Dimension-8 operators in $W^+W^-$ production via gluon fusion

Adam Martin; Andrea Banfi; Daniel Gillies; Matthew A. Lim

REVIEW 4 major objections 4 minor 1 cited by

Dimension-8 operators in $W^+W^-$ production via gluon fusion

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Dimension-8 interference with the Standard Model is negligible in gluon-fusion W-pair production, justifying EFT fits that keep dimension-6 squared terms.

desk verdict 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. read the letter →

arxiv 2412.16020 v2 pith:JYKIKU56 submitted 2024-12-20 hep-ph hep-ex

Daniel Gillies , Andrea Banfi , Adam Martin , Matthew A. Lim This is my paper · ORCID

classification hep-phhep-ex

keywords SMEFTdimension-8operatorsgluonfusionW+W-productionhelicityamplitudesjetvetoLHCEFTvalidity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

I 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.

For 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.

Referee Report

4 major / 4 minor

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.

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 (4)

[Sec. 2.2, Sec. 4, and Appendix C] 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.
[Eqs. (2.22)-(2.23) and Fig. 4] 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.
[Sec. 4.2 and Fig. 14] 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.
[Sec. 5, Eqs. (5.1)-(5.2)] 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.

minor comments (4)

[Eq. (2.14)] The second occurrence of M(5)+- in Eq. (2.14) should be M(5)-+; as written, the same helicity label appears twice.
[Fig. 18 caption] 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.
[Sec. 4.1] 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.
[Eq. (2.21)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the D8-interference claim follows from independently computed amplitudes and external data; self-citations are to public code and prior classifications, not to the target conclusion.

full rationale

The paper's central claim, that dimension-8 interference with the Standard Model is negligible in the EFT regime, is derived from explicit helicity amplitudes computed in Section 2.1 and compared numerically with the loop-suppressed SM gg amplitude in Section 3.3 and Figure 11. The conclusion is not an input: it follows from the bounded inequality 2|Re(M_SM^gg M_8^*)| <= 2|M_SM^gg||M_8| combined with the numerically small SM gg amplitude, and the amplitudes were cross-checked against MadGraph/UFO. The dimension-6 fits use external ATLAS data and standard chi-square methods, with the EFT-validity criterion in Eqs. (2.21)-(2.23) acting only as a bin-selection rule; that rule is empirical and arbitrary, and Figure 4 exposes its effect, but it is not a fitted parameter renamed as a prediction and it does not force the reported constraints by construction. The later dimension-8 fits are explicitly presented under a postulated c6 -> 0 scenario, and the a posteriori check of the c6c8 term is a consistency test, not a circular derivation. Self-citations to MCFM-RE and Ref. [44] are for the public code and an error-prescription method, while the dimension-8 operator basis from Ref. [37] is a parameter-free classification that does not include the target result; none of these citations is used to forbid alternatives or to substitute for the numerical derivation. The main weakness identified by the authors, the hand-chosen and ambiguously implemented EFT-validity cutoff, is a robustness concern, not a circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper relies on standard SMEFT background assumptions, a hand-chosen EFT validity threshold, and a postulated c6 -> 0 scenario for the dimension-8 constraints. No new particles, forces, or conserved quantities are introduced.

free parameters (3)

EFT validity threshold factor = 2 (sigma6 > 2 * sigma8)
Section 2.2 defines the empirical Lambda_min by requiring the largest dimension-8 squared contribution to be no more than half the dimension-6 squared contribution (Eq. 2.22-2.23). The factor 2 is chosen by hand, and Fig. 4 shows the constraints depend strongly on it.
HL-LHC systematic error linear extrapolation = 4.8637 + 19.543 * (Me/TeV) percent
Section 4.2 projects current ATLAS systematic errors to HL-LHC using a linear fit in the dilepton invariant mass; the HL-LHC sensitivity projections depend on this extrapolation.
c6c8 consistency threshold = 1/4
Section 5 allows the c6 -> 0 scenario only if the largest dimension-6-dimension-8 interference is no more than 1/4 the size of the dimension-8 squared contribution; this ratio is chosen by hand.

assumptions (6)

domain assumption SMEFT assumptions: SM gauge symmetries, linear electroweak symmetry breaking, and a gap between the electroweak scale and the new-physics scale Lambda.
Invoked in the Introduction to justify the 1/Lambda expansion and the operator basis.
domain assumption Four-flavour scheme PDFs make top-quark interference negligible in the gg channel.
Section 3.1: 'we neglect it in the present study by utilising a four-flavour scheme for parton distribution functions, the NNPDF31_nnlo_as_0118_luxqed_nf_4 PDF set'.
ad hoc to paper The c6 -> 0 scenario: dimension-6 operators are negligible relative to dimension-8, motivated by strong existing constraints from on-shell Higgs data.
Section 5 postulates a scenario in which the dimension-6 and dimension-8 terms are decoupled or dimension-6 operators are not generated; the dimension-8 constraints are conditional on this assumption.
domain assumption NLL resummation is sufficient for the gluon-fusion channel under the jet veto.
Section 3.1 states 'Resummation for the gg contribution is only implemented at NLL accuracy in MCFM-RE' and this accuracy is used for all gg predictions.
domain assumption The multiplicative combination of NNLL+NNLO QCD with NLO EW corrections adequately estimates the SM background.
Section 3.1 uses Eq. (3.1) following the prescription of ref. [34]; missing QCD-EW cross terms are estimated by scheme differences and found to be within QCD scale uncertainties up to Me ~ 1 TeV.
ad hoc to paper The empirical condition sigma6 > 2 * sigma8 is sufficient to guarantee EFT validity for the bins used.
The paper adopts this criterion for all fits at the end of Section 2.2 without a derivation from first principles; the resulting constraints vary with the criterion (Fig. 4).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Dimension-8 operators in $W^+W^-$ production via gluon fusion." pith.science (2026). https://pith.science/paper/JYKIKU56

@misc{pith2026241216020,
  author       = {Pith},
  title        = {Pith review of: Dimension-8 operators in $W^+W^-$ production via gluon fusion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JYKIKU56}},
  note         = {Machine review of arXiv:2412.16020}
}

abstract

We investigate the impact of dimension-8 operators on $W^+W^-$ production at the LHC for the incoming gluon-gluon channel. To this end, we have identified all dimension-8 CP-even operators contributing to the process in question, and computed the corresponding tree-level helicity amplitudes for fully-leptonic decays of the $W$ bosons. These are implemented in the program MCFM-RE, which automatically incorporates the effect of a jet-veto to reduce the otherwise overwhelming $t\bar t$ background. We find that, unless we break the hierarchy of the effective field theory (EFT), the interference of the dimension-8 operators with the Standard Model is negligible across the considered distributions. This justifies including the square of dimension-6 operators when performing EFT fits with this channel. We then present new constraints on CP-even and CP-odd dimension-6 operators within the EFT regime. Lastly, we postulate a scenario in which the hierarchy of the EFT is broken, justified by the strong constraints on dimension-6 operators from existing on-shell Higgs data. In this scenario, we discuss the constraints that can be reasonably set on CP-even dimension-8 operators with current and future data. We remark that the effect of the jet-veto on the ability to constrain new physics in the $W^+W^-$ channel is quite dramatic and must be properly taken into account.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Anomalous triple gauge couplings in the light of dimension-8 operators in $W^+W^-$
hep-ph 2026-07 conditional novelty 6.0 of 10

Bosonic dimension-8 operators in γγ-initiated WW production dominate over qqbar and set the practical EFT validity scale, yielding validity-aware constraints on dimension-6 Wilson coefficients.

Reference graph

Works this paper leans on

63 extracted references · 17 canonical work pages · cited by 1 Pith paper

[1]

collaboration, Summary Plots for Heavy Particle Searches and Long-lived Particle Searches - March 2023 ,

ATLAS collaboration, A. collaboration, Summary Plots for Heavy Particle Searches and Long-lived Particle Searches - March 2023 ,

work page 2023
[2]

Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns

CMS collaboration, A. Hayrapetyan et al., Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns , 2405.18661

work page Pith review arXiv
[3]

Aad et al., Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS experiment , Phys

ATLAS collaboration, G. Aad et al., Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS experiment , Phys. Rev. D 101 (2020) 012002, [1909.02845]

arXiv 2020
[4]

https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsCombined

work page
[5]

Brivio and M

I. Brivio and M. Trott, The Standard Model as an Effective Field Theory , Phys. Rept. 793 (2019) 1–98, [ 1706.08945]

arXiv 2019
[6]

Buchm¨ uller and D

W. Buchm¨ uller and D. Wyler,Effective lagrangian analysis of new interactions and flavour conservation, Nuclear Physics B 268 (1986) 621–653

work page 1986
[7]

Grzadkowski, M

B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian , JHEP 10 (2010) 085, [ 1008.4884]

arXiv 2010
[8]

Carrillo Gonz´ alez, C

M. Carrillo Gonz´ alez, C. de Rham, S. Jaitly, V. Pozsgay and A. Tokareva, Positivity-causality competition: a road to ultimate EFT consistency constraints , JHEP 06 (2024) 146, [ 2307.04784]

arXiv 2024

Show all 63 references

[9]

Adams, N

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion , JHEP 10 (2006) 014, [hep-th/0602178]

2006 arXiv
[10]

Ellis, C

J. Ellis, C. W. Murphy, V. Sanz and T. You, Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data , JHEP 06 (2018) 146, [ 1803.03252]

2018 arXiv
[11]

Butter, O

A. Butter, O. J. P. ´Eboli, J. Gonzalez-Fraile, M. C. Gonzalez-Garcia, T. Plehn and M. Rauch, The Gauge-Higgs Legacy of the LHC Run I , JHEP 07 (2016) 152, [1604.03105]

2016 arXiv
[12]

D. R. Green, P. Meade and M.-A. Pleier, Multiboson interactions at the LHC , Rev. Mod. Phys. 89 (2017) 035008, [ 1610.07572]

2017 arXiv
[13]

Zhang, Time to Go Beyond Triple-Gauge-Boson-Coupling Interpretation of W Pair Production, Phys

Z. Zhang, Time to Go Beyond Triple-Gauge-Boson-Coupling Interpretation of W Pair Production, Phys. Rev. Lett. 118 (2017) 011803, [ 1610.01618]

2017 arXiv
[14]

Baglio, S

J. Baglio, S. Dawson and I. M. Lewis, An NLO QCD effective field theory analysis of W +W − production at the LHC including fermionic operators , Phys. Rev. D 96 (2017) 073003, [ 1708.03332]

2017 arXiv
[15]

Baglio, S

J. Baglio, S. Dawson and I. M. Lewis, NLO effects in EFT fits to W +W − production at the LHC , Phys. Rev. D 99 (2019) 035029, [ 1812.00214]. – 42 –

2019 arXiv
[16]

Baglio, S

J. Baglio, S. Dawson and S. Homiller, QCD corrections in Standard Model EFT fits to W Zand W Wproduction, Phys. Rev. D 100 (2019) 113010, [ 1909.11576]

2019 arXiv
[17]

Bellan et al., A sensitivity study of VBS and diboson WW to dimension-6 EFT operators at the LHC , JHEP 05 (2022) 039, [ 2108.03199]

R. Bellan et al., A sensitivity study of VBS and diboson WW to dimension-6 EFT operators at the LHC , JHEP 05 (2022) 039, [ 2108.03199]

2022 arXiv
[18]

E. d. S. Almeida, A. Alves, O. J. P. ´Eboli and M. C. Gonzalez-Garcia, Electroweak legacy of the LHC run II , Phys. Rev. D 105 (2022) 013006, [ 2108.04828]

2022 arXiv
[19]

Degrande, N

C. Degrande, N. Greiner, W. Kilian, O. Mattelaer, H. Mebane, T. Stelzer et al., Effective Field Theory: A Modern Approach to Anomalous Couplings , Annals Phys. 335 (2013) 21–32, [ 1205.4231]

2013 arXiv
[20]

Falkowski, M

A. Falkowski, M. Gonzalez-Alonso, A. Greljo, D. Marzocca and M. Son, Anomalous Triple Gauge Couplings in the Effective Field Theory Approach at the LHC , JHEP 02 (2017) 115, [ 1609.06312]

2017 arXiv
[21]

Aoude and W

R. Aoude and W. Shepherd, Jet Substructure Measurements of Interference in Non-Interfering SMEFT Effects , JHEP 08 (2019) 009, [ 1902.11262]

2019 arXiv
[22]

Ellis, S.-F

J. Ellis, S.-F. Ge and K. Ma, Hadron collider probes of the quartic couplings of gluons to the photon and Z boson , JHEP 04 (2022) 123, [ 2112.06729]

2022 arXiv
[23]

Martin, A case study of SMEFT O 1/Λ4 effects in diboson processes: pp → W(ℓν )γ, JHEP 05 (2024) 223, [ 2312.09867]

A. Martin, A case study of SMEFT O 1/Λ4 effects in diboson processes: pp → W(ℓν )γ, JHEP 05 (2024) 223, [ 2312.09867]

2024 arXiv
[24]

Degrande and H.-L

C. Degrande and H.-L. Li, Impact of dimension-8 SMEFT operators on diboson productions, JHEP 06 (2023) 149, [ 2303.10493]

2023 arXiv
[25]

Bellm, S

J. Bellm, S. Gieseke, N. Greiner, G. Heinrich, S. Pl¨ atzer, C. Reuschle et al., Anomalous coupling, top-mass and parton-shower effects in W +W − production, JHEP 05 (2016) 106, [ 1602.05141]

2016 arXiv
[26]

Rossia, M

A. Rossia, M. Thomas and E. Vryonidou, Diboson production in the SMEFT from gluon fusion , JHEP 11 (2023) 132, [ 2306.09963]

2023 arXiv
[27]

Azatov and A

A. Azatov and A. Paul, Probing Higgs couplings with high pT Higgs production, JHEP 01 (2014) 014, [ 1309.5273]

2014 arXiv
[28]

Grojean, E

C. Grojean, E. Salvioni, M. Schlaffer and A. Weiler, Very boosted Higgs in gluon fusion, JHEP 05 (2014) 022, [ 1312.3317]

2014 arXiv
[29]

Banfi, A

A. Banfi, A. Martin and V. Sanz, Probing top-partners in Higgs+jets , JHEP 08 (2014) 053, [ 1308.4771]

2014 arXiv
[30]

Azatov, C

A. Azatov, C. Grojean, A. Paul and E. Salvioni, Taming the off-shell Higgs boson , Zh. Eksp. Teor. Fiz. 147 (2015) 410–425, [ 1406.6338]

2015 arXiv
[31]

Azatov, C

A. Azatov, C. Grojean, A. Paul and E. Salvioni, Resolving gluon fusion loops at current and future hadron colliders , JHEP 09 (2016) 123, [ 1608.00977]

2016 arXiv
[32]

Celada, T

E. Celada, T. Giani, J. ter Hoeve, L. Mantani, J. Rojo, A. N. Rossia et al., Mapping the SMEFT at high-energy colliders: from LEP and the (HL-)LHC to the FCC-ee , JHEP 09 (2024) 091, [ 2404.12809]. – 43 –

2024 arXiv
[33]

SMEFiT collaboration, J. J. Ethier, G. Magni, F. Maltoni, L. Mantani, E. R. Nocera, J. Rojo et al., Combined SMEFT interpretation of Higgs, diboson, and top quark data from the LHC , JHEP 11 (2021) 089, [ 2105.00006]

2021 arXiv
[34]

Grazzini, S

M. Grazzini, S. Kallweit, J. M. Lindert, S. Pozzorini and M. Wiesemann, NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production, JHEP 02 (2020) 087, [ 1912.00068]

2020 arXiv
[35]

Kallweit, J

S. Kallweit, J. M. Lindert, S. Pozzorini and M. Sch¨ onherr, NLO QCD+EW predictions for 2ℓ2ν diboson signatures at the LHC , JHEP 11 (2017) 120, [1705.00598]

2017 arXiv
[36]

Banerjee, D

S. Banerjee, D. Reichelt and M. Spannowsky, Electroweak corrections and EFT operators in W+W- production at the LHC , Phys. Rev. D 110 (2024) 115012, [2406.15640]

2024 arXiv
[37]

Lehman and A

L. Lehman and A. Martin, Low-derivative operators of the Standard Model effective field theory via Hilbert series methods , JHEP 02 (2016) 081, [ 1510.00372]

2016 arXiv
[38]

https://github.com/danieljgillies/MCFM-RE
[39]

Darm´ e et al.,UFO 2.0: the ‘Universal Feynman Output’ format , Eur

L. Darm´ e et al.,UFO 2.0: the ‘Universal Feynman Output’ format , Eur. Phys. J. C 83 (2023) 631, [ 2304.09883]

2023 arXiv
[40]

Alwall, R

J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations , JHEP 07 (2014) 079, [1405.0301]

2014 arXiv
[41]

Aad et al., CP Properties of Higgs Boson Interactions with Top Quarks in the t¯tH and tH Processes Using H → γγ with the ATLAS Detector, Phys

ATLAS collaboration, G. Aad et al., CP Properties of Higgs Boson Interactions with Top Quarks in the t¯tH and tH Processes Using H → γγ with the ATLAS Detector, Phys. Rev. Lett. 125 (2020) 061802, [ 2004.04545]

2020 arXiv
[42]

Aad et al., Constraints on Higgs boson properties using W W∗(→ eνµν )jj production in 36.1 fb−1 of √s = 13 TeV pp collisions with the ATLAS detector, Eur

ATLAS collaboration, G. Aad et al., Constraints on Higgs boson properties using W W∗(→ eνµν )jj production in 36.1 fb−1 of √s = 13 TeV pp collisions with the ATLAS detector, Eur. Phys. J. C 82 (2022) 622, [ 2109.13808]

2022 arXiv
[43]

Aad et al., Probing the CP nature of the top–Higgs Yukawa coupling in tt¯H and tH events with H →bb¯ decays using the ATLAS detector at the LHC , Phys

ATLAS collaboration, G. Aad et al., Probing the CP nature of the top–Higgs Yukawa coupling in tt¯H and tH events with H →bb¯ decays using the ATLAS detector at the LHC , Phys. Lett. B 849 (2024) 138469, [ 2303.05974]

2024 arXiv
[44]

Arpino, A

L. Arpino, A. Banfi, S. J¨ ager and N. Kauer, BSM W Wproduction with a jet veto , JHEP 08 (2019) 076, [ 1905.06646]

2019 arXiv
[45]

Cacciari, G

M. Cacciari, G. P. Salam and G. Soyez, The anti- kt jet clustering algorithm , JHEP 04 (2008) 063, [ 0802.1189]

2008 arXiv
[46]

Aaboud et al., Measurement of fiducial and differential W +W − production cross-sections at √s = 13 TeV with the ATLAS detector , Eur

ATLAS collaboration, M. Aaboud et al., Measurement of fiducial and differential W +W − production cross-sections at √s = 13 TeV with the ATLAS detector , Eur. Phys. J. C 79 (2019) 884, [ 1905.04242]

2019 arXiv
[47]

Gehrmann, M

T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierh¨ ofer, A. von Manteuffel, – 44 – S. Pozzorini et al., W +W − Production at Hadron Colliders in Next to Next to Leading Order QCD, Phys. Rev. Lett. 113 (2014) 212001, [ 1408.5243]

2014 arXiv
[48]

Grazzini, S

M. Grazzini, S. Kallweit, S. Pozzorini, D. Rathlev and M. Wiesemann, W +W − production at the LHC: fiducial cross sections and distributions in NNLO QCD , JHEP 08 (2016) 140, [ 1605.02716]

2016 arXiv
[49]

Grazzini, S

M. Grazzini, S. Kallweit, M. Wiesemann and J. Y. Yook, W +W − production at the LHC: NLO QCD corrections to the loop-induced gluon fusion channel , Phys. Lett. B 804 (2020) 135399, [ 2002.01877]

2020 arXiv
[50]

Kallweit, E

S. Kallweit, E. Re, L. Rottoli and M. Wiesemann, Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RADISH: W+W− production at the LHC , JHEP 12 (2020) 147, [ 2004.07720]

2020 arXiv
[51]

J. M. Campbell, R. K. Ellis, T. Neumann and S. Seth, Jet-veto resummation at N3LLp + NNLO in boson production processes , JHEP 04 (2023) 106, [ 2301.11768]

2023 arXiv
[52]

Gavardi, M

A. Gavardi, M. A. Lim, S. Alioli and F. J. Tackmann, NNLO+PS W +W− production using jet veto resummation at NNLL’ , JHEP 12 (2023) 069, [ 2308.11577]

2023 arXiv
[53]

Denner and S

A. Denner and S. Rode, Automated resummation of electroweak Sudakov logarithms in diboson production at future colliders , Eur. Phys. J. C 84 (2024) 542, [2402.10503]

2024 arXiv
[54]

Bertone, S

NNPDF collaboration, V. Bertone, S. Carrazza, N. P. Hartland and J. Rojo, Illuminating the photon content of the proton within a global PDF analysis , SciPost Phys. 5 (2018) 008, [ 1712.07053]

2018 arXiv
[55]

I. W. Stewart and F. J. Tackmann, Theory Uncertainties for Higgs and Other Searches Using Jet Bins , Phys. Rev. D 85 (2012) 034011, [ 1107.2117]

2012 arXiv
[56]

Aaboud et al., Measurement of the W +W − production cross section in pp collisions at a centre-of-mass energy of √s = 13 TeV with the ATLAS experiment, Phys

ATLAS collaboration, M. Aaboud et al., Measurement of the W +W − production cross section in pp collisions at a centre-of-mass energy of √s = 13 TeV with the ATLAS experiment, Phys. Lett. B 773 (2017) 354–374, [ 1702.04519]

2017 arXiv
[57]

Tumasyan et al., Search for CP violation in ttH and tH production in multilepton channels in proton-proton collisions at √s = 13 TeV , JHEP 07 (2023) 092, [ 2208.02686]

CMS collaboration, A. Tumasyan et al., Search for CP violation in ttH and tH production in multilepton channels in proton-proton collisions at √s = 13 TeV , JHEP 07 (2023) 092, [ 2208.02686]

2023 arXiv
[58]

H. Bahl, P. Bechtle, S. Heinemeyer, J. Katzy, T. Klingl, K. Peters et al., Indirect CP probes of the Higgs-top-quark interaction: current LHC constraints and future opportunities, JHEP 11 (2020) 127, [ 2007.08542]

2020 arXiv
[59]

Cepeda et al., Report from Working Group 2: Higgs Physics at the HL-LHC and HE-LHC, CERN Yellow Rep

M. Cepeda et al., Report from Working Group 2: Higgs Physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr. 7 (2019) 221–584, [ 1902.00134]

2019 arXiv
[60]

Englert, A

C. Englert, A. Freitas, M. M. M¨ uhlleitner, T. Plehn, M. Rauch, M. Spira et al., Precision Measurements of Higgs Couplings: Implications for New Physics Scales , J. Phys. G 41 (2014) 113001, [ 1403.7191]

2014 arXiv
[61]

CMS collaboration, A. M. Sirunyan et al., W+W− boson pair production in – 45 – proton-proton collisions at √s = 13 TeV, Phys. Rev. D 102 (2020) 092001, [2009.00119]

2020 arXiv
[62]

https://github.com/danieljgillies/Dim8-Operators-in-ggWW
[63]

H. K. Dreiner, H. E. Haber and S. P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry , Phys. Rept. 494 (2010) 1–196, [0812.1594]. – 46 –

2010 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

collaboration, Summary Plots for Heavy Particle Searches and Long-lived Particle Searches - March 2023 ,

ATLAS collaboration, A. collaboration, Summary Plots for Heavy Particle Searches and Long-lived Particle Searches - March 2023 ,

work page 2023

[2] [2]

Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns

CMS collaboration, A. Hayrapetyan et al., Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns , 2405.18661

work page Pith review arXiv

[3] [3]

Aad et al., Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS experiment , Phys

ATLAS collaboration, G. Aad et al., Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS experiment , Phys. Rev. D 101 (2020) 012002, [1909.02845]

arXiv 2020

[4] [4]

https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsCombined

work page

[5] [5]

Brivio and M

I. Brivio and M. Trott, The Standard Model as an Effective Field Theory , Phys. Rept. 793 (2019) 1–98, [ 1706.08945]

arXiv 2019

[6] [6]

Buchm¨ uller and D

W. Buchm¨ uller and D. Wyler,Effective lagrangian analysis of new interactions and flavour conservation, Nuclear Physics B 268 (1986) 621–653

work page 1986

[7] [7]

Grzadkowski, M

B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian , JHEP 10 (2010) 085, [ 1008.4884]

arXiv 2010

[8] [8]

Carrillo Gonz´ alez, C

M. Carrillo Gonz´ alez, C. de Rham, S. Jaitly, V. Pozsgay and A. Tokareva, Positivity-causality competition: a road to ultimate EFT consistency constraints , JHEP 06 (2024) 146, [ 2307.04784]

arXiv 2024