{"id":"af1c97ab-b06e-4339-be25-5db293c73103","arxiv_id":"2411.13231","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"For a Majorana fermion coupled to quarks via a dimension-six vector-vector operator, the observed baryon asymmetry can be reproduced across a wide mass range, with scattering processes dominating and with testable neutron-antineutron oscillation rates.","lead":"This paper solves the early-Universe Boltzmann equations for a baryogenesis model with a Majorana fermion coupled to quark-like fermions, using decay and scattering rates from the authors' previous work. It finds parameter regions that produce the observed matter-antimatter asymmetry and estimates neutron-antineutron oscillation rates accessible to future experiments.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The numerical BAU results depend entirely on unvalidated fit functions for CP-violating rates from Ref [5]; without a direct check, the claimed mass range is not established.","rationale":"The paper's central claim is that the observed BAU can be reproduced in this effective theory over a wide mass range Mχ∈(10^4,10^16) GeV. That is an existence claim, and the couplings are tuned to match Yobs, so the claim is not a prediction. What must be true for the existence claim to hold is that the collision terms—especially the CP-violating rate differences ΔΓ and Δσv—are accurate enough that the tuned parameter regions remain viable. The paper imports these rates from Ref [5] in the form of ad hoc fit functions with no uncertainty estimates, and one of the three benchmark families (BP-C) is not computed from the model at all but constructed by hand. Because YB is linear in ΔΓ and Δσv in the linearized BE (Eq. (17)), even a factor-of-two error in a fit normalization directly changes the required couplings and can shift or close the claimed mass windows. This is the most load-bearing assumption in the paper: every benchmark point and contour in Figs. 4-5 inherits it. No other identified issue is equally structural. The sphaleron washout in Sec. 5 is treated as an adjustable factor, and the vector-operator n-nbar matrix element is acknowledged as an estimate, so both affect quantitative prospects but not the core baryogenesis existence argument. The paper does deserve credit for setting up a complete BE system, including scattering processes that many baryogenesis studies omit, and for clearly exposing the CPT/unitarity structure of the rates. If the exact rates from Ref [5] reproduce the fits to within the accuracy needed, the central claim would be supported; if not, the claimed mass range and the experimental reach derived from it would have to be revised. The reader's weakest_assumption already identified this same structural dependence, and the CONDITIONAL verdict appropriately encodes it until the rate inputs are validated.","tokens_in":28120,"tokens_out":8164,"duration_ms":92867,"concrete_test":"Recompute YB(x_e) for BP-A and BP-B using the exact thermally averaged rates from Ref [5] (evaluated by integrating the Ref [5] matrix elements over initial-state thermal distributions) over x∈[0.1,10], and compare with the Appendix C fit-based solution. If YB shifts by more than a factor of 2, or if the Mχ interval giving YB/Yobs=1 moves by more than a decade, the mass-range claim is not robust; report the ΔΓ and Δσv residuals at the x values that dominate the integral.","verdict_should_be":"UNCHANGED","load_bearing_attack":"All nine benchmark solutions in Sec. 4.2 are obtained by solving the Boltzmann equations with collision terms taken from Appendix C. Eqs. (33)-(35) are explicitly fit functions that 'mimic adequately well the magnitude and x dependence' of the rates computed in Ref [5]; no residuals, error bars, or validation plots are given. The CP-violating input rates ΔΓ and Δσv enter linearly in the YB source term (Eq. (17)), so any error in their normalization or in their x dependence directly rescales YB and therefore rescales the couplings g and Mχ/Λ needed to hit YB/Yobs=1. The claimed range Mχ∈(10^4,10^16) GeV is extracted from contours in Figs. 4-5 built from these fits. Worse, BP-C is not derived from any loop computation: Table 1 assigns it ΔΓ and Δσv normalizations by hand and copies BP-A's x dependence, so results for BP-C do not test the model, only a toy variant. Because the fits are unquantified and the companion rates are not independently verified in this paper, the central existence claim—that this theory explains the observed BAU—is conditional on inputs whose accuracy is unknown.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the authors' earlier effective-theory framework for baryogenesis with a Majorana fermion X coupled to quark-like fermions Q via a dimension-six vector-vector four-fermion operator. The authors set up Boltzmann equations for the X yield and the baryon yield, using thermally averaged decay and scattering rates imported from Ref. [5], including X -> QQQ decay, X Qc -> QQ scattering, and Delta B=2 scattering. They linearize the equations for small YB, solve numerically for nine benchmark points (BP-nX with mass scales M_chi = 10^6, 10^9, 10^12 GeV and rate families A, B, C), and choose the coupling g and mass-to-cutoff ratio M_chi/Lambda so that YB/Y_obs = 1. They find the observed BAU can be obtained for M_chi in (10^4, 10^16) GeV, with scattering processes dominant in families A and B and decay dominant in family C. They also translate the viable low-mass region into neutron-antineutron oscillation rates and compare with Super-Kamiokande and future HIBEAM/NNBAR sensitivity.","tokens_in":28551,"tokens_out":4223,"duration_ms":47075,"significance":"If the central numerical claim holds, the paper provides explicit parameter choices in a concrete effective theory for which the observed BAU is reproduced, and it highlights an experimentally testable low-mass window via n-nbar oscillation. The Boltzmann-equation framework is standard, the linearization in YB is appropriate, and the numerical solutions in Figs. 3-6 appear internally consistent. The authors are also transparent that g and M_chi/Lambda are calibrated to YB/Y_obs = 1, which is parameter fitting rather than a derivation from independent inputs; this is not circular. The main significance is therefore conditional on the reliability of the imported rate functions, which are the load-bearing input to every numerical result. The n-nbar oscillation rate provides a genuinely external observable that could falsify the low-mass part of the claimed parameter space, and the emphasis on scattering over decays is a useful contrast to the usual decay-only treatments.","major_comments":[{"comment":"The paper states that the fit functions in Eqs. (33)-(35) \"mimic adequately well the magnitude and x dependence\" of the rates computed in Ref. [5], but it provides no residuals, validation plots, or uncertainty estimates. Since Delta Gamma and Delta sigma v enter linearly in the source term of Eq. (17), an unquantified error in their normalization or x dependence directly rescales YB and therefore shifts the g and M_chi/Lambda values needed to reach YB/Y_obs = 1. The claimed mass range M_chi in (10^4, 10^16) GeV in Sec. 4.2 is extracted from contours built on these fits, so this is not a cosmetic issue. Please provide a direct comparison of the fit functions to the original computed rates, or give an estimate of the induced error on YB.","section":"Appendix C, Eqs. (33)-(35)"},{"comment":"BP-C is not derived from any loop computation: its Delta Gamma and Delta sigma v normalizations are hand-assigned and its x dependence is copied from BP-A, as stated in Sec. 4.1. The BP-nC families therefore test a toy parameterization rather than the model of Sec. 2, and the statement in the Abstract that \"this theory\" explains the BAU over M_chi in (10^4, 10^16) GeV includes the 10^4 GeV lower bound coming from BP-nB and BP-nC. Either restrict the central model claim to BP-A and BP-B, or justify BP-C as an independent representative of other related theories and clearly label the BP-nC results as such.","section":"Table 1 and Sec. 4.2 (BP-C)"},{"comment":"The sign structure of the source term in Eq. (13), including the imaginary-part and real-intermediate-state cancellations, is imported from Ref. [5] without re-derivation, and the paper notes the sign of the n_X^eq term is opposite to a naive calculation. Given that this sign determines whether the source term has the assumed form, a concise derivation or a reference to the specific equations in Ref. [5] would substantially strengthen the paper. As written, the reader cannot independently verify the most delicate ingredient of the Boltzmann equation.","section":"Eq. (13) and Sec. 5"}],"minor_comments":[{"comment":"There is a typo: \"neucleosynthesis\" should be \"nucleosynthesis\", and in Sec. 5 the phrase \"washed out significantly due by\" should be corrected.","section":"Sec. 6"},{"comment":"The red kappa_nbar contours are hard to distinguish from the BAU contours in Fig. 5; plotting them in a separate panel or with clearer line styles would improve readability. The text states the same kappa_nbar dependence holds for all three columns, but only the right column is shown; a brief explanation of why would be helpful.","section":"Fig. 5 and Sec. 4.3"},{"comment":"The variable x_b is defined as M/\\Lambda only in Appendix B, but it is used earlier in Sec. 4.2. Please define it in the main text or use a consistent notation.","section":"Appendix B, Eq. (29)"},{"comment":"For BP-1B the final YB depends on the initial overdensity delta_X(x_b), and the value delta_X = 8 is chosen to reproduce the observed BAU; this dependence on UV-completion details should be stated prominently when BP-1B is used to support the claimed mass range.","section":"Sec. 4.2 (BP-1B)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a direct continuation of the authors' program, and the self-citation pattern is appropriate given that the rates come from their earlier work. The main technical reservation is the unvalidated nature of the fit functions in Appendix C; if the authors can show that these fits reproduce the rates of Ref. [5] within, say, a few percent across the relevant x range, or can provide error bars that propagate to YB, the central claim would be substantially strengthened. The BP-C family should be either better motivated or excluded from the model-specific mass-range claim. The paper fits the scope of the journal and the topic is of interest to the BAU community."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a genuine extension of the authors' earlier program: the microscopic CP-violating decay and scattering rates were computed in Refs. [4,5], and here they put those rates into Boltzmann equations, solve them numerically, and map the parameter space that gives the observed BAU. The genuinely new results are the demonstration that scattering, not decay, drives the asymmetry in two of the three benchmark families, the new BP-C benchmark that isolates the decay-driven regime, and the neutron-antineutron (n-nbar) oscillation reach overlay. The Boltzmann setup is standard and the linearization about YB=0 is appropriate. If I worked in this area I would cite this paper.\n\nThe soft spots. All the numerical results hang on the fit functions in Eqs. (33)-(35). The paper says they \"mimic adequately well\" the rates computed in the companion paper, but no residuals, error bars, or validation plots are shown. Any error in the normalization or x-dependence of ΔΓ or Δσv directly rescales YB and therefore the couplings needed to hit YB/Yobs=1. The claimed mass range Mχ∈(10^4,10^16) GeV is extracted from contours built on these fits. That is a real weakness, and the stress-test note is right to flag it. It is not fatal—the fits come from actual loop computations in Ref. [5], and a referee can ask for code or validation plots—but it means the central existence claim is conditional on inputs whose accuracy is unquantified. BP-C is more of a toy: its x-dependence is copied from BP-A and its normalizations are hand-picked, so results there illustrate a regime rather than test the model.\n\nTwo smaller caveats. The BAU is used to fix couplings, so this is parameter-space existence, not prediction; the authors are appropriately careful about that, and the n-nbar handle provides an independent check. Sphaleron washout (Sec. 5, via the survival fraction αw) and the Fierz-rearranged n-nbar matrix element add unquantified uncertainties.\n\nWho this is for: baryogenesis practitioners, especially those working on EFTs where scattering contributions are often ignored. The scattering-dominance result is the most useful observation in the paper.\n\nRecommendation: send it to peer review, with a referee asked to validate the rate fits—either by checking them against the Ref. [5] computations with error estimates, or by requesting the numerical code. If the fits check out, the paper is a solid, citable model-building contribution. If they don't, the mass range is not established. So: conditional acceptance, with fit validation as the load-bearing condition.","headline":"A legitimate Boltzmann-equation extension of the authors' earlier rate computations, with a novel scattering-dominance result and a useful n-nbar reach overlay, but the central mass-range claim rests on unvalidated fit functions from the companion paper.","tokens_in":29023,"tokens_out":2912,"would_cite":true,"duration_ms":29844,"reading_group":"yes","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 a Majorana fermion coupled to quark-like fermions through a dimension-six vector-vector interaction can generate the observed baryon asymmetry of the Universe from a baryon-symmetric start, over a mass range from…","keywords":["baryogenesis","baryon asymmetry of the Universe","Majorana fermion","dimension-six effective operator","Boltzmann equations","neutron-antineutron oscillation","CP violation","early Universe"],"falsifier":"Compute the exact one- and two-loop thermally averaged rates for the decay, scattering, and $\\Delta B=2$ channels at the benchmark points and re-solve the Boltzmann equations; if the resulting yield contours move away from $Y_B^{\\rm obs}$ by more than the observational precision, the claimed mass range is not robust. Alternatively, a null result from a neutron-antineutron oscillation search reaching the sensitivity the paper associates with $M_\\chi\\sim 10^4$–$10^6$ GeV would rule out the low-mass branch of the viable parameter space.","tokens_in":27870,"feed_emoji":"🌌","tokens_out":6407,"duration_ms":57682,"temperature":0.7,"pith_summary":"This paper argues that a single effective theory—a Majorana fermion $X$ coupled to quark-like fermions $Q$ through a dimension-six four-fermion vector-vector interaction—can generate the observed baryon asymmetry of the Universe starting from a baryon-symmetric state. The authors set up the Boltzmann equations for the $X$ and net baryon number densities in the expanding early Universe, import the thermally averaged decay and scattering rates from their earlier computation, and solve the equations numerically at nine benchmark points. They find that the observed yield $Y_B \\approx 0.85\\times10^{-10}$ is reproduced for masses $M_\\chi\\in(10^4,10^{16})$ GeV with appropriately chosen couplings, and that scattering processes play the dominant role in two of the three benchmark classes. The low-mass end of this region predicts neutron-antineutron oscillation rates that upcoming experiments could test, which is why the claim matters beyond cosmology.","feed_headline":"Scattering, not decay, can seed the Universe's matter excess","feed_subtitle":"Boltzmann solutions tie a Majorana fermion's mass from 10^4 to 10^16 GeV to the observed baryon asymmetry.","key_machinery":"The load-bearing object is the dimension-six four-fermion vector-vector effective operator $(g/\\Lambda^2)(\\overline{D^c}\\gamma_\\mu D)(\\bar{X}\\gamma^\\mu U)$, with a Majorana mass splitting for the fermion $X$ that violates baryon number and supplies the CP-violating phases. The cosmological machinery is the pair of coupled Boltzmann equations for the yield $Y_X=n_X/s$ and $Y_B=n_B/s$, whose collision terms are the thermally averaged rates for decay $X\\to QQQ$, scattering $X Q^c\\to QQ$, and $\\Delta B=2$ scattering $QQQ\\to Q^c Q^c Q^c$, together with their conjugate and inverse processes. A CPT-unitarity relation, imported from the earlier study, fixes the sign of the inverse-decay contribution and turns the departure of $Y_X$ from equilibrium into a net baryon number. The terrestrial probe is the neutron-antineutron oscillation rate $\\Delta m_{n\\bar n}=g^2 s_{\\rm eff}^2/(\\Lambda^4 M_\\chi)\\,\\langle\\bar n|Q_{VV}|n\\rangle$, which connects the BAU-compatible parameter region to experiments.","core_discovery":"The central claim is that, beginning from a baryon-antibaryon symmetric early Universe, the decay and scattering of a pseudo-Dirac Majorana fermion $X$ with quark-like partners $Q$ can produce the presently observed baryon asymmetry over a very wide range of mass scales. Solving the coupled Boltzmann equations for $Y_X(x)$ and $Y_B(x)$ with the thermally averaged rates of Ref. [5], the paper exhibits explicit benchmark points where the asymptotic yield equals $Y_B^{\\rm obs}\\approx 0.85\\times10^{-10}$. In benchmark classes BP-A and BP-B the asymmetry builds up mainly through the scattering channel $X\\,Q^c\\to QQ$; in BP-C, constructed with a suppressed scattering rate, decay $X\\to QQQ$ dominates. The paper further derives the induced neutron-antineutron oscillation rate in the viable region and maps the current Super-Kamiokande bound onto the parameter space, showing that the lower mass branch is already being probed.","pith_inferences":["Because the Boltzmann solutions rely on fit functions that only mimic the loop rates and carry no uncertainty estimates, the claimed mass range should be read as indicative; a direct evaluation of the exact thermally averaged rates is the natural next test.","BP-C is constructed by copying BP-A's $x$-dependence with rescaled normalizations, so its 'decay-dominated' conclusion is less independent than the BP-A/BP-B results and should be treated as an illustrative scenario.","The neutron-antineutron reach currently uses a Fierz-rearranged scalar-operator lattice matrix element; a direct lattice computation for the vector operator would sharpen or shift the mass reach shown in the paper.","The same Boltzmann framework, with the rates replaced, could be applied to other four-fermion operators (for example scalar-scalar interactions), which the paper's model-independent presentation invites."],"forward_implications":["If the central claim is right, the observed baryon asymmetry can be produced by new physics at any mass between roughly $10^4$ and $10^{16}$ GeV, so low-energy experiments, not just high-energy colliders, can test baryogenesis.","In the BP-A and BP-B benchmark classes, scattering generates most of the asymmetry; any related theory that keeps only decay channels would underestimate the yield and misidentify the viable parameter region.","The low-mass branch, $M_\\chi\\sim 10^4$–$10^6$ GeV, predicts neutron-antineutron oscillation rates within about three orders of magnitude of the current Super-Kamiokande bound, so next-generation searches have a concrete target.","If electroweak sphalerons partially wash out the generated baryon number, the viable parameter contours shift to the $1/w_{\\rm tot}$ level, but the mechanism still has regions that reproduce the observed asymmetry."],"supporting_citations":[{"why":"Supplies the effective theory, the baryon number assignments, and the neutron-antineutron operator used in the analysis.","marker":"[4]"},{"why":"Provides the thermally averaged decay and scattering rates and their temperature dependence used as collision terms in the Boltzmann equations.","marker":"[5]"},{"why":"Establishes the CPT and unitarity sign relation for inverse decay that is built into the Boltzmann equation.","marker":"[14]"},{"why":"Supplies the lattice QCD matrix element used to estimate the neutron-antineutron oscillation rate.","marker":"[27]"},{"why":"Gives the Super-Kamiokande bound that defines the current experimental sensitivity benchmark.","marker":"[24]"},{"why":"Describes the future HIBEAM/NNBAR sensitivity used for the reach projections.","marker":"[26]"},{"why":"Provides the early-Universe thermodynamics and Boltzmann-equation formalism the paper follows.","marker":"[2]"}],"fun_headline_variants":["Scattering drives baryon excess from Majorana quark coupling","Boltzmann solutions tie fermion mass to matter asymmetry","Neutron oscillation probes baryogenesis window","Baryon asymmetry from Majorana fermion decays and scattering","Matter excess explained by Majorana fermion over wide mass range"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the thermally averaged rates imported from the earlier work—especially the CP-violating differences $\\Delta\\Gamma$ and $\\Delta\\sigma v$ and the $\\Delta B=2$ rate $\\Gamma_1$—are represented accurately enough by the fit functions used here. The fits are said only to mimic the magnitude and $x$ dependence, with no uncertainty estimates, and BP-C's $x$-dependence is copied from BP-A; if the true rates differ, the computed baryon yield, the claimed mass range, and the neutron-antineutron reach all shift.","fun_headline_variants_meta":{"raw":{"variants":["Scattering drives baryon excess from Majorana quark coupling","Boltzmann solutions tie fermion mass to matter asymmetry","Neutron oscillation probes baryogenesis window","Baryon asymmetry from Majorana fermion decays and scattering","Matter excess explained by Majorana fermion over wide mass range"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00017,"raw_usage":{"total_tokens":1298,"prompt_tokens":1007,"completion_tokens":291,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":623,"completion_tokens_details":{"reasoning_tokens":211}},"tokens_in":623,"tokens_out":291,"duration_ms":3620,"temperature":1.0,"reasoning_tokens":211,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:41:51.952185+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact one- and two-loop thermally averaged rates for the decay, scattering, and $\\Delta B=2$ channels at the benchmark points and re-solve the Boltzmann equations; if the resulting yield contours move away from $Y_B^{\\rm obs}$ by more than the observational precision, the claimed mass range is not robust. Alternatively, a null result from a neutron-antineutron oscillation search reaching the sensitivity the paper associates with $M_\\chi\\sim 10^4$–$10^6$ GeV would rule out the low-mass branch of the viable parameter space.","supporting_citations":[{"cited_title":"Effective Theory for Baryogenesis with a Majorana Fermion Pair Coupled to Quarks","cited_arxiv_id":"2211.12115","evidence_quote":"Supplies the effective theory, the baryon number assignments, and the neutron-antineutron operator used in the analysis."},{"cited_title":"Baryon Asymmetry from the Decay and Scattering of a Majorana Fermion Pair Coupled to Quarks","cited_arxiv_id":"2311.14636","evidence_quote":"Provides the thermally averaged decay and scattering rates and their temperature dependence used as collision terms in the Boltzmann equations."},{"cited_title":"Neutron-antineutron oscillation search using a 0.37 megaton-years exposure of Super-Kamiokande,","cited_arxiv_id":null,"evidence_quote":"Gives the Super-Kamiokande bound that defines the current experimental sensitivity benchmark."}],"review_version":1}