{"id":"3a96678b-e476-4265-9161-bfafa801f78f","arxiv_id":"1908.05685","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Thermal corrections to a mediator mass can open kinematically forbidden decays and produce dark matter, with a relic abundance nearly independent of the dark matter mass for renormalizable couplings.","lead":"A process called 'forbidden freeze-in' can make dark matter when a mediator particle gains a large thermal mass in the hot early Universe, so it can decay into dark matter even though the decay is impossible at zero temperature. The paper derives the relic abundance for this process and finds new allowed regions in a dark Higgs portal model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Forbidden-freeze-in production peaks below x=0.1, where the code assumes S is in equilibrium; the scan permits A and λHS as small as 1e-8, and footnote 16's assertion that this is always safe is not verified point-by-point.","rationale":"The reader's weakest_assumption is that S is in chemical equilibrium at early times, and my independent read identifies the same spot as the most load-bearing condition. The geometric point that makes it acute is quantitative: in the forbidden regime the production peak lies at x < 0.1 whenever α ≲ 0.3, which is precisely the region where the code substitutes an equilibrium S abundance instead of solving its Boltzmann equation. Since the scan admits A and λHS as small as 1e-8, the portal interaction may be far too weak to establish chemical equilibrium before production begins, and footnote 16's reassurance is not backed by a per-point check. I do not see an internal inconsistency or a flaw in the general thermal-mass derivation; the paper gives a clear analytic setup, a plausible model, and several cross-checks such as the subdominance of 2→2 production. The weakness is therefore a conditional one: the forbidden regions as plotted are only robust if the equilibrium condition is imposed or shown to hold. The reader's CONDITIONAL verdict is the right level, so I leave it unchanged rather than escalating to rejection.","tokens_in":20291,"tokens_out":11333,"duration_ms":124525,"concrete_test":"For every scan point classified as forbidden freeze-in, compute the S↔SM number-changing rate Γ_eq(T) = n_S^eq(T)⟨σv(SS→HH)⟩ at T_peak = 2mχ/(α⟨z⟩) and at T = 10mS, and compare it with H(T). If any forbidden-region points have Γ_eq < H, rerun the relic-density calculation for those points with n_S(x_R) = 0 and the full coupled Boltzmann equations including SS→HH and H†H→SS production; if the yχ required for Ωh^2 shifts by more than ~50%, the forbidden band in Figs. 3b and 8 requires an explicit equilibrium cut and the paper should state that condition.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central mechanism requires that, at the temperatures where S→χχ is kinematically opened by the thermal mass, the mediator S has an equilibrium abundance and a thermal mass mS,T^2 = mS^2 + α^2 T^2. In the forbidden regime mS < 2mχ with small α, the production peaks at x = mS/T ≈ 0.17 α mS/mχ, which is below 0.1 whenever α ≲ 0.3. The numerical setup in Sec. 3.2 assumes S traces its equilibrium abundance for x < 0.1 and only solves the coupled Boltzmann equations for x > 0.1, so essentially all forbidden-freeze-in production is computed under an assumed equilibrium S population. The scan in Table 1 allows A and λHS down to 1e-8; for such portal couplings, the S↔SM number-changing rates, which scale roughly as λHS^2 T in the symmetric phase, can fall below H at the production peak T_peak ≈ 2mχ/(α⟨z⟩), which can be hundreds of GeV for mS ~ GeV and α ~ 0.01. Footnote 16 explicitly concedes that the thermal mass formula (2.3) fails once S is chemically frozen out and then asserts, without a scan-level check, that this caveat does not affect the studied model. If S is underabundant at early times, the DM yield from S decay is suppressed relative to eq. (2.23), and the quoted yχ values and relic-density contours for the small-portal part of the forbidden region are not reliable. This does not invalidate the generic forbidden-freeze-in mechanism for benchmark points with sufficiently large λHS, but it makes the presented model region conditional on an unverified equilibrium assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces and studies a 'forbidden freeze-in' mechanism for dark matter production. The central observation is that a mediator S in thermal equilibrium with the Standard Model bath develops a temperature-dependent mass m_{S,T}^2 ≈ m_S^2 + α^2 T^2; even if the vacuum decay S→χχ is kinematically forbidden (m_S < 2m_χ), it becomes allowed at high temperature. In Sec. 2 the authors derive analytic estimates for the DM yield. For dimension-four operators the yield is nearly independent of m_χ and the required Yukawa coupling y_χ is larger than in standard freeze-in; for higher-dimensional operators production is dominated at high temperatures. In Sec. 3 they implement this in a dark Higgs portal model with Dirac fermion dark matter, solve the coupled S/χ Boltzmann equations, scan the parameter space with MultiNest, and apply BBN, SN1987, CHARM, E949, LHCb, FASER, and SHiP constraints, finding new viable regions in the m_S–m_χ–λ_S–y_χ parameter space.","tokens_in":20762,"tokens_out":10599,"duration_ms":104381,"significance":"The forbidden freeze-in mechanism is a genuinely useful generalization of freeze-in: it is generic whenever a bath particle has a sizable thermal self-mass, and it produces distinctive phenomenology, notably a relic abundance nearly independent of m_χ and a stronger DM–mediator coupling than standard freeze-in. The closed-form limits in Eqs. (2.19) and (2.23) are clearly derived and reproduce the correct limiting behavior in Fig. 3, and the presentation of the experimental constraints is a service to the community. The use of the observed Ωh² as an external constraint is standard and not circular. However, the quantitative results of the scan are conditional on a chemical-equilibrium assumption for S that is not verified for the smallest allowed portal couplings, and the analytic thermal-mass formula omits a contribution that is not negligible in part of the scanned model range; these points must be addressed before the model regions can be considered robust.","major_comments":[{"comment":"The numerical setup assumes S is in chemical equilibrium for x < 0.1 and only solves the coupled S–χ Boltzmann equations for x > 0.1. For the forbidden regime, production peaks at z ≈ ⟨z⟩ = 0.34, i.e. at T_peak ≈ 2m_χ/(α⟨z⟩). With the ranges in Table 1 this can exceed 10^4 GeV for m_χ = 50 GeV and α = 0.01, where number-changing S↔SM rates mediated by A, λHS ~ 10^-8 fall well below the Hubble rate (a rough λHS^2 T/H estimate gives ~10^-3). In such cases S cannot be assumed to track its equilibrium abundance, and footnote 16 itself concedes that the thermal mass formula (2.3) fails once S is chemically frozen out; the statement that this 'has no implications for our results' is not checked point-by-point in the scan. Since the equilibrium initial abundance of S is an input to the yield in Eq. (2.23), the small-portal part of the forbidden region in Fig. 8 and the associated y_χ values are not yet reliable. Please verify the equilibrium condition by computing the relevant rates at each scan point, or extend the numerical integration to x < 0.1 with a well-defined initial condition for S.","section":"§3.2, footnote 16; Table 1"},{"comment":"The analytic treatment uses α^2 = λS/24 in Eq. (2.14), i.e. the thermal mass from the S self-interaction alone. In the model of Sec. 3.1, the quartic portal λHS S^2 H†H also contributes to the thermal mass of S, by an amount of order λHS T^2 (for instance λHS T^2/6 for the four real Higgs degrees of freedom). For λHS = 10^-2 and λS = 10^-4, both within the Table 1 ranges, this contribution is much larger than λS T^2/24, so the 'α' appearing in Eqs. (2.16), (2.22), and (2.23) is not simply the combination of scan parameters used in the model. If the numerical code includes the full thermal mass, the analytic closed forms and the plotted α are not the same quantity; if it uses only Eq. (2.3), a relevant physical effect is omitted. Please specify the full thermal-mass expression used in the numerical computation and either include the λHS contribution in the definition of α or demonstrate that it is negligible throughout the region shown in the plots.","section":"§2.1, Eq. (2.3); §3.1"}],"minor_comments":[{"comment":"The sentence 'in which the scenario can natually be realised' contains a typo: 'natually' should be 'naturally'.","section":"§1"},{"comment":"The phrase 'aboundance' in 'the final dark matter aboundance' and similar places should be 'abundance'.","section":"§2.3"},{"comment":"In the discussion of Fig. 7a, the text says 'In Fig. 6a the final DM abundance is determined by the branching fraction...'; this cross-reference appears to be mislabeled and should refer to Fig. 7a.","section":"Fig. 7 and surrounding text"},{"comment":"The relation between the summed |M|² and Γ_χ should clarify whether Γ_χ is the width for S→χχ with χ and χ̄ counted together or separately; the current notation is slightly ambiguous.","section":"Eq. (2.6)"},{"comment":"The 'additional 10% theoretical uncertainty' used with the Planck relic-density constraint is not described; please state how it was implemented in the MultiNest likelihood.","section":"§3.2.2"}],"recommendation":"major_revision","confidential_remarks":"This is a solid phenomenology paper whose core mechanism is interesting and likely correct in the equilibrium regime. The main technical issue is that the scan claims to cover very small portal couplings without verifying that the equilibrium assumption underpinning the thermal mass and initial S abundance actually holds; this is fixable by adding rate checks or extending the integration range. The relation to Ref. [14] is handled honestly, and the paper's contribution—the general treatment of the d≤4 case and the specific Higgs-portal realization—is appropriate for JHEP."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this paper is more than a re-run of the earlier gravitino/axino observation. It isolates a regime that had been noted in passing, gives it a name, derives closed-form yields, and builds a zero-VEV dark-Higgs example that is cleanly different from ref. [14]. The central physics checks out: with mS,T^2 = mS^2 + alpha^2 T^2, decays that are kinematically forbidden in vacuum open at high temperature, and for dimension-four operators the relic abundance is almost mchi-independent. That is a real and useful result, and the paper is honest about the earlier literature.\n\nThe strongest part is Sec. 2. The analytic approximation for the yield, eq. (2.23), is simple enough to reproduce and matches the numerical curves. The paper also carefully walks through why d>4 operators behave differently. In the model section, the zero-VEV choice avoids a complication present in earlier constructions, and the experimental constraints are applied sensibly.\n\nThe soft spots are real but not fatal. The numerical scan assumes S was in chemical equilibrium for x < 0.1 and solves the coupled Boltzmann equations only for x > 0.1. But the forbidden production peaks at x ~ alpha <z> mS/(2mchi), which is below 0.1 for alpha < 0.3. That means most of the forbidden production is computed under exactly the equilibrium assumption. Footnote 16 explicitly concedes that the thermal mass formula fails once S is chemically frozen out, and it asserts without a scan-level check that this does not affect the studied model. With A and lambdaHS allowed down to 1e-8, that assertion deserves a real check. For the smallest portal couplings, the quoted ychi and relic-density contours are conditional, not wrong in mechanism. There is also a minor tension between that concession and the introduction's claim that the equilibrium assumption can be relaxed. The private code makes verification harder, though the analytic formulas give enough to reconstruct the main claims.\n\nFor a benchmark point with adequately large lambdaHS, the forbidden freeze-in mechanism holds up. The paper is aimed at freeze-in model builders and anyone computing relic abundances with thermal-mass corrections; they should read it and revisit earlier models. I would send it to peer review and ask for either a point-by-point verification of S equilibrium in the scanned region or a restriction of the claimed region to where it is verified.","headline":"A solid and useful paper that names a real freeze-in regime and derives clean formulas; the main caveat is that part of the model scan leans on an unverified mediator-equilibrium assumption at small portal couplings.","tokens_in":21250,"tokens_out":4582,"would_cite":true,"duration_ms":46838,"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 mediator that cannot decay into dark matter at zero temperature can do so once its thermal mass grows, and this 'forbidden freeze-in' can dominate dark-matter production.","keywords":["forbidden freeze-in","thermal mass","dark Higgs portal","dark matter relic density","freeze-in mechanism","long-lived mediator","early universe cosmology"],"falsifier":"For a scan point with very small mediator–Standard Model couplings (near the lower edge of the scanned ranges, e.g. mixing parameters around $10^{-8}$), solve the coupled Boltzmann equations without assuming $S$ was in equilibrium at early times, tracking $S$'s full phase-space distribution; if the resulting relic abundance departs from the mass-independent $Y_{DM,0}$ formula, the claim that forbidden freeze-in dominates in that region is wrong.","tokens_in":20094,"feed_emoji":"🌡️","tokens_out":9335,"duration_ms":83416,"temperature":0.7,"pith_summary":"This paper identifies a dark-matter production regime it calls 'forbidden freeze-in': a mediator particle that cannot decay into dark matter at zero temperature can develop a large thermal mass in the hot early Universe, making the decay energetically allowed. The paper argues that this thermally opened decay channel, rather than standard freeze-in processes computed with zero-temperature masses, can dominate the production of dark matter. For decays through dimension-four operators, the resulting relic abundance is nearly independent of the dark-matter mass and requires a larger coupling than ordinary freeze-in; for higher-dimensional operators the production becomes sensitive to the reheating temperature. A scalar 'dark Higgs' portal model provides a concrete realisation, and the paper maps the parameter regions that give the observed relic density and survive current and future experimental constraints.","feed_headline":"Thermal mass unlocks a forbidden dark-matter production route","feed_subtitle":"A mediator too light to decay to dark matter at rest can do so in the hot early universe, altering relic predictions.","key_machinery":"The load-bearing object is the thermally corrected mediator mass, $m_{S,T}^2 \\simeq m_S^2 + \\alpha^2 T^2$, where $\\alpha^2 = \\lambda_S/24$ comes from the scalar self-interaction. With the vacuum decay width $\\Gamma_{S\\to\\chi\\bar\\chi} = (y_\\chi^2/8\\pi)(m_S^2-4m_\\chi^2)^{3/2}/m_S^2$, the allowed window is controlled by the ratio $z = 2m_\\chi/(\\alpha T)$: the decay is open for $z<1$ and shuts off at $z=1$. Substituting the thermally varying mass into the freeze-in Boltzmann equation turns the yield evolution into $dY_{DM}/dz \\propto K_1(\\alpha)(1-z^2)^{3/2}/\\sqrt{g h}$ times the derivative of the entropy degrees of freedom, and integrating from $z=0$ to $z=1$ produces the closed-form abundance. The mechanism is carried by the combined $\\alpha^4$ and $K_1(\\alpha)$ prefactors: they set the production efficiency and make the final abundance nearly mass-independent for dimension-four operators.","core_discovery":"The paper's central claim is that 'forbidden frozen-in dark matter' is a generic freeze-in sub-regime. Once a bath particle $S$ in equilibrium with the Standard Model plasma acquires a thermal correction to its mass, $m_{S,T}^2 \\simeq m_S^2 + \\alpha^2 T^2$ with $\\alpha^2 = \\lambda_S/24$ for a quartic self-interaction, the decay $S \\to \\chi\\bar\\chi$ can proceed at high temperature even when the zero-temperature mass satisfies $m_S < 2m_\\chi$. For a dimension-four decay operator the production peaks just before the decay closes, at $z \\equiv 2m_\\chi/(\\alpha T) \\approx 1$, and the final yield is approximately $Y_{DM,0} = (\\alpha^2 y_\\chi / 5\\times10^{-9})^2 (1\\,\\mathrm{GeV}/(2m_\\chi)) K_1(\\alpha)/\\sqrt{g h}$ evaluated at $\\langle z\\rangle \\approx 0.34$. The relic abundance $\\Omega h^2$ is then, up to order-one corrections, independent of $m_\\chi$, in contrast to the linear mass dependence of standard freeze-in, and the required Yukawa coupling is typically larger. For dimension-five and higher operators the yield is dominated by the highest temperatures, so the abundance depends on the reheating temperature. The paper's dark Higgs portal example produces both regimes in a numerical scan and shows the allowed regions are constrained by and partially testable through long-lived scalar searches.","pith_inferences":["Because the mechanism only requires that the mediator be in kinetic equilibrium, it should extend to models where the mediator is chemically decoupled from the Standard Model but self-interacting; the paper notes this possibility but does not include it in the numerical scan.","The near mass-independence for dimension-four decays implies a degeneracy: different dark-matter masses can share the same thermal-mass parameter and coupling while all matching the observed abundance, which would make the mechanism difficult to pin down by relic-density measurements alone.","Vector and fermion mediators with large thermal masses should exhibit the same forbidden window, so the regime is likely not limited to scalar portals; checking this would require only replacing the thermal-mass and decay-rate formulas."],"forward_implications":["Parameter regions with $m_S < 2m_\\chi$ that standard freeze-in would rule out can now yield the observed dark-matter abundance, so the viable space of portal models is larger than previously thought.","For dimension-four decay operators, the dark-matter mass and the production coupling are effectively decoupled from the relic abundance, so attempts to match the observed density must use larger couplings than standard freeze-in suggests.","For higher-dimensional operators, the forbidden freeze-in contribution is dominated by the highest temperatures, making the final abundance dependent on the reheating temperature rather than only on particle masses.","Around the transition point $m_S \\approx 2m_\\chi$, the predictions become sharply mass-sensitive over a width of order $\\alpha m_S$, which is a direct consequence of the thermal mass opening the decay.","In the concrete dark Higgs model, the viable forbidden-freeze-in points populate long-lived-mediator regions that upcoming forward and beam-dump experiments can begin to probe."],"supporting_citations":[{"why":"Defines the standard freeze-in framework of production through feebly interacting particles that this paper extends.","marker":"[5]"},{"why":"Introduces the dynamic freeze-in treatment with thermal masses and phase transitions that motivates the scalar-mediator setup.","marker":"[14]"},{"why":"First identifies thermally induced forbidden decays as a production channel, here for gravitinos.","marker":"[11]"},{"why":"Supplies the Boltzmann-equation formulation for decay-driven freeze-in used to derive the yield formulas.","marker":"[34]"},{"why":"Provides the big-bang-nucleosynthesis lifetime bounds that delimit the allowed dark-Higgs parameter space.","marker":"[40]"},{"why":"Provides the decay and detection treatment for a light scalar mixing with the Higgs, used for collider and beam-dump constraints.","marker":"[41]"}],"fun_headline_variants":["Thermal mass turns on dark matter decay, new production route","Heated mediator spawns dark matter via forbidden decay","Forbidden decays become allowed in hot early universe","Thermal correction flips switch on dark matter freeze-in","Hot plasma mass shift opens dark matter production window"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes the mediator $S$ was in equilibrium with the hot plasma in the early Universe, because that is what justifies the thermal-mass formula $m_{S,T}^2 \\simeq m_S^2 + \\alpha^2 T^2$; if $S$ was never abundant or interacting enough to be in equilibrium, the forbidden decay window would not open.","fun_headline_variants_meta":{"raw":{"variants":["Thermal mass turns on dark matter decay, new production route","Heated mediator spawns dark matter via forbidden decay","Forbidden decays become allowed in hot early universe","Thermal correction flips switch on dark matter freeze-in","Hot plasma mass shift opens dark matter production window"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000407,"raw_usage":{"total_tokens":2135,"prompt_tokens":987,"completion_tokens":1148,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":1071}},"tokens_in":603,"tokens_out":1148,"duration_ms":8442,"temperature":1.0,"reasoning_tokens":1071,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:07:35.872438+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a scan point with very small mediator–Standard Model couplings (near the lower edge of the scanned ranges, e.g. mixing parameters around $10^{-8}$), solve the coupled Boltzmann equations without assuming $S$ was in equilibrium at early times, tracking $S$'s full phase-space distribution; if the resulting relic abundance departs from the mass-independent $Y_{DM,0}$ formula, the claim that forbidden freeze-in dominates in that region is wrong.","supporting_citations":[],"review_version":1}