{"id":"57d76f1c-6091-4b01-8277-22cd9d601d1d","arxiv_id":"2608.05401","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The HiggsTools toolbox is upgraded for LHC Run 3 with 13.6 and 14 TeV cross-sections, resonant and non-resonant di-Higgs predictions including interference, and a recast four-top search limit.","lead":"This paper describes version 1.3 of HiggsTools, the standard software suite that tests new physics models against LHC measurements of Higgs bosons. It adds predictions at the new LHC collision energy, Higgs-pair production cross-sections with interference effects, and a recast of the CMS four-top-quark search, keeping the community's interpretation tools ready for Run 3 and the HL-LHC.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (9)'s geometric-mean K-factors for the two resonant-interference terms are unvalidated; a wrong K_RT/K_RB would bias the headline full hh cross-section and any limits derived from it.","rationale":"The paper is a software-release and validation paper whose central new capability is the full Higgs-pair production cross-section (resonant plus non-resonant plus all interference terms, Eq. 7) and its use in HiggsBounds. For that claim to hold, the multiplicative K-factors attached to the interference terms must be reliable. The geometric-mean approximation in Eq. (9) is load-bearing because the paper provides no independent check for the two resonant-interference K-factors, despite noting that interference can be significant for resonant di-Higgs limits. The 1% validation of the analogous box–triangle K-factor is useful evidence but does not cover the resonant case, which has a different analytic structure due to the s-channel propagator, width, and off-shell effects. A wrong K_RT or K_RB would propagate directly into σtot and into any exclusion limit derived from it, undermining a headline claim of the release. I agree with the reader that this is the weakest assumption. The proposed HPAIR-based check is concrete and uses tools already employed in the paper, so it should settle the question with modest effort. I also note, as the reader did, the secondary concern that the six-parameter rational fit of Eq. (22) is fitted to only three points in Appendix B; that issue is localized to one limit implementation, whereas Eq. (9) affects all full cross-section predictions. Given that both concerns are documented but unresolved, the reader's conditional verdict remains appropriate; no further verdict change is needed.","tokens_in":35612,"tokens_out":11886,"duration_ms":111130,"concrete_test":"Use the HPAIR NLO QCD (heavy-top limit) setup already shown in Fig. 5, with a single heavy scalar H and a grid of masses and widths (e.g. mH = 300–1000 GeV, ΓH/mH = 1% and 5%). Evaluate the full gg→hh cross-section at LO and NLO for sign-flipped values of c3 and κλ so that the c3·ct·κλ and c3·ct^2 interference contributions are isolated; their NLO/LO ratios give K_RT and K_RB. Compare these with sqrt(K_R K_T) and sqrt(K_R K_B) using the same K_R, K_T, K_B definitions as in §2.3. If either differs by more than about 5%, Eq. (9) is unsupported and the Eq. (7) predictions need either a revised treatment or an explicit uncertainty estimate.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.3 builds the central new prediction σtot on six terms (Eq. 7) and assigns K-factors K_RT = sqrt(K_R K_T) and K_RB = sqrt(K_R K_B) (Eq. 9) to the two resonant–non-resonant interference terms. The only test offered is for the box–triangle interference: K_TB = 2.735 versus sqrt(K_T K_B) ≈ 2.729, a 1% deviation. No such check is given for K_RT or K_RB. These interference terms are not generically small: the paper itself notes that full interference can matter for resonant di-Higgs limits, especially when κλ deviates from its SM value or c3 is non-negligible. The resonant contributions involve an s-channel propagator with width and off-shell effects, so their higher-order corrections need not follow the same factorization as the box–triangle term. If the true NLO K-factors for ART and ARB differ from the geometric-mean values by more than a few percent, the predicted σtot, and therefore any HiggsBounds limits derived from it, are biased without an estimate of the uncertainty. This is a genuine correctness risk, not a matter of convention.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents HiggsTools 1.3, comprising HiggsPredictions 2.0, HiggsBounds 6.1, and HiggsSignals 3.1, with the stated goal of preparing the HiggsTools framework for LHC Run 3 and the HL-LHC. The main new features are cross-section predictions at 13.6 and 14 TeV, an interpolated gluon-fusion reference model (SMHiggsInterp), predictions for resonant, non-resonant, and combined Higgs-pair production including interference terms, a recast of the CMS four-top-quark search with coupling-dependent acceptances, coupling-dependent non-resonant di-Higgs limits, improved handling of pre-Higgs-discovery searches, and several HiggsSignals improvements for scalars with mass uncertainties. The implementations are validated against the CMS four-top limits (Fig. 9) and against anyHH/HPAIR for di-Higgs production (Fig. 5), and the code is publicly available.","tokens_in":35987,"tokens_out":4701,"duration_ms":46546,"significance":"If the central approximations are reliable, this is a valuable and timely community resource: it lets arbitrary BSM scalar sectors be tested against current and upcoming LHC results without the user having to recompute cross-sections or recast searches. The paper is strong in providing open-source code, explicit validation plots against CMS four-top limits, and a documented comparison with HPAIR for di-Higgs production. The authors also state several limitations clearly, including the use of a single signal region in the four-top recast and the neglect of signal-signal interference. The main significance risk is that the headline di-Higgs cross-section and the new coupling-dependent limits rely on approximations whose numerical uncertainty is not quantified, as detailed in the major comments.","major_comments":[{"comment":"The geometric-mean K-factors for the resonant-interference terms, K_RT = sqrt(K_R K_T) and K_RB = sqrt(K_R K_B), are load-bearing for the full hh cross-section in Eq. (7), but they are not validated. The only explicitly checked interference term is the box-triangle one, where sqrt(K_T K_B) deviates from K_TB by only about 1%. The resonant interference terms involve an s-channel propagator with a width and off-shell effects, so their higher-order QCD corrections need not follow the same factorization. Since this full cross-section is the basis for the resonant di-Higgs limits and for the example applications, the authors should either validate K_RT and K_RB against a full NLO calculation for representative (mH, GammaH, kappa_lambda, c3) values or provide a quantitative estimate of the resulting uncertainty on sigma_tot. The related choice to fix KR(mH) at GammaH/mH = 1% while the amplitudes AR, ART, ARB are stored as functions of the width also deserves a comment for broad resonances, where the width dependence of the K-factor is not included.","section":"Section 2.3, Eq. (9)"},{"comment":"The coupling-dependent limit shape in Eq. (22) is underdetermined for the presented Run-3 ATLAS bbbar-gamma-gamma example: six coefficients (five independent after the overall normalization) are fitted to only three kappa_lambda points, namely kappa_lambda = -1.7, 1, and 6.6. The resulting acceptance factor is therefore not unique, and the derived limit for intermediate kappa_lambda values depends on the arbitrary rational ansatz. This is load-bearing for the new coupling-dependent non-resonant di-Higgs limits and for the example in Fig. 14. The authors should either use the full experimental limit curves where available, constrain the functional form using additional physics input, or explicitly quantify the systematic uncertainty introduced by the choice of fit ansatz.","section":"Appendix B, Eq. (22)"},{"comment":"The four-top recast is a central new feature, but its validation in Fig. 9 covers only the cases with cV = 0 (pure CP-even scalar and pure pseudoscalar). The acceptance fit functions for the cV-dependent terms, which enter Eqs. (16) and (17) and are needed for the more general coupling structure, are not validated against any external limit or against the CMS results for cV != 0. Given that the paper advertises the recast as applicable to CP-mixed scalars and to scalars with non-zero vector-boson couplings, the authors should demonstrate the reliability of the cV-dependent coefficients, for example by comparing the resulting limits with those from other analyses that constrain vector-coupled scalars, or by quantifying the associated uncertainty from the fitting procedure.","section":"Section 3.1.1, Eqs. (16)-(17)"}],"minor_comments":[{"comment":"Equation (16) contains a typo: the second term in the first bracket is written with b1,tot,X again instead of a distinct coefficient for the c_tilde_t^2 term. The expansion on the right-hand side suggests the intended structure has separate coefficients for c_V^2 c_t^2, c_V^2 c_tilde_t^2, etc.","section":"Section 3.1.1, Eq. (16)"},{"comment":"Equation (36) refers to an undefined symbol 'ctW phi(mphi)' in the second term on the right-hand side; this should presumably be c3,tot,tW phi(mphi) as in Eq. (33).","section":"Appendix A.1.2, Eq. (36)"},{"comment":"The text in Appendix B says the coefficients 'E, F and G' are specified in the denominator, but Eq. (22) defines the denominator coefficients as D, E, and F. This inconsistency should be corrected.","section":"Section 3.2, Eq. (22) and Appendix B"},{"comment":"In Table 1, the gg->hh row lists the mass range as '251-3000' GeV, but the non-resonant contribution is for two 125 GeV Higgs bosons; the table entry should clarify that this mass range refers to the mass of the heavy resonance mH in the resonant contribution, not to the mass of the produced h pairs.","section":"Section 2.1, Table 1"},{"comment":"The SMHiggsInterp reference model is a new default, but the interpolation procedure itself is not described in the text; the authors should state how the interpolation between SMHiggsEW and SMHiggs is performed (e.g., the functional form and the transition mass range).","section":"Section 2.2, Fig. 1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid, honest software-release paper for the standard BSM Higgs toolbox. The new features are genuinely useful and mostly well validated. There are two real soft spots—the geometric-mean K-factors for the resonant-interference terms in Eq. (9), and the underdetermined kappa_lambda-dependent limit fit in App. B—but neither invalidates the core of the paper.\n\nWhat's actually new: cross-section tables at 13.6 and 14 TeV, the SMHiggsInterp reference model, the full resonant + non-resonant hh production cross-section with interference (Eq. 7), the recast of the CMS four-top search into coupling-dependent acceptances, and coupling-dependent non-resonant di-Higgs limits. The four-top recast is validated against the CMS limits and shows good agreement (Fig. 9); the di-Higgs implementation is checked against anyHH and HPAIR (Fig. 5). The example applications—2HDM exclusions, the top-philic ALP, and a CP-mixed heavy scalar—demonstrate that the new functionality actually works. The paper is also commendably explicit about the limitations of its approximations.\n\nNow the soft spots. The stress-test note holds up on reading. Eq. (9) assigns K_RT = sqrt(K_R K_T) and K_RB = sqrt(K_R K_B) to the two resonant–non-resonant interference terms, and the only check offered is for the box–triangle interference K_TB, where the approximation works to 1%. The resonant terms go through an s-channel propagator with width and off-shell effects; their higher-order corrections need not factor the same way. If K_RT or K_RB are off by a few percent, the predicted full cross-section—and any limits derived from it—are biased with no uncertainty estimate. This is a genuine correctness risk, not a matter of convention. The authors flag it as an approximation, but a validation or a conservative uncertainty band should be provided.\n\nSecond, the kappa_lambda-dependent limit fit in App. B fits six parameters (A–F in Eq. 22) to only three points. That is underdetermined. The resulting acceptance factor could be unreliable away from the fitted points. This is the lesser issue because the limits are approximate anyway, but it should be cleaned up—fit to more points or impose a theoretically motivated functional form.\n\nOverall: a well-executed update of a community-standard tool. The code is available, the validations are reasonable, and the caveats are in the text. The two issues are fixable and should be addressed before final publication, but they do not sink the paper.\n\nThis is for anyone doing BSM Higgs phenomenology at the LHC—scans, limit-setting, interpretations of Run 3 data. It deserves a serious referee. My recommendation: accept with minor-to-moderate revision, and ask the referee specifically to request validation or an uncertainty estimate for the K-factor approximation, and a better-posed fit for the kappa_lambda acceptance.","headline":"A solid, honest update of the community-standard BSM Higgs toolbox; two documented numerical approximations need tightening, but the core new functionality is real and well validated.","tokens_in":36490,"tokens_out":3337,"would_cite":true,"duration_ms":29644,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.60.Fr","14.80.Bn","14.80.Cp"],"model":"deepseek-v4-flash","headline":"HiggsTools 1.3 combines resonant, non-resonant, and interference contributions into a single validated di-Higgs cross-section prediction, so any BSM scalar model can be tested against LHC Run 3 and HL-LHC data out of the box.","keywords":["HiggsTools","BSM scalar phenomenology","Higgs pair production","LHC Run 3","HiggsBounds","HiggsSignals","four-top searches","trilinear Higgs coupling"],"falsifier":"Run a complete next-to-leading-order QCD calculation of $gg \\to H \\to hh$ with a generic scalar resonance, isolate the triangle–resonance and box–resonance interference contributions, and compare their K-factors with the geometric-mean values $\\sqrt{K_R K_T}$ and $\\sqrt{K_R K_B}$ used in the paper; a deviation of more than a few percent would falsify the central approximation of the full-cross-section implementation.","tokens_in":35405,"feed_emoji":"⚛️","tokens_out":7589,"duration_ms":64635,"temperature":0.7,"pith_summary":"This paper presents HiggsTools 1.3, a software release that lets any model with extra scalar particles be tested automatically against the full set of LHC Higgs searches and measurements. The centrepiece is a new prediction for Higgs-boson pair (hh) production that computes the resonant, non-resonant and interference contributions together, as a function of the Higgs self-coupling $\\kappa_\\lambda$, the top-quark Yukawa coupling, and the mass, width, and couplings of a heavy BSM scalar. On the limits side, the paper adds a recast of the CMS four-top-quark search with coupling-dependent acceptances, and coupling-dependent non-resonant di-Higgs limits. If the implementation is right, a BSM parameter point can be confronted with Run 3 and HL-LHC results out of the box, and the full di-Higgs cross section replaces the common resonant-only or non-resonant-only approximations that can miss significant interference effects.","feed_headline":"Full di-Higgs cross sections, interference and all, now in HiggsTools","feed_subtitle":"One combined prediction lets any BSM scalar face Run 3 and HL-LHC di-Higgs searches.","key_machinery":"Eq. (7), the master formula for the full di-Higgs cross section: $\\sigma_{\\rm tot} = c_t^2 \\kappa_\\lambda^2 K_T A_T + c_t^4 K_B A_B + c_t^3 \\kappa_\\lambda K_{TB} A_{TB} + c_3^2 K_R A_R + c_t \\kappa_\\lambda c_3 K_{RT} A_{RT} + c_t^2 c_3 K_{RB} A_{RB}$, where the $A$'s are integrated amplitudes stored as two-dimensional grids in $(m_H, \\Gamma_H)$. The approximation that carries the argument is Eq. (9), $K_{RT} = \\sqrt{K_R K_T}$ and $K_{RB} = \\sqrt{K_R K_B}$, which assigns higher-order QCD corrections to the two resonance-vs-non-resonance interference terms without computing them directly; the one interference that has been checked, $K_{TB}$, deviates from this geometric-mean rule by only 1%. The non-resonant K-factors are fixed constants ($K_T = 2.989$, $K_B = 2.492$, $K_{TB} = 2.735$) obtained from the ratio of LHCHWG NNLO-based predictions to the anyHH LO result, and the resonant K-factor $K_R(m_H)$ is the ratio of the SusHi-based resonant cross section to the anyHH one.","core_discovery":"The central claim is that the total $gg \\to hh$ cross section for the SM-like Higgs boson plus one heavy CP-even resonance decomposes into six terms—squared triangle, box, and resonance amplitudes plus three interferences—each with its own multiplicative K-factor, and that the two resonant-interference K-factors can be approximated by the geometric mean of the resonant and non-resonant K-factors (Eq. 9). This lets the code combine precision NLO/NNLO/N3LO predictions for the individual pieces with the LO interference structure obtained from a minimal UFO model, while keeping resonant production at the narrow-width-plus-off-shell-improvements level. The paper also claims that the CMS four-top search can be recast as a coupling-dependent acceptance limit in the most sensitive signal region, with signal-yield fit functions in $c_t$, $\\tilde{c}_t$, and $c_V$, and that non-resonant di-Higgs limits can be made $\\kappa_\\lambda$-dependent via a rational fit (Eq. 22). Together these amount to the claim that the whole Run 3 di-Higgs and multi-top programme is now usable as a generic BSM constraint.","pith_inferences":["If the geometric-mean K-factor approximation fails for $K_{RT}$ and $K_{RB}$ at the level of a few percent, the derived limits on $\\kappa_\\lambda$ and on resonant production—and any exclusion plots made with the full cross section—would inherit that bias, so a direct NLO computation of those two interference terms is the natural next validation step.","The four-top recast is deliberately limited to the single most sensitive signal region because signal-region correlations are not public, so the new limit is systematically weaker than the full CMS analysis; implementing the corresponding ATLAS search would sharpen the strongest constraints on top-philic scalars.","The coupling-dependent-acceptance infrastructure used for the four-top recast is general, and the same pattern could be applied to other future final states (for example $t\\bar{t} b\\bar{b}$ or $H \\to t\\bar{t}$ with associated jets), turning the recast machinery into a reusable template for Run 3 and HL-LHC searches.","The combination of the full di-Higgs cross-section prediction with the $\\kappa_\\lambda$-dependent non-resonant limits makes global fits of the Higgs self-coupling inside concrete BSM models (like the 2HDM) feasible in a single tool, and would readily accommodate HL-LHC projection studies."],"forward_implications":["A BSM model with one heavy CP-even scalar can now obtain a Run-3-ready full $gg \\to hh$ cross section (resonant + non-resonant + all interferences) directly from effective couplings and feed it into HiggsBounds for limit setting.","The CMS four-top search becomes usable for arbitrary top-philic scalars—CP-even, CP-odd, or CP-mixed—and for scalars with non-zero vector-boson couplings, not just the pure $c_t = 1$, $c_V = 0$ points published by CMS.","Non-resonant di-Higgs limits from ATLAS, CMS, and their combination become coupling-dependent, so $\\kappa_\\lambda$ can be constrained within full BSM model scans rather than only at the SM point.","Pre-Higgs-discovery searches are no longer selected by default for scalars whose mass is compatible with 125 GeV within the experimental resolution, allowing newer searches such as invisible Higgs decays or non-resonant di-Higgs to be applied when they are more sensitive.","HiggsSignals now rescales model-predicted rates to the reference mass of each measurement, so that scalars with large mass uncertainties (as in supersymmetric models) no longer spuriously worsen the global fit."],"supporting_citations":[{"why":"The CMS four-top search whose cross-section limits are recast into the new HiggsBounds limit via coupling-dependent acceptances.","marker":"[12]"},{"why":"Provides the MadAnalysis implementation of the CMS four-top search, supplying the signal-region event counts and efficiencies used in the fit.","marker":"[57]"},{"why":"LHCHWG Higgs-pair production recommendations that supply the non-resonant $\\sigma(\\kappa_\\lambda)$ fit formula and the 13.6/14 TeV energy rescaling.","marker":"[33]"},{"why":"anyHH/anyH3 provides the LO amplitudes for the interference terms and the trilinear-coupling tools used for both predictions and validation.","marker":"[21, 22]"},{"why":"SusHi supplies the resonant $gg \\to H$ cross sections that set the resonant K-factor normalization in the full di-Higgs formula.","marker":"[15, 16]"},{"why":"The previous HiggsTools release defines the framework, input structure, and interfaces that this version extends.","marker":"[8]"},{"why":"The HEFT fit formula used as the cross-check for the $c_t$-dependence of the non-resonant cross section.","marker":"[43]"},{"why":"Shows that interference effects have a significant impact on the di-Higgs limits in the 2HDM, motivating the full cross-section implementation.","marker":"[44]"}],"fun_headline_variants":["Di-Higgs interference K-factors via geometric mean in HiggsTools","HiggsTools adds full di-Higgs interference for Run 3","HiggsTools recasts multi-top searches for BSM scalars"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The full cross-section formula assumes that the unknown higher-order QCD corrections to the two resonance-vs-non-resonance interference terms equal the geometric mean of the corresponding resonant and non-resonant corrections; only the box–triangle interference has been checked (it is off by 1%), so if the true corrections to those two terms differ substantially, the predicted cross sections and the limits derived from them would be biased.","fun_headline_variants_meta":{"raw":{"variants":["Di-Higgs interference K-factors via geometric mean in HiggsTools","HiggsTools adds full di-Higgs interference for Run 3","HiggsTools recasts multi-top searches for BSM scalars"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000914,"raw_usage":{"total_tokens":3954,"prompt_tokens":1000,"completion_tokens":2954,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":2903}},"tokens_in":616,"tokens_out":2954,"duration_ms":21375,"temperature":1.0,"reasoning_tokens":2903,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T13:50:34.936501+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a complete next-to-leading-order QCD calculation of $gg \\to H \\to hh$ with a generic scalar resonance, isolate the triangle–resonance and box–resonance interference contributions, and compare their K-factors with the geometric-mean values $\\sqrt{K_R K_T}$ and $\\sqrt{K_R K_B}$ used in the paper; a deviation of more than a few percent would falsify the central approximation of the full-cross-section implementation.","supporting_citations":[],"review_version":1}