{"id":"0c6942e7-934f-40c8-b18c-44f0f9ef9137","arxiv_id":"2507.11532","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Scatterings of heavy particles off a hot bath can grow faster than cosmic expansion and efficiently produce the observed matter-antimatter asymmetry, even with small couplings.","lead":"This paper proposes a new way to generate the matter-antimatter asymmetry of the universe, using scatterings whose rates grow relative to cosmic expansion as the universe cools. The mechanism could make baryogenesis work at lower energy scales, potentially closer to experimental reach.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Super-criticality hinges on a single unverified tree-level topology for X2ρ→X1ρ; if the charge assignments do not forbid the second diagram, the 1/k_CM^2 scaling cancels and the mechanism collapses.","rationale":"The reader's weakest_assumption correctly identifies the tree-level topology of X2ρ→X1ρ as the load-bearing structural condition for super-criticality. Every other issue in the paper, such as the ad hoc cutoff in the CP asymmetry computation or the deferred non-perturbative CP violation, affects the numerical benchmark but not the qualitative mechanism; if the 1/k_CM^2 scaling is absent, the central claim fails regardless of those details. I therefore agree with the reader's choice. The proposed check is concrete and decisive: it directly tests the charge-conservation selection of tree diagrams and the persistence of the 1/k_CM^2 scaling when the mass splitting is retained. Because the concern is presently unresolved but addressable by an explicit calculation, the verdict should remain CONDITIONAL rather than ACCEPT or REJECT.","tokens_in":17639,"tokens_out":37168,"duration_ms":437929,"concrete_test":"From the Lagrangian in Eq. (3), write the explicit Feynman rules for the ρ† \\bar{X^c} X and ρ \\bar{X} X^c vertices, draw all tree-level diagrams for X2 ρ(∗) → X1 ρ(∗) and for the CP-conjugate process, and check charge conservation at each vertex by assigning incoming charge = outgoing charge under the U(1)_{B−L} current. Then compute the squared amplitude at leading order in k_CM/m_X without taking Δm_X → 0, using the mass eigenvalues m1, m2. If more than one diagram survives, sum them and verify whether the 1/k_CM^2 leading terms cancel. A positive outcome (single diagram, no cancellation) confirms the super-critical scaling; any surviving destructive interference disproves it.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (3) defines the Yukawa interactions with ρ† \\bar{X^c} X. The entire super-critical mechanism depends on the assertion (between Figs. 1 and 2) that the U(1)_{B−L} charges −1 for X_i and −2 for ρ leave only one of the s- and u-channel fermion-exchange diagrams for X2ρ→X1ρ, so that the two leading 1/k_CM pieces do not cancel and σ ∝ 1/k_CM^2. This is the structural reason n < −1. The paper does not display the explicit charge-flow analysis; the Appendix B cross-sections are quoted in the Δm_X→0 limit, which obscures the propagator structure. If both diagrams are actually present (e.g., because the exchanged particle can be an antiparticle with charge +1 in the u-channel), the leading terms cancel and σ becomes k-independent, reducing the rate to sub-Hubble. Since the benchmark and the 'super-critical' label in the abstract both rest on this scaling, this is the single most load-bearing assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper identifies a class of early-universe scattering processes in which the rate per non-relativistic particle can grow relative to the Hubble rate as the universe cools. Parametrizing the thermally averaged cross-section as <σv> ∝ T^n, the authors call n=-1 critical and n<-1 super-critical. The general argument is clean: a non-relativistic particle scattering off a relativistic bath with σ ∝ 1/k_CM^2 has Γ = n_T<σv> ∝ T, while H ∝ T^2. As a concrete realization, they construct a U(1)_{B-L} model with two heavy Dirac fermions X1,X2 (charge -1) and a complex scalar ρ (charge -2), in which CP-violating X2ρ→X1ρ scattering is claimed to have σ ∝ 1/k_CM^2, producing a rapidly growing asymmetry that freezes out when X2 is depleted. A Boltzmann calculation with a benchmark parameter set yields an asymmetry near the observed value. The paper also addresses thermal corrections to the X mass matrix and the IR-divergent t-channel V_μ exchange.","tokens_in":17899,"tokens_out":22569,"duration_ms":288842,"significance":"The general scaling argument is simple, correct, and potentially important: it shows that scattering processes need not become inefficient in an expanding universe if the target is relativistic and the cross-section grows fast enough, and it correctly notes that this evades the unitarity obstruction that applies to non-relativistic DM annihilation. If the model's topology claim holds, the mechanism offers a new and efficient route to baryogenesis/leptogenesis with possibly smaller couplings and lower scales. The manuscript is largely self-contained, with explicit appendices for decay rates, cross-sections, thermal mass corrections, and the Boltzmann decomposition. The main caveats are that the crucial topology assertion is not demonstrated and the numerical illustration is a benchmark fit rather than a predictive scan.","major_comments":[{"comment":"The entire super-critical behavior in the model rests on the statement that the U(1)_{B-L} charges of X_i (-1) and ρ (-2) leave only one of the s- and u-channel fermion-exchange diagrams for X2ρ→X1ρ, so that the two leading 1/k_CM contributions do not cancel and σ ∝ 1/k_CM^2. This claim is asserted but not demonstrated. Table III quotes cross-sections only in the Δm_X→0 limit, which obscures the propagator structure. Please provide an explicit charge-flow or amplitude-level demonstration that exactly one diagram contributes, and in particular rule out an antiparticle-exchange (crossed) diagram; if both diagrams contribute, the leading 1/k_CM terms cancel and the super-critical scaling disappears.","section":"Figs. 1-2 and the text between them"},{"comment":"The t-channel V_μ exchange divergences are regularized by introducing an angular cutoff θ_min and retaining only the finite parts (I1≈-2ln2, I2≈-1/3). No physical regulator (Debye screening, thermal width) is introduced, and no proof of scheme independence is given. Since the CP asymmetry coefficients in Table III contain terms proportional to g_{B-L}^2 ln2, the size of ε and hence the final asymmetry shown in Fig. 3 may depend on this ad hoc prescription. Please replace the cutoff by a physical regulator or demonstrate that the quoted results are regulator-independent.","section":"Appendix B, Eqs. (B5)-(B6)"},{"comment":"The benchmark parameters in Table I are chosen so that the final asymmetry matches the observed value; the numerical agreement is therefore an illustration, not a prediction. The abstract and discussion claim that the mechanism is efficient 'even at low scales and with small couplings,' but the benchmark uses m1=30 PeV and no parameter scan is presented. A scan or at least a sensitivity estimate in (m1, Δm_X, α_ij) is needed to support the low-scale claim and to show that the freeze-out behavior in Fig. 3 is generic rather than selected.","section":"Results, Table I and Fig. 3"}],"minor_comments":[{"comment":"The definition of Y just above Table III is garbled by the typesetting ('Y≡16· |y11y∗12+ y12y∗22|2'); it should read |y11 y12^* + y12 y22^*|^2 (or whichever combination is intended) so that the cross-sections can be checked.","section":"Table III, definition of Y"},{"comment":"Equation (11) quotes d ln ΔX/d ln x ≈ -α11 α_B-L M_Pl/m1 without a numerical coefficient or derivation; please provide the numerical factor or a reference.","section":"Eq. (11)"},{"comment":"The statement in Eq. (12) that |Δρ| ≃ |ε| Y_1^FO is presented as a numerical observation; it would be useful to state whether this is a fitted relation or a derived consequence of the Boltzmann system.","section":"Eq. (12)"},{"comment":"There are several typographical artifacts in the text, including 'raison d'ˆetre' in the Discussion and the typesetting of T_{B-L} in the cosmology section; a careful proofreading pass would improve readability.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The general scaling argument is solid and the paper is likely to be of interest to the hep-ph community. The main risks are the model-specific topology claim and the regulator dependence of the CP asymmetry; both are fixable in a revision. I would be comfortable with a major revision that adds an explicit amplitude-level proof of the one-diagram topology and a physical treatment of the IR divergences. The benchmark agreement with the observed baryon asymmetry should be framed as an illustration rather than a prediction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"New here is the scaling observation, and it is a good one: scatterings of non-relativistic heavy particles off a relativistic bath can have rates that do not fall below Hubble, provided the thermally averaged cross-section grows like T^n with n ≤ -1. For n < -1 the rate inevitably overtakes H at low T, and this is consistent with unitarity, unlike the DM-annihilation case where γ ≥ 3 runs into the unitarity bound. That is a conceptually new handle on baryogenesis, and the paper builds a concrete U(1)_{B−L} model with two Dirac fermions and a charged scalar to realize it.\n\nThe Boltzmann machinery is handled with care. The authors integrate the full set of equations, track flavor and total asymmetries, and check thermal corrections to the X mass matrix; those corrections are shown to be small in the parameter region used. The identification of X2ρ→X1ρ scattering as the super-critical driver, and the freeze-out when X2 is depleted, is coherent.\n\nThe soft spots are real but mostly addressable. The most load-bearing is that the 1/k^2 scaling rests on the assertion that the charge assignments forbid one of the two s/u fermion-exchange diagrams, so the leading 1/k_CM pieces do not cancel. The paper states this but never shows the charge-flow analysis; the Table III cross-sections are quoted in the Δm_X→0 limit, which obscures the propagator structure. I could not rule out the stress-test worry from the text alone. A referee should demand the explicit derivation. Second, the CP-violating coefficients use an angular cutoff in the t-channel Vµ exchange and keep only the finite parts. That is ad hoc; a proper treatment with thermal masses for Vµ is needed before the numerical CP asymmetries are trustworthy. Third, the benchmark parameters are chosen to hit the observed asymmetry, so this is an existence proof, not a prediction. Fourth, a significant part of the model's CP violation (the long-range resummed processes) is deferred to a companion paper; the present results cover only perturbative CP violation.\n\nNone of these is a demonstrated collapse of the mechanism. But the paper, as written, does not close the loop on the two most important points: the topology that gives 1/k^2, and the IR behavior of the Vµ loop. Both are checkable, and a serious referee is the right way to get them checked. I would accept this for peer review and send it to someone who can verify the charge-flow argument and the IR regularization. If those survive, this is a solid contribution that opens up a new class of low-scale asymmetry models.","headline":"New scaling route to asymmetry generation that deserves a referee, but the concrete model has two load-bearing gaps: the s/u topology proof and the Vµ IR cutoff.","tokens_in":18447,"tokens_out":5358,"would_cite":true,"duration_ms":69693,"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":"A class of scatterings with rates that grow as the universe cools can generate the observed cosmic matter excess.","keywords":["baryogenesis","leptogenesis","CP violation","scattering rates","super-critical scattering","early universe cosmology","U(1)B-L model","Boltzmann equations"],"falsifier":"Compute the tree-level amplitude for $X_i \\rho \\to X_j \\rho$ with generic $U(1)$ charges, allowing both $s$- and $u$-channel fermion exchanges: if the $1/k_{\\mathrm{CM}}$ terms cancel and the thermally averaged cross-section stops growing as $1/T^2$, the claimed super-critical rate does not occur. A second check is to vary parameters until the condition of Eq. (6) is violated; the resulting O(1) thermal mixing would rotate the mass eigenstates and quench the asymmetry below the observed baryon-to-entropy ratio.","tokens_in":17383,"feed_emoji":"🌌","tokens_out":10997,"duration_ms":127036,"temperature":0.7,"pith_summary":"Baryogenesis and leptogenesis usually assume that scattering rates fall behind the Hubble expansion as the universe cools, leaving decays to do the work. The paper identifies a class of scatterings between non-relativistic heavy fermions and a relativistic scalar bath for which the opposite happens: the cross-section grows as $1/T^2$, so the scattering rate decreases only as $T$ while the Hubble parameter decreases as $T^2$. In a minimal $U(1)_{B-L}$ extension of the Standard Model, gauge-charge assignments forbid the $s$- and $u$-channel destructive interference that normally makes such amplitudes momentum-independent, and the CP-violating downscattering $X_2 \\rho \\to X_1 \\rho$ consequently becomes super-critical. The authors solve the coupled Boltzmann equations and show that the asymmetry generated this way freezes out only when the heavier fermion is depleted, reproducing the observed baryon-to-entropy ratio with small couplings at a 10 PeV scale.","feed_headline":"Scatterings that beat cosmic expansion can explain matter","feed_subtitle":"Falling temperatures make these particle scatterings stronger, so asymmetry generation stays efficient at low energies.","key_machinery":"The machinery is the interaction topology forced by $U(1)_{B-L}$ charge assignments: $\\rho$ carries charge $-2$, and $X_1$ and $X_2$ carry charge $-1$. For a non-relativistic $X$ and a relativistic $\\rho$, each of the $s$- and $u$-channel fermion-exchange diagrams in $X_i \\rho \\to X_j \\rho$ contributes $\\delta M \\propto 1/k_{\\mathrm{CM}}$ at leading order, but if both channels are present their leading terms cancel destructively, leaving a momentum-independent amplitude. The charge assignment admits only one channel per flavour-changing process, so no cancellation occurs and the cross-section scales as $1/k_{\\mathrm{CM}}^2$, i.e. as $1/T^2$ in the bath; with $n_\\rho \\propto T^3$ the rate $R \\propto T$, while $H \\propto T^2/M_{\\mathrm{Pl}}$. This 'super-critical' scaling is what lets the scattering rate outlive the Hubble rate. The companion processes $X_i V_\\mu \\leftrightarrow \\bar X_j \\rho$ have one gauge vertex, which is momentum suppressed, giving $\\sigma \\propto 1/k_{\\mathrm{CM}}$ and a critical rate $\\propto H$; these together with $X_2 \\to \\bar X_1 \\rho$ deplete the heavier species and freeze out the asymmetry.","core_discovery":"The central claim is that particle-number- or CP-violating scatterings with thermally averaged cross-sections scaling as $T^n$ with $n \\le -1$ can drive asymmetry generation more efficiently than decays, because their rates track or overtake the Hubble rate at late times. For $n=-1$ the rate is Hubble-like ('critical'); for $n<-1$ it inevitably exceeds Hubble ('super-critical'), regardless of coupling strength. The paper realizes this in a two-flavour $U(1)_{B-L}$ model with heavy Dirac fermions $X_1, X_2$ at roughly 10 PeV and a complex scalar $\\rho$: the charge assignments leave only one of the $s$- and $u$-channel fermion-exchange diagrams available for $X_i \\rho \\to X_j \\rho$, so the leading $1/k_{\\mathrm{CM}}$ terms do not cancel and $\\sigma \\propto 1/k_{\\mathrm{CM}}^2$, or $1/T^2$ after thermal averaging. The CP-violating process $X_2 \\rho \\to X_1 \\rho$ seeds a flavour asymmetry that becomes a global $B-L$ asymmetry, with freeze-out set by depletion of $X_2$; the benchmark numerical solution yields $|\\Delta_\\rho| \\approx |\\varepsilon| Y_1^{\\mathrm{FO}}$, close to maximal efficiency, and matches the observed $Y_B$. Unlike super-critical dark-matter annihilation, the relativistic-target kinematics requires only $\\gamma \\ge 1$, consistent with unitarity at low momentum.","pith_inferences":["Beyond the paper: a purely group-theoretic diagnostic could classify $U(1)$ charge assignments by whether the $s$- and $u$-channel topologies interfere, turning the mechanism into a model-selection criterion.","Beyond the paper: if the mechanism is generic, low-scale searches for $B-L$ gauge bosons and CP-odd scalars become telling probes, because the couplings need not be small enough to suppress the scattering rate.","Beyond the paper: the same rate-scaling logic suggests that scatterings with $n<-1$ could dominate other rare processes at late times, so bounds on washout should be re-derived in models with scalar mediators carrying gauge charge."],"forward_implications":["Asymmetry generation can remain efficient down to scales well below the heavy fermion mass, because the scattering rate grows rather than decays as temperature drops.","The required CP-violating phases and $B-L$-violating couplings can be much smaller than in ordinary decay-based leptogenesis, since the super-critical rate overtakes Hubble independently of the coupling strength.","Freeze-out is fixed not by the expansion rate but by the depletion of the heavier fermion population through decays and critical scatterings.","Models in which the CP-violating scalar mediator carries a gauge charge and participates in symmetry breaking should generically exhibit the same super-critical dynamics.","The same mechanism can serve asymmetric dark matter and low-scale leptogenesis scenarios, where only one relativistic target species is needed."],"supporting_citations":[{"why":"Introduces (super-)critical annihilations in dark-matter production and supplies the thermal-exponent language $n \\le -1$ that this paper adapts to scatterings on relativistic targets.","marker":"[18]"},{"why":"Shows that $\\sigma \\propto 1/k_{\\mathrm{CM}}^\\gamma$ with $\\gamma \\ge 3$ in dark-matter annihilation violates unitarity at low momentum, providing the contrast for why $\\gamma \\ge 1$ here is consistent.","marker":"[19]"},{"why":"Demonstrates how proper unitarization restores dark-matter freeze-out, framing why the relativistic-target version avoids the unitarity pathology.","marker":"[20]"},{"why":"Establishes sphaleron reprocessing of lepton number into baryon number, required to connect the generated $B-L$ asymmetry to the observed baryon asymmetry.","marker":"[23]"},{"why":"Cutkosky rules are the method used to compute the one-loop CP asymmetry coefficients $\\varepsilon$ in Table III.","marker":"[25]"},{"why":"Supplies the standard thermal-averaging procedure with the Møller velocity that underlies the Boltzmann rates.","marker":"[26]"},{"why":"Provides the numerical implementation of thermal averaging used in the computations.","marker":"[27]"},{"why":"Gives the thermal field theory formalism used to derive the temperature-dependent $X$ mass matrix and to assess thermal mixing.","marker":"[33–35]"},{"why":"Defines the finite-temperature mass shift used in the non-relativistic self-energy calculation of Appendix C.","marker":"[34]"}],"fun_headline_variants":["Scatterings that beat cosmic expansion can generate matter","Cooling universe ramps up scatterings, producing matter asymmetry","Super-critical scatterings: a new source of matter-antimatter imbalance","When collisions outpace cosmic expansion, matter appears","Falling temperatures amplify scatterings, seeding the matter surplus"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mechanism rests on the charge assignments under $U(1)_{B-L}$ leaving only one of the $s$- and $u$-channel fermion-exchange diagrams, so the leading $1/k_{\\mathrm{CM}}$ terms in the amplitude do not cancel; if both channels contribute, or if thermal mixing restores the interfering topology, the cross-section becomes momentum-independent and the super-critical growth is lost.","fun_headline_variants_meta":{"raw":{"variants":["Scatterings that beat cosmic expansion can generate matter","Cooling universe ramps up scatterings, producing matter asymmetry","Super-critical scatterings: a new source of matter-antimatter imbalance","When collisions outpace cosmic expansion, matter appears","Falling temperatures amplify scatterings, seeding the matter surplus"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000398,"raw_usage":{"total_tokens":2082,"prompt_tokens":942,"completion_tokens":1140,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":558,"completion_tokens_details":{"reasoning_tokens":1058}},"tokens_in":558,"tokens_out":1140,"duration_ms":14790,"temperature":1.0,"reasoning_tokens":1058,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:09:52.273640+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the tree-level amplitude for $X_i \\rho \\to X_j \\rho$ with generic $U(1)$ charges, allowing both $s$- and $u$-channel fermion exchanges: if the $1/k_{\\mathrm{CM}}$ terms cancel and the thermally averaged cross-section stops growing as $1/T^2$, the claimed super-critical rate does not occur. A second check is to vary parameters until the condition of Eq. (6) is violated; the resulting O(1) thermal mixing would rotate the mass eigenstates and quench the asymmetry below the observed baryon-to-entropy ratio.","supporting_citations":[{"cited_title":"Petraki, A","cited_arxiv_id":null,"evidence_quote":"Demonstrates how proper unitarization restores dark-matter freeze-out, framing why the relativistic-target version avoids the unitarity pathology."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the finite-temperature mass shift used in the non-relativistic self-energy calculation of Appendix C."}],"review_version":1}