{"id":"4b4841e7-e748-46d9-a417-99c90fea1d33","arxiv_id":"1909.00784","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In the general 2HDM with unitarity, bounded-from-below, and T parameter constraints, the Higgs triple coupling ranges up to 1.6 times the SM value and can be negative, while the quartic coupling remains positive and reaches up to four times SM.","lead":"This paper scans the general two Higgs doublet model under unitarity and stability constraints and finds the Higgs self-couplings can deviate widely from the Standard Model: the cubic coupling can reach 1.6 times the SM value or even be negative, while the quartic coupling stays positive and can be four times larger. A generalist should read this because Higgs self-coupling measurements at future colliders are a direct test of such models.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quoted g3/g4 extremes may come from parameter points with new scalars below 114 GeV that direct searches exclude; the scan imposes only T and c1>0.9, so the phenomenological claim is not yet secured.","rationale":"The reader's weakest assumption identifies the same load-bearing issue: the scan permits new scalars lighter than 125 GeV with only a weak coupling constraint and the T bound, omitting LEP/LHC direct searches and Higgs signal-rate constraints. Since the paper's abstract explicitly claims agreement with phenomenology, the numerical extremes must come from parameter points that survive direct searches. The paper does not report the masses of the scalars at the extreme g3 and g4 points, so it is possible that the negative-g3 or maximum-g4 points are in the region M2,M3 < M1 that is most likely to be excluded. My read therefore does not change the reader's conditional verdict; the paper is plausible but requires the additional phenomenological check before the headline claim can be accepted. I find no internal mathematical inconsistency in the unitarity/BFB implementation, and the positivity of g4 is consistent with bounded-from-below along the h1 direction, but the viability of the claimed parameter-space envelope is the weakest point.","tokens_in":4196,"tokens_out":8923,"duration_ms":97629,"concrete_test":"Re-run the same scan after adding a direct-search cut: reject every point in which either neutral new scalar h2 or h3 has mass below 114.4 GeV and (R21^2 + R31^2) > 0.02, and also reject points where the 125 GeV h1 signal rates deviate by more than 2 sigma from LHC measurements (e.g., with HiggsSignals). Then recompute the extrema of g3/gSM3 and g4/gSM4 and the existence of g3 < 0 points. If the 1.6x/4x maxima and negative g3 disappear, the central claim depends on excluded parameter space; if they persist with only minor shifts, the reader's concern is not load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the general 2HDM can produce g3 up to 1.6 times the SM value, even zero or negative, and g4 up to four times the SM value, while remaining in agreement with phenomenology. That claim rests on the scan exploring phenomenologically viable parameter space. The scan imposes unitarity, bounded-from-below, vacuum-stability, T in [-0.04, 0.20], and c1 > 0.9, but explicitly allows M2 and M3 below 125 GeV without any direct search limits. A neutral scalar below about 114 GeV with a non-negligible coupling to W/Z is excluded by LEP; with c1 > 0.9, R21^2 + R31^2 can be as large as 0.19, so the new scalars are not automatically safe. The paper's own mass-binned statement shows that for masses up to 125 GeV, g3 is bounded below by 0.3; the zero/negative g3 points and the maximal g4 may occur in the low-mass or intermediate-mass region, but the text does not specify. If the extreme points lie in the excluded low-mass region, the headline envelope and the claim of agreement with phenomenology fail. The absence of LHC 125 GeV signal-rate constraints and of S/U bounds makes the viability check still weaker.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the general two-Higgs-doublet model in the Higgs basis, imposing unitarity, bounded-from-below, and vacuum-stability conditions together with the experimental bound on the oblique parameter T. Using a numerical scan over input masses and angles, the authors compute the cubic (g3) and quartic (g4) self-couplings of the 125 GeV Higgs through eqs. (1.7)–(1.8). They report that g3 can be up to 1.6 times the Standard Model value, can vanish or become negative, and that g4 is always positive and up to four times the SM value. The paper is a short proceedings contribution that refers to a companion paper for details.","tokens_in":4478,"tokens_out":5884,"duration_ms":59359,"significance":"If correct, the result is phenomenologically relevant: it maps out a wide allowed envelope for the SM-like Higgs self-couplings in the 2HDM, including a sign flip of g3, which could be probed at high-luminosity colliders. The authors provide explicit expressions for g3 and g4 in the Higgs basis and correctly implement known basis-invariant constraints. However, the central numerical claims are not yet supported at the level of a journal publication because the scan is underspecified and the phenomenological viability checks are incomplete; this limits the strength of the conclusions.","major_comments":[{"comment":"The headline numbers ('g3 up to 1.6 times the SM value, possibly zero or negative; g4 up to four times the SM value') are extrema of a numerical scan, but the ranges and densities of the scanned parameters (M2, M3, MC, ϑ1, ϑ2, λ2, λ3, ℜ(λ6λ7*), ℜ(λ5*λ6λ7)) are not specified, nor is the number of sampled points. Without this information the quoted extremes are not reproducible and cannot be regarded as rigorous bounds; they might be isolated outliers. The statement 'For the masses up to 500 GeV the couplings reach their maximal values' is presented without supporting data or error estimates.","section":"Section 2 and Figure 1"},{"comment":"The claim that 'g4 is always positive because of the boundedness from below of the potential' is asserted without derivation. Equation (1.8) is a combination of λ1...λ7 with coefficients xk that can have either sign; the BFB conditions from refs. [3,4] do not transparently imply positivity of this combination. The paper should either prove the statement or give a precise reference. As written, this is an unsupported claim about a central result.","section":"Section 2"},{"comment":"The sentence 'We do not impose any lower limit on M2,3; we allow them to be lower than M1' exposes a load-bearing gap. The only constraints applied are T ∈ [−0.04, 0.20] and c1 > 0.9. Since c1 > 0.9 permits R21^2 + R31^2 up to 0.19, neutral new scalars below ~114 GeV can have non-negligible couplings to W/Z and are directly constrained by LEP searches; no LHC 125 GeV signal-rate constraints or S/U bounds are applied. The paper therefore does not establish that the scanned points are phenomenologically allowed. In particular, the paper's own mass-binned summary shows that for masses below 125 GeV g3 is bounded below by 0.3, so the negative/zero-g3 points and the maximal g4 values may arise in the low-mass region; the text does not identify where they occur, so the headline envelope could fail if those points are excluded.","section":"Section 2, paragraph on phenomenological constraints"}],"minor_comments":[{"comment":"The text refers to the 'Standart Model' twice; this should be corrected to 'Standard Model'.","section":"Final paragraph before references"},{"comment":"The phrase 'we require the m to satisfy' is a typo; it should read 'we require them to satisfy'.","section":"Section 2"},{"comment":"The notation √MC, √M2, and √M3, where M_i denote squared masses, could be confusing; please define the convention explicitly in the text and in the figure caption.","section":"Section 1 and Figure 1"},{"comment":"The caption says the plot shows 'various values of c1' but does not provide a legend or a description of the line styles; without this the reader cannot interpret which curve corresponds to which c1 value.","section":"Figure 1"},{"comment":"The phrase 'The squared mass M1 = (125 GeV)^2' is slightly ambiguous because equation (1.5b) uses M1 as an eigenvalue; clarifying that all M_i are squared masses would prevent confusion.","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, and the brevity is understandable, but the central quantitative claims (the 1.6 and 4.0 factors, the sign flip of g3, and the positivity of g4) are presented as phenomenological results without a reproducible scan specification or adequate direct-search constraints. If the companion paper [2] contains the missing details, the authors should cite it more precisely and indicate exactly which results are transferred; otherwise the manuscript needs to be extended. I would like to see a revision that addresses the three major points above before publication in a journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a short proceedings write-up of a numerical scan, and the headline result is plausible but oversold. It reports that in the general 2HDM, after imposing unitarity, bounded-from-below, vacuum stability, and the T-parameter bound, the cubic Higgs coupling g3 can be up to 1.6 times the SM value and can be zero or negative, while the quartic coupling g4 stays positive and can reach four times the SM value. That is the thing to remember: an interesting, concrete envelope that directly speaks to Higgs self-coupling measurements.\n\nWhat is new: I am not aware of another scan that applies this particular combination of constraints in the Higgs basis to the general 2HDM and reports the resulting g3/g4 ranges. The explicit formulas (1.7) and (1.8) are useful, and the paper is honest that most of the technical apparatus comes from their own earlier work (ref [2]). The basis-invariance point is well made.\n\nThe soft spots are in proportion. The bounds are numerical extrema, not proved inequalities; the scan ranges and densities are not given, so the reader cannot judge coverage. The statement that g4 is always positive is attributed to boundedness but not derived. More importantly, the paper claims agreement with phenomenology while only applying T and c1 > 0.9. They allow the new scalars to be below 125 GeV and do not apply LEP, LHC, S, U, or 125-GeV signal-rate constraints. The text's mass-binned statement shows that for new scalars up to 125 GeV the trilinear stays above 0.3, so the zero/negative g3 cases probably come from heavier points, but the maximal g4 may also sit in regions where the missing constraints bite. So the phenomenological envelope as stated is not yet secure.\n\nOverall the central calculation is likely sound. The paper would be improved by giving scan parameters and by rewriting the phenomenological claim to say which constraints were actually applied. For a proceedings version this is a reasonable contribution; a journal version would need the additional constraints and a more careful derivation of g4 positivity.\n\nI would send it to a referee if it were submitted to a regular journal: the result is nontrivial and the issues are fixable. I would not cite it as it stands, though — I would wait for the version that closes those gaps.","headline":"The reported g3/g4 ranges are plausible and worth knowing, but the paper oversells its phenomenological reach: the scan applies only T and c1>0.9 and lacks direct search constraints.","tokens_in":5064,"tokens_out":4209,"would_cite":false,"duration_ms":42012,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The general two-Higgs-doublet model allows the 125 GeV Higgs cubic self-coupling to reach 1.6 times the Standard Model value and even to turn negative, while the quartic coupling stays positive and can reach four times the SM value.","keywords":["two Higgs doublet model","Higgs self-couplings","cubic Higgs coupling","quartic Higgs coupling","unitarity bounds","bounded-from-below conditions","oblique parameter T","Higgs basis"],"falsifier":"Re-run the same scan with the S and U oblique parameters added and with current LEP and LHC lower bounds on the charged and neutral scalar masses; if the points that give g3 equal to zero or negative, or g4 above three times the Standard Model value, all disappear, then the quoted envelope is not the envelope of a fully phenomenologically valid 2HDM.","tokens_in":3946,"feed_emoji":"⚛️","tokens_out":4049,"duration_ms":44984,"temperature":0.7,"pith_summary":"This paper asks how much the cubic and quartic self-couplings of the 125 GeV Higgs can differ from their Standard Model values while the underlying theory still makes sense. It works in the most general two-Higgs-doublet model and imposes three sets of restrictions at once: tree-level unitarity of scalar scattering, a potential that is bounded from below, and the experimentally measured T parameter. The numerical result is that the cubic coupling can be up to 1.6 times the Standard Model value, but can also be zero or negative, while the quartic coupling is always positive and can reach four times its Standard Model value. The paper maps where these deviations occur in terms of the new-scalar masses, so the result gives a concrete target for future collider measurements of Higgs self-interactions.","feed_headline":"2HDM Higgs self-couplings: up to 4x SM, cubic can flip sign","feed_subtitle":"New scalars lighter than 500 GeV produce the largest deviations, so collider searches can test this window.","key_machinery":"The central object is the 11-parameter scalar potential of the 2HDM written in the Higgs basis, together with the 3x3 mass matrix of the neutral scalars and its orthogonal diagonalizing matrix R, parametrized by three rotation angles. The argument runs by taking the masses and mixing angles as input, computing the remaining quartic couplings, and then enforcing unitarity (the eigenvalues of the two-particle scalar scattering matrices must be below 4π), boundedness from below, vacuum stability, and the T-parameter bound. The explicit formulas for the cubic coupling g3 and quartic coupling g4 in terms of R and the potential parameters are the quantities whose allowed envelopes are then scanned numerically.","core_discovery":"The central claim is that, within the parameter space that satisfies unitarity, boundedness from below, vacuum stability, and the T-parameter constraint, the general 2HDM permits a wide and partly sign-flipped range for the 125 GeV Higgs self-couplings. For new scalar masses up to 125 GeV, the cubic coupling lies in the range 0.3–1.6 times the Standard Model value and the quartic coupling lies in the range 0–3 times its Standard Model value; for masses up to about 500 GeV both couplings reach their maximal deviations, and for masses above 1 TeV they approach their Standard Model values. The paper also finds that the new scalars cannot be arbitrarily heavy: with cos(theta1) below about 0.99 they must be no heavier than roughly 700 GeV, and with cos(theta1) below 0.95 no heavier than about 550 GeV, while in the nearly SM-like limit they can become TeV-scale and almost degenerate.","pith_inferences":["The paper uses only the T oblique parameter among electroweak precision constraints; including S and U as well would likely narrow the quoted envelope, so the 1.6x and 4x maxima should be read as an upper bound on the currently allowed range, not a definitive prediction.","If existing LEP and LHC direct searches already exclude neutral or charged scalars below about 125 GeV with the required couplings, then the low-mass region that produces the largest and sign-flipped deviations would be closed, and the remaining envelope would be considerably smaller.","The same input-mass-and-angles scan could be repeated with S and U constraints added, and the resulting allowed regions for g3 and g4 would give a sharper, more conservative test of this model class."],"forward_implications":["If the paper is right, a future measurement of the triple-Higgs coupling could see an enhancement of up to 60 percent over the Standard Model, or even a negative value, rather than only a modest upward shift.","The quartic self-coupling is predicted to be strictly positive in this framework, so a measured negative quartic coupling would rule out this entire parameter space.","Large deviations require new scalars that are relatively light, roughly below 500 GeV, making them directly accessible to LHC searches and giving a concrete discovery target.","For nearly SM-like Higgs couplings (cos(theta1) close to 1), the new scalars can be TeV-scale and almost degenerate, which would make them far harder to see at current colliders."],"supporting_citations":[{"why":"Supplies the unitarity conditions for the 2HDM scattering matrices, whose eigenvalues are bounded by 4π.","marker":"[1]"},{"why":"Provides the calculation method, the explicit scattering matrices, and the parameter-scan technique used throughout the numerical analysis.","marker":"[2]"},{"why":"Gives necessary and sufficient conditions for the 2HDM potential to be bounded from below, which the paper implements.","marker":"[3]"},{"why":"Provides a further derivation of bounded-from-below conditions used to constrain the potential parameters.","marker":"[4]"},{"why":"Gives the conditions ensuring the chosen vacuum is the global minimum over all other stationary points of the potential.","marker":"[5]"},{"why":"Supplies the formula used to compute the oblique parameter T in the 2HDM.","marker":"[6]"},{"why":"Provides the experimentally allowed domain for the T parameter, -0.04 < T < 0.20, used as a phenomenological constraint.","marker":"[7]"}],"fun_headline_variants":["2HDM Higgs cubic can flip sign, quartic up to 4x SM","Cubic Higgs coupling in 2HDM: sign flip, up to 1.6x SM","Unitarity bounds widen 2HDM Higgs self-couplings","New scalars in 2HDM capped near 700 GeV by unitarity","Higgs self-couplings: cubic negative possible, quartic 4x SM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper treats a parameter point as phenomenologically acceptable if it passes only the T-parameter bound and cos(theta1) > 0.9, allowing new scalars to be lighter than 125 GeV without applying LEP or LHC direct-search limits or the S and U oblique parameters.","fun_headline_variants_meta":{"raw":{"variants":["2HDM Higgs cubic can flip sign, quartic up to 4x SM","Cubic Higgs coupling in 2HDM: sign flip, up to 1.6x SM","Unitarity bounds widen 2HDM Higgs self-couplings","New scalars in 2HDM capped near 700 GeV by unitarity","Higgs self-couplings: cubic negative possible, quartic 4x SM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000245,"raw_usage":{"total_tokens":1504,"prompt_tokens":885,"completion_tokens":619,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":501,"completion_tokens_details":{"reasoning_tokens":508}},"tokens_in":501,"tokens_out":619,"duration_ms":6185,"temperature":1.0,"reasoning_tokens":508,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:36:06.318795+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same scan with the S and U oblique parameters added and with current LEP and LHC lower bounds on the charged and neutral scalar masses; if the points that give g3 equal to zero or negative, or g4 above three times the Standard Model value, all disappear, then the quoted envelope is not the envelope of a fully phenomenologically valid 2HDM.","supporting_citations":[{"cited_title":"The three- and four-Higgs couplings in the general two-Higgs-doublet model","cited_arxiv_id":"1807.04244","evidence_quote":"Provides the calculation method, the explicit scattering matrices, and the parameter-scan technique used throughout the numerical analysis."},{"cited_title":"Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential","cited_arxiv_id":"1705.08965","evidence_quote":"Gives the conditions ensuring the chosen vacuum is the global minimum over all other stationary points of the potential."},{"cited_title":"Patrignani et al","cited_arxiv_id":null,"evidence_quote":"Provides the experimentally allowed domain for the T parameter, -0.04 < T < 0.20, used as a phenomenological constraint."}],"review_version":1}