{"id":"2855356e-d87a-4303-902c-593bb9fe20e5","arxiv_id":"hep-ph/0008138","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Heavy sterile neutrinos of 10 to 200 MeV mixed with active neutrinos are excluded over most of the mass-mixing plane by big-bang nucleosynthesis and the SN 1987A neutrino burst.","lead":"Physicists computed how a hypothetical heavy sterile neutrino, 10 to 200 MeV in mass and mixed with ordinary neutrinos, would alter big-bang nucleosynthesis and the neutrino burst from supernova 1987A, then drew exclusion regions in the mass-mixing plane. The result is a map of which heavy sterile neutrinos cosmology and astrophysics already rule out, useful to anyone interpreting short-baseline anomalies or planning sterile-neutrino searches.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The BBN curves below 140 MeV are actually computed and hold up; the softer element of Fig. 3 is the SN 1987A band, whose extension from the 33.9 MeV case of Ref. [3] to M_s ~ 100 MeV rests on a one-line thermal-tail argument rather than a production calculation.","rationale":"The core of the paper is the BBN calculation for 10 < M_s < 140 MeV, and it is done with real machinery: coupled Boltzmann equations for ν_s and ν_a (Eqs. 10-11), explicit decay terms per mixing channel (Eqs. 13-16), a temperature equation (Eq. 17), an 800-point momentum grid, and the Kawano nucleosynthesis code. The fitting formulae in Table 1 compress Figs. 1-2, and the internal consistency check at M_s = 60 and 140 MeV is reported. That part of the central claim is supported and I would not downgrade it. The reader's weakest_assumption, the M_s > 140 MeV pion channel, is correctly identified as heuristic, but the authors flag it themselves in Section 5 and Section 7 and exclude it from Fig. 3, so it is an acknowledged limitation rather than a new finding, and it sits outside the 10-140 MeV claim the reader states. Where I would push further is the SN 1987A band: it is anchored to a published source (Ref. [3], Nucl. Phys. B580 (2000) 331), so restating it is not itself a concern under the citation rule, but the mass extrapolation from 33.9 MeV to ~100 MeV is new here and is argued only from the mean thermal energy. That is the one load-bearing element of Fig. 3 that is neither computed nor acknowledged as approximate. Two smaller points: the NOMAD region comes from a paper in preparation and should be treated as provisional, though it is a comparison overlay and not load-bearing; and the Section 7 assertion that Eq. (7) holds across the whole excluded region is marginal at the low-mass end (at M_s = 10 MeV, ΔN = 1, sin^2 2θ ~ 0.54 and δm^2 ~ 100 MeV^2 give a product near 540, just above the stated 500), which would slightly weaken the lowest-mass bound if taken literally. Neither of these changes the verdict. The BBN result stands; the SN band's upper mass reach is the item worth checking, and it does not move the paper below CONDITIONAL, so I recommend UNCHANGED.","tokens_in":11726,"tokens_out":8256,"duration_ms":130263,"concrete_test":"Compute the ν_s production rate in a SN core (T ~ 30 MeV, ρ ~ 3e14 g/cm^3) for M_s = 50, 100 and 150 MeV, including the full Boltzmann suppression and Pauli blocking on the final-state active neutrinos, and compare the resulting energy-loss rate against the Raffelt trapping criterion used in Ref. [3]. If the M_s = 100 MeV rate is suppressed by more than roughly an order of magnitude relative to the massless case, the lower edge of the SN band in Fig. 3 must move up and the 'up to 100 MeV' claim in Section 6 does not survive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest_assumption targets the M_s > 140 MeV pion channel, but that region is explicitly fenced off: Section 5 says 'we cannot directly apply our numerical program' and Section 7 says the estimates are 'less precise' and are omitted from Fig. 3. It is an acknowledged limitation, and it also lies outside the 10-140 MeV window the reader's strongest_claim actually asserts, so it cannot be the load-bearing soft spot for that claim. The genuinely unaddressed element of the headline exclusion map is the horizontal SN 1987A band in Fig. 3 (3e-8 < sin^2 2θ < 0.1). Section 6 imports this band from Ref. [3], which treated a 33.9 MeV neutrino, and then asserts it 'pertains at least to masses up 100 MeV' on the grounds that 'the average thermal neutrino energy exceeds about 100 MeV so that threshold effects should not become important until the mass significantly exceeds this limit.' That is a statement about the mean energy, not about the number density above threshold, which is what controls production. For M_s = 100 MeV in a T ~ 30 MeV core the equilibrium abundance of the heavy state is suppressed by roughly e^{-M_s/T} ~ 0.04, and the energy-loss rate scales as M_s e^{-M_s/T} ~ 3.7 T, i.e. an order of magnitude below the massless case. Since the lower edge of the SN band is set by requiring enough production to drain the core, that suppression should raise the lower edge and shrink the band, not leave it unchanged to 100 MeV. The paper does not compute this; it asserts it. This is a real, unacknowledged soft spot in one of the two headline exclusion regions, distinct from the acknowledged pion-channel caveat.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript extends the authors' earlier work (Ref. [3], Nucl. Phys. B580) on a heavy sterile Dirac neutrino mixed with an active flavour, lifting the fixed 33.9 MeV mass and treating mixing with ν_e, ν_μ and ν_τ separately. Below M_s = 140 MeV the authors solve a coupled system of Boltzmann equations for the sterile and active neutrino distributions together with the energy-conservation equation for the plasma (Eqs. 10, 11, 17), with channel-specific decay terms (Eqs. 13-16), and feed the resulting distorted spectra into a modified Kawano nucleosynthesis code at η_10 = 5. For each mass they extract a minimum allowed mixing (Fig. 1) and a maximum allowed lifetime (Fig. 2) for ΔN = 0.2 and ΔN = 1.0, and tabulate fitting formulae and coefficients (Eqs. 18, 19; Table 1). Above the pion threshold they give an order-of-magnitude estimate of the ν_2 → π^0 + ν_a channel (Eq. 25), explicitly not plotted. The supernova bound is imported from Ref. [3] and asserted to hold up to M_s ≈ 100 MeV. The results are collected in the exclusion map of Fig. 3.","tokens_in":12174,"tokens_out":14845,"duration_ms":275896,"significance":"If the BBN exclusion curves hold, they close a substantial region of heavy sterile neutrino parameter space with no laboratory input, and they do so with a calculation that is unusually well documented for this literature: the full kinetic system is printed, the collision and decay terms are given channel by channel, both an optimistic and a conservative ΔN tolerance are reported, and the fitting coefficients of Table 1 make the result reproducible without digitising the figures. The exclusion map is falsifiable and directly comparable to laboratory searches such as NOMAD. The paper is also candid about its approximations: §5 states that the numerical program cannot be applied above the pion threshold, and §7 states that those estimates are less precise and are omitted from Fig. 3. I do not regard the reuse of the supernova band from the authors' own published Ref. [3] as circularity; quoting a published result is normal practice. The issue is narrower and is taken up below: the extension of that band to masses far above the 33.9 MeV case actually computed in Ref. [3] is a new claim made here, and it is argued only qualitatively.","major_comments":[{"comment":"Eq. (3) as printed, τ_νs = 1.0 sec (M_s/10 MeV)^5 sin^2 2θ, has both the mass and the mixing dependence inverted relative to the decay width it is meant to represent, and it contradicts the paper's own text and Table 1. The text immediately below it says that 'for a sufficiently large mass and non-negligible mixing, the ν2 lifetime given in Eq. (3) would be quite short', and §3 says that for sin^2 2θ < 8×10^-6 'the life-time of the heavy ν2 would exceed the nucleosynthesis time'; both statements require τ ∝ M_s^-5 sin^-2 2θ, the opposite of what is printed. Eq. (21) for the pion channel has the correct sign structure, τ ∝ [sin^2θ M_s (M_s^2 - m_π^2)]^-1. A numerical cross-check against the paper's own Table 1 confirms the misprint: at M_s = 100 MeV the ν_μ,τ, ΔN = 0.2 row gives τ_max ≈ 0.064 s and (sin^2θ)_min ≈ 5×10^-5, which are mutually consistent only with τ ≈ 1.0 sec (M_s/10 MeV)^-5 sin^-2 2θ; the printed form would instead imply sin^2θ ≈ 1.6×10^-7, three orders of magnitude away. Since Eq. (3) is the bridge between the mixing angle and the lifetime used throughout Figs. 1-3, Table 1 and Eq. (25), the missing minus signs should be corrected explicitly.","section":"§2, Eq. (3)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The horizontal band 3×10^-8 < sin^2 2θ < 0.1 in Fig. 3 is carried over from Ref. [3], which treated a 33.9 MeV neutrino, and §6 extends it to M_s ≈ 100 MeV on the grounds that 'the average thermal neutrino energy exceeds about 100 MeV so that threshold effects should not become important until the mass significantly exceeds this limit'. That argument addresses the mean energy, whereas what controls the energy-loss bound is the number density of sterile states above production threshold, which for M_s ≳ T_core is Boltzmann suppressed. For M_s = 100 MeV in a core with T ≈ 30 MeV the equilibrium abundance is suppressed by roughly e^{-M_s/T} ≈ 0.04, and the energy-loss rate scales as M_s e^{-M_s/T}, an order of magnitude below the massless case. Because the lower edge of the band is set by requiring enough production to drain the core, that suppression should raise the lower edge by a comparable factor and shrink the band, not leave it unchanged to 100 MeV. The paper does not compute this. A concrete test would be to evaluate the sterile production rate with the relativistic occupation factor retained, or, more simply, to restrict the band in Fig. 3 to the mass range where M_s/T_core is small (say M_s ≲ 50 MeV) and state that the extension to 100 MeV is not established. The upper edge, which follows from trapping and the mean free path, is less affected by this argument.","section":"§6 and Fig. 3 (supernova band)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The statement that 'BBN excludes the area below the two upper dashed lines if the heavy neutrinos were abundant in the early universe' needs rewording, because the following sentence says that below the lowest dashed curve the heavy states are not efficiently produced and their impact is negligible. The excluded region is the band between the lowest (production) curve and the ΔN curves, and the caption should say so directly.","section":"§7 and Fig. 3 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract advertises bounds over 10-200 MeV, but Fig. 3 stops at 140 MeV and the 140-200 MeV results of §5 are order-of-magnitude estimates that are deliberately not plotted. The abstract should state the range actually covered by the quantitative results.","section":"Abstract and §7","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The upper limit in Eq. (25) as printed, 5.8×10^-8 m_π M_s/((M_s/m_π)^2 - 1), carries dimensions of MeV^2 unless the factor is m_π/M_s; inverting Eq. (21) at τ = 0.1 s gives sin^2θ ≈ 5.8×10^-8 m_π^3/[M_s(M_s^2 - m_π^2)], which differs from the printed expression by a factor (M_s/m_π)^2. The sentence preceding Eq. (25) also quotes the bound in terms of sin 2θ while the equation itself uses sin^2θ; the two should be made consistent.","section":"§5, Eq. (25)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The fitting form (sin^2θ)_min = s1 M_s^α + s2 has a negative constant s2, so for the ν_μ,τ, ΔN = 0.2 row it crosses zero near M_s ≈ 186 MeV and becomes unphysical beyond that. The fitted mass range should be stated explicitly and the formula should not be presented as extrapolable outside it.","section":"Table 1 and Eq. (18)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The NOMAD exclusion curve shown in Fig. 3 rests on Ref. [2], which is listed as 'paper in preparation'. The curve should be labelled preliminary in the figure and the numerical values or the analysis assumptions should be given, so that the comparison does not depend on an unpublished source.","section":"§1 and Fig. 3 (NOMAD)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that for Majorana neutrinos 'the cosmological number density of the heavy neutrinos would be twice smaller and corresponding bounds would be changed in an evident way and rather weakly' should be quantified or softened; 'twice smaller' is also awkward phrasing for a factor of two.","section":"§7 (Majorana case)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The bounds depend on the adopted ΔN tolerance through ΔY = 0.013 ΔN and on the fixed η_10 = 5. A sentence stating the provenance of the ΔY-ΔN relation and noting that the quoted limits scale with the adopted tolerance would help the reader judge how conservative the ΔN = 1.0 curves really are.","section":"§4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The supernova constraint is an order-of-few energy-loss argument, but the report of it in §6 and in Fig. 3 does not state the confidence level or the factor by which the core energy loss may exceed the standard rate. Stating this would let the band be compared on equal footing with the BBN curves.","section":"§6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The medium mixing formula is quoted from Ref. [13] with a numerical coefficient but no statement of its range of validity or of the approximations behind it; a brief remark would help readers who wish to reproduce the production curve of Eq. (8).","section":"§3, Eq. (5)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"It would be useful to mark on these figures the mass range over which the numerical code was actually run, as distinct from the range covered by the fitting formulae, since §4 notes that the temperature treatment changes between small and large masses.","section":"Figs. 1 and 2","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The BBN calculation below 140 MeV is solid and well documented, and I would support publication once the two major points are addressed. The first is a straightforward misprint in Eq. (3) that is contradicted by the paper's own Table 1 and text. The second is the supernova band: the import from Ref. [3] is fine for the 33.9 MeV case, but the extension to 100 MeV is new to this paper and is argued only from the mean thermal energy. The editor may also wish to note that §6 overlaps substantially with Ref. [3] and that the NOMAD comparison curve depends on a result still in preparation; the genuinely new content here is the flavour-by-flavour BBN treatment and the pion-channel estimate."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"The real contribution is the BBN calculation for 10-140 MeV, and it is done properly. Full Boltzmann system for the sterile and active distributions, collision and decay terms written out channel by channel, temperature evolution from energy conservation, and the whole thing run through Kawano's code. Extending their earlier 33.9 MeV nu_tau case to all three flavors and the full mass range is incremental but real, and the Table 1 fits are a useful compression of Figs. 1 and 2. If you work in this window, these are the curves to quote, and the authors are honest that their approximations weaken the bounds rather than strengthen them. The Delta N = 0.2 and 1.0 pair is the right way to present it given the 4He systematic.","headline":"The BBN curves for 10-140 MeV are genuinely computed and will be the reference for that window; the SN 1987A band borrowed from their earlier paper is the part that doesn't survive scrutiny at the high-mass end.","tokens_in":12893,"tokens_out":2082,"would_cite":true,"duration_ms":35148,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["14.60.St","26.50.+x","95.30.Cq"],"model":"selfhosted/deepseek-v4.1-flash","headline":"Heavy sterile neutrinos mixed with the known flavours are largely ruled out by big-bang nucleosynthesis and by the neutrino burst of SN 1987A, for masses between 10 and 140 MeV.","keywords":["sterile neutrinos","big-bang nucleosynthesis","SN 1987A","neutrino mixing","primordial helium abundance","neutrino decoupling","extra neutrino species","heavy neutral leptons"],"falsifier":"A full non-equilibrium kinetic calculation of the $ν_2 → π^0 + ν_a$ channel, replacing the instantaneous-decay estimate, would either confirm or erase the $M_s > 140$ MeV band of Eq. (25); independently, a primordial helium or deuterium abundance determination that pushes the tolerated $ΔN$ far below 0.2 would move the nucleosynthesis curves, and a laboratory detection of a 10–140 MeV sterile neutrino with mixing inside the excluded region would contradict the bound outright.","tokens_in":13064,"feed_emoji":"💥","tokens_out":3632,"duration_ms":68173,"temperature":0.7,"pith_summary":"The paper asks how much room is left for a fourth, sterile neutrino — one with no weak couplings of its own — in the mass range of tens of MeV, where it can mix with $ν_e$, $ν_μ$ or $ν_τ$ and decay into a light neutrino plus an electron-positron pair. The authors answer with two independent exclusions. First, if such a state was ever populated in the early plasma, its energy density and its decay products distort the neutron-to-proton ratio and the expansion rate, shifting the primordial helium abundance; solving the coupled kinetic equations for sterile and active occupation numbers and feeding the result into a nucleosynthesis code gives a minimum allowed mixing angle for each mass, and an equivalent maximum allowed lifetime. Second, if the same particle escapes a supernova core too freely it drains energy and shortens the observed neutrino burst, which excludes a broad band of mixing angles for masses up to about 100 MeV. The point of the exercise is that cosmology and one historical supernova together close a large slice of parameter space that no laboratory experiment had touched.","feed_headline":"Heavy sterile neutrinos of 10-200 MeV mostly ruled out","feed_subtitle":"Nucleosynthesis and the 1987A neutrino burst together exclude a wide band of mass and mixing, with no lab input.","key_machinery":"The engine is a set of Boltzmann equations in scaled variables $x = m_0 a(t)$ and $y = p a(t)$, one for the sterile occupation number with a production term driven by the matter-suppressed mixing angle $sin 2θ_M$ and one for the departure of each active flavour from equilibrium, coupled to an energy-conservation equation $x dρ/dx = -3(ρ+p)$ that tracks how the electromagnetic plasma is heated by decay products. The decay terms are written channel by channel, with the $ν_2 → ν_1 ℓ^+ℓ^-$ rate set by the lifetime $τ_{ν_s} = 1.0 s (M_s/10 MeV)^5 sin^2 2θ$ (0.7 s for the $ν_e$ channel). The resulting photon temperatures and distorted $ν_e$ spectra are passed to a modified Kawano nucleosynthesis code at $η_{10} = 5$, and the helium shift is converted to an effective extra-neutrino number through $ΔY = 0.013 ΔN$. The supernova bound is not a simulation but an energy-loss/energy-transfer argument: a sterile state that escapes the core too freely accelerates cooling, and one that decays or scatters inside the core still transports energy outward, so both extremes are excluded while an intermediate window remains.","core_discovery":"For Dirac sterile neutrinos of mass $10 < M_s < 140$ MeV mixed with a single active flavour, the authors find that big-bang nucleosynthesis forbids mixing angles below a mass-dependent curve: a sterile neutrino produced abundantly through mixing in the early universe either survives long enough to add energy density at the nucleosynthesis epoch or decays into $e^+e^-$ and neutrinos that reshape the neutron-proton ratio, and either way the primordial helium yield moves outside the tolerated range. The curves are given both for an optimistic tolerance of $ΔN = 0.2$ and a conservative $ΔN = 1.0$ extra light neutrino species, and are fitted by $(sin^2θ)_{min} = s_1 M_s^{α} + s_2$ with the coefficients tabulated. Equivalently, a maximum lifetime $τ_{max}$ is derived as a function of mass. Superimposed on the same plane, the SN 1987A energy-loss and energy-transfer argument excludes roughly $3×10^{-8} < sin^2(2θ) < 0.1$ for masses below about 100 MeV. A separate production-efficiency estimate, $(δm^2/MeV^2) sin^2 2θ < 2.3×10^{-7}$, marks the region where sterile states were never abundant and the nucleosynthesis bound therefore does not apply. Above $M_s = 135$ MeV the two-body decay $ν_2 → π^0 + ν_a$ takes over, and the authors give an order-of-magnitude exclusion band for that regime rather than a numerical one.","pith_inferences":["Because the exclusion curves are driven by the helium yield, a future measurement that tightens the primordial helium or deuterium abundance — and hence pushes the tolerated $ΔN$ well below 0.2 — would extend the excluded band downward in mixing angle without any new particle physics.","The two constraints are complementary in a way the figure makes visible: supernova physics bites at larger mixing angles where the sterile state is strongly coupled, nucleosynthesis bites at smaller mixing angles where it is long-lived, so the surviving window is a diagonal strip that a next-generation calculation would have to close from both ends.","The acknowledged gap above 140 MeV is the natural place for a follow-up: a full kinetic treatment of the pion channel, including the non-equilibrium $ν_e$ it injects into neutron-proton reactions, could turn the order-of-magnitude band of Eq. (25) into a bound comparable in status to the lower-mass curves.","The same machinery would apply almost unchanged to any new light singlet that mixes with one active flavour and decays visibly in the early plasma, so the paper's real export is a method for converting a mixing angle into a helium-abundance shift."],"forward_implications":["Any heavy sterile neutrino with mass between 10 and 140 MeV and mixing below the tabulated $(sin^2θ)_{min}$ curve is excluded if it was ever in equilibrium in the early plasma, independent of any laboratory measurement.","The same particle is excluded for mixing angles between roughly $3×10^{-8}$ and $0.1$ in $sin^2(2θ)$ by the duration of the SN 1987A neutrino burst, up to masses near 100 MeV.","A sterile state that mixes more weakly than $(δm^2/MeV^2) sin^2 2θ < 2.3×10^{-7}$ was never abundant, so the nucleosynthesis constraint on it disappears and only direct experiment can reach it.","For masses above 135 MeV the pion channel $ν_2 → π^0 + ν_a$ dominates and shortens the lifetime so sharply that lifetimes above roughly 0.1 s are excluded except near a narrow cancellation window around 0.2 s.","Majorana rather than Dirac heavy neutrinos would halve the cosmological number density and weaken all of these bounds, but only mildly.","The NOMAD limit on $ν_τ$–sterile mixing covers part of the same plane, so the cosmological and astrophysical bounds and the accelerator bound can be read as one combined exclusion map."],"supporting_citations":[{"why":"The authors' own earlier work supplying the kinetic-equation framework, the numerical nucleosynthesis treatment, and the SN 1987A energy-transfer argument that this paper generalises in mass and flavour.","marker":"[3]"},{"why":"Supplies the matter-suppressed mixing angle $sin 2θ_M$ used to compute the sterile production rate in the plasma.","marker":"[13]"},{"why":"Source of the production-rate estimate $Γ_s/H ≈ sin^2 2θ_M (T_γ/T_w)^3$ on which the abundance and freeze-out discussion rests.","marker":"[12]"},{"why":"The Kawano nucleosynthesis code, modified here to accept the computed photon temperature and distorted neutrino spectra.","marker":"[17]"},{"why":"Provides the $π^0 → ν {bar ν}$ lifetime that is translated into the $ν_2 → π^0 + ν_a$ rate governing the high-mass regime.","marker":"[18]"},{"why":"Second calculation of the pion-to-neutrino decay width used for the same translation above $M_s = 135$ MeV.","marker":"[19]"},{"why":"The NOMAD limit on $ν_τ$–sterile mixing, plotted alongside the cosmological and supernova regions for direct comparison.","marker":"[2]"},{"why":"Background on how a neutrino heavier than an MeV disturbs light-element abundances, the premise the whole nucleosynthesis calculation builds on.","marker":"[14]"}],"fun_headline_variants":["BBN and SN 1987A exclude wide sterile-neutrino mass-mixing bands","10-200 MeV sterile neutrinos: nucleosynthesis sets a mass-dependent mixing floor","Nucleosynthesis alone forbids mixing below a mass-dependent curve for 10-140 MeV","Limitation: above 135 MeV the pion decay channel gets only an order-of-magnitude bound","SN 1987A excludes 3e-8 < sin^2(2θ) < 0.1 for masses below about 100 MeV"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The exclusion curves assume that the distortion a heavy sterile neutrino imprints on primordial helium can be traded for a tolerated number of extra light neutrino species, $ΔN$ between 0.2 and 1.0, and — for the $M_s > 140$ MeV tail, as the authors themselves acknowledge — that the dominant pion decay channel can be handled by an instantaneous-decay estimate rather than by the numerical code, with the cancellation window near 0.2 s left to future non-equilibrium calculations.","fun_headline_variants_meta":{"raw":{"variants":["BBN and SN 1987A exclude wide sterile-neutrino mass-mixing bands","10-200 MeV sterile neutrinos: nucleosynthesis sets a mass-dependent mixing floor","Nucleosynthesis alone forbids mixing below a mass-dependent curve for 10-140 MeV","Limitation: above 135 MeV the pion decay channel gets only an order-of-magnitude bound","SN 1987A excludes 3e-8 < sin^2(2θ) < 0.1 for masses below about 100 MeV"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1437,"prompt_tokens":915,"completion_tokens":522,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":404}},"tokens_in":915,"tokens_out":522,"duration_ms":9423,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":404,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T18:05:41.983096+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A full non-equilibrium kinetic calculation of the $ν_2 → π^0 + ν_a$ channel, replacing the instantaneous-decay estimate, would either confirm or erase the $M_s > 140$ MeV band of Eq. (25); independently, a primordial helium or deuterium abundance determination that pushes the tolerated $ΔN$ far below 0.2 would move the nucleosynthesis curves, and a laboratory detection of a 10–140 MeV sterile neutrino with mixing inside the excluded region would contradict the bound outright.","supporting_citations":[{"cited_title":"Fermilab-Pub-92/04-A","cited_arxiv_id":null,"evidence_quote":"The Kawano nucleosynthesis code, modified here to accept the computed photon temperature and distorted neutrino spectra."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The authors' own earlier work supplying the kinetic-equation framework, the numerical nucleosynthesis treatment, and the SN 1987A energy-transfer argument that this paper generalises in mass and flavour."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the matter-suppressed mixing angle $sin 2θ_M$ used to compute the sterile production rate in the plasma."},{"cited_title":"Restrictions on neutrino oscillations from BBN. Non-resonant case","cited_arxiv_id":"hep-ph/0006103","evidence_quote":"Source of the production-rate estimate $Γ_s/H ≈ sin^2 2θ_M (T_γ/T_w)^3$ on which the abundance and freeze-out discussion rests."},{"cited_title":"Fishbach et al, Phys","cited_arxiv_id":null,"evidence_quote":"Provides the $π^0 → ν {bar ν}$ lifetime that is translated into the $ν_2 → π^0 + ν_a$ rate governing the high-mass regime."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Second calculation of the pion-to-neutrino decay width used for the same translation above $M_s = 135$ MeV."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The NOMAD limit on $ν_τ$–sterile mixing, plotted alongside the cosmological and supernova regions for direct comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Background on how a neutrino heavier than an MeV disturbs light-element abundances, the premise the whole nucleosynthesis calculation builds on."}],"review_version":1}