{"id":"e8ef81c2-24c2-4c67-ad1c-1859925dd35e","arxiv_id":"2505.02947","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"One-loop corrected triple Higgs couplings in the 2HDM can boost e+e- to Zhh cross sections by factors up to about 6 and can make a heavy-Higgs resonance peak accessible at the ILC.","lead":"This paper computes how one-loop quantum corrections to Higgs self-couplings in a two-Higgs-doublet model can make the production of Higgs pairs at future electron-positron colliders several times more likely than the tree-level expectation. It matters for planning future collider measurements of the Higgs potential, because the corrections can create or hide beyond-Standard-Model signals in the double Higgs-strahlung channel.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"One-loop THC substitution is not validated against the full one-loop Zhh calculation; the H-mediated contribution may miss large HZZ corrections.","rationale":"The paper's central claim has two legs: (i) one-loop 2HDM THCs can be much larger than their tree-level values, and (ii) using those loop-corrected THCs in e+e-→Zhh leads to strong cross-section enhancements and visible H resonances. Leg (i) is well supported: the λ_hhh enhancement for BPal is reproduced by two independent codes (BSMPT and anyH3) with small momentum effects, and the parameter scan in Sec. 3 gives consistent allowed ranges. Leg (ii) rests on the assumption that the THC insertions capture the dominant electroweak corrections to the process. The paper gives a plausible power-counting argument for this—large scalar self-couplings versus gauge couplings—but does not verify it with a full one-loop calculation. The H-resonance benchmarks are particularly vulnerable because the HZZ coupling is suppressed by small cβ-α, so loop corrections to HZZ could be relatively large. The no-background assumption for the significances is a real caveat, but it is explicitly stated and mitigated by App. C, where significances remain above ~5 for several points; hence it is less decisive than the unvalidated THC-substitution approximation. A full one-loop computation of the process would settle the issue; if it confirms the approximation, the paper's conclusions stand, and if it does not, the numerical predictions require revision. Given that the concern is real but not yet demonstrated to fail, the conditional verdict is appropriate and unchanged.","tokens_in":49179,"tokens_out":15196,"duration_ms":164820,"concrete_test":"Compute the full one-loop electroweak corrections to e+e-→Zhh in the 2HDM for the six benchmark points in Tab. 4 using an automated tool (e.g., FeynArts/FormCalc or MadGraph5_aMC@NLO with a 2HDM UFO model), matching the BSMPT renormalization scheme for the scalar sector. Compare the resulting total cross sections and mhh distributions with the THC-substitution results in Figs. 2, 4–8 and with Tabs. 6–7. If the total rate shifts by more than ~20% relative to the THC-substitution prediction for BPal, or the H-peak significances change by more than ~1 unit for any resonance benchmark, the Sec. 4.1 dominance assumption fails and the headline enhancement factors and Z values lose their nominal precision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.1 states that inserting one-loop THCs into tree-level Zhh formulas 'includes the full subset of the one-loop purely scalar corrections' and that other one-loop contributions are 'expected to be subleading' because they carry a factor of g. This is an expectation, not a demonstrated result. The consistency check in Sec. 5.1.2 (BSMPT vs. anyH3 for λ_hhh at BPal) validates only the momentum dependence of the THC, not the complete one-loop process. In the SM, the full EW corrections to e+e-→Zhh are O(10%) [105,106] even when the -9% κλ correction is included, showing that vertex and box corrections are not automatically negligible. The danger is sharpest for the H-resonance benchmarks (BP1, BP2, BP3, BPsign, BPext): their tree-level HZZ coupling is cβ-α ≈ 0.1–0.18, so a one-loop correction to HZZ of ordinary size (g^2/16π^2 times mass ratios) can shift the H-peak amplitude by tens of percent, directly altering the significances in Tab. 6. The paper flags this at the end of Sec. 4.1 but does not quantify it.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript studies the impact of one-loop corrected triple Higgs couplings (THCs) on e+e- -> Zhh double Higgs production in the 2HDM. The authors compute the one-loop couplings lambda_hhh and lambda_hhH with the effective-potential code BSMPT and, for lambda_hhh, also with the diagrammatic code anyH3/anyBSM. They scan the 2HDM parameter space with ScannerS, HiggsTools and HDECAY, and find that the one-loop corrected kappa_lambda can reach about 5.8 even in the alignment limit. Inserting the loop-corrected THCs into the tree-level Zhh cross section formulas of Refs. [31,32], they find large enhancements (up to a factor 5.9 at 500 GeV for the benchmark BPal) and study the H-resonance peak in the m_hh distribution. Using a profile-likelihood significance with Gaussian smearing and binning, they report significances above 10 for several benchmark points, and conclude that future e+e- colliders may give access to lambda_hhH.","tokens_in":49418,"tokens_out":7181,"duration_ms":87165,"significance":"If the central approximation is valid, the paper makes a strong phenomenological point: one-loop THCs can dramatically modify double Higgs production in a parameter region (the alignment limit) where all tree-level Higgs couplings are SM-like, so di-Higgs production would be a unique probe. The paper has genuine strengths: the parameter scan is based on public constraint tools, the benchmark points are explicitly specified, the one-loop THCs are cross-checked between two independent public codes, and the finite-momentum dependence of lambda_hhh is quantified in Fig. 3. These features make the analysis largely reproducible. The main caveat, discussed below, is that the cross-section computation is not a complete one-loop calculation, and the size of the omitted contributions is not quantified.","major_comments":[{"comment":"The central approximation - replacing the tree-level THCs by one-loop THCs in the tree-level Zhh amplitude - is not validated against a complete one-loop computation. The text states that this 'includes the full subset of the one-loop purely scalar corrections' and that other one-loop contributions are 'expected to be subleading', but this is an expectation, not a demonstrated result. Refs. [105,106] show that in the SM the full electroweak corrections to e+e- -> Zhh are O(10%) even when the -9% correction to kappa_lambda is included, so box diagrams, wave-function corrections, and gauge-boson vertex corrections are not automatically negligible. The danger is most acute for the H-resonance benchmarks BP1, BP2, BP3, BPsign and BPext, whose tree-level HZZ coupling is only c_beta-alpha ~ 0.1-0.18 (Table 4): an ordinary one-loop correction to the HZZ vertex can shift the resonant amplitude by tens of percent and directly change the significances in Table 6. The paragraph at the end of Sec. 4.1 flags this issue, but does not quantify it. I request either a full one-loop calculation of e+e- -> Zhh in the 2HDM, or a concrete estimate showing that the omitted one-loop contributions are subleading in the parameter regions of the benchmark points.","section":"Section 4.1"},{"comment":"The finite-momentum comparison between the effective-potential and diagrammatic computations is performed only for lambda_hhh at the benchmark BPal (Fig. 3). For the H-peak analysis, the coupling that matters most is lambda_hhH, which is taken entirely from the effective-potential calculation and is not cross-checked against any diagrammatic result. Since the resonant H -> hh amplitude is evaluated at timelike momentum m_hh = m_H, and since lambda_hhH receives sizable loop corrections in the benchmarks of Table 4, the paper should either provide an analogous momentum-dependent check for lambda_hhH or justify why the zero-momentum effective-potential value is adequate in the resonance region. Without this check, the H-peak significances in Table 6 rest on an unvalidated ingredient.","section":"Section 5.1.2 and Table 4"},{"comment":"The reported significances for the H resonance are computed under a no-background assumption: the quantity b_i in Eq. (30) is the continuum prediction from the same parameter point with lambda_hhH set to zero, not the Standard Model or SM-like backgrounds such as ZZZ, ZZh, or top-quark final states. The text is honest about this in Sec. 5.2.1 and Sec. 6, and App. C partially addresses it by rescaling the event number by 17%, but the abstract and the main conclusion present the Z > 10 numbers without the no-background caveat. I ask that the paper either provide, for at least one benchmark, an estimate with a plausible background shape and normalization, or state explicitly in the abstract and conclusions that the quoted significances are discovery significances only under a background-free assumption.","section":"Section 5.2.1 and Table 6"}],"minor_comments":[{"comment":"There is a duplicated word in the sentence 'The 2HDM Higgs couplings to the SM particles are modified w.r.t. to the corresponding SM Higgs couplings. The modification factors for the h,H,A couplings to the massive massive gauge bosons...'.","section":"Section 2"},{"comment":"The caption reads 'T able 1' instead of 'Table 1'.","section":"Table 1 caption"},{"comment":"In the flavor-observables bullet point, '2DHM' should be '2HDM'.","section":"Section 3.1"},{"comment":"The sentence 'This implies that the the finite-momentum effects are very small' contains a duplicated 'the'.","section":"Section 5.1.2"},{"comment":"In the discussion of BP1, 'the resonance peak becomes less prominent and broader' is fine, but the phrase 'resonace peak' appears in the text and should be corrected.","section":"Section 5.2.2"},{"comment":"The caption contains 'for Pe− = −80% and Pe+ = +30%. The color coding is the same as in Fig. 4' but has a typo 'f or' in the first line.","section":"Figure 12 caption"}],"recommendation":"major_revision","confidential_remarks":"The central result is plausible but relies on a truncated one-loop treatment; in my view this is fixable with a dedicated validation section or a quantitative estimate of omitted contributions, rather than a fatal flaw. I do not see circularity: the one-loop THCs are computed from the model potential, not fitted to the Zhh cross section. The no-background caveat should be elevated in the abstract and conclusions. I recommend major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe paper is worth knowing because it shows that in the 2HDM, one-loop corrections to λhhh can push κλ up to ~6 even in the alignment limit, and that inserting these loop-corrected couplings into e+e−→Zhh can boost the cross section by a factor of ~5 and make the H resonance peak visible with high significance at the ILC. The qualitative message is solid. The two strongest pieces are the cross-check between the effective-potential (BSMPT) and diagrammatic (anyH3/anyBSM) calculations of λhhh, which agree to a few percent, and the use of public constraint tools (ScannerS, HiggsTools, HDECAY) for the parameter scan.\n\nWhat is new is applying the loop-corrected THCs to e+e− di-Higgs, including the λhhH resonant contribution and a careful study of mhh smearing and binning. That part is done responsibly: the paper does not hide that this is not a complete one-loop calculation of e+e−→Zhh. In Sec. 4.1 it states clearly that only the 'purely scalar corrections' are included and that other contributions are 'expected' to be subleading; and the significance analysis explicitly assumes negligible background. So the reader is told where the idealizations are.\n\nThe soft spot, as your stress-test notes, is that the THC-substitution approximation is not validated against a full one-loop calculation. The concern is sharpest for the H-resonance benchmarks, where cβ−α is only ~0.1–0.18 and a one-loop correction to HZZ could shift the peak amplitude by tens of percent. In the SM, the full EW corrections to Zhh are O(10%) even after the κλ correction, so 'large scalar couplings dominate' is plausible but not demonstrated. The paper’s caveat at the end of Sec. 4.1 acknowledges this, but the abstract and conclusions present the large enhancement factors and significances without that caveat. The no-background assumption is also optimistic, though explicitly flagged in Sec. 5.2.\n\nThat said, the central qualitative claim almost certainly survives a complete calculation: the corrections are large (factors of 5–6 in cross section, significance >10) and the missing EW pieces would need to be anomalously large to erase the effect. So the paper is not over-selling in a way that undermines its main point.\n\nWho is this for? People working on 2HDM phenomenology, di-Higgs at lepton colliders, and ILC projections. It deserves a serious referee. I would send it to review with a request that the authors either add a sanity check against a full one-loop e+e−→Zhh calculation for one benchmark, or at least give a parametric estimate of the HZZ one-loop correction.\n\nBest,\n[Name]","headline":"In the 2HDM, one-loop corrections to triple Higgs couplings can boost e+e−→Zhh by factors of ~5 and make the H resonance visible at the ILC; the paper is solid but the THC-substitution approximation is not checked against a full one-loop calculation, a limitation explicitly acknowledged.","tokens_in":49990,"tokens_out":3817,"would_cite":true,"duration_ms":37572,"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":"One-loop corrections to triple Higgs couplings in the 2HDM can make the Higgs self-coupling up to six times its Standard Model value and boost e+e- → Zhh cross sections by a factor of about six, even in the alignment limit.","keywords":["triple Higgs couplings","two-Higgs-doublet model","di-Higgs production","e+e- colliders","one-loop corrections","effective potential","ILC","Higgs self-coupling"],"falsifier":"A complete one-loop computation of $e^+e^-\\to Zhh$ in the 2HDM, including all non-THC diagrams, that yields total cross sections differing from the THC-insertion approximation by more than about 5–10% for the benchmark points considered would falsify the claim that the one-loop THCs are the leading corrections. Experimentally, an ILC measurement of the $Zhh$ cross section at 500 GeV that does not show a large enhancement for a parameter point predicting $\\kappa_\\lambda^{(1)}\\approx 5.75$ would equally call the central claim into question.","tokens_in":48944,"feed_emoji":"⚛️","tokens_out":6173,"duration_ms":62178,"temperature":0.7,"pith_summary":"In the two-Higgs-doublet model, the paper argues, one-loop corrections can change the triple Higgs self-coupling $\\lambda_{hhh}$ by up to a factor of about six relative to the Standard Model value, even when the light Higgs boson is exactly SM-like (the alignment limit). Inserting these loop-corrected couplings into the $e^+e^- \\to Zhh$ cross section enhances the predicted di-Higgs production rate by factors of about 5.9 at 500 GeV and 4.8 at 1 TeV for their benchmark BPal. The same corrections can make the heavy-Higgs resonance in the $m_{hh}$ distribution visible at the ILC, with projected significances above 10 for several benchmarks even with 10% smearing of the invariant mass and under a no-background assumption. The paper establishes that the effective-potential approximation for the loop-corrected couplings is sufficient, since a full diagrammatic calculation changes the prediction by only 1–5%. This matters because the Higgs self-coupling is the least constrained part of the Standard Model and a potential window into new physics that otherwise hides in loop corrections.","feed_headline":"Loop effects can boost Higgs-pair rates sixfold at e+e- colliders","feed_subtitle":"Even an SM-like Higgs can hide a self-coupling up to six times larger, visible in e+e- → Zhh.","key_machinery":"The working machinery is the one-loop corrected triple Higgs coupling, $\\lambda_{hhh}$ and $\\lambda_{hhH}$, in the 2HDM. The one-loop corrections are obtained as third derivatives of the Coleman-Weinberg effective potential (implemented in the code BSMPT) and cross-checked with the diagrammatic code anyH3, which includes finite-momentum dependence. These corrected couplings are then substituted into the tree-level analytic formulas for $e^+e^-\\to Zhh$ (from Refs. [31,32]), replacing the tree-level vertices. The chain works because heavy scalar loops with large quartic couplings—enabled by large mass splittings between the heavy Higgs bosons—can generate large positive corrections to the self-coupling, even where the tree-level coupling is exactly the SM value.","core_discovery":"The central claim is that BSM effects in the Higgs potential can be large even when the observable Higgs looks completely SM-like. In the 2HDM, the one-loop corrected triple Higgs couplings $\\lambda_{hhh}$ and $\\lambda_{hhH}$, computed from the effective potential and confirmed diagrammatically, can exceed their tree-level values by factors of several: $\\kappa_\\lambda^{(1)}$ up to about 6 in all Yukawa types, and $\\lambda_{hhH}$ up to about $\\pm 2$. Inserting these into the analytic tree-level cross section for $e^+e^-\\to Zhh$, the paper finds the total cross section enhanced by a factor of 5.9 at $\\sqrt{s}=500$ GeV and 4.8 at 1 TeV for the alignment benchmark BPal ($\\kappa_\\lambda^{(1)}=5.75$). It also finds that for benchmark points where the one-loop $\\lambda_{hhH}$ is enhanced, the $H$-resonance peak in the $m_{hh}$ distribution can be statistically significant at the ILC—$Z>10$ for BP1, BP2 and BPext even with 10% Gaussian mass smearing, assuming no background. The paper concludes that future $e^+e^-$ colliders could access these loop-induced couplings, and that a $\\sim$10% measurement of $\\kappa_\\lambda$ would be achievable.","pith_inferences":["Editorial inference: the same loop-correction mechanism—large scalar quartic couplings feeding the self-coupling—likely operates in other extended scalar sectors, so a tree-level SM-like Higgs self-coupling does not imply a SM-like loop-corrected one.","Editorial inference: if these corrections are real, they should also enter other observables such as single-Higgs production via loop-induced $hZZ$/$h\\gamma\\gamma$ couplings, meaning consistency checks across Higgs precision measurements could confirm or exclude the large corrections.","A testable extension, not in the paper: recompute the significances including realistic SM backgrounds (e.g., $ZZZ$, $ZZh$) and a full detector simulation; based on the 17% event retention in Ref. [40], the discovery reach for $\\lambda_{hhH}$ is likely weaker than the quoted $Z$ values but may still be significant for the strongest benchmarks."],"forward_implications":["Di-Higgs production at $e^+e^-$ colliders can be enhanced by up to a factor of about six in the 2HDM, even in the exact alignment limit where all other Higgs couplings are SM-like.","An observable $H$-resonance peak in the $m_{hh}$ distribution at the ILC would give direct access to the coupling $\\lambda_{hhH}$, with projected significances above 10 for several benchmarks under the assumed no-background scenario.","Because the effective-potential and diagrammatic computations agree to within 1–5%, the simpler effective-potential evaluation of one-loop THCs is adequate for future phenomenological studies of this process.","A measurement of $\\kappa_\\lambda$ at $e^+e^-$ colliders with ~10% accuracy would be sensitive to the loop-enhanced values found in the 2HDM, making di-Higgs production a strong probe of BSM scalar sectors.","Detector resolution on $m_{hh}$ (smearing) is the main experimental limit on $\\lambda_{hhH}$ access; a high-resolution detector is necessary to see narrow resonance peaks."],"supporting_citations":[{"why":"Supplies the analytic one-loop formula for $\\lambda_{hhh}$ showing the large scalar-loop corrections in the 2HDM.","marker":"[15]"},{"why":"Provides the diagrammatic one-loop computation of $\\lambda_{hhh}$ (anyH3) used to compare finite-momentum effects against the effective-potential result.","marker":"[17]"},{"why":"Supplies the tree-level analytic $e^+e^-\\to Zhh$ cross-section formula adapted to the 2HDM.","marker":"[31]"},{"why":"Companion derivation of the analytic cross-section formulas used in the paper.","marker":"[32]"},{"why":"Prior sensitivity analysis of di-Higgs production at $e^+e^-$ colliders in the 2HDM, extended here with one-loop THCs and polarization.","marker":"[35]"},{"why":"ILC experimental analysis providing the event-selection cuts, b-tagging efficiency, and event-retention factors used for acceptance and significance estimates.","marker":"[40]"},{"why":"BSMPT effective-potential code used to compute the one-loop triple Higgs couplings.","marker":"[58]"},{"why":"Asymptotic profile-likelihood formulae used to compute the statistical significances of the $H$-resonance peaks.","marker":"[63]"}],"fun_headline_variants":["Sixfold self-coupling boost from 2HDM loops lights up e+e- → Zhh","One-loop 2HDM Higgs couplings amplify di-Higgs cross section nearly 6x","Loop-corrected Higgs trilinear can enhance di-Higgs rates 6x at ILC","Triple Higgs coupling hidden in 2HDM can make e+e- → Zhh 6x stronger"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument rests on the assumption that replacing the tree-level triple-Higgs vertices in the $e^+e^-\\to Zhh$ amplitude with the one-loop corrected couplings captures the dominant one-loop electroweak corrections; other one-loop contributions such as box diagrams, one-loop $ZZH$ couplings, and wave-function corrections are assumed to be subleading.","fun_headline_variants_meta":{"raw":{"variants":["Sixfold self-coupling boost from 2HDM loops lights up e+e- → Zhh","One-loop 2HDM Higgs couplings amplify di-Higgs cross section nearly 6x","Loop-corrected Higgs trilinear can enhance di-Higgs rates 6x at ILC","Triple Higgs coupling hidden in 2HDM can make e+e- → Zhh 6x stronger"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.002047,"raw_usage":{"total_tokens":8115,"prompt_tokens":1230,"completion_tokens":6885,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":846,"completion_tokens_details":{"reasoning_tokens":6781}},"tokens_in":846,"tokens_out":6885,"duration_ms":47717,"temperature":1.0,"reasoning_tokens":6781,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:39:18.153293+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A complete one-loop computation of $e^+e^-\\to Zhh$ in the 2HDM, including all non-THC diagrams, that yields total cross sections differing from the THC-insertion approximation by more than about 5–10% for the benchmark points considered would falsify the claim that the one-loop THCs are the leading corrections. Experimentally, an ILC measurement of the $Zhh$ cross section at 500 GeV that does not show a large enhancement for a parameter point predicting $\\kappa_\\lambda^{(1)}\\approx 5.75$ would equally call the central claim into question.","supporting_citations":[{"cited_title":"Testing Higgs selfcouplings at e+ e- linear colliders,","cited_arxiv_id":null,"evidence_quote":"Supplies the tree-level analytic $e^+e^-\\to Zhh$ cross-section formula adapted to the 2HDM."}],"review_version":1}