{"id":"1f3cdfae-dd6d-439e-966b-f57044d34aaa","arxiv_id":"2507.01137","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A combined fit of LHC and LEP data constrains the five four-heavy-quark Wilson coefficients, and shows that gamma5-scheme choices can shift the resulting bounds.","lead":"This paper combines LHC and LEP measurements to narrow the allowed strength of four-heavy-quark interactions in the Standard Model Effective Field Theory. It also shows that the mathematical scheme used for gamma5 in Higgs calculations can change the extracted limits.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The linear c1_tt bound excluding zero is driven by the A_b,FB discrepancy; a leave-one-out test for that observable is needed before crediting the combined EWPO+LHC constraint.","rationale":"The reader's weakest_assumption is exactly the load-bearing concern I identify: the fit uses the A_b,FB discrepancy as signal without a robustness test, and this drives the linear c1_tt bound away from zero. The evidence in the paper supports this: Eq. (C.10) shows A_b,FB is the only EWPO with a significant c1_tt coefficient; Table 5 shows the EWPO-only bound on c1_tt is [-14.92,-1.68]; and Section 5.3 explicitly attributes the EWPO-only exclusion of the SM to A_b,FB. Removing A_b,FB from the fit should therefore dramatically change the c1_tt interval, and if it includes zero, the central claim that the combination significantly reduces the parameter space for this operator is contingent on a single disputed observable. The gamma5 scheme issue is real but less load-bearing for the final Tables 5 and 6, because the paper itself states that inclusive Higgs production has no significant impact on the final combination; it matters mainly for the standalone single-Higgs interpretation in Section 4. The paper is honest about both caveats, and the derived two-loop EWPO expressions and tabulated predictions are useful, so a CONDITIONAL verdict is appropriate. No change to the reader's verdict is needed.","tokens_in":28753,"tokens_out":3900,"duration_ms":124408,"concrete_test":"Re-run the linear O(Lambda^-2) combined chi2 fit of Section 5.3 twice: once with the EWPO2 dataset (A_b and A_b,FB) removed entirely, and once with A_b,FB shifted upward by +1 sigma and +2 sigma toward its SM prediction while keeping all other inputs unchanged. If the 95% CL interval for c1_tt in Table 6 no longer excludes zero in either variant, the headline combined bound is not robust against the known A_b,FB discrepancy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central combined-fit result in Section 5.3, specifically the O(Lambda^-2) individual 95% CL interval for c1_tt in Table 6, [-9.12, -0.89], excludes the SM. The EWPO-only bound in Table 5 is [-14.92, -1.68], and the dominant driver is the well-known discrepancy in A_b,FB: Eq. (C.10) gives delta(A_b,FB)/A_b,FB = 51.083e-4 * c1_tt, while the contributions of c1_tt to delta(Gamma_b), R_c, R_l, and R_b are all O(1e-6). Thus c1_tt is constrained almost entirely by A_b,FB, and the fit attributes the full 1.5-3 sigma experimental discrepancy to this single Wilson coefficient. The paper states in Section 5.3 that the EWPO-only contours exclude the SM at 95% CL because of the A_b,FB discrepancy, but it provides no robustness test such as dropping or shifting this observable. If other SMEFT operators (e.g., Zbb vertex corrections) or unknown systematics contribute to A_b,FB, the quoted tight linear bound on c1_tt would not be a genuine constraint. This is the weakest load-bearing assumption of the paper's main phenomenological claim, more so than the gamma5 scheme dependence because Section 5.3 itself notes that inclusive Higgs production has no significant impact on the final combination.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper derives constraints on the five dimension-six four-heavy-quark operators in the SMEFT by combining LHC measurements of four-top, top-pair, top-pair-plus-Higgs, and inclusive single-Higgs production with LEP electroweak precision observables. The theoretical predictions include tree-level contributions to four-top production, NLO contributions to t-tbar and t-tbar-H production, two-loop contributions to gluon-fusion Higgs production and Higgs decays, and one- and two-loop contributions to EWPO. The authors also study the dependence of the single-Higgs constraints on the gamma5 continuation scheme, finding that NDR and BMHV give different bounds on the two operators that contribute to gg->H. A combined chi-square fit yields 95% CL intervals for the five Wilson coefficients in both linear and quadratic EFT expansions, reported in Tables 5 and 6.","tokens_in":28994,"tokens_out":14666,"duration_ms":169157,"significance":"If the quoted constraints are robust, this is a useful step toward pinning down a class of SMEFT operators that is otherwise very weakly bounded. The paper provides detailed analytic expressions for the gg->H and gamma-gamma-H matrix elements and for the EWPO shifts, and it makes the numerical predictions available in tabulated form. The gamma5-scheme comparison for single-Higgs observables is a valuable methodological point for the SMEFT community. However, the main combined-fit result contains a load-bearing dependence on the A_b,FB observable, and the operator normalisation for the colour-octet four-heavy operator is not fully pinned down across all datasets, so the numerical bounds in Tables 5 and 6 should be treated with caution until these points are clarified.","major_comments":[{"comment":"The linear-order 95% CL interval for c1_tt in Table 6, [-9.12, -0.89], excludes the SM, and the corresponding EWPO-only interval in Table 5 is [-14.92, -1.68]. From Eq. (C.10), the contribution of c1_tt to delta A_b,FB / A_b,FB is 51.083e-4 c1_tt, whereas its contributions to the other EWPO in Eq. (3.1) are of order 1e-6 or smaller. The bound is therefore driven almost entirely by the well-known A_b,FB discrepancy, which the paper acknowledges in Section 5.3 but does not subject to any robustness test. Because the fit assumes that no other SMEFT operators or unknown systematics contribute to A_b,FB, the quoted exclusion of zero is not yet supported. Please add a leave-one-out analysis that drops or shifts A_b,FB, and/or a fit that includes the Zbb-vertex operators that are known to affect this observable. The quadratic-order interval [-1.66, 1.49] already includes the SM, which further motivates this test before the linear-order exclusion is presented as a central result.","section":"5.3, Table 6, Eq. (C.10)"},{"comment":"The operator normalisation for the colour-octet four-heavy operator is not pinned down consistently across the datasets. Section 2.1 states that all computations use O8_QQ = Q_qq^(3)/8 + Q_qq^(1)/24, while Section 3.3 explains that the EWPO results in Eq. (3.1) are extracted in the original Warsaw basis and that the alternative definition with two colour-octet currents differs by an evanescent operator that can be numerically significant. Since Eq. (3.1) and the SMEFT@NLO predictions may therefore refer to different operator normalisations for c8_QQ, the combined bounds on c8_QQ in Tables 5 and 6 could be shifted. Please state unambiguously which operator definition is used for each dataset and quantify the size of the evanescent shift on the combined c8_QQ bounds.","section":"2.1, 3.3, Eq. (2.4), Eq. (3.1)"}],"minor_comments":[{"comment":"The text says the theoretical signal strengths are 'expanded to linear order in the WCs', but Eqs. (4.3) and (4.4) contain quadratic terms in the Wilson coefficients. Please clarify the intended expansion order and make the wording consistent with the displayed expressions.","section":"4, Eqs. (4.3) and (4.4)"},{"comment":"The same K-factor is used for the SM and for the O(Lambda^-2) EFT contributions to the production cross section. This assumes that the higher-order QCD corrections factorise in the same way for the SM and interference terms; please state this approximation explicitly.","section":"4, Eq. (4.1)"},{"comment":"In the rows for EWPO1 and EWPO2, the 'n dat' column lists '1' although each row contains multiple observables. Please clarify whether the column counts datasets or observables, and how the correlation between observables is implemented in the chi-square.","section":"Table 1"},{"comment":"The labels 'comb-2D' and 'comb-profiled' are used in the figure captions and text but are not defined in the captions themselves. Please define them there for clarity.","section":"5.3, Figs. 4 and 5"},{"comment":"The SMEFT predictions for t-tbar-b-bar production are taken from Ref. [5] 'as in [5]' with no details of the exact process definition, scale choice, or PDF set used. Please provide a fuller specification of these inputs in the text or a table.","section":"5.2, pp->t-tbar-b-bar"},{"comment":"The abstract highlights the gamma5-scheme dependence as a main result, but the final combined fit is performed only in the NDR scheme and Section 5.3 states that inclusive Higgs production has no significant impact on the final combination. Please add a sentence noting that the quoted combined limits are NDR-specific and that the scheme dependence is demonstrated for the single-Higgs sector only.","section":"Abstract and Section 5.3"}],"recommendation":"major_revision","confidential_remarks":"The paper is squarely within the scope of JHEP and makes a useful technical contribution through the detailed analytic expressions and the gamma5-scheme comparison. My main concern is that the linear-order exclusion of the SM for c1_tt rests on the A_b,FB discrepancy, with no leave-one-out test; the operator-normalisation issue for O8_QQ should also be resolved before the bounds in Tables 5 and 6 are relied upon. I do not see grounds for rejection, but I would not recommend acceptance without these robustness checks."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuinely useful SMEFT paper. It combines direct four-top, ttbar, ttbar H, and ttbar bbbar measurements with two-loop EWPO and ggH constraints on the five four-heavy-quark operators, and it gives per-coefficient two-loop EWPO expressions in Eq. (3.1) that I have not seen written out that cleanly before. The NDR-versus-BMHV comparison for single-Higgs production is also a real service: the flat direction in BMHV and its lifting in NDR is a concrete warning for anyone who uses these operators in loop calculations.\n\nWhat the paper does well: the computational setup is standard and transparent, the MC predictions are tabulated, the analytic matrix elements in Appendix A and the EWPO coefficients in Appendix C are detailed enough to reproduce, and the authors flag their own caveats explicitly. The combined-fit result—significantly reducing the allowed parameter space, especially for the c1_QQ–c8_QQ plane—is plausible and supported by the shown contours.\n\nThe soft spot is real and load-bearing. The tight linear bound on c1_tt in Table 6, [-9.12, -0.89], is driven almost entirely by the A_b,FB discrepancy. Equation (C.10) shows that c1_tt enters A_b,FB with a coefficient 51e-4 while its effects on R_b, R_c, and R_l are at the 1e-6 level. The fit effectively assigns the whole well-known experimental discrepancy to this single Wilson coefficient. The paper notes this in Section 5.3 but does not provide a robustness test, such as dropping or shifting A_b,FB, or checking whether a Zbb-type operator absorbs the discrepancy. Until that test is done, the marginalised linear c1_tt bound should not be treated as a genuine SMEFT constraint.\n\nThe gamma5 scheme issue is real but less damaging for the final combination: the paper itself says inclusive Higgs production has no significant impact on the combined fit. Still, quoting only NDR numbers in the final fit, without a scheme-uncertainty band, is a small gap between the paper's own warning and its practice.\n\nThe citation pattern looks honest; the two-loop ggH matrix element comes from the authors' own Ref. [22] but is reproduced in the appendix, so the constraint is not self-referential. No code is shipped, but the analytic expressions and tables make independent reproduction feasible.\n\nBottom line: this paper deserves a serious referee. I would ask for an A_b,FB leave-one-out test and a sentence on how the final bounds shift if that observable is removed. Once that is in place, the per-coefficient EWPO results and the combined constraints are a solid contribution to the SMEFT literature.","headline":"A useful and careful SMEFT fit combining direct top and loop-induced probes; the c1_tt bound, however, leans on the A_b,FB discrepancy and needs a robustness test before it can be taken at face value.","tokens_in":29633,"tokens_out":2889,"would_cite":true,"duration_ms":32728,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.60.-i","14.65.Ha","14.80.Bn"],"model":"deepseek-v4-flash","headline":"This paper establishes that direct LHC top and Higgs measurements combined with loop-level precision probes bound the five four-heavy-quark SMEFT operators, and that the gamma5 scheme choice changes the single-Higgs limits.","keywords":["SMEFT","four-heavy-quark operators","four-top-quark production","electroweak precision observables","gluon-fusion Higgs production","gamma5 schemes","Wilson coefficients","top-quark pair production"],"falsifier":"Re-run the combined fit with the $A_{b,FB}$ measurement either removed or shifted to its Standard Model prediction. If the 95% confidence-level interval on $c^1_{tt}$ (reported as $[-9.12,-0.89]$ in the linear individual fit) then no longer excludes zero, the claim that the combination of electroweak precision, top-pair, and four-top data constrains this operator is settled; a full global fit that adds $Z b\\bar b$ vertex operators to absorb the $A_{b,FB}$ discrepancy would provide the same test.","tokens_in":28496,"feed_emoji":"🎯","tokens_out":12367,"duration_ms":125774,"temperature":0.7,"pith_summary":"The paper sets out to show that the five dimension-six four-heavy-quark operators of the Standard Model Effective Field Theory, long considered among the least constrained new-physics interactions, can be pinned down by combining direct LHC production measurements with loop-level indirect probes. It combines four-top, top-pair, top-pair-plus-Higgs, and top-pair-bottom-pair cross sections with gluon-fusion Higgs production, Higgs decays, and electroweak precision observables, and it reports 95% confidence-level intervals for the five Wilson coefficients in both linear and quadratic fits. The paper also demonstrates that the way $\\gamma_5$ is continued to $d=4-2\\epsilon$ dimensions in the two-loop single-Higgs calculation changes the extracted bounds, so a fit restricted to four-quark operators must be interpreted scheme by scheme. If the claims hold, the four-heavy-quark sector is no longer a nearly flat direction of the SMEFT, and electroweak precision data become an indispensable complement to multi-top searches.","feed_headline":"Top, Higgs, and LEP data squeeze four-quark new-physics bounds.","feed_subtitle":"Combined LHC top and Higgs measurements with LEP precision data shrink limits and lift flat directions.","key_machinery":"The machinery is a $\\chi^2$ fit whose theory inputs come from three layers: tree-level SMEFT matrix elements for $t\\bar t t\\bar t$ and $t\\bar t b\\bar b$; automated one-loop predictions for $t\\bar t$ and $t\\bar t H$; and two-loop analytic results for gluon-fusion Higgs production, $H\\to gg$, $H\\to\\gamma\\gamma$, and the $Z$-pole observables. The central objects are the five four-heavy-quark contact operators, colour-singlet and colour-octet combinations of third-generation quark currents. The load-bearing identities are the linear two-loop electroweak shifts of Eq. (3.1) and the renormalised $ggH$ matrix element of Eq. (3.2), whose $K_{tG}$ and $K_{t\\varphi}$ terms vanish in the BMHV $\\gamma_5$ continuation scheme (Breitenlohner--Maison--'t Hooft--Veltman) and are nonzero in the NDR scheme (naive dimensional regularisation); that difference creates the flat direction in a BMHV-only single-Higgs fit.","core_discovery":"The central claim is that combining electroweak precision observables with LHC top-quark and single-Higgs data substantially reduces the parameter space allowed for the dimension-six four-heavy-quark operators $O^1_{QQ}$, $O^8_{QQ}$, $O^1_{Qt}$, $O^8_{Qt}$, and $O^1_{tt}$. In the linear fit, the combination of electroweak precision data, top-quark pair production, and four-top-quark production is what shrinks the allowed region; in the quadratic fit, four-top production gives the dominant pull and electroweak precision observables are needed to lift degeneracies such as the near-blind direction in the $(c^8_{QQ}, c^1_{QQ})$ plane. The paper further claims that two-loop electroweak corrections are numerically significant for the asymmetry observables $A_b$ and $A_{b,FB}$, and that the choice of $\\gamma_5$ scheme in the two-loop gluon-fusion Higgs calculation propagates into the Wilson-coefficient bounds: in the Breitenlohner--Maison--'t Hooft--Veltman scheme a flat direction $c^1_{Qt}+c_F c^8_{Qt}$ appears, whereas the naive dimensional regularisation scheme lifts it, so the two restricted fits correspond to different classes of ultraviolet models.","pith_inferences":["Inference: taking the reported $c^1_{tt}$ interval at face value and using the convention $c/\\Lambda^2$ with $\\Lambda=1$ TeV, an order-one Wilson coefficient corresponds to a new-physics scale around $0.3$ TeV for this contact interaction; the exact number is not stated in the paper.","Inference: the $A_{b,FB}$ discrepancy is a sensitive lever arm, and the paper gives no robustness check against removing or reweighting that single observable; a future fit that does so would reveal how much of the $c^1_{tt}$ exclusion is carried by one dataset.","Inference: the scheme-shift relations in the appendix provide a dictionary between the NDR and BMHV results for the single-Higgs sector, so a future global fit could quote bounds in either scheme without recomputing the two-loop matrix elements."],"forward_implications":["The five four-heavy-quark operators move from being nearly unconstrained to having 95% confidence-level intervals of order one to a few tens in the linear fit; for example, the combined individual bound on $c^1_{tt}$ is $[-9.12,-0.89]$, and the quadratic fit tightens the four-top-driven bounds.","Electroweak precision observables are not marginal: in the linear fit they are part of the combination that shrinks the parameter space, and in the quadratic fit they lift the almost-blind direction in the $(c^8_{QQ}, c^1_{QQ})$ plane.","Two-loop electroweak corrections matter, particularly for $A_b$ and $A_{b,FB}$, so one-loop-only electroweak constraints on these operators are not numerically reliable.","Single-Higgs bounds inferred from the four-top operators are $\\gamma_5$-scheme dependent; a scheme-independent bound requires including operators that enter at one loop, such as $O_{t\\varphi}$, $O_{tG}$, and $O_{\\varphi G}$.","A single-Higgs fit restricted to the four-top operators has different meaning in the two schemes: it probes two distinct classes of ultraviolet models, and a full global fit in the BMHV scheme is left for future work."],"supporting_citations":[{"why":"Provides the one- and two-loop matching results for third-generation four-quark operators to $Z$-pole observables, from which Eq. (3.1) is drawn.","marker":"[20]"},{"why":"Supplies the two-loop $gg\\to H$ and $H\\to\\gamma\\gamma$ matrix elements and the NDR/BMHV scheme-dependent $K$-terms that drive the single-Higgs fit.","marker":"[22]"},{"why":"The automated one-loop SMEFT generator used to compute $t\\bar t$ and $t\\bar t H$ production predictions in the top basis.","marker":"[23]"},{"why":"Establishes the one-loop collider sensitivity to these heavy-quark operators, which the present electroweak and two-loop analysis extends.","marker":"[24]"},{"why":"The recent global SMEFT fit whose loose constraints motivate this work and whose database supplies the $t\\bar t b\\bar b$ measurements and predictions.","marker":"[5]"},{"why":"Provides the measured gluon-fusion Higgs signal strengths used as inputs to the single-Higgs toy fit.","marker":"[67]"},{"why":"Supplies the electroweak precision observables and their correlations used in the EWPO fit, including the discrepant $A_{b,FB}$.","marker":"[83]"},{"why":"The NLO (QCD+EW)+NLL four-top-quark cross-section prediction adopted as the SM reference for the four-top datasets.","marker":"[88]"},{"why":"Shows the subleading weak-interference contributions to four-top production that are included in the tree-level SMEFT prediction.","marker":"[52]"}],"fun_headline_variants":["Combined top, Higgs, LEP data shrink four-heavy-quark operator space","EW precision plus top/Higgs data lifts four-quark operator degeneracies","Four-heavy-quark SMEFT operators constrained by top, Higgs, LEP data","Combining LHC top and Higgs data with LEP precision shrinks four-quark bounds","Top, Higgs, and LEP data resolve four-heavy-quark operator flat directions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The fit assumes the five four-heavy-quark operators are the only beyond-Standard-Model contributions to the measured observables, so the well-known discrepancy in the bottom-quark forward--backward asymmetry $A_{b,FB}$ is charged entirely to these operators; if additional SMEFT operators or unknown experimental systematics contribute, the quoted bounds, especially on $c^1_{tt}$, would not be the true constraints.","fun_headline_variants_meta":{"raw":{"variants":["Combined top, Higgs, LEP data shrink four-heavy-quark operator space","EW precision plus top/Higgs data lifts four-quark operator degeneracies","Four-heavy-quark SMEFT operators constrained by top, Higgs, LEP data","Combining LHC top and Higgs data with LEP precision shrinks four-quark bounds","Top, Higgs, and LEP data resolve four-heavy-quark operator flat directions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00123,"raw_usage":{"total_tokens":5021,"prompt_tokens":877,"completion_tokens":4144,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":493,"completion_tokens_details":{"reasoning_tokens":4051}},"tokens_in":493,"tokens_out":4144,"duration_ms":36086,"temperature":1.0,"reasoning_tokens":4051,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:00:54.018742+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the combined fit with the $A_{b,FB}$ measurement either removed or shifted to its Standard Model prediction. If the 95% confidence-level interval on $c^1_{tt}$ (reported as $[-9.12,-0.89]$ in the linear individual fit) then no longer excludes zero, the claim that the combination of electroweak precision, top-pair, and four-top data constrains this operator is settled; a full global fit that adds $Z b\\bar b$ vertex operators to absorb the $A_{b,FB}$ discrepancy would provide the same test.","supporting_citations":[],"review_version":1}