{"id":"cb0ae1bb-5644-4cb9-a263-c2f512285cfd","arxiv_id":"2608.03936","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"In the scNMSSM at large lambda and low tan(beta), all surviving SM-like points have kappa_lambda between 0.884 and 0.982 and di-Higgs cross section 30.3-36.9 fb.","lead":"A scan of one million parameter points in a supersymmetric extension of the Standard Model finds 66 viable cases where the Higgs self-coupling is always slightly suppressed below the Standard Model value. The result gives future colliders a narrow, testable target and links the suppression to a stronger early-universe phase transition.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Tree-level κλ universality is not established at the quoted precision: the paper's own NLO estimate lets the most SM-like benchmark cross κλ=1.","rationale":"The paper is transparent about the tree-level nature of the κλ calculation, but the abstract and conclusions state the universal suppression as a robust prediction. The reader's identified weakest assumption—that the ±(3–8)% NLO band preserves κλ<1—is exactly the load-bearing point. The paper's own Table 5 demonstrates that the most SM-like benchmark can cross unity under a plausible +8% shift, so the central qualitative claim is not yet secure. No machine-checked proof or independent NLO computation is provided. The rest of the paper—the scan, the mass spectrum, the di-Higgs cross-section range—is conditional on this tree-level result; the cross-section predictions use the Carvalho parametrization and internal benchmarks, but the primary novelty is the claimed universal suppression. A full one-loop calculation for the 66 points is a concrete, feasible check that would settle the issue. If it confirms κλ<1 for all points, the conditional verdict should stand; if not, the headline claim should be weakened. The paper's honest deferral of the NLO computation supports a conditional accept rather than rejection, so I do not change the reader's verdict.","tokens_in":14951,"tokens_out":21043,"duration_ms":214780,"concrete_test":"Run a full one-loop calculation of κλ for all 66 surviving scan points using NMSSMCALC (as the paper itself proposes), keeping the same input parameters and renormalization scheme. If any point yields κλ_NLO ≥ 1, the universal suppression claim is falsified; if all 66 points remain below 1, the concern is resolved. As a minimal first check, recompute Point A of Table 4 with the full one-loop corrections: if κλ_NLO ≥ 1, the upper endpoint of Eq. (8) is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—Eq. (8) and the abstract's 'universally suppressed' κλ=0.884–0.982—is computed at tree level with Eq. (6). The only NLO estimate is a uniform ±(3–8)% rescaling, and Table 5 shows that Point A, the most SM-like point (κλ_tree=0.982), reaches κλ_NLO,max=1.061. Because the spread across the 66 points (Δκλ≈0.10) is comparable to the quoted NLO band (≈±0.03 to ±0.08), a full one-loop calculation is required before 'universal suppression' can be asserted. The paper itself defers this to future work, so the strongest claim is not yet established at the precision the headline implies. If NLO corrections are correlated with the singlet fraction, the upper endpoint of Eq. (8) could cross unity for more than just Point A. The qualitative EWPT motivation depends on κλ<1 for all surviving points, so this is load-bearing. The abstract's 'full two-loop precision' applies to the NMSSMTools Higgs-mass calculation, not to the trilinear coupling, which the text explicitly states is computed at tree level.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies di-Higgs production and the trilinear Higgs self-coupling in the semi-constrained NMSSM (scNMSSM) at large lambda and low tan(beta). A random scan of one million parameter points, with NMSSMTools 6.1.2 applying theoretical, collider, flavor, and dark matter constraints, yields 66 SM-like points with singlet fraction S13^2 < 0.05. Using a tree-level NMSSM formula (Eq. 6), the author finds kappa_lambda = 0.884-0.982 with mean 0.944 +/- 0.018 (Eq. 8), and using the Carvalho parametrization (Eq. 9) obtains non-resonant di-Higgs cross sections sigma(gg->h1h1) = 30.3-36.9 fb (0.880-1.050 sigma_SM) at 13.6 TeV (Eq. 10), with the h3-mediated resonant contribution negligible. The paper interprets the universal suppression of kappa_lambda as qualitatively consistent with a strengthened electroweak phase transition, though a finite-temperature computation is deferred to future work.","tokens_in":15329,"tokens_out":8856,"duration_ms":85879,"significance":"If the quantitative claims were established at the quoted precision, the paper would provide a valuable first systematic map of trilinear self-coupling and di-Higgs phenomenology in the large-lambda, low-tan(beta) scNMSSM, with explicit benchmark points and concrete collider predictions that could be tested at the HL-LHC and future lepton colliders. The use of a large random scan with public tools, the provision of benchmark points, and the honest placement of the EWPT discussion at a qualitative level are strengths. However, the central claims are currently weakened by three load-bearing issues: the 'universal suppression' is only a tree-level statement and can fail under the paper's own NLO estimate; the stated systematic uncertainty from kappa_t != 1 in the di-Higgs parametrization appears to be wrong by at least a factor of several; and the claim that no h2->h1h1 resonant contribution is kinematically accessible is contradicted by the reported mass ranges. These issues need to be resolved before the headline predictions can be taken at face value.","major_comments":[{"comment":"The headline claim of universal suppression kappa_lambda < 1 is a tree-level result. Eq. (6) is evaluated at tree level, and the only NLO estimate is a uniform rescaling by ±(3–8%). Table 5 shows that Point A, the most SM-like point (kappa_lambda^tree = 0.982), reaches kappa_lambda^NLO,max = 1.061 under the +8% rescaling. Since the spread in Eq. (8) (Delta kappa_lambda ≈ 0.10) is comparable to the quoted NLO band, the statement 'No enhancement of kappa_lambda above unity was found' is not established at loop level. The text itself defers the full NMSSMCALC computation to future work. Moreover, the abstract's phrase 'full two-loop precision' is misleading when applied to kappa_lambda and the di-Higgs cross section, which are computed at tree level or via a fitted parametrization. Either a full one-loop calculation should be provided, or the claims should be explicitly rephrased as tree-le","section":"§4.2, Eq. (8), Table 5"},{"comment":"The treatment of kappa_t != 1 is not quantitatively reliable. Linearizing Eq. (9) around kappa_t = 1 and kappa_lambda = 1 gives a coefficient [4(A1+A3)+2(A2+A4)+2A5]/(sum A_i) ≈ 9.2/1.83 ≈ 5.0. For the sample range kappa_t ∈ [0.97, 1.01], this implies corrections of order +5% to -15%, not the ~2% quoted in the text. The expression 'delta sigma/sigma ~ 4(kappa_t-1)(A1+A3+A5)/(sum A_i)' also appears numerically/algebraically incorrect and omits the derivative contributions from the A2 and A4 terms. Consequently, the lower end of Eq. (10) and the statement that 35/31 points lie above/below sigma_SM are not justified with the stated uncertainty. The cross-section ratio should be recomputed using a parametrization that keeps kappa_t explicitly, or using the underlying public code, and the uncertainty should be reassessed.","section":"§4.3, Eq. (9)"},{"comment":"The text states that 'no resonant h2→h1h1 decay is kinematically accessible for any of the 66 points,' but Table 3 reports m_h2 ∈ [131, 268] GeV and m_h1 ∈ [122, 125] GeV. For points with m_h2 > ~250 GeV, the 2*m_h1 threshold is exceeded, so h2→h1h1 is kinematically open. The resonant calculation in §4.3 considers only gg→h3→h1h1, not h2 mediation. If h2→h1h1 is allowed, its contribution to sigma(gg->h1h1) should be included or explicitly shown to be negligible. This is directly relevant to the claim that the resonant contribution is ≤ 0.004 fb and that any di-Higgs deviation is purely non-resonant.","section":"§4.1 vs §4.3"}],"minor_comments":[{"comment":"'full two-loop precision' should be qualified: the two-loop precision applies to the NMSSMTools Higgs-mass calculation, while kappa_lambda is tree-level and the di-Higgs cross section uses an external parametrization. Also, 'is expected to be probed' should be 'are expected to be probed'.","section":"Abstract"},{"comment":"Typo: 'and and' appears in the caption. The caption also refers to the 122–128 GeV window while Table 3 and the abstract report 122.0–125.0 GeV for the surviving points; please clarify that the 66 final points lie in the narrower range.","section":"Figure 1 caption"},{"comment":"The notation 'kappa_t = C_t(h1) = S12/sin beta kappa_t = 1' is self-contradictory. Define kappa_t unambiguously and state that the Carvalho parametrization was calibrated for kappa_t = 1.","section":"§4.3, Eq. (9)"},{"comment":"The uncertainty in '<kappa_lambda> = 0.944 ± 0.018' is not defined; please state whether it is the standard deviation of the sample or the standard error of the mean.","section":"§4.2"},{"comment":"Whenever the range for kappa_lambda is quoted (e.g., Eq. 8), it should be labelled 'tree-level' to avoid implying NLO precision, unless the NLO calculation is actually performed.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a relevant and timely topic, and the benchmark-point information is a useful contribution. However, the main quantitative claims need additional work: the NLO crossing issue in Table 5 directly undermines the 'universal suppression' headline; the kappa_t uncertainty in §4.3 appears to be numerically wrong; and the h2 kinematic statement is internally inconsistent. These are fixable in a revision, but together they currently preclude acceptance. The finite-temperature EWPT discussion is appropriately framed as qualitative and is not the main basis for my recommendation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing to know: this is a clean, reproducible scan of one million scNMSSM points in the large-lambda, low-tan(beta) region with GUT boundary conditions, and it returns a tight window: kappa_lambda 0.884-0.982, sigma(hh) 30-37 fb at 13.6 TeV. The paper is honest about what it computed and what it defers. That is the good news.\n\nWhat is actually new: the combination of GUT-scale scNMSSM constraints, the SM-like selection, and the simultaneous look at kappa_lambda and non-resonant di-Higgs, with the observation that doublet-dominated h1 is confined below ~125 GeV in this regime. The scan itself appears competently done: NMSSMTools, standard constraints, benchmark points A and B for reproducibility, and a clear statement that the resonant h3 channel is negligible because h3 is singlet-like. That last point is a genuinely useful negative result for collider searches.\n\nWhere it gets soft: the central quantitative claim, 'universal suppression' kappa_lambda < 1, is computed at tree level. The only NLO input is an estimate from the literature of ±3-8%, and the paper's own Table 5 shows the most SM-like point (A) can cross 1 at +8%. Since the spread across the 66 points is only ~0.1, which is comparable to the NLO band, the robustness argument 'the range exceeds the loop corrections' does not hold. The abstract's 'full two-loop precision' applies to the NMSSMTools Higgs mass calculation, not to the trilinear coupling; the text says this, but the abstract invites a stronger reading. The EWPT section is explicitly qualitative: no finite-T potential, no v_c/T_c. That is fine as motivation, but it should not be billed as support for baryogenesis.\n\nAlso, the non-resonant cross section prediction inherits the Carvalho parametrization's approximation kappa_t = 1; the authors estimate a ~2% shift, which is minor and handled.\n\nBottom line: this is a solid phenomenology scan with an overreaching headline. The honest version is: 'in this corner of the scNMSSM, tree-level kappa_lambda is predicted to be 0.88-0.98, pending one-loop confirmation, with a distinctive non-resonant di-Higgs rate.' A full one-loop calculation would settle it. I would send it to a referee—the scan is reproducible and the benchmark region is useful—but the referee should be told to focus on whether the suppression claim survives NLO.\n\nFor your reading group: maybe, if you care about NMSSM collider phenomenology. I would cite it for the benchmark points and the h3 channel suppression.","headline":"Useful scNMSSM scan in a motivated corner, but the 'universal suppression' claim overreaches the tree-level calculation and the paper's own NLO estimate.","tokens_in":15826,"tokens_out":1956,"would_cite":true,"duration_ms":19448,"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":"In the scNMSSM at large λ and low tan β, every viable SM-like point has a suppressed Higgs self-coupling, κλ = 0.884–0.982, and a narrow non-resonant di-Higgs rate of 30.3–36.9 fb at 13.6 TeV.","keywords":["scNMSSM","Higgs self-coupling","di-Higgs production","electroweak phase transition","singlet-doublet mixing","large lambda low tan beta","Higgs mass","HL-LHC prospects"],"falsifier":"Compute the full one-loop κλ for all 66 points rather than estimating it; if any SM-like point with S13²<0.05 has NLO κλ > 1, the claimed universal suppression is false. Experimentally, a future lepton-collider measurement excluding κλ < 1 at 95% CL would also rule out the prediction.","tokens_in":14855,"feed_emoji":"⚛️","tokens_out":12915,"duration_ms":126126,"temperature":0.7,"pith_summary":"This paper investigates the semi-constrained NMSSM in the region of large λ and low tan β, the regime that most naturally raises the Higgs mass through the tree-level λ²v² sin²2β contribution. Out of one million randomly generated parameter points, 66 survive all theoretical, collider, flavor, and dark matter constraints as SM-like Higgs configurations. The paper's central result is that every one of those 66 points has a trilinear Higgs self-coupling below the Standard Model value: κλ = 0.884–0.982, with mean 0.944 ± 0.018. The corresponding non-resonant di-Higgs production cross section at 13.6 TeV is 30.3–36.9 fb (0.88–1.05 times the SM), while the resonant h3→h1h1 channel contributes at most 0.004 fb. If true, this gives a concrete, testable collider footprint of a modified Higgs potential that could support a strong first-order electroweak phase transition, and motivates a future finite-temperature analysis of the transition strength.","feed_headline":"All 66 viable points suppress the Higgs self-coupling","feed_subtitle":"In the large-λ low-tanβ slice, κλ = 0.884–0.982, making the di-Higgs rate a concrete HL-LHC target.","key_machinery":"The load-bearing object is the ratio κλ = λ_{h1h1h1}/λ_{SM}, defined from the tree-level NMSSM self-coupling (Eq. 6), which decomposes into a doublet term ∝ C_V³, where C_V = S11 cosβ + S12 sinβ is the reduced coupling of h1 to W/Z, plus singlet corrections ∝ S13 C_V² and ∝ S13³. Because the SM-like selection demands S13² < 0.05, the dominant C_V³ term is always slightly suppressed, and this single fact drives the universal κλ<1 result. The second machine is the analytic parametrization of non-resonant gg→h1h1 production (Eq. 9), which converts κλ and κt into σ/σSM through interference coefficients A1...A5; the sign structure of these coefficients is why lowering κλ below one can raise the c","core_discovery":"Central claim: in this parameter region every SM-like point that survives all constraints has a trilinear Higgs self-coupling below the SM value, κλ = 0.884–0.982 (mean 0.944 ± 0.018), from the tree-level mixing formula (Eq. 6). Doublet–singlet mixing is the mechanism: h1's small singlet fraction (S13²<0.05) lowers C_V, reducing the dominant C_V³ term. The same mixing generates a tree-level cubic barrier of strength λµeff ∈ [55,102] GeV, qualitatively connecting κλ<1 to a strengthened first-order electroweak phase transition. Collider-wise, the non-resonant di-Higgs cross section is bounded to 30.3–36.9 fb (0.88–1.05 σSM) at 13.6 TeV, because a smaller κλ weakens the triangle amplitude and r","pith_inferences":["Beyond the paper: because the suppression tracks the singlet fraction rather than the scanned coupling ranges, a percent-level κλ measurement could serve as a practical surrogate for measuring doublet–singlet mixing even if h2 and h3 are too heavy to produce directly.","Beyond the paper: the claimed kinematic confinement of SM-like h1 below ~125 GeV is directly testable by scanning the same λ–tanβ window with wider λ, κ, and A-terms; finding a SM-like h1 above 125 GeV with S13²<0.05 would falsify that structural prediction.","Beyond the paper: a rate-only di-Higgs measurement near 1.0 σSM would not discriminate this model from the SM; the discriminating information lives in the extracted κλ and the shape of the m_hh distribution, so κλ-fits matter more than total-rate limits.","Beyond the paper: since the mechanism is purely tree-level mixing, the same qualitative suppression pattern should appear in any NMSSM-like model with a light doublet and a small singlet admixture; the specific 0.884–0.982 window is a benchmark that other singlet-extended models can be compared against."],"forward_implications":["A future measurement of κλ that resolves a 2–12% suppression would single out this scNMSSM region; the MSSM, by contrast, predicts only a weak suppression (κλ ≳ 0.97).","The predicted di-Higgs cross sections, 30.3–36.9 fb at 13.6 TeV, are all below current experimental upper limits, so the model is not yet constrained; the HL-LHC global combination and future lepton colliders are the settings that can test the range.","Because the resonant h3→h1h1 contribution is at most 0.004 fb, a detectable deviation from the SM would appear in the non-resonant di-Higgs kinematics rather than as a resonance peak.","The universal κλ suppression is tied to the same doublet–singlet mixing that builds a tree-level cubic barrier, so it is a zero-temperature signpost for a potentially strong first-order electroweak phase transition; quantifying vc/Tc remains the next step.","Observing a suppressed κλ together with a h2 in 131–268 GeV and a singlet-like h3 in 383–581 GeV would be a combined multi-scalar signature of this region."],"supporting_citations":[{"why":"Supplies the spectrum and constraint machinery used to scan one million points and to select the 66 SM-like survivors.","marker":"[11–15]"},{"why":"Supplies the analytical parametrization (Eq. 9) that turns κλ and κt into the non-resonant gg→h1h1 cross-section.","marker":"[23]"},{"why":"Provides the SM reference cross section (33.33 fb at 13.6 TeV) against which σ/σSM is normalized.","marker":"[24]"},{"why":"Provides the estimated ±(3–8)% one-loop shift in κλ used to argue the suppression survives loop corrections.","marker":"[20]"},{"why":"Gives the observed upper limit from combined Run 2 di-Higgs searches against which the predicted rates are checked.","marker":"[25]"},{"why":"Gives the general-NMSSM di-Higgs range (0.7–2.4 σSM) used as the comparison that motivates the narrower scNMSSM prediction.","marker":"[8]"},{"why":"Establishes the singlet-sector route to a strong first-order electroweak phase transition that the qualitative EWPT discussion builds on.","marker":"[4]"},{"why":"Supplies benchmark lines/planes for NMSSM Higgs-to-Higgs decays, the most directly comparable study that this work complements.","marker":"[9]"}],"fun_headline_variants":["No viable scNMSSM point exceeds SM κλ","κλ = 0.884–0.982 in all surviving points","Di-Higgs rate 0.88–1.05 σSM in scNMSSM large-λ","κλ suppressed across all scNMSSM viable points","scNMSSM large-λ: all viable points give κλ<1"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The universal suppression claim rests on the tree-level self-coupling formula plus an assumed ±3–8% one-loop correction band; if radiative corrections push the least-suppressed point above κλ = 1 (as the paper's own table allows), universality fails.","fun_headline_variants_meta":{"raw":{"variants":["No viable scNMSSM point exceeds SM κλ","κλ = 0.884–0.982 in all surviving points","Di-Higgs rate 0.88–1.05 σSM in scNMSSM large-λ","κλ suppressed across all scNMSSM viable points","scNMSSM large-λ: all viable points give κλ<1"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001531,"raw_usage":{"total_tokens":6092,"prompt_tokens":1000,"completion_tokens":5092,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":744,"completion_tokens_details":{"reasoning_tokens":4990}},"tokens_in":744,"tokens_out":5092,"duration_ms":35979,"temperature":1.0,"reasoning_tokens":4990,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T05:24:15.324903+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full one-loop κλ for all 66 points rather than estimating it; if any SM-like point with S13²<0.05 has NLO κλ > 1, the claimed universal suppression is false. Experimentally, a future lepton-collider measurement excluding κλ < 1 at 95% CL would also rule out the prediction.","supporting_citations":[{"cited_title":"Analytical parametrization of HH production at the LHC","cited_arxiv_id":null,"evidence_quote":"Supplies the analytical parametrization (Eq. 9) that turns κλ and κt into the non-resonant gg→h1h1 cross-section."},{"cited_title":"de Florian et al","cited_arxiv_id":null,"evidence_quote":"Provides the SM reference cross section (33.33 fb at 13.6 TeV) against which σ/σSM is normalized."},{"cited_title":"Baglio, R","cited_arxiv_id":null,"evidence_quote":"Provides the estimated ±(3–8)% one-loop shift in κλ used to argue the suppression survives loop corrections."},{"cited_title":"Higgs pair production in the NMSSM at the LHC","cited_arxiv_id":null,"evidence_quote":"Gives the general-NMSSM di-Higgs range (0.7–2.4 σSM) used as the comparison that motivates the narrower scNMSSM prediction."},{"cited_title":"Huber, Thomas Konstandin, Tomislav Prokopec, and Michael G","cited_arxiv_id":null,"evidence_quote":"Establishes the singlet-sector route to a strong first-order electroweak phase transition that the qualitative EWPT discussion builds on."},{"cited_title":"Benchmark Lines and Planes for Higgs-to-Higgs Decays in the NMSSM","cited_arxiv_id":"2403.15046","evidence_quote":"Supplies benchmark lines/planes for NMSSM Higgs-to-Higgs decays, the most directly comparable study that this work complements."}],"review_version":1}