{"id":"40b26111-ad5e-412e-84e6-0607275b43fd","arxiv_id":"2508.13155","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"For Higgs-portal reheating with a light inflaton, the combination of vacuum stability, perturbativity, and LHC constraints limits the reheating temperature to between roughly 3.4e6 and 3.9e12 GeV.","lead":"This paper derives allowed ranges for the inflaton mass and the reheating temperature in models where the inflaton decays into Higgs bosons. It connects early-universe reheating to collider data and Higgs vacuum stability, giving targets for model building and searches.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed T_rh window appears to rely on the zero-temperature perturbative width; for T_rh ≫ m_phi, thermal Higgs masses suppress φ→HH, so the window is not robust until this is checked.","rationale":"The reader correctly identified the perturbative T_rh mapping as the weakest load-bearing premise. My read agrees and sharpens it: in the claimed window T_rh ≫ m_phi, which is exactly the regime where zero-temperature two-body decay widths can fail because of the thermal Higgs mass. I am not claiming the paper is wrong; the source text is too corrupted to tell whether finite-temperature effects were already included. The Boltzmann check above would settle the issue. Since the reader already returned UNVERDICTED and my concern does not by itself change that state, the verdict remains UNVERDICTED.","tokens_in":16256,"tokens_out":13928,"duration_ms":153364,"concrete_test":"Obtain a clean PDF and locate the reheating equations (the φ→HH width and T_rh formula). Then take the two boundary points quoted in the abstract (m_phi=260 GeV with T_rh=3.4e6 GeV, and m_phi=3.8e10 GeV with T_rh=3.9e12 GeV) and solve dρ_φ/dt + 3Hρ_φ = −Γ_eff ρ_φ, dρ_R/dt + 4Hρ_R = +Γ_eff ρ_φ, with H^2 = (ρ_φ+ρ_R)/(3M_Pl^2), Γ_eff = Γ0 Θ(m_phi − 2 m_h(T)), m_h(T)^2 = 125^2 + c_H T^2, c_H ≈ 0.1, and g_* ≈ 106.75. If the resulting final T_rh for either boundary point is orders of magnitude below the quoted value, the central window is not robust. If the paper already implements this calculation, reproduce the boundary plot instead.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline result is obtained by converting (μ, m_phi) constraints into a T_rh window through the two-body decay width Γ(φ→HH) and the standard relation T_rh ~ sqrt(Γ M_Pl). The abstract, and the corrupted full text, give no evidence that finite-temperature corrections are included. For the boundary values quoted, T_rh is orders of magnitude above m_phi: 3.4e6 GeV versus 260 GeV at the low end, and 3.9e12 GeV versus 3.8e10 GeV at the high end. At the epoch H ~ Γ the ambient bath therefore has T ≫ m_phi/2. The SM Higgs then has a thermal mass m_h(T) ~ O(0.1-0.6) T, which exceeds m_phi/2, so at-rest φ→HH is kinematically blocked and the zero-temperature width is not the correct decay rate. Unless the paper solves the Boltzmann equations with, e.g., Γ_eff = Γ0 Θ(m_phi − 2 m_h(T)), the quoted T_rh window is not established. Because the supplied text is unreadable, this is the single check that determines whether the headline claim survives.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the scenario in which reheating proceeds through the interaction μ φ |H|^2 between a light inflaton φ and the Standard Model Higgs doublet H, with a bare inflaton mass m_phi. The authors combine renormalization-group requirements that the Higgs potential remain stable and perturbative up to high scales with LHC constraints evaluated with HiggsTools, and they translate the resulting constraints on (μ, m_phi) into a prediction for the reheating temperature using the two-body decay φ→HH. Their headline result is 3.4×10^6 GeV ≲ T_rh ≲ 3.9×10^12 GeV and 260 GeV ≲ m_phi ≲ 3.8×10^10 GeV. The version of the full text supplied to me is heavily corrupted, so the underlying equations and numerical steps could not be independently checked; the abstract is legible and is the basis for this report.","tokens_in":16481,"tokens_out":4408,"duration_ms":46174,"significance":"If the claimed window is correct, the paper gives a sharp, falsifiable correlation between an electroweak-scale inflaton mass, the Higgs-inflaton coupling, and the reheating temperature, which is directly relevant for Higgs-portal reheating models and for LHC searches. The use of the public code HiggsTools and the explicit RG analysis are strengths, and the constraints appear to be externally imposed benchmarks rather than derived from the desired T_rh interval, so there is no evident circularity. The main caveats are that the central derivation is not legible in the supplied text and that the zero-temperature decay treatment needs justification at the quoted high reheating temperatures.","major_comments":[{"comment":"The quoted window rests on the standard mapping T_rh ~ sqrt(Γ M_Pl) with the zero-temperature two-body width Γ(φ→HH). At the claimed endpoints T_rh is many orders of magnitude above m_phi (3.4×10^6 GeV vs. 260 GeV; 3.9×10^12 GeV vs. 3.8×10^10 GeV), so at the epoch H ~ Γ the ambient plasma has T ≫ m_phi/2. The SM Higgs then acquires a thermal mass m_h(T) ~ O(0.1–0.6)T, which typically exceeds m_phi/2 and kinematically blocks at-rest φ→HH decays. The manuscript, in the legible parts, does not address this. Please either solve the Boltzmann equation with a temperature-dependent width (e.g., Γ_eff = Γ_0 Θ(m_phi − 2 m_h(T))), or provide a concrete argument that decays complete before the thermal bath is established. Without this, the T_rh bounds are not established beyond the zero-temperature approximation.","section":"Abstract / reheating calculation"},{"comment":"Because the full text I received is corrupted, I cannot verify the β-functions, the treatment of the dimensionful coupling μ, or the threshold corrections used to conclude that the Higgs potential remains stable and perturbative. Please make sure the published version explicitly lists the renormalization-group equations, the matching scale, and the criteria for 'stable' and 'perturbative' (including the upper bound on μ). These are load-bearing for the derived allowed region.","section":"RG analysis / Section 2 (unreadable in supplied text)"},{"comment":"The abstract states that LHC constraints are applied through HiggsTools, but the legible text does not specify which observables are used (e.g., Higgs signal strengths, exotic Higgs decays, or direct searches for a new scalar) or how the code translates a given (μ, m_phi) into an exclusion. Please spell out the relevant processes and give the numerical likelihood or chi-square treatment, since the lower bound m_phi > 260 GeV appears to follow from this step.","section":"LHC constraints / HiggsTools implementation"}],"minor_comments":[{"comment":"The supplied full text is garbled; please ensure the final manuscript has intact display equations and section numbers, since this prevented verification.","section":"Overall presentation"},{"comment":"Define T_rh precisely (e.g., T at H = Γ versus instantaneous decay temperature) and state whether the quoted range assumes instant thermalization.","section":"Reheating definition"},{"comment":"The mention of the 'HiggsTools public code' should include a version or arXiv reference and the specific input parameters used.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The finite-temperature decay issue is the key technical risk; if the authors can show that the thermal mass does not shut off the decay (or that the quoted window survives a full Boltzmann treatment), I would view the paper favorably. The corrupted full text prevented me from checking the RG and HiggsTools steps, so a clean revised version is essential."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know about this paper. It assembles a genuinely useful chain: SM RG running, vacuum stability/perturbativity, and LHC constraints via HiggsTools, applied to the μ φ |H|² portal with an electroweak-scale inflaton. The specific combined window, 3.4×10⁶ GeV ≲ T_rh ≲ 3.9×10¹² GeV with 260 GeV ≲ m_φ ≲ 3.8×10¹⁰ GeV, is the kind of bound model builders want. None of the ingredients is new, but the application to a bare-mass-dominated inflaton is a fair target.\n\nThe soft spot is the conversion from (μ, m_φ) to T_rh. The abstract gives no hint that finite-temperature effects are included. At the quoted lower end T_rh is five orders of magnitude above m_φ; the SM Higgs thermal mass at that temperature is of order 0.1–0.6 T, well above m_φ/2. That kinematically blocks φ→HH, so the zero-temperature width is not the right input for T_rh ~ sqrt(Γ M_Pl). If the paper solved the Boltzmann equations with a temperature-dependent effective width, the window might survive in modified form. If it used the zero-temperature width, the headline bound is not established. I could not check this because the full text provided to me is a character-corrupted blob; the RG beta functions, threshold corrections, decay-width formula, and HiggsTools interface are all illegible.\n\nOn the positive side, the conceptual machinery is honest and standard. No circular reasoning is apparent: the stability and collider constraints are external benchmarks, and T_rh is a derived output. The citation pattern is clean for this subfield.\n\nBottom line: if you send this to a referee, the decisive question to pose is precise — did you include thermal-mass blocking or an effective phase-space factor when computing T_rh? If not, the bounds are likely too optimistic. If yes, this is a useful constraint on the μφ|H|² reheating portal. Given the use of public code and the relevance to Higgs-portal inflation, I would not desk-reject it. It deserves peer review with that thermal question explicitly flagged. It is a borderline-major-revision candidate rather than a clear accept.","headline":"Useful RG-plus-LHC constraint for the μφ|H|² portal, but the quoted T_rh window relies on a decay-width treatment that thermal effects may invalidate.","tokens_in":17020,"tokens_out":3565,"would_cite":false,"duration_ms":41759,"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":"The paper derives a narrow allowed window for Higgs-portal reheating: vacuum stability, perturbativity, and LHC constraints together force $3.4\\times10^6\\,\\mathrm{GeV}\\lesssim T_{\\rm rh}\\lesssim 3.9\\times10^{12}\\,\\mathrm{GeV}$ and…","keywords":["Higgs reheating","inflaton","reheating temperature","Higgs vacuum stability","renormalization group running","perturbativity","collider constraints","inflaton decay"],"falsifier":"Recompute the reheating temperature at a representative allowed point, say $m_\\phi=300\\,\\mathrm{GeV}$ with $\\mu$ chosen to give $T_{\\rm rh}\\approx10^7\\,\\mathrm{GeV}$, using a lattice or full Boltzmann treatment that includes resonant and backreaction effects; if the resulting radiation temperature differs from the instantaneous-decay formula by an order of magnitude, the window's edge moves. Independently, a collider discovery of a Higgs-coupled scalar at $250\\,\\mathrm{GeV}$ would directly contradict the $260\\,\\mathrm{GeV}$ lower bound.","tokens_in":16044,"feed_emoji":"🌡️","tokens_out":7045,"duration_ms":74670,"temperature":0.7,"pith_summary":"This paper asks what happens when the inflaton reheats the universe by decaying into Higgs bosons through the interaction $\\mu \\phi |\\mathcal{H}|^2$, rather than through the high-scale couplings usually assumed in inflation models. It argues that in potentials where the inflaton is massless without a bare mass term, the inflaton can sit near the electroweak scale, where collider and vacuum-stability constraints become relevant. Combining renormalization-group running of the Higgs quartic coupling with LHC bounds, the paper derives a finite allowed window for the reheating temperature and the inflaton bare mass. If correct, any Higgs-portal reheating mechanism of this type must land inside that window, giving concrete targets for both cosmological and collider searches.","feed_headline":"Reheating via the Higgs is confined to one temperature window","feed_subtitle":"Stability, perturbativity, and LHC data force the inflaton mass between 260 GeV and 3.8e10 GeV.","key_machinery":"The load-bearing object is the Higgs-portal interaction $\\mu \\phi |\\mathcal{H}|^2$, where $\\phi$ is the inflaton and $\\mathcal{H}$ the Standard Model Higgs doublet, together with the standard perturbative relation between the reheating temperature and the inflaton decay width, $T_{\\rm rh}\\propto \\sqrt{M_{\\rm Pl}\\,\\Gamma}$. The paper runs renormalization-group equations for the Higgs quartic coupling, the coupling $\\mu$, and the inflaton bare mass, imposing that the Higgs potential remain stable and perturbative to high energies, and then overlays LHC constraints from a public collider code. The two-body decay width for $\\phi\\to \\mathcal{H}\\mathcal{H}$ is what carries $\\mu$ into the reheating temperature and closes the chain from RG and collider bounds to the quoted temperature window.","core_discovery":"The central claim is that the requirement that the Higgs potential stay stable and perturbative up to high energies, together with LHC limits on a new scalar coupled to the Higgs, leaves only a narrow allowed region in the $(m_\\phi,\\mu)$ plane for the interaction $\\mu \\phi |\\mathcal{H}|^2$. Within that region the reheating temperature is confined to $3.4\\times10^6\\,\\mathrm{GeV}\\lesssim T_{\\rm rh}\\lesssim 3.9\\times10^{12}\\,\\mathrm{GeV}$, and the inflaton bare mass to $260\\,\\mathrm{GeV}\\lesssim m_\\phi\\lesssim 3.8\\times10^{10}\\,\\mathrm{GeV}$. The paper also provides the resulting relations between $T_{\\rm rh}$ and $m_\\phi$, and between $\\mu$ and $m_\\phi$, so that reheating is turned from a free parameter into a derived quantity for this portal.","pith_inferences":["Beyond the paper: the $260\\,\\mathrm{GeV}$ lower bound turns collider searches for new scalars in Higgs final states into a direct test of reheating; a discovery of a Higgs-coupled scalar below that mass would break the claimed window.","Beyond the paper: if the window holds, high-temperature mechanisms requiring $T_{\\rm rh}\\gtrsim10^{12}\\,\\mathrm{GeV}$, such as some leptogenesis scenarios, are disfavoured for this portal because the upper edge sits near $3.9\\times10^{12}\\,\\mathrm{GeV}$.","Beyond the paper: a full preheating simulation including parametric resonance and backreaction would provide a sharper test, because the perturbative two-body decay assumption is the step that maps $\\mu$ and $m_\\phi$ onto $T_{\\rm rh}$."],"forward_implications":["For this portal, reheating temperatures below about $3\\times10^6\\,\\mathrm{GeV}$ and above about $4\\times10^{12}\\,\\mathrm{GeV}$ are excluded, so viable models must reheat inside that band.","The inflaton mass is forced above $260\\,\\mathrm{GeV}$ and below $3.8\\times10^{10}\\,\\mathrm{GeV}$, ruling out electroweak-scale inflatons below $260\\,\\mathrm{GeV}$ under the stated stability plus collider logic.","Vacuum stability and perturbativity alone already bracket the allowed $\\mu$–$m_\\phi$ relation, with LHC data further tightening it.","The explicit $T_{\\rm rh}$–$m_\\phi$ and $\\mu$–$m_\\phi$ relations make the reheating temperature a derived quantity rather than a freely chosen model parameter for this reheating portal."],"supporting_citations":[],"fun_headline_variants":["Higgs reheating squeezed into a single temperature window","Stability and LHC data narrow Higgs-reheating window","Reheating temperature fixed by Higgs stability and colliders","One window for Higgs reheating: 3.4e6 to 3.9e12 GeV","Inflaton mass bound yields a unique reheating window"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that reheating is set by the single-particle decay rate $\\phi\\to\\mathcal{H}\\mathcal{H}$ with instant thermalization, so that $T_{\\rm rh}\\propto\\sqrt{M_{\\rm Pl}\\,\\Gamma}$; if parametric resonance, backreaction, or a different thermalization history matters, the quoted temperature window need not hold.","fun_headline_variants_meta":{"raw":{"variants":["Higgs reheating squeezed into a single temperature window","Stability and LHC data narrow Higgs-reheating window","Reheating temperature fixed by Higgs stability and colliders","One window for Higgs reheating: 3.4e6 to 3.9e12 GeV","Inflaton mass bound yields a unique reheating window"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000698,"raw_usage":{"total_tokens":3228,"prompt_tokens":1093,"completion_tokens":2135,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":709,"completion_tokens_details":{"reasoning_tokens":2045}},"tokens_in":709,"tokens_out":2135,"duration_ms":15782,"temperature":1.0,"reasoning_tokens":2045,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:14:39.300681+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the reheating temperature at a representative allowed point, say $m_\\phi=300\\,\\mathrm{GeV}$ with $\\mu$ chosen to give $T_{\\rm rh}\\approx10^7\\,\\mathrm{GeV}$, using a lattice or full Boltzmann treatment that includes resonant and backreaction effects; if the resulting radiation temperature differs from the instantaneous-decay formula by an order of magnitude, the window's edge moves. Independently, a collider discovery of a Higgs-coupled scalar at $250\\,\\mathrm{GeV}$ would directly contradict the $260\\,\\mathrm{GeV}$ lower bound.","supporting_citations":[],"review_version":1}