{"id":"4ae9671a-917f-41ff-8306-6b3f5aa01c3e","arxiv_id":"2502.03878","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the real singlet extension of the Standard Model, the di-Higgs mass spectrum at the HL-LHC and at ILC1000 carries a measurable imprint of the triple Higgs coupling λhhH, and the pure-resonant approximation used by ATLAS and CMS is not reliable.","lead":"This paper studies whether a new type of Higgs self-coupling can be measured by producing two Higgs bosons together at the LHC and at a future electron-positron collider. It shows that the simplified search method used by ATLAS and CMS may miss important interference effects, and that a 1 TeV linear collider could help recover the new coupling.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The benchmark plane is explicitly not checked against existing LHC di-Higgs bounds (Sect. 2.2); if current resonant or non-resonant HH limits exclude it, the ATLAS/CMS-approximation argument loses its target. A recast of published limits would settle this.","rationale":"The reader's weakest-assumption analysis points to the missing LHC di-Higgs constraint check, and I agree that this is the single load-bearing item. The paper's most consequential claim is not that RxSM has interesting interference structure (that is standard and supported by the LO plots), but that ATLAS/CMS resonant-search approximations 'may fail to capture the relevant effects and lead to erroneous results.' That claim becomes practically relevant only for a benchmark plane that could actually be confronted with LHC data. The paper's own Sect. 2.2 lists the omitted check, and Table 2 gives all parameters needed to test it. Because sin theta is 0.12-0.18 and lambda_hhH is 0.32-0.52, the predicted gg -> H -> hh rates are not obviously negligible; existing resonant HH limits could plausibly cut into the plane. If they do, the comparisons in Figs. 9-12 and the ILC section lose their concrete target. If they do not, the paper's conditional is resolved and no objection remains. I am not claiming the plane is in fact excluded; I am identifying this as the load-bearing unknown. The LO-only distributions and the 15% smearing/50 GeV binning are a secondary concern because the authors acknowledge them (Sect. 3.1) and because the qualitative peak-broadening effect is not likely to vanish at NLO, though a full NLO reweighting would still be valuable. The suggested test is a direct recast of existing public limits; it is feasible with the parameters listed in Table 2 and would settle the issue.","tokens_in":26743,"tokens_out":6860,"duration_ms":77112,"concrete_test":"For each point P1-P8 in Table 2, compute the resonant signal sigma(pp -> H -> hh) using the finite-width HPAIR resonant-only mhh distribution with the Tab. 2 parameters (mH, sin theta, lambda_hhH, Gamma_H), apply the event selection and mhh binning of the ATLAS/CMS Run-2 resonant HH combination cited as Refs. [15,16], and compare the predicted yields with the observed 95% CL upper limit at the corresponding mH. Also compare the non-resonant sigma(gg -> hh) at kappa_lambda about 1.45 with the same combination's kappa_lambda limit. If any point lies above an observed limit, the benchmark plane is excluded; if all pass, the missing check is closed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim is that the pure-resonant approximation used by ATLAS and CMS can fail for RxSM di-Higgs production, leading to erroneous limits. The concrete stage for this demonstration is the FOEWPT benchmark plane defined in Sect. 2.3 and the eight points in Table 2. But Sect. 2.2 explicitly states \"we did not check for constraints arising from di-Higgs measurements at the LHC.\" The plane has mH in [458, 660] GeV and sin theta in [0.12, 0.18], so every point predicts a resonant gg -> H -> hh signal whose rate scales roughly as sin^2(theta) x BR(H -> hh), plus a non-resonant contribution with kappa_lambda about 1.45. These are precisely the channels covered by existing ATLAS and CMS di-Higgs searches. If the predicted resonant cross sections exceed the observed 95% CL upper limits at the corresponding mH, the benchmark plane is already excluded; the mhh broadening shown in Figs. 9-12 and the resulting statement that current search designs may miss the signal would then describe a region that is not viable. Conversely, if the plane survives, the conditional is satisfied and the central argument stands. This is not a modeling subtlety but an external-data check, and the authors explicitly leave it unresolved.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies di-Higgs production in the real singlet extension of the Standard Model (RxSM) at the HL-LHC and at a future e+e− collider (ILC1000), with the goal of assessing sensitivity to the BSM triple Higgs coupling λhhH. The analysis is anchored to a two-dimensional benchmark plane, taken from Ref. [25], that is designed to feature a strong first-order electroweak phase transition. At the HL-LHC, the authors compute gg→hh cross sections and mhh distributions using a RxSM-adapted version of HPAIR. They find that the full, interference-inclusive mhh distribution is substantially broader than the pure-resonant template used by the ATLAS and CMS resonant di-Higgs searches, and they argue on this basis that the experimental approximation can fail for the RxSM. For the ILC1000, they compute e+e−→Zhh at tree level with MadGraph/SARAH, apply simple acceptance cuts, and use the same R estimator to characterize the visibility of the H resonance. The central qualitative result is that resonant-continuum interference broadens the apparent resonance and can shift the peak-dip structure, so that a pure-resonant template may misrepresent the model's prediction.","tokens_in":26996,"tokens_out":3923,"duration_ms":45011,"significance":"If the benchmark plane survives existing constraints, the paper makes a useful and concrete point: for a well-motivated FOEWPT scenario in the RxSM, the simplified resonant signal models used in current ATLAS/CMS searches are not an adequate description of the full leading-order prediction, because interference with the non-resonant diagrams substantially broadens the mhh structure. This extends earlier 2HDM-based criticism (Ref. [21]) to a model with a strong first-order phase transition, which is a phenomenologically relevant target. The authors are also honest about the limitations of their R estimator, repeatedly stating that it is not an experimental significance. The quantitative claims (R values, 'visibility', and the ILC sensitivity statement) are weaker than the qualitative shape argument, and one load-bearing input, the viability of the benchmark plane against current LHC di-Higgs constraints, is explicitly left unchecked. The paper does not ship machine-checked proofs or public code, but it uses established public tools (HPAIR, HiggsTools, MadGraph, SARAH, BSMPT) and cross-checks the benchmark points with BSMPTv3.","major_comments":[{"comment":"Section 2.2 explicitly states 'we did not check for constraints arising from di-Higgs measurements at the LHC', yet the benchmark plane has mH in [458, 660] GeV, sinθ in [0.12, 0.18], and κλ ≈ 1.45. These are precisely the parameter ranges probed by current ATLAS and CMS non-resonant and resonant di-Higgs searches. If the plane is excluded by those data, the concrete demonstration in Sect. 3.3.3 loses its target. The Conclusions claim that 'the plane under consideration is in agreement with all theoretical and experimental constraints' is therefore inaccurate. This must be fixed, either by performing a recast or proper reference to existing HH limits for these eight points, or by explicitly reframing the plane as illustrative and not yet confronted with HH data.","section":"Sect. 2.2 and Conclusions"},{"comment":"The quantitative claims about 'visibility' of the resonance and the R values rest on LO mhh distributions with a 15% smearing and 50 GeV bins. The authors justify using LO distributions by concerns about NLO mass effects, but they do not quantify how NLO corrections might shift the peak-dip position or the R values. Since the abstract and conclusions draw on these R values to support the claim that the full signal would be visible or missed by current searches, the analysis needs either an estimate of the associated theory uncertainty or a clear statement that the quantitative R values are illustrative only, with the robust claim being the qualitative shape difference.","section":"Sect. 3.1 and Sect. 3.3 (Eq. (28), Figs. 9-12)"},{"comment":"The abstract concludes 'We demonstrate the potential sensitivity to λhhH via an experimental determination at the ILC1000.' The body, however, uses the theory-level estimator R, explicitly stated not to be a true experimental significance, and applies only parton-level acceptance cuts without background or systematic uncertainties. The ILC analysis therefore does not demonstrate an experimental determination of λhhH; it shows that the mhh distribution has a feature that a future experimental analysis might exploit. The abstract and conclusions should be reworded to reflect this distinction.","section":"Sect. 4 and Abstract"}],"minor_comments":[{"comment":"The caption says '√s = 14 GeV'; this should be 14 TeV.","section":"Fig. 8 caption"},{"comment":"In the text preceding the figures, the green curve is first defined as σNoH, but then it says 'For comparison, the green curve indicates the SM result (σSM)'; these statements are inconsistent and the figure legend should be checked.","section":"Sect. 4.2, Figs. 15-16"},{"comment":"There are several typographical errors: 'Acknoledgements' should be 'Acknowledgements', 'Shakharov' should be 'Sakharov', 'occurence' should be 'occurrence', and 'the the di-Higgs' appears twice in Sect. 2.3.","section":"Throughout"},{"comment":"Reference [28] (Dawson, Dittmaier, Spira) is missing its arXiv number.","section":"Ref. [28]"},{"comment":"The definition of N^C_i for the ILC estimator differs from the HL-LHC definition (non-resonant instead of SM), and this difference is only explained in a footnote; it would help to unify the notation or explain the distinction in the main text.","section":"Sect. 4.1, Eq. (30)"}],"recommendation":"major_revision","confidential_remarks":"The paper's central qualitative claim is credible and the authors are appropriately careful in labeling their R estimator. The main blocker is the self-acknowledged absence of any check of the benchmark plane against existing LHC di-Higgs constraints; given that the entire ATLAS/CMS approximation argument is staged on that plane, this is a load-bearing omission rather than a minor caveat. The ILC part also claims more than it delivers. With those reframed, the paper would be a solid contribution. The novelty relative to Refs. [20] and [21] is incremental, but the FOEWPT benchmark context gives it additional phenomenological relevance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent, honest phenomenological paper that does something genuinely new — it computes full di-Higgs m_hh distributions (including all interferences) on an RxSM benchmark plane that is simultaneously constrained to give a strong first-order electroweak phase transition. The warning that the ATLAS/CMS pure-resonant template may be misleading is not new in general (the 2HDM version is in their Ref. [21]), but showing it in this FOEWPT-motivated RxSM context is a real addition. The ILC1000 analysis is a straightforward but solid extension, with a sensible treatment of acceptance and b-tagging.\n\nThe paper also does things right. It uses HPAIR adapted to the RxSM, applies HiggsBounds/HiggsSignals for the usual constraints, and is explicit about the LO-only distributions, the smearing/binning, and the fact that the R estimator is not a real significance. The qualitative interference-broadening mechanism is standard physics and is supported by the shown distributions. Credit is due for the honest wording in Sect. 2.2.\n\nThe soft spot is the one the stress-test flags: the benchmark plane is never checked against existing LHC di-Higgs limits. With m_H in [458, 660] GeV and sinθ in [0.12, 0.18], every point predicts a resonant rate that current searches may constrain. The authors say they did not check, and the paper's strongest claim is precisely that the experimental limits are unreliable for this model. That is an argument, but it is not a substitute for a recast or at least a rough estimate of whether the plane is excluded under the full-interference treatment. If a simple recast rules out the plane, the quantitative conclusions (cross sections, R values, ILC sensitivities) lose their concrete target. The qualitative point about template broadening would probably still stand, but it would stand in a different, more general form.\n\nThis is not a fatal flaw in the sense of incoherence — the paper is clear on its own terms — but it is a load-bearing gap that a referee should ask to be closed. The LO-only m_hh shapes are a lesser concern, and the authors acknowledge them.\n\nWho is this for: people working on singlet extensions, di-Higgs phenomenology, and future e+e- collider studies. It deserves a serious referee. I would send it to review, with the di-Higgs constraint check as the main required revision.","headline":"A competent RxSM di-Higgs study whose new piece is the full m_hh distributions on a FOEWPT benchmark plane; the central caveat is that the plane is not checked against existing LHC di-Higgs limits, which the authors admit.","tokens_in":775,"tokens_out":738,"would_cite":true,"duration_ms":36643,"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 real singlet extension of the Standard Model, the heavy Higgs boson that enables a strong first-order electroweak phase transition leaves a broadened, interference-shaped imprint in the di-Higgs mass distribution; the paper argues…","keywords":["real singlet extension of the SM","triple Higgs couplings","di-Higgs production","first-order electroweak phase transition","resonant heavy Higgs","mhh invariant mass distribution","ILC1000","Higgs self-coupling"],"falsifier":"Re-run the current resonant di-Higgs search with the full leading-order RxSM m_hh templates for benchmark points P1-P8 instead of the pure-resonant template; if the exclusion status of the plane is unchanged, the claim that the approximation can lead to erroneous results would be refuted for these points. A complementary check is to compute NLO QCD m_hh distributions with full top-mass dependence for P1, P4, and P7 and see whether the broadened peak-dip structure survives the same smearing and binning.","tokens_in":26494,"feed_emoji":"⚛️","tokens_out":9260,"duration_ms":89268,"temperature":0.7,"pith_summary":"The paper studies di-Higgs production in the real singlet extension of the Standard Model (RxSM), the simplest Higgs-sector model that can produce a strong first-order electroweak phase transition, on a benchmark plane where the heavy Higgs mass lies between about 460 and 660 GeV and the light-Higgs trilinear coupling is kappa_lambda = 1.45. Its central claim is that the BSM trilinear coupling lambda_hhH leaves a visible imprint in the m_hh distribution through interference between the resonant heavy-Higgs diagram and the non-resonant box and light-triangle diagrams, even after detector smearing and binning. The paper argues that the pure-resonant signal template used in current LHC searches for resonant di-Higgs production does not represent this RxSM signal, because the full distribution is broadened into a peak-dip structure, so applying those templates can exclude points erroneously or miss real signals. For a 1 TeV e+e- collider (ILC1000) it argues that e+e- -> Zhh can give access to lambda_hhH, with theoretical R-values indicating a visible resonance peak for all eight benchmark points. If true, this would provide a route toward the first measurement of a beyond-Standard-Model triple Higgs coupling, a key step for reconstructing the Higgs potential behind electroweak baryogenesis.","feed_headline":"Double-Higgs signals are broader than LHC search templates assume","feed_subtitle":"Interference with background diagrams could hide or move heavy-Higgs peaks; ILC1000 may still see them.","key_machinery":"The load-bearing object is the differential di-Higgs invariant-mass distribution d(sigma)/dm_hh computed at leading order with the full set of diagrams: the top-quark box, the light-Higgs triangle (controlled by kappa_lambda), and the heavy-Higgs s-channel triangle (controlled by sin(theta)*lambda_hhH). Interference between the resonant and non-resonant amplitudes produces the characteristic peak-dip structure; the paper's observability measure is the estimator R, defined as the summed bin-by-bin difference between RxSM and SM event counts, normalized by the SM count, restricted to bins where the difference exceeds 20 GeV times the bin size (or a threshold of two events at the ILC). The benchmark plane itself is the second piece of machinery: it is defined by fixing the singlet VEV x and quartic b4 with relations a1*x = -32000, lambda = 0.18, and b3 = -560*sqrt(b4), which guarantees a strong first-order electroweak phase transition and keeps kappa_lambda = 1.45 with m_H between 458 and 660 GeV.","core_discovery":"On its own terms, the paper establishes that in the RxSM benchmark plane the process gg -> hh receives a resonant contribution from the heavy Higgs boson H through the coupling lambda_hhH, and that this contribution interferes with the SM-like continuum. The resulting m_hh distribution is not a narrow resonance but a peak-dip structure whose position and shape depend on m_H and on the sign and size of the couplings. After a 15% Gaussian smearing and 50 GeV binning, the dip is largely washed out, but a sizeable excess over the SM remains around m_hh ~ m_H for benchmark points in all three regions defined by the total-cross-section significance; the paper's R estimator ranges from about 230 down to 80 at the HL-LHC. Comparing the full calculation with the resonant-only calculation used by the experimental collaborations, the paper finds that the full distribution is substantially broadened, especially toward lower m_hh, and concludes that the resonant-only approximation may fail to capture the relevant effects and lead to erroneous results. At the ILC1000, the m_hh distribution of e+e- -> Zhh shows a resonance structure whose R value is largest for the smallest lambda_hhH, giving a potential sensitivity to this coupling.","pith_inferences":["The paper explicitly does not check against non-resonant di-Higgs data at the LHC; if those data already exclude the kappa_lambda = 1.45, m_H < 660 GeV plane, the claim's concrete target disappears. The authors' own caveat makes this the first thing to test.","The same interference-broadening argument likely extends beyond the RxSM to other heavy-scalar models; one direct test would be to recast current resonant di-Higgs exclusions using full-interference templates for a range of singlet and doublet models and see how many excluded points move.","The LO m_hh distributions are used with 15% smearing and 50 GeV bins because NLO distributions with full mass dependence are not available; if NLO corrections shift the dip position or smear the peak further, the quantitative R values and the 'visible after binning' conclusion could change. This is an editorial caution, not a paper claim.","A natural future extension is to repeat the ILC analysis with polarized beams and a full detector simulation of the 4b+Z final state; the public R values suggest the coupling could be extracted, but only a complete experimental study can confirm the precision."],"forward_implications":["If the approximation critique is right, existing LHC exclusion limits for resonant di-Higgs production cannot be applied directly to singlet-extension models; each model needs a full-interference signal template or a reinterpretation of the limits.","The HL-LHC can distinguish this RxSM benchmark plane from the SM in the m_hh distribution even when the total cross section shows no significant deviation, because of the broadened excess around the heavy-Higgs mass.","The ILC1000 (or any e+e- collider at 1 TeV with 8 ab^-1) could determine lambda_hhH from e+e- -> Zhh; within this benchmark plane the sensitivity is largest for small lambda_hhH and decreases as m_H grows.","A first measurement of a BSM triple Higgs coupling would allow the reconstruction of the scalar potential in a model that can explain the baryon asymmetry via a strong first-order electroweak phase transition.","Because the plane has kappa_lambda = 1.45 but is not in the alignment limit, the same m_hh analysis indirectly tests the cosmological scenario of electroweak baryogenesis that motivated the model."],"supporting_citations":[{"why":"It supplies the eight FOEWPT benchmark points and the plane-defining parameter relations that the paper re-constrains and uses for all signal predictions.","marker":"[25]"},{"why":"It provides the HPAIR code for the gg -> hh cross section and m_hh distributions that the authors adapted to the RxSM and used at leading order.","marker":"[28]"},{"why":"It introduces the 15% smearing, 50 GeV binning, and the R estimator that the HL-LHC analysis uses to judge visibility.","marker":"[20]"},{"why":"It previously showed for the 2HDM that resonant-only di-Higgs searches can exclude points erroneously, the argument this paper extends to the RxSM.","marker":"[21]"},{"why":"It is the LHC resonant di-Higgs search whose pure-resonant signal template the paper argues is inadequate for this model.","marker":"[15]"},{"why":"It is the companion search with the same template, cited with [15] as the current experimental procedure.","marker":"[16]"},{"why":"It provides the anticipated 4.5 sigma SM di-Higgs significance at the HL-LHC, used to rescale uncertainties and define Delta s.","marker":"[76]"},{"why":"It supplies the ILC event-selection scheme (four b-jets plus Z, acceptance cuts) and the R-based sensitivity treatment used for e+e- -> Zhh.","marker":"[35]"},{"why":"It provides the e+e- m_hh and R methodology from the 2HDM that is adapted to the ILC1000 analysis.","marker":"[36]"}],"fun_headline_variants":["Interference shifts double-Higgs peaks, LHC templates miss them","Heavy-Higgs interference leaves dip-peak in di-Higgs mass spectrum","Peak-dip from heavy Higgs eludes LHC search templates","ILC1000 can probe the triple-Higgs coupling that LHC misses"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the FOEWPT benchmark plane, which the authors explicitly did not test against existing LHC di-Higgs measurements, is not already excluded; if those data rule out the plane, all the cross-section predictions, m_hh shapes, and the critique of the experimental approximation lose their concrete target.","fun_headline_variants_meta":{"raw":{"variants":["Interference shifts double-Higgs peaks, LHC templates miss them","Heavy-Higgs interference leaves dip-peak in di-Higgs mass spectrum","Peak-dip from heavy Higgs eludes LHC search templates","ILC1000 can probe the triple-Higgs coupling that LHC misses"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000658,"raw_usage":{"total_tokens":3138,"prompt_tokens":1202,"completion_tokens":1936,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":818,"completion_tokens_details":{"reasoning_tokens":1853}},"tokens_in":818,"tokens_out":1936,"duration_ms":14698,"temperature":1.0,"reasoning_tokens":1853,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T00:23:40.922686+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the current resonant di-Higgs search with the full leading-order RxSM m_hh templates for benchmark points P1-P8 instead of the pure-resonant template; if the exclusion status of the plane is unchanged, the claim that the approximation can lead to erroneous results would be refuted for these points. A complementary check is to compute NLO QCD m_hh distributions with full top-mass dependence for P1, P4, and P7 and see whether the broadened peak-dip structure survives the same smearing and binning.","supporting_citations":[{"cited_title":"Dawson, S","cited_arxiv_id":null,"evidence_quote":"It provides the HPAIR code for the gg -> hh cross section and m_hh distributions that the authors adapted to the RxSM and used at leading order."},{"cited_title":"Sensitivity to Triple Higgs Couplings via Di-Higgs Production in the 2HDM at e+e- Colliders","cited_arxiv_id":"2106.11105","evidence_quote":"It supplies the ILC event-selection scheme (four b-jets plus Z, acceptance cuts) and the R-based sensitivity treatment used for e+e- -> Zhh."},{"cited_title":"Triple Higgs Couplings in the 2HDM: The Complete Picture","cited_arxiv_id":"2203.12684","evidence_quote":"It provides the e+e- m_hh and R methodology from the 2HDM that is adapted to the ILC1000 analysis."}],"review_version":1}