{"id":"d46fa989-701a-430c-8bce-e7394113ecd7","arxiv_id":"2412.16020","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The full set of CP-even dimension-8 SMEFT amplitudes for gluon-fusion W+W- production is computed; their SM interference is shown to be negligible under EFT hierarchy, and new operator constraints are derived.","lead":"This paper computes all six CP-even dimension-8 operator effects on W+W- production through gluon fusion at the LHC. It finds their interference with the Standard Model is negligible unless the EFT hierarchy is broken, and it sets new constraints on dimension-6 and dimension-8 coefficients.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'D8 interference is negligible' physics claim is well supported, but the reported EFT fits depend on a hand-chosen and ambiguously implemented validity cutoff, so the quoted constraints are not robust.","rationale":"The reader's weakest assumption is correct. The high-level result that D8 interference with the SM is negligible in gg->WW is strongly supported: the interference is bounded by the product of the small SM gg amplitude and the D8 amplitude, and the explicit helicity amplitudes were checked against MadGraph. The fragile part is the claim that D6^2-only fits are justified, because this requires the D8^2 contribution to be small in the fitted bins, which is enforced only by the ad hoc criterion of Eqs (2.22)-(2.23). The paper itself shows in Fig 4 that the contours depend sensitively on the chosen threshold, and Section 4's reference to eq (2.21) rather than eq (2.23) makes the actual bin selection ambiguous. Since the reported constraints on both D6 and D8 operators are a central deliverable, this warrants a conditional verdict. No issue is taken with the amplitude computation itself; the concern is a methodological choice that should be settled by a robustness check.","tokens_in":31545,"tokens_out":14240,"duration_ms":136250,"concrete_test":"Recompute the kappa_g-tilde_kappa_g contours of Figs 13 and 15 (and the D8 contours of Figs 17-18) under three alternative EFT-validity prescriptions: (i) keep all bins but add a per-bin theory uncertainty equal to the D8-squared contribution at that bin; (ii) use the eq (2.21) cut Lambda_min=2M_eµ; (iii) use the eq (2.23) cut with the 'half' factor replaced by 0.1 and by 1. If the 95% CL contours shift by more than the reported 1-sigma band, or if prescriptions (i) and (iii) disagree, the quoted constraints are dominated by the arbitrary cutoff choice and should be presented as illustrative rather than as robust bounds.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's qualitative central claim survives scrutiny: because the SM gg amplitude is loop-suppressed, the D8-SM interference is bounded by 2|M_SM^gg||M8| and is numerically small wherever the EFT is valid (Fig 11), and the helicity amplitudes are cross-checked against MadGraph. The load-bearing weakness is in the step from that observation to EFT fits. The fits in Sections 4-5 select bins using an EFT-validity criterion, Eqs (2.22)-(2.23), that demands the largest D8 squared contribution be below half the D6 squared contribution. Nothing derives this 'half' factor; Fig 4 shows the inferred contours depend strongly on it. Worse, the implementation is ambiguous: Section 4 says bins are kept up to the largest bin satisfying eq (2.21) (Lambda_min = 2 M_eµ), while Section 2.2 says the adopted rule is eq (2.23), which is coefficient-dependent. These are different cuts, and eq (2.21) was shown in Fig 3 to be inaccurate. If the fits used eq (2.21), they can include bins where D8^2 is not subdominant, undermining the D6^2-only truncation; if they used eq (2.23), the bin set changes discontinuously with the fit parameters, and Appendix C's manual smoothing can bias the quoted bounds. Either way, the D6 and D8 constraints rest on an unproven, parameter-dependent cutoff rather than on the robust interference suppression.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper constructs the six CP-even dimension-8 operators contributing to gg -> W+W- with fully leptonic decays, derives the corresponding tree-level helicity amplitudes, implements them in MCFM-RE with jet-veto resummation, and cross-checks them against MadGraph/UFO. It finds that, under the usual EFT hierarchy, the interference of the dimension-8 operators with the SM is numerically negligible across the considered Me-mu distributions because the SM gluon-fusion amplitude is loop-suppressed and small at high energies. This is used to justify retaining only the dimension-6 squared contribution in EFT fits to this channel. The paper then presents constraints on CP-even and CP-odd dimension-6 operators from current ATLAS data and HL-LHC projections, and, in a postulated c6 -> 0 scenario, constraints on the two largest CP-even dimension-8 operators. The role of the jet veto, including its suppression of the BSM signal, is emphasized throughout.","tokens_in":31892,"tokens_out":8381,"duration_ms":70827,"significance":"The central qualitative result is significant and practically useful: if confirmed, it justifies dropping dimension-8-SM interference in gg -> WW EFT fits under ordinary EFT power counting, and it fills a gap left by earlier single-operator dimension-8 studies. The paper has strong reproducibility credentials: the amplitudes are cross-checked against an independent UFO/MadGraph implementation, the code and data are made available, and the SM predictions include state-of-the-art NNLL+NNLO QCD, NLO electroweak corrections, and jet-veto resummation applied to the BSM signal. The quantitative constraints, however, are conditional on hand-chosen EFT-validity thresholds and on an ambiguously specified bin-selection rule, so the quoted bounds should be regarded as illustrative until those choices are justified or varied.","major_comments":[{"comment":"The bin-selection rule is implemented inconsistently with the stated EFT-validity criterion. Section 4 says that fits use bins up to the largest N satisfying Eq. (2.21), Lambda_min = 2 Me-mu, while Section 2.2 concludes by adopting the coefficient-dependent condition sigma_6 > 2 sigma_8 of Eq. (2.23), and the text around Fig. 15 says the cutoff is applied 'in accordance with Eq. (2.23)'. Equation (2.21) is explicitly shown in Fig. 3 to be inaccurate at low Me-mu and to yield the strongest constraints in Fig. 4. If Eq. (2.21) is used, bins can enter where the dimension-8 squared term is not subdominant to the dimension-6 squared term, undermining the truncation in Eq. (2.20); if Eq. (2.23) is used, the bin set changes discontinuously with the fitted coefficients, and the manual ellipse smoothing described in Appendix C can bias the quoted bounds. Please state unambiguously which rule was used and rerun the fits with a single, justified rule.","section":"Sec. 2.2, Sec. 4, and Appendix C"},{"comment":"The 'half' threshold in Eq. (2.23) is ad hoc and load-bearing for all quoted constraints. Figure 4 shows that varying the condition from sigma_6 > sigma_8 to sigma_6 > 4 sigma_8 and replacing it with the naive Lambda_min > 2 Me-mu changes the inferred kappa_g-kappa-tilde_g contours by roughly a factor of two in the couplings; the same threshold determines the bins used in the dimension-6 fits of Section 4 and, through Eq. (2.23) applied at the dimension-8 scale, the dimension-8 fits of Section 5. Since Eqs. (2.22)-(2.23) are introduced as an 'empirical approach' with no uncertainty, the bounds emphasized in the abstract and conclusions (e.g. Lambda > 5 TeV for the dimension-6 operators and Lambda > 900 GeV / 2-3 TeV for the dimension-8 operators) should be presented as functions of the threshold, or the threshold should be assigned and propagated as a theoretical uncertainty.","section":"Eqs. (2.22)-(2.23) and Fig. 4"},{"comment":"The HL-LHC projections rely on a linear extrapolation of current ATLAS systematic errors, shown as the curve 4.86 + 19.5 Me-mu/TeV in Fig. 14, without any uncertainty band or justification. Because the EFT-validity cutoff removes much of the high-Me-mu tail, the slope and normalization of this extrapolation directly determine which bins dominate the projected constraints in Figs. 15 and 18, and hence the quoted projections such as |kappa-tilde_g| < 0.9 and Lambda > 2-3 TeV. Please justify this extrapolation or show the sensitivity of the projections to alternative systematic-error assumptions.","section":"Sec. 4.2 and Fig. 14"},{"comment":"The dimension-8 constraints in Section 5 are presented as a 'motivated scenario' with c6 -> 0, which is a transparent assumption; however, the additional consistency check that the c6-c8 interference term be below one quarter of the dimension-8 squared term in the bins used introduces a second unquantified threshold. The quoted constraints Lambda > 900 GeV (current data) and Lambda > 2-3 TeV (HL-LHC) are therefore conditional on both the c6 -> 0 postulate and this 1/4 criterion. The paper should either derive the 1/4 factor from a systematic EFT-error prescription or show how the dimension-8 bounds shift when it is varied.","section":"Sec. 5, Eqs. (5.1)-(5.2)"}],"minor_comments":[{"comment":"The second occurrence of M(5)+- in Eq. (2.14) should be M(5)-+; as written, the same helicity label appears twice.","section":"Eq. (2.14)"},{"comment":"The caption states that 'contours on the right panel correspond to the situation in which a jet-veto condition is applied, whereas those on the right are obtained without a jet-veto'; the first clause should refer to the left panel, since the sentence is otherwise self-contradictory.","section":"Fig. 18 caption"},{"comment":"The statement that the first three Me-mu bins are neglected because they 'did not agree perfectly with data' should be accompanied by a check that this exclusion does not bias the fit, even if those bins are at low energy and expected to be insensitive to the higher-dimensional operators.","section":"Sec. 4.1"},{"comment":"The notation 'Lambda_min = 2 sqrt(c_i) Me-mu ~ 2 Me-mu' is confusing because the coefficient sqrt(c_i) is silently dropped in the final estimate; please clarify that c_i is set to one in that step.","section":"Eq. (2.21)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of JHEP and the main technical content, namely the complete set of dimension-8 operators and helicity amplitudes for gg -> WW with a jet veto, is solid and independently cross-checked. The stress-test concern about the discrepancy between Eq. (2.21) and Eq. (2.23) is confirmed by the manuscript text: Section 4 says the fits use Eq. (2.21), while Section 2.2 adopts Eq. (2.23). I do not see grounds for rejection, because the central qualitative claim about the smallness of dimension-8 interference is robust and the fit-level issues can be addressed by rerunning the analysis with a single, justified validity criterion and by showing threshold dependence. The reported numerical constraints should be treated as conditional until that is done."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a good SMEFT paper with a robust central physics claim and a wobbly constraints section. The new things are the complete set of six CP-even dimension-8 operators for gg->W+W-, the helicity amplitudes, and their implementation in MCFM-RE with the jet veto. The amplitudes are cross-checked against MadGraph/UFO, which gives me confidence in them. The central observation that D8 interference with the SM is negligible under EFT hierarchy is well supported: the SM gg amplitude is loop-suppressed, and the interference is bounded by 2|M_SM||M8|, numerically small wherever the EFT is valid. That justifies fitting with dimension-6 squared and dropping D8 interference. The paper also gives first constraints on operators 2 and 3, and the jet-veto effect on sensitivity is a genuinely useful point.\n\nThe soft spot is exactly where your stress-test note lands. The EFT validity cut used in the fits is ambiguous. Section 2.2 derives an empirical criterion comparing the largest D8 squared contribution to half of the D6 squared contribution (eq. 2.23) and says that is the adopted rule. Section 4, however, says bins are kept up to the largest bin satisfying eq. (2.21), the naive Lambda_min = 2 M_eµ relation. Those are different cuts. Figure 4 shows the inferred contours depend strongly on which assumption you make. Since the quoted D6 and D8 constraints are the paper's main quantitative results, this ambiguity matters. The constraints also rely on hand-chosen threshold factors, a c6->0 postulate for the D8 fits, and manual contour smoothing. All of this is transparently disclosed, but the constraint numbers are not on as firm ground as the amplitude work.\n\nI would not call this a fatal flaw. The physics claim about interference survives because it follows from the explicit amplitudes and the smallness of the loop-induced SM amplitude. A serious referee should ask the authors to clarify which cut they actually used, to show sensitivity of the contours to the 'half' factor and to the bin-selection rule, and to provide a numerical implementation note. With those clarifications the paper would be much stronger.\n\nFor a reader, the amplitudes and the interference result are worth citing; the constraints should be treated as provisional. The paper deserves a serious referee — not a desk reject.","headline":"Solid and useful first full set of D8 operators for gg->WW; central claim about negligible D8-SM interference holds, but the EFT-fit constraints rest on an ambiguous and hand-chosen validity cutoff.","tokens_in":32375,"tokens_out":2472,"would_cite":true,"duration_ms":21417,"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":"Dimension-8 interference with the Standard Model is negligible in gluon-fusion W-pair production, justifying EFT fits that keep dimension-6 squared terms.","keywords":["SMEFT","dimension-8 operators","gluon fusion","W+W- production","helicity amplitudes","jet veto","LHC","EFT validity"],"falsifier":"Compare the measured $M_{e\\mu}$ distribution in the gluon-fusion $WW$ channel with the prediction that includes only the Standard Model plus the dimension-6 squared term in the bins admitted by the EFT-validity criterion; if the data show an excess that grows with energy faster than the dimension-6 square prediction, the claim that dimension-8 interference is negligible is falsified. A direct calculation-based check is to compute the $c_6 c_8$ interference term in Eq. (5.2) for operators $O_2$ and $O_3$ and verify whether it changes the predicted cross section in those bins by more than the quoted theoretical uncertainties.","tokens_in":31348,"feed_emoji":"⚛️","tokens_out":12439,"duration_ms":95902,"temperature":0.7,"pith_summary":"This paper asks whether dimension-8 operators can be probed in W+W- production at the LHC when the W pair is produced by gluon fusion, the channel through which the Standard Model contribution is loop-induced and small. The authors identify all six CP-even dimension-8 operators that contribute at tree level, write down their helicity amplitudes, and implement them in a Monte Carlo program that includes the jet veto (a cut rejecting events with extra hard jets) used to suppress top backgrounds. Their main finding is that, as long as the effective field theory expansion is valid, the interference of these dimension-8 operators with the Standard Model is much smaller than the square of the dimension-6 contributions, so EFT fits can safely keep the dimension-6 squared terms and ignore dimension-8 interference. They then derive constraints on dimension-6 operators from current and projected LHC data, and show that the jet veto suppresses the gluon-initiated signal far more than the quark-initiated background. Under a hierarchy-breaking scenario in which dimension-6 operators are negligible, they bound two of the six dimension-8 operators to new-physics scales above roughly 900 GeV with current data and up to about 3 TeV at the High-Luminosity LHC.","feed_headline":"Dimension-8 operators stay hidden in gluon-fusion W-pair events","feed_subtitle":"All six contributing CP-even operators are computed; only the dimension-6 squared term matters for LHC EFT fits.","key_machinery":"The central object is the set of tree-level helicity amplitudes $\\mathcal{M}^{(i)}_{\\lambda_1\\lambda_2}$ for the six CP-even dimension-8 operators contributing to $gg\\to W^+W^-\\to e^+\\nu\\,\\mu^-\\bar\\nu$, expressed in spinor products. The argument runs on the size comparison between the squared dimension-8 amplitudes and the squared dimension-6 amplitude: the empirical criterion of Eq. (2.23) admits only bins where $\\sigma_8^2 < \\sigma_6^2/2$, so that the EFT hierarchy holds. A second structural feature is that operators $O_2$ and $O_3$ have equal squared amplitudes in this channel (their interference with each other and with the SM vanishes), which makes them indistinguishable in the $M_{e\\mu}$ distribution.","core_discovery":"The paper establishes that in gluon-gluon fusion to $W^+W^-$ with fully leptonic decays, the Standard Model amplitude is loop-induced and decreases with partonic energy, while the six CP-even dimension-8 contact amplitudes grow as $\\hat{s}^2/\\Lambda^4$. As a result, the SM--dimension-8 interference, though formally of order $1/\\Lambda^4$, is much smaller than the squared dimension-6 amplitude in the regime where the EFT expansion is valid, and can therefore be neglected in fits. The paper justifies keeping the square of the dimension-6 amplitude on these grounds, and then uses current $WW$ data to constrain the dimension-6 operators of the gluon--Higgs type and their CP-odd counterparts, finding that the bounds are not competitive with on-shell Higgs data unless the jet veto is relaxed and systematics improve. Among the six dimension-8 operators, only operators $O_2$ and $O_3$, which have identical squared amplitudes in this channel, can be constrained: $\\Lambda \\gtrsim 0.9$ TeV with current data, and $\\Lambda \\gtrsim 2$--$3$ TeV at the HL-LHC depending on the jet-veto and systematic-error assumptions.","pith_inferences":["Inference: The same small-interference argument should hold for other loop-induced diboson channels such as $gg\\to ZZ$, so dimension-6-squared fits are probably safe there as well until the loop-induced SM amplitude grows.","Inference: The $O_2/O_3$ degeneracy implies that the $M_{e\\mu}$ distribution alone cannot separate these operators; angular observables or other diboson final states are a natural testable route to lift it.","Inference: The strong dependence of the contours on the EFT-validity threshold (Fig. 4) indicates that global SMEFT fits using this channel carry a hidden systematic associated with the expansion-validity cut; profiling over the threshold or attaching an 'EFT uncertainty' per bin would change the reported exclusions.","Inference: If 1%-precision data arrive at the HL-LHC, dimension-6--dimension-10 cross terms will matter before robust dimension-8 bounds can be claimed, since the omitted $c_6 c_{10}$ terms enter at the same order as the kept $c_8^2$ term."],"forward_implications":["Within the EFT regime, dimension-8 interference can be dropped from $gg\\to WW$ fits, and the dimension-6 squared terms are consistently the next-order contribution to keep.","The jet veto suppresses the gluon-fusion signal by up to an order of magnitude more than the quark-initiated background, so relaxing it (for example via b-tagging) is the main lever for improving gluon-operator sensitivity; without improved systematics, however, the relaxation alone does not help.","Only operators $O_2$ and $O_3$ among the six CP-even dimension-8 operators can be constrained with current data ($\\Lambda \\gtrsim 0.9$ TeV); the other four need roughly 1-percent-level theoretical and statistical uncertainties to become reachable.","The HL-LHC $WW$ channel will remain less competitive than on-shell Higgs data for the CP-even dimension-6 gluon--Higgs coupling, but may become competitive for the CP-odd coupling if the jet veto is lifted.","The naive mapping $M_{e\\mu} \\simeq M_{WW}/2$ overestimates the EFT-valid region; adopting the empirical criterion of Eq. (2.23) gives more conservative and more reliable constraints."],"supporting_citations":[{"why":"Supplies the complete set of dimension-8 SMEFT operators from which the six CP-even operators for gluon-fusion WW are selected.","marker":"[37]"},{"why":"Identifies the six dimension-6 operators entering gluon-fusion WW and their energy growth, giving the baseline for the dimension-6 contributions used throughout.","marker":"[26]"},{"why":"The earlier study of higher-order EFT effects in gg->WW that considered only one dimension-8 operator, which this work extends to the full CP-even set.","marker":"[25]"},{"why":"Provides the NLO electroweak corrections and photon-induced contribution used in the best Standard Model prediction for the high-energy tails.","marker":"[34]"},{"why":"Supplies the jet-veto resummed Monte Carlo framework used to predict both SM and BSM signals in the WW channel.","marker":"[44]"},{"why":"Gives the current LHC differential WW production data used in the dimension-6 and dimension-8 fits.","marker":"[46]"},{"why":"Provides the on-shell Higgs constraints on dimension-6 operators that motivate the hierarchy-breaking scenario for dimension-8 bounds.","marker":"[3]"}],"fun_headline_variants":["Dim-8 operators hide in gluon-fusion W pairs","Gluon-fusion W pairs: dim-8 negligible, dim-6 squared wins","Jet veto quashes dim-8 signals in W-pair production","Only two dim-8 operators constrainable in WW via gluon fusion","Dim-8 interference negligible; dim-6 squared dominates EFT fit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis assumes that the effective field theory expansion is valid only in kinematic bins where the largest dimension-8 squared contribution is less than half the dimension-6 squared contribution, a threshold chosen by hand that determines which bins enter the fits.","fun_headline_variants_meta":{"raw":{"variants":["Dim-8 operators hide in gluon-fusion W pairs","Gluon-fusion W pairs: dim-8 negligible, dim-6 squared wins","Jet veto quashes dim-8 signals in W-pair production","Only two dim-8 operators constrainable in WW via gluon fusion","Dim-8 interference negligible; dim-6 squared dominates EFT fit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000945,"raw_usage":{"total_tokens":4097,"prompt_tokens":1071,"completion_tokens":3026,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":687,"completion_tokens_details":{"reasoning_tokens":2929}},"tokens_in":687,"tokens_out":3026,"duration_ms":19667,"temperature":1.0,"reasoning_tokens":2929,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:52:40.185352+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the measured $M_{e\\mu}$ distribution in the gluon-fusion $WW$ channel with the prediction that includes only the Standard Model plus the dimension-6 squared term in the bins admitted by the EFT-validity criterion; if the data show an excess that grows with energy faster than the dimension-6 square prediction, the claim that dimension-8 interference is negligible is falsified. A direct calculation-based check is to compute the $c_6 c_8$ interference term in Eq. (5.2) for operators $O_2$ and $O_3$ and verify whether it changes the predicted cross section in those bins by more than the quoted theoretical uncertainties.","supporting_citations":[{"cited_title":"Diboson production in the SMEFT from gluon fusion","cited_arxiv_id":"2306.09963","evidence_quote":"Identifies the six dimension-6 operators entering gluon-fusion WW and their energy growth, giving the baseline for the dimension-6 contributions used throughout."},{"cited_title":"Anomalous coupling, top-mass and parton-shower effects in ${W^+W^-}$ production","cited_arxiv_id":"1602.05141","evidence_quote":"The earlier study of higher-order EFT effects in gg->WW that considered only one dimension-8 operator, which this work extends to the full CP-even set."},{"cited_title":"BSM WW production with a jet veto","cited_arxiv_id":"1905.06646","evidence_quote":"Supplies the jet-veto resummed Monte Carlo framework used to predict both SM and BSM signals in the WW channel."}],"review_version":1}