{"id":"c6ded38a-5726-43bb-ac64-2f6cc5d04a6c","arxiv_id":"2506.15485","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A model with a bulk sterile neutrino and a Majoron claims to unify dark matter, dark radiation, and invisible neutrino decay, but its quoted parameter space is internally inconsistent.","lead":"This paper proposes that a sterile neutrino living in extra dimensions, coupled to a particle called a Majoron, can simultaneously explain dark matter, extra dark radiation, and neutrino decay. A generalist might read it to see whether one extra-dimensional framework can plausibly tie together three unrelated cosmic puzzles.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"At g~1e-6, the 2 keV DM candidate ν(1) decays via ν(1)→ν+J with lifetime ~1e-5 s; making m_J heavy enough to stabilize it forbids the claimed eV-scale active-neutrino decay, so the unified DM+neutrino-decay claim is internally inconsistent.","rationale":"The reader's weakest assumption focuses on the dark-radiation timing contradiction (g~1e-6, m_n~1/R~10^6 GeV gives τ_n~10^-17 s instead of 0.1-1 s). That is a valid and concrete problem, and it independently supports rejection. However, I judge the more load-bearing flaw to be the DM stability versus neutrino-decay tension: the same coupling required for observable active-neutrino decay makes the 2 keV DM candidate decay in ~10^-5 s if the Majoron is light, and if the Majoron is heavy enough to prevent that decay, the eV-scale active-neutrino decay is kinematically forbidden. This is not a quantitative mistuning but a structural incompatibility of the unification claim. The paper's own text provides no stabilization mechanism: Section 2 says ν(1) is 'assumed to be cosmologically stable' with no symmetry or kinematic argument. The freeze-in normalization error (Eqs. 6-7 have dimension M^-3) and the decay-timing inconsistency reinforce the rejection, but the DM/neutrino-decay incompatibility is the cleanest single test: one decay-width calculation with the paper's own Eq. 14 decides it. I therefore keep the REJECT verdict and rate agreement with the reader as partial: we identify different primary weaknesses that point the same direction.","tokens_in":9149,"tokens_out":15900,"duration_ms":167162,"concrete_test":"Use Eq. 14 with m_ν1=2 keV, g=10^-6, m_J=0 to compute Γ(ν1→ν_i+J); if τ≈1.6×10^-5 s, the DM candidate is not stable. Then repeat with m_J=1 MeV: verify the decay ν_i(0.1 eV)→ν_j+J is kinematically forbidden, so the active-neutrino decay signal in Section 5 disappears. This two-step kinematics/lifetime check settles whether all three pillars can coexist in one parameter point.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim requires the same Majoron coupling (Eq. 3) with g~1e-6 to provide a stable warm-DM candidate, ν(1), at m_ν(1)~2 keV, and to mediate invisible decay of eV-scale active neutrinos (Section 5). These two requirements are incompatible. If m_J < m_ν(1) − m_ν_i, the decay ν(1)→ν_i+J is kinematically open. Using the paper's own width formula (Eq. 14), Γ_ν(1) ≈ g^2 m_ν(1)/(16π) ≈ 4×10^-20 GeV for g=10^-6 and m_ν(1)=2 keV, giving τ≈1.6×10^-5 s. The DM particle would vanish microseconds after production, not survive to the present. The only way to forbid this decay is to take m_J > m_ν(1) (or decouple ν(1) from J, which the model does not do). But then the same channel ν_i→ν_j+J for active neutrinos with m_ν_i~0.1 eV is kinematically forbidden, eliminating the claimed neutrino-decay signature and the associated IceCube/DUNE sensitivity claimed in Sections 5-6. Section 2 merely 'assumes' ν(1) is cosmologically stable; no symmetry, mass threshold, or coupling suppression is given. Thus the three pillars of the abstract cannot coexist: stable keV DM and observable decay of eV active neutrinos cannot both arise from the same g~1e-6 Majoron coupling. This internal tension is independent of the additional decay-timing and freeze-in normalization problems noted by the reader.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a model in which a bulk right-handed neutrino propagating in large extra dimensions is coupled to a pseudo-Nambu-Goldstone Majoron, aiming to simultaneously explain warm dark matter (the lightest Kaluza-Klein sterile neutrino produced by freeze-in), dark radiation (from decays of heavier KK modes into Majorons), and invisible decay of active neutrinos. The manuscript presents the model Lagrangian, freeze-in production estimates, a Boltzmann system for Majoron injection, neutrino decay widths, and a claimed viable parameter region around R^{-1} ~ 10^3 TeV, g ≲ 10^{-6}, and m_{ν(1)} ~ 2 keV - 1 MeV, with prospective sensitivity for CMB-S4, DUNE, and IceCube-Gen2.","tokens_in":9603,"tokens_out":4931,"duration_ms":48923,"significance":"If the framework were internally consistent, it would offer an economical unification of three beyond-Standard-Model phenomena with correlated, testable signatures. The conceptual appeal is genuine: a single Majoron portal connecting a sterile-neutrino KK tower to dark matter, dark radiation, and neutrino decay is a natural idea. However, the manuscript as written contains several load-bearing technical errors and internal contradictions that invalidate the central claims: the freeze-in equations are dimensionally inconsistent, the phase-space factors are incorrect, the 'stable' dark-matter candidate decays far too rapidly under the same coupling used for neutrino decay, the quoted compactification scale is incompatible with the claimed lightest KK mass, and the heavier KK modes have lifetimes many orders of magnitude too short to produce the claimed ΔNeff. Because these problems affect the core derivation and the stated parameter region, the paper cannot be accepted in its present form.","major_comments":[{"comment":"The same Majoron coupling g ~ 10^{-6} that is invoked to make ν(1) a stable warm dark-matter candidate also mediates its decay. Using the paper's own width formula in Eq. (14) with m_{ν(1)} = 2 keV and g = 10^{-6} gives Γ ≈ g^2 m/(16π) ≈ 4×10^{-20} GeV, corresponding to a lifetime τ ≈ 1.6×10^{-5} s. Thus the lightest KK mode would decay practically instantaneously after production, contradicting the assumption in §2 that ν(1)_R is 'cosmologically stable'. No symmetry, mass-threshold, or coupling-suppression mechanism is provided to protect ν(1). Conversely, if m_J > m_{ν(1)} is imposed to forbid this decay, the active-neutrino decay channel ν_i → ν_j + J of §5 is kinematically closed for eV-scale neutrinos, eliminating the claimed IceCube/DUNE sensitivity. The three central pillars of the abstract therefore cannot coexist.","section":"§2, §5, Eqs. (3), (14), (16)"},{"comment":"The Boltzmann equation for the freeze-in yield is dimensionally inconsistent. The left-hand side dY_{ν(1)}/dT has mass dimension -1 (in units where ℏ=c=1), while the right-hand side contains M_Pl Γ_H T^6, which has mass dimension 8, multiplied by dimensionless factors. Consequently Eq. (7) is also dimensionally incorrect. As a result, the derived Yukawa value y ~ 10^{-10} and the claimed relic-abundance contour in Fig. 2 are not supported by a valid calculation.","section":"§3, Eqs. (6)–(7)"},{"comment":"The partial width for H → ν_L ν(1) uses the phase-space factor (1 - 4m_{ν(1)}^2/m_H^2)^{3/2}, which is the factor for a two-body decay into two identical final-state masses. Here the final states are a massless active neutrino and a massive sterile neutrino, so the correct kinematic factor is different, e.g. involving [(1 - (m_1+m_2)^2/m_H^2)(1 - (m_1-m_2)^2/m_H^2)]^{1/2} times the appropriate spin factors. The numerical width entering the freeze-in calculation is therefore in error.","section":"§3, Eq. (5)"},{"comment":"The claimed allowed parameter space in Eq. (16) is internally inconsistent with the KK mass formula in Eq. (2). If R^{-1} ~ 10^3 TeV, the first KK mode has mass m_1 ≈ 1/R ≈ 10^3 TeV, not 2 keV - 1 MeV as stated unless one reinterprets m_{ν(1)} as the zero mode, which is not a KK excitation. Furthermore, for the heavier KK modes with mass ~10^3 TeV and g ~ 10^{-6}, Eq. (10) gives lifetimes τ_n ≈ 16π/(g^2 m_n) ~ 3×10^{-17} s, many orders of magnitude below the τ_n ~ 0.1–1 s window that §4 identifies as necessary for a nonthermal ΔNeff signature consistent with BBN. The dark-radiation mechanism therefore cannot operate as described.","section":"§4, §6, Eq. (16)"}],"minor_comments":[{"comment":"The initial abundances of the heavier KK modes that decay into Majorons are not derived; the Boltzmann system in Eqs. (11)–(12) requires initial conditions that are not computed from any production mechanism.","section":"§4, Eq. (13)"}],"recommendation":"reject","confidential_remarks":"This manuscript appears to be an early draft with several fundamental issues. The central inconsistencies—the instab stability of the dark-matter candidate under the same coupling used for neutrino decay, the dimensionally invalid freeze-in equations, and the mismatched KK mass scale and decay timing—mean that the proposed scenario, as stated, cannot realize its claimed unified picture. A major revision would require a substantially new construction rather than local repairs. In addition, the citation of an apparently unrelated machine-learning paper (ref. [8]) and several typos suggest the manuscript has not yet reached the standard for formal review."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This one is easy to summarize. The paper assembles a plausible-sounding combination of large extra dimensions, a Majoron portal, freeze-in sterile neutrino dark matter, and invisible neutrino decay, but the central mechanism is internally inconsistent and the quantitative formulas contain basic errors. I agree with the reader's rejection, and the stress-test note lands.\n\nWhat is genuinely new is minimal: the ingredients all appear in the cited literature (LED sterile neutrinos, Majorons, freeze-in, invisible decay). The contribution is the specific assembly and the claimed unified parameter space. That assembly is not realized. The stress-test gets to the heart of it: with g~1e-6 and m_ν(1)~2 keV, Eq. (14) gives τ ≈ 1.6e-5 s for ν(1)→ν+J, so the dark matter candidate decays away microseconds after production. The paper simply 'assumes' stability in Section 2, with no symmetry or mass threshold to enforce it. Raising m_J to forbid the DM decay kills the claimed eV-scale active-neutrino decay. The three pillars cannot coexist.\n\nThe reader's other concerns are real and independent. Eqs. (6)-(7) have inconsistent mass dimensions. Eq. (5) uses the wrong phase-space factor for a two-body decay with one light and one heavy final state—minor relative to the stability problem, but still an error. Eq. (16) quotes R^-1 ~ 10^3 TeV while claiming m_ν(1) ~ 2 keV–1 MeV, which is impossible for the first KK mode if 1/R sets the KK spacing. The paper also claims a Boltzmann treatment but gives only schematic equations and no numerical solution; Fig. 3 is illustrative, not computed.\n\nTo give credit: the author frames the three phenomena clearly, cites the relevant freeze-in and Majoron literature, and is explicit that only a narrow sub-MeV window could work. Those are marks of an honest attempt, not a crank write-up. But the errors are load-bearing, not cosmetic. The proposed viable parameter space is not realized by the model as written.\n\nWho is this for? A reader who wants a list of ingredients for a combined LED-Majoron DM/DR/neutrino-decay model might skim the introduction. But nobody should build on the quantitative claims. I would not cite it, and I would not bring it to reading group.\n\nRecommendation: desk reject. A referee report would be a list of the same internal contradictions. The author needs to fix the stability problem and the mass relation before the model deserves referee time.","headline":"Assembles familiar ingredients into a unified LED-Majoron story, but the central mechanism is internally inconsistent and the quantitative formulas have load-bearing errors.","tokens_in":770,"tokens_out":797,"would_cite":false,"duration_ms":37362,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"One Majoron portal yields dark matter, dark radiation, and neutrino decay.","keywords":["Sterile neutrino","Majoron","Large extra dimensions","Warm dark matter","Dark radiation","ΔN_eff","Freeze-in","Neutrino decay"],"falsifier":"Compute the KK lifetime from Eq. (10) for a representative heavy mode with m_n ~ $10^{3}$ TeV and g = $10^{-6}$. If the result is far below 0.1 s—as a direct scaling suggests—the dark-radiation mechanism of Section 4 fails, and the model cannot produce the claimed ΔN_eff. Observationally, a CMB-S4 measurement of ΔN_eff consistent with zero to a precision of ~0.01 would exclude the predicted nonthermal radiation injection.","tokens_in":8917,"feed_emoji":"🌌","tokens_out":7881,"duration_ms":70797,"temperature":0.7,"pith_summary":"This paper proposes that a single portal—sterile neutrinos living in large extra dimensions and coupled to a pseudo-Goldstone Majoron—can simultaneously explain the dark matter, an excess of dark radiation, and invisible neutrino decay. In the model the lightest Kaluza–Klein sterile neutrino is produced out of equilibrium through Higgs decays and survives as warm dark matter, while heavier KK modes decay into active neutrinos plus relativistic Majorons, shifting the effective number of neutrino species ΔN_eff. The same Majoron coupling makes active neutrinos decay invisibly with lifetimes near current bounds. A sympathetic reader would care because the three phenomena are not independent: they are controlled by the same volume-suppressed coupling g ≲ $10^{-6}$ and a compactification scale of 1/R ~ $10^{3}$ TeV, so one positive detection would predict the others. The paper maps the allowed parameter region to a narrow sub-MeV window for the dark-matter candidate and identifies targets in CMB-S4, Lyman-$\\alpha$ surveys, and neutrino telescopes.","feed_headline":"One Majoron portal yields dark matter, dark radiation, neutrino decay","feed_subtitle":"A single 10^-6 coupling links warm dark matter, extra radiation, and invisible neutrino decay.","key_machinery":"The central objects are a Kaluza–Klein tower of bulk right-handed neutrinos and a pseudo-Nambu–Goldstone Majoron from spontaneous lepton-number violation. The tower's volume-suppressed coupling, Eq. (3), gives every KK mode the same portal to the Standard Model: the lightest mode is long-lived and builds up its abundance through freeze-in H → ν_L $ν^{{(1)}}$_R decays, while heavier modes decay $ν^{{(n)}}$_R → ν + J with the width of Eq. (10), Γ ∝ $g^{2}$ m_n. The mechanism is completed by the Boltzmann system of Eqs. (11)–(12), which tracks the injection of Majorons into the radiation bath and converts it into ΔN_eff through Eq. (13).","core_discovery":"The central claim of the paper is that the allowed parameter space given in Eq. (16), $R^{-1}$ ~ $10^{3}$ TeV, g ≲ $10^{-6}$, and m_{ν(1)} ~ 2 keV to O(MeV), produces all three phenomena from one mechanism. The lightest KK sterile neutrino is produced by freeze-in from Higgs decays and constitutes a warm dark matter candidate with mass 2 keV–1 MeV that evades Lyman-$\\alpha$ constraints. Heavier KK modes decay into ν + J, and the paper solves a coupled Boltzmann system showing that decays in the time window τ_n ~ 0.1–1 s generate a nonthermal Majoron population that raises ΔN_eff without destroying BBN concordance. Active neutrinos decay invisibly with lifetime/mass ratios near $10^{9}$ s/eV, saturating the current bounds from solar, atmospheric, and astrophysical data. In short, the paper claims that a single, predictive, testable region of parameter space addresses dark radiation, dark matter, and neutrino anomalies simultaneously.","pith_inferences":["The same lifetime formula that produces the ΔN_eff window could be turned around: measuring the diffuse supernova neutrino spectrum would fix g and thereby predict the exact dark-matter freeze-in abundance, closing the loop.","If the internal lifetime hierarchy does not hold (heavy KK modes decaying far earlier than 0.1–1 s), the dark-radiation component might instead come from a different relativistic relic, but the paper's specific correlation between neutrino decay and warm dark matter would remain a distinctive test of the Majoron portal.","The volume suppression that leads to g ~ 10^-6 also predicts anomalously suppressed but nonzero couplings for all higher KK modes; existing searches for rare Higgs decays to invisible states could already place independent bounds on the model.","One could extend the framework to two extra-dimensional radii to separate the dark-matter KK mass from the compactification scale, which would loosen the overclosure and Lyman-alpha tension while preserving the ΔN_eff link."],"forward_implications":["If the scenario is right, CMB-S4 and Simons Observatory should see a positive shift in ΔN_eff at the level of the model's allowed band, not an exact zero.","The dark matter is warm with mass in the 2 keV–1 MeV range, so high-resolution Lyman-alpha data either confirms the free-streaming scale or excludes the model.","The active-neutrino lifetime/mass ratio should sit near 10^9 s/eV, making invisible decay potentially observable at IceCube-Gen2 and DUNE.","Detection of any one of the three signatures forces the other two to appear in the same correlated region.","Supernova cooling bounds on Majoron emission constrain the same coupling, so the allowed g ~ 10^-6 window is testable by both cosmology and stellar astrophysics."],"supporting_citations":[{"why":"Introduces the Majoron as the pseudo-Nambu–Goldstone boson from spontaneous lepton number violation, providing the interaction structure in Eq. (3).","marker":"[11]"},{"why":"Provides an alternative Majoron realization and supports the invisible decay channel used throughout the paper.","marker":"[12]"},{"why":"Establishes the large-extra-dimensions framework with bulk neutrinos, giving the volume suppression and the origin of small active neutrino masses.","marker":"[16]"},{"why":"Derives the Kaluza–Klein tower spectrum that Eq. (2) uses for the sterile neutrino masses.","marker":"[17]"},{"why":"Develops the freeze-in production mechanism used to compute the dark matter abundance in Eqs. (6)–(7).","marker":"[21]"},{"why":"Supplies the neutrino decay lifetime bounds that translate into the g ≲ 10^-6 constraint in Eq. (15).","marker":"[25]"},{"why":"Provides high-energy neutrino decay constraints, motivating the IceCube observability of invisible neutrino decay.","marker":"[26]"},{"why":"Defines the CMB-S4 sensitivity forecast that sets the experimental target for the predicted ΔN_eff excess.","marker":"[33]"}],"fun_headline_variants":["Extra dimensions unify dark matter, dark radiation, neutrino decay","Single sterile neutrino portal explains three cosmic puzzles","Neutrino portal to extra dimensions solves dark sector trio","One coupling yields warm dark matter, radiation, neutrino decay","Majoron portal to extra dims: DM, DR, and neutrino decay"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model requires a precise lifetime hierarchy in the KK tower: the lightest mode (2 keV–1 MeV) must survive to today as dark matter, while the heavier modes (mass ~1/R ~ $10^{3}$ TeV) must decay in the narrow window 0.1–1 s, even though all modes share the same coupling g ~ $10^{-6}$; using Eq. (10) with these numbers the heavy-mode lifetimes come out many orders of magnitude shorter, so this hierarchy is the premise on which everything else rests.","fun_headline_variants_meta":{"raw":{"variants":["Extra dimensions unify dark matter, dark radiation, neutrino decay","Single sterile neutrino portal explains three cosmic puzzles","Neutrino portal to extra dimensions solves dark sector trio","One coupling yields warm dark matter, radiation, neutrino decay","Majoron portal to extra dims: DM, DR, and neutrino decay"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1179,"prompt_tokens":891,"completion_tokens":288,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":205}},"tokens_in":507,"tokens_out":288,"duration_ms":3424,"temperature":1.0,"reasoning_tokens":205,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:35:01.302597+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the KK lifetime from Eq. (10) for a representative heavy mode with m_n ~ $10^{3}$ TeV and g = $10^{-6}$. If the result is far below 0.1 s—as a direct scaling suggests—the dark-radiation mechanism of Section 4 fails, and the model cannot produce the claimed ΔN_eff. Observationally, a CMB-S4 measurement of ΔN_eff consistent with zero to a precision of ~0.01 would exclude the predicted nonthermal radiation injection.","supporting_citations":[],"review_version":2}