{"id":"3eeb2060-8863-46e5-8139-931ba5434e3b","arxiv_id":"2505.10625","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A CMA-ES scan with novelty reward finds valid C3HDM parameter points with large pseudoscalar hbb, htt and htautau couplings that previous alignment-biased scans had missed.","lead":"An evolutionary algorithm with a novelty bonus maps allowed regions of a 20-parameter three-Higgs-doublet model and finds valid points where the 125 GeV Higgs has large CP-odd couplings to bottom quarks and tau leptons that earlier biased scans missed. The broader point is that machine-learning-guided scanning can uncover valid phenomenology in high-dimensional beyond-Standard-Model spaces, motivating new LHC searches.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Direct CP-odd ttH limits are drawn as contours but never enforced in the loss, so the advertised large-co_tt points are not shown to satisfy all known constraints.","rationale":"The reader's weakest-assumption assessment already flags the unenforced ttH CP limits, along with the broader concern about the in-house black-box implementation of eEDM and HiggsTools outputs. Among these, the omitted direct CP-odd ttH constraint is the most load-bearing for the specific novelty claim: the paper's headline new feature is the discovery of regions with large |co_tt|, which uncorrelate co_bb and co_tautau and invalidate Eq. (38). Unlike the eEDM concern, which is about numerical correctness and scale choice, the ttH issue is a clear logical gap between what is imposed in L(theta) and what is claimed as satisfied. The paper explicitly draws the 1sigma and 2sigma contours in Fig. 6, so the authors are aware of the measurement; yet Section III only says the limits are shown, not that they are encoded in the loss. A rate-only ttH constraint is insufficient because the direct CP measurements use angular and kinematic distributions that can exclude points even when the total rate is SM-like. The proper response is not to accuse the authors of hiding anything but to require a reproducible check: impose the direct CP likelihood and see whether the large-co_tt region survives. If it does not, the central phenomenological conclusion fails; if it does, the claim is strengthened. Because this is exactly the kind of condition that the reader's CONDITIONAL verdict anticipated, no verdict change is needed, but the concrete test should be part of the acceptance criteria.","tokens_in":19758,"tokens_out":5080,"duration_ms":55214,"concrete_test":"Add the direct ttH CP observable from Ref. [26] (or [28]) as an explicit C(O) term in Eq. (44) with the published 2sigma bound, rerun the focused co_tt scans, and compare the number of accepted points with |sign(kV)*co_tt| > 0.3 and the co_bb-co_tautau coverage in Fig. 5. If those points disappear or become rare, the claimed uncorrelated large-co_tt region is an artifact of an unenforced constraint; if they survive, the omission is immaterial to the central claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the generated points satisfy all known experimental constraints, but the CP-odd top-Higgs limits are not implemented in the constraint set. In Section III, under 'Direct searches for CP-violation', the tau CP bound |theta_tau| < 34 deg is enforced as a strict constraint, while the ttH limits from Refs. [26-28] are only described as contours 'shown in the relevant figures'. No corresponding C(O) term appears in the list feeding L(theta) in Eq. (44). Equation (42) only rescales the ttH production rate by (ce_tt)^2 + 0.416*(co_tt)^2; a rate constraint is not equivalent to the CP-sensitive differential observables used in Refs. [26-28]. Thus the red/green points with large sign(kV)*co_tt displayed in Fig. 6 and discussed in Section V.D have not been shown to satisfy a known experimental constraint. This directly undermines the abstract's 'concordance with all known experimental constraints' and the paper's central phenomenological claim that large co_tt is a viable feature of the model.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies a machine-learning black-box optimization scheme (CMA-ES with a histogram-based novelty reward) to explore the 20-dimensional parameter space of the softly-broken Z2×Z2' three-Higgs-doublet model with explicit CP violation. The authors claim that this method finds points satisfying all implemented theoretical and experimental constraints at orders-of-magnitude higher efficiency than previous random scans, and, more importantly, uncovers new phenomenologically viable regions: large CP-odd couplings of the 125 GeV Higgs to b quarks, tau leptons, and top quarks, including the wrong-sign regime for hbb and htautau. They further claim that the earlier correlation co_tautau = -tan^2(beta1) co_bb reported in Ref. [13] is not a property of the model but an artifact of starting scans near the real alignment limit with co_tt ≈ 0, and that by allowing large co_tt this correlation dissolves. The methodology, the constraint list, the loss function, and the resulting coupling-plane plots are presented in Sections II-V.","tokens_in":19947,"tokens_out":4676,"duration_ms":48917,"significance":"If the results are correct, the paper provides a useful methodological demonstration that evolutionary strategies combined with novelty rewards can find previously unreachable CP-violating regions in a high-dimensional multi-Higgs model, and the claim that Eq. (38) is an artifact of the earlier scanning strategy is physically interesting and instructive for future phenomenology scans. The authors deserve credit for being explicit that the generated points have no statistical interpretation and for cross-checking the Higgs-signal part with HiggsTools-1.1.3. However, the central claim of concordance with 'all known experimental constraints' is not yet established: the direct CP-odd ttH limits from Refs. [26-28] appear only as contours in Fig. 6 and are not enforced in the loss, and the black-box implementation is not released, so its completeness cannot be independently verified. The headline regions with large |co_tt| are therefore conditional on missing validation.","major_comments":[{"comment":"The direct CP-odd ttH limits from Refs. [26-28] are described in Section III but are not included in the constraint loss L(theta) of Eq. (44); they appear only as contour lines in Fig. 6. The only ttH-related expression, Eq. (42), rescales the ttH production rate by (ce_tt)^2 + 0.416 (co_tt)^2, which is a rate-level rescaling and does not encode the CP-sensitive angular observables used in Refs. [26-28]. Consequently, the red/green points with |co_tt| larger than about 0.3 shown in Fig. 6 and discussed in Section V.D are not demonstrated to satisfy the CP-odd ttH constraints, and the abstract's claim of concordance with all known experimental constraints is unsupported for those points. This is load-bearing because large co_tt is one of the two headline new phenomenological features, so the paper should either implement the CP-sensitive constraints, restrict the claim to the implemented constraints, or explicitly verify that the displayed points satisfy the contours.","section":"Section III/V.D, Eq. (42), Fig. 6"},{"comment":"The central existence claim depends on an in-house black-box implementation of the eEDM calculation at the MZ scale and on the HiggsTools/HiggsSignals/HiggsBounds interfaces, but no code, configuration files, or generated parameter sets are released. The completeness and correctness of the implemented constraints therefore cannot be checked by a reader. In particular, Section IV.A's black-box treatment and Section V's color-code definition of red points as passing all constraints in Section III require either a data release of the surviving points together with the exact constraint list, or a detailed validation of the eEDM and collider-constraint routines. I recommend release of at least the generated point files and the precise list of constraints with their bounds.","section":"Section IV/V (reproducibility)"}],"minor_comments":[{"comment":"The caption fragment 'Blue the paper.' is incomplete and should be reworded, for example as 'Blue points are taken from Ref. [13].'.","section":"Fig. 8 and Fig. 9 captions"},{"comment":"There is a typo in the sentence 'we make the choice of optmising a single loss function'; it should read 'optimising'.","section":"Section IV (text)"},{"comment":"The bullet on CP-violation gives an explicit bound for the tau-channel angle but merely says the ttH limits from Refs. [26-28] are shown as contours; it should state explicitly whether these limits are enforced as constraints or are only overlays for comparison.","section":"Section III, 'Direct searches for CP-violation'"},{"comment":"The sentence 'The experimental results are shown as 1σ (solid) and 2σ contour lines [26], indicate consistency with co_tt≠0' is grammatically ambiguous; clarify whether the data allow co_tt nonzero or whether the plotted points are required to lie inside the contours.","section":"Section V.D, Fig. 6 discussion"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal as a phenomenological techniques paper. The missing enforcement of the direct CP-odd ttH limits is the key blocking issue; if the authors can implement or properly caveat those constraints and release at least the data, I would be willing to accept a revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"A couple of things you should know. The paper does deliver a real phenomenological result: the CMA-ES + novelty-reward scan reaches regions of the Z2xZ2' C3HDM that the earlier scans in Ref. [13] missed. It fills the ce_bb-co_bb circle, finds wrong-sign fermion couplings, and produces points where co_bb and co_tautau are uncorrelated. The blue-point comparison makes a fair case that Eq. (38) was a scanning artifact, not a model property. Credit where it's due.\n\nThe soft spot is not minor. The abstract says points are in concordance with 'all known experimental constraints,' but the CP-odd ttH limits from Refs. [26-28] are only shown as contours in Fig. 6; they never enter the loss L(θ) of Eq. (44). The tau CP bound is enforced as a strict constraint; the ttH ones are not. That matters because the uncorrelation result rests on allowing large co_tt. If those differential ttH observables were imposed, the large-co_tt points might not survive, and the paper's central claim about restoring the type-Z decoupling would weaken substantially. At minimum, this is a load-bearing overstatement.\n\nThere's also the artifact problem: no code or data is released. The constraint stack is an in-house black box, with the eEDM calculation at the MZ scale described but not shipped. For an existence claim, that makes independent verification harder. The paper does honestly say the scans carry no statistical interpretation, which is good, but the red/green coverage plots are illustrations of reach, not probability statements.\n\nNone of this sinks the paper. The existence claim for the smaller-co_tt regions (large |co_bb|, wrong-sign ce_bb, and the co_bb/co_tautau decorrelation for moderate co_tt) is plausible and well-motivated. The main fix is straightforward: either put the ttH CP limits into the loss and re-run, or state plainly that they were not imposed, and scale the abstract and Section V.D claims accordingly. Releasing the scan data would also go a long way.\n\nWho is this for? BSM phenomenologists working on multi-Higgs models, CP violation, and ML-driven parameter-space exploration. It deserves a serious referee, not a desk reject; I would send it to peer review with the requirement that the ttH constraint gap be addressed and the artifacts either released or clearly specified.","headline":"Genuine new scan regions in the C3HDM, but the abstract overclaims all known constraints because the ttH CP-odd limits are drawn, not enforced in the loss.","tokens_in":20563,"tokens_out":3201,"would_cite":false,"duration_ms":30604,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A machine-learning scan of a CP-violating three-Higgs-doublet model finds experimentally allowed parameter points with large pseudoscalar Higgs couplings and shows that a previously reported correlation was a scanning artifact.","keywords":["three-Higgs-doublet model","CP violation","pseudoscalar Higgs couplings","evolutionary strategy","novelty reward","electron electric dipole moment","Higgs signal strengths","LHC phenomenology"],"falsifier":"Take a representative published point with large $|c^o_{bb}|$ or $|c^o_{tt}|$ and recompute its electron electric dipole moment, $B\\to X_s\\gamma$ rate, Higgs signal strengths, and direct new-scalar search exclusions with independent published codes; if any recomputed observable exceeds its experimental bound, the claim that such regions satisfy all known constraints falls. A separate direct measurement excluding $|c^o_{bb}|$ near one would rule against the model space itself, not against the search technique.","tokens_in":19562,"feed_emoji":"⚛️","tokens_out":11838,"duration_ms":108007,"temperature":0.7,"pith_summary":"This paper tries to establish that a CP-violating three-Higgs-doublet model has far more experimentally viable parameter space than earlier scans indicated, and that a machine-learning search can find it. The authors replace the slow random-scan strategy, which could only find valid points by starting near the real-scalar alignment limit, with an evolutionary-strategy optimiser augmented by a novelty reward that pushes the search into unexplored regions. Using this tool on the model's 20 free parameters, they obtain points that pass all implemented theoretical and experimental constraints while displaying large pseudoscalar couplings of the 125 GeV Higgs to bottom quarks, top quarks, and tau leptons. They conclude that a correlation previously found between the bottom and tau pseudoscalar couplings was an artifact of the old sampling method, not a property of the model. If correct, this matters because it reopens experimentally testable channels (large CP-odd Higgs couplings to $b$, $t$, and $\\tau$) that earlier scans had effectively ruled out.","feed_headline":"Machine-learning scan uncovers large pseudoscalar Higgs couplings","feed_subtitle":"It reaches regions previous scans missed, reopening CP-odd couplings of b, t, and tau.","key_machinery":"The engine is a black-box loss function $L(\\theta)=\\sum_i C(O_i(\\theta))$, where each constraint function $C$ returns zero inside the allowed interval and a positive penalty proportional to the distance outside it; a point is valid exactly when $L=0$. This loss is minimised by a covariance-matrix-adaptation evolutionary strategy (CMA-ES), a derivative-free optimiser suited to rough, high-dimensional landscapes. To prevent the optimiser from collapsing into the first valid basin, a novelty reward is added: a histogram-based outlier score estimates the local density of previously found valid points in parameter and observable space, and the loss is shifted so that revisiting dense regions carries a penalty. Seeded runs, which start from already valid points and optionally include extra constraints forcing large $|c^o_{bb}|$ or negative $c^e_{bb}$, then populate the coupling planes systematically. This machinery carries the argument because it explores the full 20-dimensional domain with no hierarchy of constraints, which is what uncovers the regions that alignment-limit seeding could not reach.","core_discovery":"In the softly-broken $Z_2\\times Z_2'$ three-Higgs-doublet model with CP-violating coefficients (a type-Z model in which the up-type, down-type, and lepton Yukawa sectors each couple to their own doublet), the paper claims that the full scalar-pseudoscalar coupling plane of the 125 GeV Higgs to bottom quarks can be populated with points consistent with every constraint it implements, including the electron electric dipole moment, $B\\to X_s\\gamma$, oblique parameters, signal strengths, and direct scalar searches. The previous scan had found only a limited wedge and an apparent anticorrelation between $c^o_{\\tau\\tau}$ and $c^o_{bb}$, which was traced to $c^o_{tt}\\approx 0$; the new search finds points with $|c^o_{tt}|\\gtrsim 0.3$, filling the $c^o_{\\tau\\tau}$--$c^o_{bb}$ plane and showing that Eq. (38), $c^o_{\\tau\\tau}/c^o_{bb}=-\\tan^2\\beta_1$, is a property of the old scanning strategy rather than of the model. The scan also populates wrong-sign couplings for leptons and down quarks while respecting the tau CP-phase bound $|\\theta_\\tau|<34^\\circ$, and it finds that large $|c^o_{tt}|$ forces a second neutral scalar to approach degeneracy with the 125 GeV Higgs.","pith_inferences":["If the central claim holds, similar artifacts may lurk in other high-dimensional BSM scans: regions dismissed because an earlier sampler could not reach them should be re-examined with novelty-guided exploration.","A natural extension is to re-run the same machinery on the complex two-Higgs-doublet model with the scalar mass range opened below 125 GeV, since the paper's check excluded the near-degenerate configurations where it did find large $|c^o_{tt}|$.","The generated points carry no statistical weight; the plots demonstrate existence of parameter regions, not likelihood, so they should not be read as probability distributions.","Releasing the constraint code and the valid-point samples would turn the claim into a reproducible benchmark: independent implementations could then recompute the observables for the published points and confirm that every bound is respected."],"forward_implications":["The whole $c^e_{bb}$--$c^o_{bb}$ circle, including pure-pseudoscalar $hbb$ couplings and the wrong-sign region, is compatible with all implemented constraints, making large CP-odd $hbb$ couplings a live experimental target.","Large $|c^o_{tt}|$ is not excluded by current $t\\bar t H$ CP measurements, so dedicated CP-odd top-Higgs searches are further justified.","$c^o_{\\tau\\tau}$ and $c^o_{bb}$ are not forced to anticorrelate, restoring the type-Z model's three decoupled fermion sectors.","The CP-violating angles $\\alpha_{14}$ and $\\alpha_{15}$ must remain small, while the other CP-violating parameters can fill their full ranges.","The method produces on the order of $10^5$ valid points in under 100 CPU hours, compared with fewer than one per $10^{13}$ for random sampling, making full-domain scans feasible for other high-dimensional models."],"supporting_citations":[{"why":"Defines the C3HDM, the previous alignment-limit scan, the blue comparison points, and Eq. (38) that the new search overturns.","marker":"[13]"},{"why":"Introduces the black-box machine-learning optimisation approach that the paper adapts.","marker":"[15]"},{"why":"Supplies the novelty-reward mechanism that combines evolutionary strategies with anomaly detection.","marker":"[16]"},{"why":"Sets the latest electron electric dipole moment bound that all accepted points must satisfy.","marker":"[12]"},{"why":"Provides the LHC Higgs signal-strength measurements used as the 2-sigma agreement baseline.","marker":"[3]"},{"why":"Supplies the CP-phase limit on the Higgs-tau coupling, $|\\theta_\\tau|<34^\\circ$, enforced as a strict constraint.","marker":"[6]"},{"why":"Gives the measured CP contours for top-Higgs production against which the large-$c^o_{tt}$ points are compared.","marker":"[26]"},{"why":"Provides the $t\\bar tH$ pseudoscalar-to-scalar cross-section ratio used for mixed-CP signal strengths.","marker":"[9]"}],"fun_headline_variants":["ML scan fills pseudoscalar Higgs coupling plane","Evolutionary strategy opens up pseudoscalar Higgs couplings","Novelty-driven ML finds large pseudoscalar Higgs couplings","ML exposes CP-odd Higgs couplings to b, t, tau"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the in-house black-box code implements every relevant constraint correctly and completely as used---especially the electron electric dipole moment at the Z-boson mass scale---since the paper releases neither the code nor the data; the direct CP-odd top-Higgs limits, shown only as contours, are not among the implemented constraints.","fun_headline_variants_meta":{"raw":{"variants":["ML scan fills pseudoscalar Higgs coupling plane","Evolutionary strategy opens up pseudoscalar Higgs couplings","Novelty-driven ML finds large pseudoscalar Higgs couplings","ML exposes CP-odd Higgs couplings to b, t, tau"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001408,"raw_usage":{"total_tokens":5721,"prompt_tokens":1005,"completion_tokens":4716,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":621,"completion_tokens_details":{"reasoning_tokens":4646}},"tokens_in":621,"tokens_out":4716,"duration_ms":34905,"temperature":1.0,"reasoning_tokens":4646,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:07:06.282840+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a representative published point with large $|c^o_{bb}|$ or $|c^o_{tt}|$ and recompute its electron electric dipole moment, $B\\to X_s\\gamma$ rate, Higgs signal strengths, and direct new-scalar search exclusions with independent published codes; if any recomputed observable exceeds its experimental bound, the claim that such regions satisfy all known constraints falls. A separate direct measurement excluding $|c^o_{bb}|$ near one would rule against the model space itself, not against the search technique.","supporting_citations":[{"cited_title":"Aad et al., cp properties of higgs boson interactions with top quarks in the tth and th processes usingh→γγ with the atlas detector , Phys","cited_arxiv_id":null,"evidence_quote":"Gives the measured CP contours for top-Higgs production against which the large-$c^o_{tt}$ points are compared."}],"review_version":1}