{"id":"1debb243-384f-4c03-b7ad-7c6414d4616f","arxiv_id":"2608.12497","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A rolling Majoron from broken global B-L symmetry generates the baryon asymmetry at TeV-scale right-handed neutrino masses in the scotogenic model, consistent with neutrino and dark matter constraints.","lead":"Physicists show that a slowly rolling field called the Majoron can bias particle-antiparticle reactions in a dark matter model, producing the observed matter abundance with right-handed neutrino masses as low as 600 GeV. The same framework explains neutrino masses, inert-scalar dark matter, and possibly a second dark matter component, making it testable at colliders and dark matter experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central result is a scan over the free initial Majoron yield Y_theta; unless its origin and persistence are demonstrated, the TeV-scale BAU claim is conditional.","rationale":"The paper is internally coherent: the strong-washout regime genuinely helps a chemical-potential source, the spectator treatment with mu_eta is careful, and the DM and neutrino constraints are folded in through micrOMEGAs and the Casas-Ibarra parametrization. The weakest point is exactly the initial Majoron yield Y_theta, which directly multiplies the final baryon asymmetry and is left as a free parameter. The paper itself flags this limitation, but the headline claim of M1 = O(600) GeV depends on it: if the required Y_theta is not generated, is damped by backreaction, or the Majoron is trapped before sphaleron freeze-out, the baryon asymmetry vanishes. My proposed coupled-system test would settle whether this concern actually lands. Since this is the same load-bearing assumption identified by the reader and the reader's CONDITIONAL verdict already reflects it, my read does not change the verdict.","tokens_in":23152,"tokens_out":38977,"duration_ms":369315,"concrete_test":"Take the representative plateau point M1 = 2 x 10^3 GeV, v_phi = 10^4 GeV, lambda_5 = 10^-4 (so M2 = v_phi = 10^4 GeV, satisfying M2 < 10 M1). Integrate the coupled system comprising the Majoron equation of motion, including the explicit-breaking potential (38) with m_J near its lifetime-allowed maximum for v_phi = 10^4 GeV, and the lepton-asymmetry Boltzmann equation (30), starting at z = M1/T = 1 with the initial Y_theta required by Eq. (36). Verify that Y_theta at T = 132 GeV agrees with the input to within 20% and that the final Y_B matches the observed value 8.7 x 10^-11. If the Majoron is trapped above T_sp or if Y_theta is damped before freeze-out, the plateau claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equations (33)-(36) make the final baryon asymmetry directly proportional to the free parameter Y_theta = v_phi^2 theta_dot/s. The paper is explicit in Sec. V: \"we remain agnostic about the underlying dynamics responsible for generating the initial condition for the Majoron motion\", so Figs. 3 and 4 are existence contours in Y_theta, not predictions. For fixed (M1, v_phi, z), any observed Y_B can be fitted by scaling Y_theta. The low-scale plateau (36) is therefore only as secure as the unquantified assumptions that some mechanism supplies the required Y_theta before inverse decays become relevant, that Y_theta is not dissipated by the same strong-washout processes that generate the asymmetry, and that the Majoron is not trapped by the potential (38) at temperatures above T_sp = 132 GeV. The damping is asserted via citations [24,84,87], not evaluated at the benchmark; if any of these conditions fails, the B-L asymmetry is wiped out and the TeV-scale claim collapses even though every particle-physics ingredient remains. This is a load-bearing initial-condition and expansion-history requirement, not a minor tuning: it separates a derived prediction from a parameter fit.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a spontaneous leptogenesis mechanism in the dynamical minimal scotogenic model, where a rolling Majoron from global U(1)_{B-L} breaking induces an effective chemical potential for B-L, and RHN decay/inverse-decay processes convert this bias into a baryon asymmetry. The authors show that the strong-washout regime, which suppresses conventional thermal leptogenesis, becomes advantageous here, and they claim that the observed baryon asymmetry can be reproduced with hierarchical RHN masses as low as O(600) GeV while remaining consistent with radiative neutrino masses and inert-scalar or Majoron dark matter. The paper derives the final Y_B from chemical equilibrium conditions, computes the spectator coefficient c_B in the appendix, and explores parameter space in Y_theta versus M1 and v_phi, including constraints from DM relic density, direct detection, kination domination, Majoron overproduction, and Majoron decay lifetime.","tokens_in":23470,"tokens_out":22697,"duration_ms":190983,"significance":"If the central claim holds, the setup provides a testable low-scale alternative to high-scale thermal leptogenesis in a well-motivated radiative neutrino mass framework, linking the baryon asymmetry to neutrino masses and a multicomponent dark sector. The chemical equilibrium derivation in the Appendix is systematic, and the identification of the lambda_5-dependent spectator effects on the final asymmetry is a useful contribution. The paper also deserves credit for explicitly delineating several cosmological consistency conditions (kination bound, Majoron stability, dark radiation). However, the headline result is an existence proof contingent on the free initial Majoron yield Y_theta, and the paper does not currently demonstrate all conditions simultaneously in a concrete benchmark.","major_comments":[{"comment":"The final baryon asymmetry, Y_B = (c_B/6) Y_theta (M1/(v_phi z_dec))^2, is directly proportional to the initial Majoron angular yield Y_theta, which the paper explicitly declares to be a free parameter in Sec. V. Figures 3 and 4 therefore show the values of Y_theta required to match the observed Y_B rather than predictions. The abstract's claim that the observed asymmetry is 'successfully generated' with M1 = O(600) GeV is accordingly an existence claim for a particular initial condition. I recommend that the authors either provide a quantitative estimate of Y_theta from the Planck-suppressed explicit breaking mechanism discussed in Sec. V, or state unambiguously that the TeV-scale result requires an ad hoc initial Majoron velocity and discuss the naturalness of the required values (e.g., Y_theta spanning roughly 10^-6 to 10^5 across the plotted range). Without this, the central claim is a parameter fit rather than a falsifiable prediction.","section":"Sec. V, Eq. (35)"},{"comment":"The kinetic misalignment condition Y_theta > Y_cr in Eq. (39) guarantees that the Majoron is not trapped at T_osc, but it does not guarantee that the Majoron is still rolling at the inverse-decay decoupling temperature T_dec. Because the kinetic energy density scales as rho_theta ∝ T^6 while T_dec can be much smaller than T_osc, one must also impose rho_theta(T_dec) > V_max, which gives an upper bound m_J < Y_theta s(T_dec)/(2 v_phi^2). This additional constraint is absent from Figs. 3-5 and from the text. For typical low-scale plateau parameters the required Y_theta appears large enough that the bound can be satisfied with sub-eV m_J, but the condition should be stated explicitly and imposed in the parameter-space analysis, especially for the higher-T_dec regime where Y_theta is smaller and the interval of allowed m_J can close.","section":"Sec. V, Eq. (39)"},{"comment":"The paper's headline claim of M1 = O(600) GeV is not backed by an explicit benchmark point. Figures 3 and 4 show contours, but no single point is given with a full specification of v_phi, M1, M2, Y_theta, m_J, m_etaI, lambda_5, the Casas-Ibarra angle, and the resulting Yukawa couplings, together with checks of neutrino masses, DM relic abundance (including the subdominant eta_I contribution), direct detection limits, the kination bound, kinetic misalignment, the rolling condition of Eq. (39), and the Majoron stability bound. I request at least one or two benchmark tables demonstrating that all these constraints can be satisfied simultaneously.","section":"Sec. VI"}],"minor_comments":[{"comment":"Equation (30) contains a typesetting error in the chemical-potential term; the source term should be typeset as (2 mu_l_alpha + 2 mu_eta - theta_dot)/T, with the fraction unambiguous.","section":"Eq. (30)"},{"comment":"The phrase 'viable explodable region' should read 'viable explorable region'.","section":"Sec. III"},{"comment":"The derivation of the factor (M1/(v_phi z))^2 would be clearer if the text explicitly stated n_B = (T^2/6) mu_B and s = (2 pi^2/45) g_*s T^3 before presenting Y_B.","section":"Eq. (33)"},{"comment":"Please clarify the meaning of the pink solid contours versus the pink shaded region; the text says the solid contours denote the Majoron yield required for the observed DM abundance while the shaded region is excluded, but the figure caption should be self-explanatory.","section":"Fig. 5"},{"comment":"The statement that dissipation of the Majoron motion is suppressed is asserted by citations [24,84,87] without a parametric estimate; a one-line estimate of Gamma_diss/H at the benchmark temperatures would strengthen the argument.","section":"Sec. V"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope as a model-building paper. The authors are honest about the free-parameter nature of Y_theta and about the radiation-domination restriction, but the abstract overstates the robustness of the TeV-scale claim. The missing rolling condition and the absence of a full benchmark point are fixable within the manuscript's scope; I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper does something real and says clearly what it does not prove. The new step is applying spontaneous leptogenesis from a rolling Majoron to the minimal two-RHN dynamical scotogenic model, and showing that the strong washout that kills conventional thermal leptogenesis becomes the asset that keeps the plasma tracking the effective chemical potential. The TeV-scale RHN claim is structurally different from earlier work, and the lambda_5 spectator analysis—where the inert doublet chemical potential either modifies c_B or erases the inert asymmetry—is a genuine addition. The DM part is competent: relic density, direct detection, LEP/EW precision, vacuum stability, and the sub-eV Majoron window with late decay constraints are assembled with the right tools.\n\nThe soft spots are exactly where the stress-test note puts them. Eq. (35) makes Y_B literally proportional to Y_theta, the initial Majoron angular yield, and Fig. 3 is the required value of Y_theta to hit the observed Y_B. The authors are explicit about this: they say they remain agnostic about the origin of the Majoron motion and treat Y_theta as a free parameter. That is honest, but it means the central 'M1 ~ 600 GeV' result is an existence proof in parameter space, not a prediction. The persistence of the rolling against thermal damping is also asserted through citations rather than evaluated at the benchmarks; given that the same strong washout processes are generating the asymmetry, a dedicated damping calculation would be the first thing I would ask for. The restriction to radiation domination and the exclusion of the kination region are stated, so that is not a flaw, just a boundary. The claim of direct testability of TeV-scale RHNs is a little optimistic—the IHD and Majoron probes are more concrete than the RHN ones.\n\nNone of this sinks the paper. The mechanism holds together, the chemistry is standard, and the honest limitation statements make it easy to see what would need to be done to turn the scan into a derivation. The paper deserves a serious referee, and a good referee will ask for the origin and damping of Y_theta rather than a redo of the Boltzmann equations.\n\nRecommendation: send it to review, with the initial-condition question as the main request. It is a solid contribution to low-scale leptogenesis model building.","headline":"A coherent and honest phenomenological study of spontaneous leptogenesis in the dynamical scotogenic model, held back only by the free initial Majoron yield that directly fixes the baryon asymmetry; worth refereeing.","tokens_in":23956,"tokens_out":1998,"would_cite":true,"duration_ms":18084,"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 shows that a rolling Majoron generated by spontaneous $U(1)_{B-L}$ breaking can produce the observed baryon asymmetry with right-handed neutrino masses as low as about 600 GeV, while the same sector explains radiative neutrino…","keywords":["spontaneous leptogenesis","scotogenic model","Majoron","baryon asymmetry","inert doublet dark matter","kinetic misalignment","TeV-scale right-handed neutrinos","U(1) B-L"],"falsifier":"A full numerical solution of the coupled equations for the Majoron velocity and the lepton asymmetries, including thermal dissipation of $\\dot\\theta$ and the expansion history, would settle the claim: if $\\dot\\theta$ decays before inverse decays decouple, or if the Universe enters a kination phase before freeze-out, the predicted $Y_B$ falls below $8.7\\times10^{-11}$. Observationally, a future CMB measurement that excludes $\\Delta N_{\\rm eff}\\simeq0.025$ would rule out the sub-eV Majoron component of this scenario.","tokens_in":22960,"feed_emoji":"🌌","tokens_out":6152,"duration_ms":53201,"temperature":0.7,"pith_summary":"The paper proposes that the observed baryon asymmetry of the Universe can be produced not by CP-violating right-handed neutrino decays but by a slowly rolling Majoron, the Goldstone boson of spontaneously broken global $U(1)_{B-L}$, which acts as a time-dependent chemical potential for $B-L$. In the dynamical scotogenic model with two hierarchical right-handed neutrinos and an inert Higgs doublet, this mechanism works precisely in the strong-washout regime where ordinary thermal leptogenesis fails, lowering the viable mass of the lightest right-handed neutrino to $M_1=\\mathcal{O}(600)$ GeV. The same framework already generates radiative neutrino masses and dark matter, so if the mechanism works, one symmetry-breaking sector simultaneously explains neutrino masses, dark matter, and the observed matter-antimatter asymmetry in a way that TeV-scale experiments can test.","feed_headline":"A rolling Majoron can make TeV-scale leptogenesis work","feed_subtitle":"The same symmetry-breaking field yields the baryon asymmetry, neutrino masses, and dark matter together.","key_machinery":"The central object is the Majoron $\\theta(x)=J(x)/v_\\phi$, the pseudo-Nambu-Goldstone boson of the spontaneously broken global $U(1)_{B-L}$ symmetry. Its derivative coupling $-\\frac{1}{2}\\,\\partial_\\mu\\theta\\,J^\\mu_{B-L}$ gives a background $\\dot\\theta$ that acts as an effective chemical potential for $B-L$; the $B-L$-violating decays and inverse decays $N_1\\leftrightarrow\\ell\\eta$ keep the plasma in equilibrium so that a lepton asymmetry is washed in while the Majoron rolls. The final baryon yield is set by $Y_B\\propto Y_\\theta\\,(M_1/v_\\phi)^2/z_{\\rm dec}^2$, with the coefficient $c_B$ fixed by the chemical potentials of the scotogenic plasma. The coupling $\\lambda_5$ does double duty: through the mass splitting of $\\eta_R$ and $\\eta_I$ it controls the one-loop neutrino mass, and through $(\\eta^\\dagger\\Phi)^2$ it determines whether an inert-doublet chemical potential participates in the spectator relations and whether a dark-matter asymmetry survives. The kinetic-misalignment condition $Y_\\theta>Y_{\\rm cr}$ selects the regime where the same rolling Majoron can supply the observed dark matter.","core_discovery":"On the paper's own terms, the discovery is that a rolling Majoron, through its derivative coupling to the $B-L$ current, induces an effective chemical potential that biases the $B-L$-violating decays and inverse decays of the lightest right-handed neutrino, and the resulting lepton asymmetry is converted by electroweak sphalerons into the observed baryon abundance $Y_B\\simeq 8.7\\times10^{-11}$. The key formula is $Y_B=(c_B/6)\\,Y_\\theta\\,(M_1/(v_\\phi z_{\\rm dec}))^2$, where $Y_\\theta=v_\\phi^2\\dot\\theta/s$ is the conserved angular yield of the Majoron, $v_\\phi$ is the $U(1)_{B-L}$ breaking scale, and $z_{\\rm dec}=M_1/T_{\\rm dec}$ is the inverse-decay decoupling point; the coefficient $c_B$ is obtained from chemical-equilibrium and spectator relations, including the role of the $\\lambda_5$ interaction that couples the inert doublet to the Higgs. Because the asymmetry is sourced by the background motion rather than by CP-violating decay amplitudes, the strong washout that suppresses conventional thermal leptogenesis instead helps the plasma track the equilibrium asymmetry, and the lightest right-handed neutrino can be as light as about 600 GeV while still being hierarchical. The same rolling Majoron can later become dark matter through kinetic misalignment, with a sub-eV Majoron that is long-lived and contributes $\\Delta N_{\\rm eff}\\simeq0.025$ as dark radiation.","pith_inferences":["Because the paper treats $Y_\\theta$ as a free initial condition, the mechanism's ultimate viability depends on an explicit ultraviolet source for the Majoron motion; a concrete inflationary or phase-transition origin would complete the story.","The same derivative-coupling trick should work in other radiative neutrino-mass models with a pseudo-Goldstone boson, so the scotogenic structure may be one of several realizations of low-scale spontaneous leptogenesis.","The radiation-domination restriction means a kination phase before freeze-out would alter the final $Y_B$; a dedicated treatment of Majoron-domination could extend the allowed $(v_\\phi, M_1)$ region or sharpen lower bounds on $v_\\phi$.","If future CMB data resolve $\\Delta N_{\\rm eff}$ around 0.025, that would be a distinctive signature distinguishing this scenario from thermal leptogenesis, which predicts no such dark-radiation component from the Majoron."],"forward_implications":["TeV-scale hierarchical right-handed neutrinos ($M_1\\simeq600$ GeV and above) become viable for leptogenesis, opening the right-handed neutrino sector to direct production and to missing-energy or displaced-vertex searches at colliders.","The strong-washout region $K_1\\gg4$, which forbids conventional thermal leptogenesis in the two-right-handed-neutrino scotogenic model, is exactly where spontaneous leptogenesis is most efficient.","The $\\lambda_5$ coupling ties neutrino mass, the inert-scalar dark-matter mass splitting, and the spectator conversion coefficient $c_B$ into one parameter, so measuring one of these quantities informs the others.","A sub-eV Majoron produced by kinetic misalignment can be the dominant dark matter while remaining cosmologically stable, and its thermal population contributes $\\Delta N_{\\rm eff}\\simeq0.025$, which is within the projected sensitivity of future CMB experiments.","Collider searches for inert scalars above roughly 550 GeV and direct-detection bounds on the Higgs-portal coupling constrain the same parameter space that produces the baryon asymmetry."],"supporting_citations":[{"why":"Supplies the scotogenic model itself: two right-handed neutrinos plus an inert doublet, radiatively generated neutrino masses, and an exact $Z_2$-stabilized dark matter candidate.","marker":"[37]"},{"why":"Provides the spontaneous-leptogenesis machinery: the derivative coupling of a rolling Majoron to the $B-L$ current acting as an effective chemical potential.","marker":"[27]"},{"why":"Gives the Boltzmann equation with the $\\dot\\theta/T$ source term used to compute the final $B-L$ asymmetry generated while inverse decays are in equilibrium.","marker":"[24]"},{"why":"Establishes the conventional thermal-leptogenesis lower bound $M_1\\gtrsim10^{11}$ GeV in the two-right-handed-neutrino scotogenic model that this mechanism is designed to bypass.","marker":"[45]"},{"why":"Supplies the kinetic-misalignment mechanism used to compute the Majoron relic abundance and the condition $Y_\\theta>Y_{\\rm cr}$.","marker":"[50]"},{"why":"Provides the standard washout and efficiency framework, including the decay parameter $K_1$ that places the model deep in the strong-washout regime.","marker":"[82]"},{"why":"The Davidson-Ibarra bound on the CP asymmetry in hierarchical thermal leptogenesis, which motivates the search for a low-scale alternative.","marker":"[13]"},{"why":"The original Fukugita-Yanagida leptogenesis mechanism that serves as the baseline conventional scenario.","marker":"[5]"}],"fun_headline_variants":["Rolling Majoron sparks TeV-scale leptogenesis","One Majoron: baryons, neutrino mass, and dark matter","Spontaneous leptogenesis from a rolling Majoron","Rolling Majoron unifies baryogenesis, neutrino mass, and dark matter","TeV-scale leptogenesis via a rolling Majoron"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mechanism needs the Majoron to start rolling with a sizable angular velocity $Y_\\theta$ that stays roughly constant until inverse decays freeze out while the Universe is radiation dominated; if that initial motion is absent or is damped away first, the baryon asymmetry vanishes.","fun_headline_variants_meta":{"raw":{"variants":["Rolling Majoron sparks TeV-scale leptogenesis","One Majoron: baryons, neutrino mass, and dark matter","Spontaneous leptogenesis from a rolling Majoron","Rolling Majoron unifies baryogenesis, neutrino mass, and dark matter","TeV-scale leptogenesis via a rolling Majoron"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00048,"raw_usage":{"total_tokens":2470,"prompt_tokens":1133,"completion_tokens":1337,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":749,"completion_tokens_details":{"reasoning_tokens":1254}},"tokens_in":749,"tokens_out":1337,"duration_ms":9917,"temperature":1.0,"reasoning_tokens":1254,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:08:13.857307+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A full numerical solution of the coupled equations for the Majoron velocity and the lepton asymmetries, including thermal dissipation of $\\dot\\theta$ and the expansion history, would settle the claim: if $\\dot\\theta$ decays before inverse decays decouple, or if the Universe enters a kination phase before freeze-out, the predicted $Y_B$ falls below $8.7\\times10^{-11}$. Observationally, a future CMB measurement that excludes $\\Delta N_{\\rm eff}\\simeq0.025$ would rule out the sub-eV Majoron component of this scenario.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the scotogenic model itself: two right-handed neutrinos plus an inert doublet, radiatively generated neutrino masses, and an exact $Z_2$-stabilized dark matter candidate."}],"review_version":1}