBooNE electron-like excess and the combined LSND plus MiniBooNE significance that motivates an eV sterile neutrino.","marker":"[4]"},{"why":"Provides the canonical type I seesaw mechanism whose mass formula the paper rescales to low energy.","marker":"[10]"},{"why":"Claims that a sub-eV pseudo-scalar with Yukawa coupling around $10^{-6}$-$10^{-5}$ to sterile neutrinos suppresses their early-universe production; the paper's cosmological viability rests on this mechanism.","marker":"[11]"},{"why":"Extends the secret-interaction reconciliation and connects it to dark matter, which the paper uses for the $I_\\varphi$ interaction and the $\\nu_6$ warm dark matter candidate.","marker":"[12]"},{"why":"Supplies the BBN cosmological constraints that eV sterile neutrinos must evade.","marker":"[5]"},{"why":"Supplies the Planck CMB constraints used to disfavor standard eV sterile neutrinos.","marker":"[6]"},{"why":"Provides large-scale-structure constraints that the secret interaction is meant to satisfy.","marker":"[7]"}],"fun_headline_variants":["Low-scale seesaw with hidden pseudo-scalar eases sterile neutrino tension","Hidden scalar couples only to sterile neutrinos, clearing cosmology","Canonical seesaw with secret sector makes eV sterile neutrinos viable","Sub-eV pseudo-scalar reconciles sterile neutrino with cosmology","Low-energy seesaw hides sterile neutrinos from early universe"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything hangs on the claim, taken from the earlier secret-interaction literature, that a pseudo-scalar lighter than $0.1\\,\\mathrm{eV}$ with a Yukawa coupling around $2\\times10^{-5}$ to sterile neutrinos really stops them from being produced in the early universe; this paper does not calculate that suppression itself.","fun_headline_variants_meta":{"raw":{"variants":["Low-scale seesaw with hidden pseudo-scalar eases sterile neutrino tension","Hidden scalar couples only to sterile neutrinos, clearing cosmology","Canonical seesaw with secret sector makes eV sterile neutrinos viable","Sub-eV pseudo-scalar reconciles sterile neutrino with cosmology","Low-energy seesaw hides sterile neutrinos from early universe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000719,"raw_usage":{"total_tokens":3323,"prompt_tokens":1136,"completion_tokens":2187,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":752,"completion_tokens_details":{"reasoning_tokens":2097}},"tokens_in":752,"tokens_out":2187,"duration_ms":14759,"temperature":1.0,"reasoning_tokens":2097,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:18:27.582043+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the early-universe production of the sterile states in this model with $m_{I_\\varphi}<0.1\\,\\mathrm{eV}$ and $Y_{S11}=2\\times10^{-5}$; if the resulting effective number of extra neutrinos or the abundance of the $7\\,\\mathrm{keV}$ state exceeds the bounds from BBN, the cosmic microwave background, and large-scale structure, the central claim fails. A laboratory bound excluding a pseudo-scalar below $0.1\\,\\mathrm{eV}$ coupled to sterile neutrinos would also undercut it.","supporting_citations":[{"cited_title":"(22) For the values of mν6 and Ue6 given above, we obtain τν6 ∼ 1028s","cited_arxiv_id":null,"evidence_quote":"Reports the MiniBooNE electron-like excess and the combined LSND plus MiniBooNE significance that motivates an eV sterile neutrino."},{"cited_title":"Hamann, S","cited_arxiv_id":null,"evidence_quote":"Claims that a sub-eV pseudo-scalar with Yukawa coupling around $10^{-6}$-$10^{-5}$ to sterile neutrinos suppresses their early-universe production; the paper's cosmological viability rests on this mechanism."},{"cited_title":"Ko et al","cited_arxiv_id":null,"evidence_quote":"Extends the secret-interaction reconciliation and connects it to dark matter, which the paper uses for the $I_\\varphi$ interaction and the $\\nu_6$ warm dark matter candidate."},{"cited_title":"Aguilar-Arevalo, et al","cited_arxiv_id":null,"evidence_quote":"Supplies the BBN cosmological constraints that eV sterile neutrinos must evade."},{"cited_title":"Mention, M","cited_arxiv_id":null,"evidence_quote":"Supplies the Planck CMB constraints used to disfavor standard eV sterile neutrinos."},{"cited_title":"Acero, Carlo Giunti, and Marco Laveder Phys","cited_arxiv_id":null,"evidence_quote":"Provides large-scale-structure constraints that the secret interaction is meant to satisfy."}],"review_version":1}