Electroweak precision observables at NLL order in the SMEFT

Ben A. Stefanek; Ulrich A. Haisch

REVIEW 3 major objections 5 minor 245 references

Electroweak precision observables at NLL order in the SMEFT

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Two-loop running upgrades electroweak precision predictions in the SMEFT to next-to-leading-logarithmic accuracy, and at that accuracy Z-pole data already set the best bounds on key four-top operators.

desk verdict A useful fixed-order two-loop EWPO package, but the 'NLL' label overclaims: the logarithms are truncated at L^2 and L, not resummed. read the letter →

arxiv 2608.10064 v1 pith:NKL5D2ER submitted 2026-08-10 hep-ph

Ulrich A. Haisch , Ben A. Stefanek This is my paper · ORCID

classification hep-ph

keywords SMEFTelectroweakprecisionobservablesnext-to-leadinglogarithmstwo-loopanomalousdimensionsWilsoncoefficientsfour-topoperatorsFCC-eecompositeHiggs

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

Electroweak precision observables—the Z and W masses and widths, cross sections, and asymmetries measured at LEP and SLC—are among the sharpest indirect tests of new physics, but their SMEFT predictions have until now been limited to leading-logarithmic and fixed-order accuracy. This paper shows that next-to-leading-logarithmic (NLL) accuracy is already achievable: combine the one-loop matching results that exist for every electroweak observable with the recently completed two-loop anomalous dimension matrix for the full set of dimension-six operators, and evolve from the new-physics scale to the Z pole. The large logarithms of the scale ratio are generated only by this running, so two-loop matching—still unavailable for most operators—is not needed. The resulting NLL formulas cover all 210 independent Wilson coefficients and, when fitted to current data, already make LEP and SLC the strongest probes of the purely right-handed four-top operator and several related third-generation four-quark operators, with projected FCC-ee sensitivity reaching effective scales of order 20 TeV.

What carries the argument

The load-bearing object is the two-loop anomalous dimension matrix of the dimension-six SMEFT operators—the $210\times 210$ matrix that describes how Wilson coefficients mix as the renormalization scale slides from $\Lambda$ down to $m_Z$. The method combines this with the complete one-loop electroweak matching conditions, in the LEP input scheme $(\alpha, G_F, m_Z)$. The step that makes the whole construction work is the scale-separation argument: logarithms of $\Lambda/m_Z$ can only arise from RG running, never from loops at the electroweak scale, so one-loop matching plus two-loop running is exactly what NLL accuracy requires. The paper also uses a consistent classification of operators by the order at which they first enter—tree, one-loop, or two-loop—with the two-loop class subdivided into operators that get LL contributions through RG mixing and those (like $Q_G$, $Q_{uH}$, $Q_{HG}$) whose EWPO sensitivity first appears as genuine two-loop NLL effects.

What would settle it

Take one specific two-loop mixing entry used in the paper—for example the coefficient of the $L$ term in $C_{HD}(m_Z)/C_{uG}^{33}(\Lambda)$ in Eq. (2.11), which is proportional to $g_s y_t\,(48\alpha_t - \tfrac{32}{3}\alpha_Y)/(16\pi^3)$—and compute it independently with a second two-loop anomalous-dimension calculation. If the coefficient differs, the NLL shifts in $m_W$, $\Gamma_Z$, and the asymmetries induced by $Q_{uG}$ change accordingly. Alternatively, compute the full two-loop matching contribution of $Q_{uu}^{3333}$ to $T$ and check whether it is free of $\ln(\Lambda/m_Z)$ terms, as the paper's claim that two-loop matching is NNLL requires.

Watch

Extended reading notes

Core claim

The central claim, stated on the authors' terms, is that the logarithmic structure of electroweak precision predictions in the SMEFT can be systematically improved one step beyond leading logarithms. Writing the large logarithm as $L=\ln(\Lambda/m_Z)$, LL terms are $\alpha^n L^n$ and NLL terms are $\alpha^n L^{n-1}$; the paper derives NLL predictions for all electroweak observables by feeding two-loop RG evolution into the known one-loop matching conditions. A key part of the claim is a structural argument, illustrated on $Q^{3333}_{uu}\to T$, that two-loop matching does not generate $\ln(\Lambda/m_Z)$ terms and therefore enters only at NNLL order. On this basis the paper classifies every dimension-six operator by the loop order at which it first affects EWPO, identifies the Higgs self-interaction operator $Q_H$ as the unique operator whose leading logarithms appear only at four-loop order, and provides numerical fits showing that existing Z-pole data already surpass LHC top-quark constraints on the third-generation four-quark operators, with FCC-ee projections extending the reach.

Load-bearing premise

The paper takes the two-loop scale-evolution matrix for all 210 operators from a separate calculation instead of deriving it, and it only demonstrates in one worked example that one-loop matching is enough; if that matrix has an error, or if the worked example does not represent every operator, every NLL number and bound in the paper shifts.

Editorial extensions

If this is right

Existing LEP and SLC electroweak data already provide stronger 95% CL bounds on the third-generation four-quark operators $Q_{qq}^{3333(1)}$, $Q_{qq}^{3333(3)}$, $Q_{qu}^{3333(1)}$, and $Q_{uu}^{3333}$ than current LHC top-quark measurements, with effective scales above 1 TeV.
Projected FCC-ee Tera-Z measurements extend these bounds to effective scales of order 20 TeV and surpass projected HL-LHC sensitivity for $Q_G$, $Q_{H\square}$, $Q_{uG}^{33}$, and $Q_{uH}^{33}$.
Operators such as $Q_{uG}^{33}$, $Q_G$, $Q_{uH}^{33}$, and $Q_{HG}$ first become accessible to electroweak precision through genuine two-loop NLL effects, while $Q_H$ remains beyond NLL reach.
NLL accuracy requires no two-loop matching; every NLO electroweak calculation whose one-loop matching is known can be upgraded to NLL by adding the two-loop RG running.
The W-boson mass is the single most important EWPO for these NLL constraints in several operator classes, dominating fits for $Q_{uu}$, $Q_{uG}$, $Q_{uH}$, and $Q_{H\square}$.

Reading between the lines

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

The strong $\Lambda$ dependence of the EWPO bounds on four-quark operators means that a global fit treating $\Lambda$ as a free parameter—rather than fixing it at 1 TeV—could change the ranking of constraints; the paper fixes $\Lambda$ but notes that larger $\Lambda$ strengthens the RG effects, leaving this a direct, testable next step.
If the same two-loop anomalous dimension matrix is applied to dimension-eight SMEFT operators when it becomes available, the same NLL counting would predict new first-access operators for EWPO; the classification logic in Section 2.3 gives a template for identifying them.
The paper's identification of $m_W$ as the dominant NLL probe for several operators suggests that the planned FCC-ee $m_W$ measurement is not just a Standard Model consistency check but a high-sensitivity search for top-quark compositeness; experiments might therefore want to optimize $m_W$ systematics beyond the S1 scenario assumptions.

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

First thing: this is a solid, useful paper, but the NLL label doesn't hold up in the way the abstract claims. What’s new and good: systematic classification of all 210 operators by EWPO sensitivity, explicit two-loop mixing examples, full numerical expressions in ancillary files, and a clean demonstration that one-loop matching suffices for the logarithms that matter. The LEP/SLC fits and the RS/CH examples are carefully done, with honest treatment of uncertainties. The paper deserves credit for making the two-loop beta functions of [20] usable in EWPO phenomenology.

The stress-test concern is real. By the paper's own definitions, LL means α^n L^n and NLL means α^n L^{n-1} for all n≥1. The central results (2.8)–(2.20) and the Section 4 formulas contain only L^2 and L terms. Solving the one-loop RGE along the Q_uu → Q_Hu → Q_HD chain generates α_t^3 L^3 and higher LL logarithms because γ_{Hu,Hu} is nonzero. Those terms are not exhibited or included. The paper is therefore a fixed-order two-loop calculation, not an NLL-resummed one. The numerical size is not negligible: α_t L ~ 0.18 at Λ = 1 TeV, so the missing α_t^3 L^3 term is an O(10–20%) correction to the α_t^2 L^2 term. For FCC-ee projections, that can shift the bounds by more than the stated experimental precision.

Also, the paper relies completely on the two-loop anomalous dimension matrix of [20] without independent check. That is a legitimate external benchmark, not a defect, but it means the central numbers inherit any errors in [20].

Soft spots in proportion: the classification and formulas are reproducible; the fits are documented. The main revision needed is to reframe the claims honestly — "log-enhanced corrections through two-loop order" rather than "NLL accuracy" — and possibly add the missing higher-log terms or estimate their size. Some of the conclusions in Sections 5 and 6 may change once those terms are included.

Bottom line: this is a paper for SMEFT phenomenologists, and it deserves a serious referee. If the authors either rename the accuracy or (better) include the higher-order logarithms, it will be a valuable reference. I would read it again, and I'd cite the operator classification.

Recommendation: send to peer review, with a request for clarification of the logarithmic counting.

Referee Report

3 major / 5 minor

Summary. The paper claims to systematically improve SMEFT predictions for electroweak precision observables (EWPO) to next-to-leading-logarithmic (NLL) accuracy by combining tree-level and one-loop matching with one- and two-loop renormalization-group evolution. It classifies operators according to the loop order at which they first enter EWPO, derives two-loop RG-induced logarithmic contributions for representative operators such as the right-handed four-top operator, the top chromomagnetic dipole, the triple-gluon operator, the top Yukawa-type operator, and the Higgs-gluon operator, and provides numerical NLL formulas for the complete set of EWPO in the LEP scheme. These results are then used to perform fits to current LEP/SLC data and projected FCC-ee data, with comparisons to LHC top-quark and Higgs constraints, and are applied to custodial Randall-Sundrum and composite Higgs models. The central claim is that the paper provides NLL-accurate EWPO expressions depending on all 210 independent Wilson coefficients, with ancillary files containing the full set of formulas.

Significance. If the NLL claim is correct, this work would be a valuable step for global SMEFT fits, since two-loop RG effects would allow EWPO to probe several operator classes that are otherwise only weakly constrained. The paper has clear strengths: it engages with the recently computed two-loop SMEFT anomalous dimension matrix, illustrates the mechanism on explicit operator-observable pairs, provides reproducible numerical inputs, includes comparisons with existing LHC constraints, and gives explicit model applications. The analytic and numerical exercises in Sections 2.3 and 4 appear internally consistent with the cited one-loop matching and two-loop beta-function results. However, the central NLL accuracy claim is not supported by the paper's own logarithmic counting, as detailed in the major comments. The significance of the phenomenological results is therefore conditional on a re-scoped or corrected treatment of higher-order logarithms.

major comments (3)

[Section 2.3, Eqs. (2.8)–(2.20)] The paper's own definitions in Eqs. (1.2)–(1.3) count LL as α^n L^n and NLL as α^n L^{n-1} for all n=1,2,..., yet the central results in Eqs. (2.8)–(2.20) and all of Section 4 contain only L^2 and L terms. Under the same counting, the one-loop RGE that generates the LL series also produces higher-order terms: for the chain Q_uu → Q_Hu → Q_HD, a non-zero one-loop diagonal anomalous dimension γ_{Hu,Hu} gives a contribution γ_{HD,Hu} γ_{Hu,Hu} γ_{Hu,uu} L^3/6 to C_HD(mZ), which is an n=3 LL term according to Eq. (1.2), together with corresponding n=3 NLL terms. Since α_t L ≈ 0.18 for Λ=1 TeV, the omitted α_t^3 L^3 term is expected to be roughly 10–20% of the retained α_t^2 L^2 term. The expressions are therefore fixed-order truncations at two-loop/order-L^2, not NLL-resummed results. The central claim of systematic NLL accuracy is not established without resumming or otherwise systematically including the all-order one-loop logarithms.
[Section 3, Eq. (3.3) and Eqs. (3.5)–(3.6)] The argument that one-loop matching suffices for NLL accuracy is incomplete for the same reason. In Eq. (3.3), the RGE solution for C_Hu(μR) is explicitly truncated at O(L). If the one-loop self-mixing of Q_Hu is retained, C_Hu(μR) receives α_t^2 L^2 and higher terms, which through the one-loop matching contribution T^(1) in Eq. (3.2) produce α_t^3 L^3 and α_t^3 L^2 contributions. These are part of the LL and NLL series by the paper's own definitions and are not contained in T_NLL defined in Eq. (3.5). The statement that the remainder T−T_NLL contains no large logarithms only isolates the two-loop matching term T^(2); it does not account for omitted higher-order RG logarithms generated by the one-loop anomalous dimensions.
[Section 4 and Section 5, Tables 5–6 and Figures 10–11] Because all numerical formulas in Section 4 contain only L^2 and L terms, the fits in Section 5, and especially the FCC-ee projections, are based on the truncated O(L^2) expressions. The projected effective scales in Table 6, such as 20.9 TeV for c_{qq}^{(1)3333}, therefore inherit the missing higher-order logarithms. The estimated numerical impact from the omitted terms is at the 10–20% level for Λ=1 TeV and grows with Λ. The quantitative sensitivities presented in Tables 5–6 and Figures 8–11 should be recomputed with a consistent treatment of higher-order logarithms, or the claims should be re-scoped to 'two-loop RG-improved predictions up to order L^2' rather than 'NLL accuracy'.

minor comments (5)

[Section 4, introductory paragraph] The sentence describing 'the L^2, L, and L dependence' appears to contain a typo or an undefined notation; please define separate symbols for ln(Λ/mZ), ln(mZ/mt), and any other logarithms appearing in the numerical formulas.
[Section 4, Eqs. (4.5)–(4.22)] The three-term notation in formulas such as Eq. (4.5) is confusing because all three terms are written with the same symbol L; please clarify which terms are L^2, which are L, and which are constants or other logarithms.
[Table 4] The column header 'Future precision 10^-4' is ambiguous for mW and ΓW, whose entries appear to have dimensionful units; please clarify the units and normalization used in that column.
[Section 1, footnote 1] The phrase 'the instant classic [20]' is colloquial and not appropriate for a journal report; please rephrase.
[Section 2.3, Eq. (2.8)] The statement that 'LL and NLL contributions are highlighted in red and green' will not be visible in black-and-white printing; please add explicit labels or a distinct notation.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the NLL EWPO construction combines external one-loop matching and two-loop RGE results; no prediction reduces to a fitted input or self-citation chain.

full rationale

The paper's central derivation is an application of two independent external inputs: the complete two-loop SMEFT anomalous dimensions of [20] and the NLO matching conditions of [11]. Equations (2.8)-(2.20) and the Section 4 numerical formulas are obtained by inserting those beta functions into the matching framework, and the Section 5 fits treat the Wilson coefficients as free parameters adjusted to LEP/SLC and LHC data; no equation equates a 'predicted' observable to the data used to fit that same observable. The only self-citations in the derivation chain are [15] and [31]. Reference [15] is used in Section 3 to exhibit the two-loop matching term for Q_uu -> T, which is then shown to be NNLL and is explicitly omitted from the NLL prediction T_NLL = T^(0)+T^(1) (Eq. 3.5); the conclusion that two-loop matching is unnecessary for NLL accuracy does not import the paper's target result. Reference [31] is cited only for the RG framework used to classify the Q_H four-loop mixing as NNLL, and Q_H is excluded from the 210-coefficient set. Neither citation carries the central claim. The skeptical concern that the RGE solution is truncated at L^2 rather than resummed to all orders concerns whether the 'NLL accuracy' label is justified by the paper's own counting; that is a completeness/correctness issue, not a circular reduction of outputs to inputs. Accordingly, no circular step can be exhibited, and the honest finding is no significant circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No ad hoc free parameters are introduced: the NLL derivation uses SM inputs and the Wilson coefficients as EFT variables, and the fits constrain rather than tune them. The main axioms are the correctness of the external two-loop beta functions, dimension-six truncation with U(1)^14 flavor and CP assumptions, and the one-loop-matching-is-NLL argument. No new particles, mediators, or forces are postulated.

free parameters (1)

High-scale Wilson coefficients c_i(Λ), 210 independent coefficients = not fixed; constrained by LEP/SLC, LHC, and projected FCC-ee data in Section 5
These are the targets of the EWPO fits rather than tuning parameters; the NLL formulas are linear in them, and no numerical values are chosen to force the derivation.

assumptions (5)

domain assumption Correctness and completeness of the two-loop SMEFT anomalous dimension matrix of [20]
All NLL logarithms in Eqs. (2.8)-(2.20) and Section 4 are generated from this matrix; it is not rederived in this paper.
domain assumption Dimension-six truncation and restriction to CP-even operators invariant under U(1)^14, with only y_t nonzero, captures all phenomenologically relevant EWPO at NLL
Sets the 210/211 operator basis in Sections 2.2 and 4 and drops light Yukawas and CP violation.
domain assumption One-loop EW matching combined with two-loop RG running is sufficient for NLL; two-loop matching is NNLL
Proved by example for Q_uu to T in Section 3 and argued generally; no general proof is given for every operator and observable.
domain assumption SM inputs from PDG 2025 and the FCC-ee Tera-Z S1 uncertainty projections are reliable
The fits in Section 5 depend directly on Table 4 values.
standard math Standard QFT and SMEFT perturbative framework, including renormalization-scale independence of physical predictions
Background for the operator product expansion, anomalous dimensions, and matching calculations.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Electroweak precision observables at NLL order in the SMEFT." pith.science (2026). https://pith.science/paper/NKL5D2ER

@misc{pith2026260810064,
  author       = {Pith},
  title        = {Pith review of: Electroweak precision observables at NLL order in the SMEFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NKL5D2ER}},
  note         = {Machine review of arXiv:2608.10064}
}

abstract

Electroweak precision observables (EWPO) remain among the most powerful indirect probes of physics beyond the Standard Model (BSM), and future $e^+ e^-$ colliders are expected to substantially enhance their sensitivity. Within the framework of the Standard Model Effective Field Theory (SMEFT), we show how EWPO predictions can be systematically improved to next-to-leading-logarithmic (NLL) accuracy by combining fixed-order tree-level and one-loop matching with two- and one-loop renormalization-group evolution. We derive NLL expressions that encode the full dependence on all 210 independent Wilson coefficients and illustrate their impact through fits to both current and projected collider measurements. This work provides a basis for global SMEFT analyses at NLL precision, thereby maximizing the indirect reach to BSM physics through EWPO measurements. The phenomenological relevance of this framework is illustrated explicitly in both the custodial Randall-Sundrum model and a custodial composite Higgs model.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

245 extracted references · 9 canonical work pages

[20]

L. Born, J. Fuentes-Martín, and A. E. Thomsen, (2026), arXiv:2601.19974 [hep-ph]. – 55 –

arXiv 2026
[1]

Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys

S. Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys. Rept.427, 257 (2006), arXiv:hep-ex/0509008

arXiv 2006
[2]

Abadaet al.(FCC), Eur

A. Abadaet al.(FCC), Eur. Phys. J. ST228, 261 (2019)

2019
[3]

Donget al.(CEPC Study Group), (2018), arXiv:1811.10545 [hep-ex]

M. Donget al.(CEPC Study Group), (2018), arXiv:1811.10545 [hep-ex]

arXiv 2018
[4]

Buchmüller and D

W. Buchmüller and D. Wyler, Nucl. Phys. B268, 621 (1986)

1986
[5]

Grzadkowski, M

B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, JHEP10, 085 (2010), arXiv:1008.4884 [hep-ph]

arXiv 2010
[6]

Brivio and M

I. Brivio and M. Trott, Phys. Rept.793, 1 (2019), arXiv:1706.08945 [hep-ph]

arXiv 2019
[7]

Isidori, F

G. Isidori, F. Wilsch, and D. Wyler, Rev. Mod. Phys.96, 015006 (2024), arXiv:2303.16922 [hep-ph]

arXiv 2024

Show all 245 references

[8]

Dawson and P

S. Dawson and P. P. Giardino, Phys. Rev. D101, 013001 (2020), arXiv:1909.02000 [hep-ph]

2020 arXiv
[9]

Dawson and P

S. Dawson and P. P. Giardino, Phys. Rev. D105, 073006 (2022), arXiv:2201.09887 [hep-ph]

2022 arXiv
[10]

Bellafronte, S

L. Bellafronte, S. Dawson, and P. P. Giardino, JHEP05, 208 (2023), arXiv:2304.00029 [hep-ph]

2023 arXiv
[11]

Biekötter and B

A. Biekötter and B. D. Pecjak, JHEP07, 134 (2025), arXiv:2503.07724 [hep-ph]

2025 arXiv
[12]

Bellafronte, S

L. Bellafronte, S. Dawson, C. Del Pio, M. Forslund, and P. P. Giardino, (2026), arXiv:2605.18679 [hep-ph]

2026 arXiv
[13]

Biekötter, B

A. Biekötter, B. D. Pecjak, D. J. Scott, and T. Smith, JHEP07, 115 (2023), arXiv:2305.03763 [hep-ph]

2023 arXiv
[14]

Biekötter, B

A. Biekötter, B. D. Pecjak, and T. Smith, JHEP04, 073 (2024), arXiv:2312.08446 [hep-ph]

2024 arXiv
[15]

Haisch and L

U. Haisch and L. Schnell, JHEP02, 038 (2025), arXiv:2410.13304 [hep-ph]

2025 arXiv
[16]

Di Noi, H

S. Di Noi, H. El Faham, R. Gröber, M. Vitti, and E. Vryonidou, JHEP01, 025 (2026), arXiv:2507.01137 [hep-ph]

2026 arXiv
[17]

E. E. Jenkins, A. V. Manohar, and M. Trott, JHEP10, 087 (2013), arXiv:1308.2627 [hep-ph]

2013 arXiv
[18]

E. E. Jenkins, A. V. Manohar, and M. Trott, JHEP01, 035 (2014), arXiv:1310.4838 [hep-ph]

2014 arXiv
[19]

Alonso, E

R. Alonso, E. E. Jenkins, A. V. Manohar, and M. Trott, JHEP04, 159 (2014), arXiv:1312.2014 [hep-ph]

2014 arXiv
[21]

Gorbahn and U

M. Gorbahn and U. Haisch, JHEP10, 094 (2016), arXiv:1607.03773 [hep-ph]

2016 arXiv
[22]

Z. Bern, J. Parra-Martinez, and E. Sawyer, JHEP10, 211 (2020), arXiv:2005.12917 [hep-ph]

2020 arXiv
[23]

Q. Jin, K. Ren, and G. Yang, JHEP04, 180 (2021), arXiv:2011.02494 [hep-ph]

2021 arXiv
[24]

Haisch, D

U. Haisch, D. J. Scott, M. Wiesemann, G. Zanderighi, and S. Zanoli, JHEP07, 054 (2022), arXiv:2204.00663 [hep-ph]

2022 arXiv
[25]

Di Noi, R

S. Di Noi, R. Gröber, G. Heinrich, J. Lang, and M. Vitti, Phys. Rev. D109, 095024 (2024), arXiv:2310.18221 [hep-ph]

2024 arXiv
[26]

E. E. Jenkins, A. V. Manohar, L. Naterop, and J. Pagès, JHEP02, 131 (2024), arXiv:2310.19883 [hep-ph]

2024 arXiv
[27]

Di Noi, R

S. Di Noi, R. Gröber, and M. K. Mandal, JHEP12, 220 (2025), arXiv:2408.03252 [hep-ph]

2025
[28]

L. Born, J. Fuentes-Martín, S. Kvedarait˙ e, and A. E. Thomsen, JHEP05, 121 (2025), arXiv:2410.07320 [hep-ph]

2025 arXiv
[29]

Naterop and P

L. Naterop and P. Stoffer, JHEP06, 007 (2025), arXiv:2412.13251 [hep-ph]

2025 arXiv
[30]

C. Duhr, A. Vasquez, G. Ventura, and E. Vryonidou, JHEP07, 160 (2025), arXiv:2503.01954 [hep-ph]

2025 arXiv
[31]

Haisch, JHEP06, 004 (2025), arXiv:2503.06249 [hep-ph]

U. Haisch, JHEP06, 004 (2025), arXiv:2503.06249 [hep-ph]

2025 arXiv
[32]

Zhang, JHEP06, 106 (2025), arXiv:2504.00792 [hep-ph]

D. Zhang, JHEP06, 106 (2025), arXiv:2504.00792 [hep-ph]

2025 arXiv
[33]

B. Assi, A. Helset, J. Pagès, and C.-H. Shen, JHEP12, 082 (2025), arXiv:2504.18537 [hep-ph]

2025 arXiv
[34]

Naterop and P

L. Naterop and P. Stoffer, JHEP02, 016 (2026), arXiv:2507.08926 [hep-ph]

2026
[35]

Di Noi and R

S. Di Noi and R. Gröber, Phys. Lett. B869, 139878 (2025), arXiv:2507.10295 [hep-ph]

2025
[36]

Haisch and M

U. Haisch and M. Niggetiedt, (2025), arXiv:2507.20803 [hep-ph]

2025 arXiv
[37]

C. Duhr, G. Ventura, and E. Vryonidou, JHEP11, 046 (2025), arXiv:2508.04500 [hep-ph]

2025 arXiv
[38]

Di Noi, B

S. Di Noi, B. A. Erdelyi, and R. Gröber, JHEP06, 177 (2026), arXiv:2510.14680 [hep-ph]

2026 arXiv
[39]

Banik, A

S. Banik, A. Crivellin, L. Naterop, and P. Stoffer, JHEP02, 017 (2026), arXiv:2510.08682 [hep-ph]

2026
[40]

Henriksson, S

J. Henriksson, S. R. Kousvos, and J. Roosmale Nepveu, JHEP05, 005 (2026), arXiv:2511.16740 [hep-th]

2026
[41]

Chala and J

M. Chala and J. López Miras, (2025), arXiv:2512.04064 [hep-ph]

2025
[42]

Guedes and J

G. Guedes and J. Roosmale Nepveu, (2025), arXiv:2512.08827 [hep-ph]

2025
[43]

C. Duhr, G. Ventura, and E. Vryonidou, (2026), arXiv:2602.01250 [hep-ph]

2026
[44]

Mantani, P

L. Mantani, P. Olgoso, and A. N. Rossia, (2026), arXiv:2604.16599 [hep-ph]

2026 arXiv
[45]

L. Born, A. Greljo, and A. E. Thomsen, (2026), arXiv:2604.26817 [hep-ph]

2026 arXiv
[46]

Greljo, A

A. Greljo, A. Palavrić, and B. A. Stefanek, (2025), arXiv:2512.04159 [hep-ph]

2025
[47]

Durieux, M

G. Durieux, M. McCullough, and E. Salvioni, JHEP12, 148 (2022), [Erratum: JHEP02, 165 (2023)], arXiv:2209.00666 [hep-ph]

2022 arXiv
[48]

B. A. Stefanek, JHEP09, 103 (2024), arXiv:2407.09593 [hep-ph]. – 56 –

2024 arXiv
[49]

Allwicher, M

L. Allwicher, M. McCullough, and S. Renner, JHEP02, 164 (2025), arXiv:2408.03992 [hep-ph]

2025 arXiv
[50]

Maura, B

V. Maura, B. A. Stefanek, and T. You, JHEP10, 022 (2025), arXiv:2412.14241 [hep-ph]

2025 arXiv
[51]

Maura, B

V. Maura, B. A. Stefanek, and T. You, Phys. Rev. Lett.135, 141802 (2025), arXiv:2503.13719 [hep-ph]

2025 arXiv
[52]

ter Hoeve, L

J. ter Hoeve, L. Mantani, J. Rojo, A. N. Rossia, and E. Vryonidou, Phys. Rev. D112, 013008 (2025), arXiv:2504.05974 [hep-ph]

2025 arXiv
[53]

Dinget al., (2026), 10.21468/SciPostPhysCommRep.24, arXiv:2601.13248 [hep-ph]

J.-L. Dinget al., (2026), 10.21468/SciPostPhysCommRep.24, arXiv:2601.13248 [hep-ph]

2026 arXiv
[54]

Zhang, N

C. Zhang, N. Greiner, and S. Willenbrock, Phys. Rev. D86, 014024 (2012), arXiv:1201.6670 [hep-ph]

2012 arXiv
[55]

J. Brod, A. Greljo, E. Stamou, and P. Uttayarat, JHEP02, 141 (2015), arXiv:1408.0792 [hep-ph]

2015 arXiv
[56]

Röntsch and M

R. Röntsch and M. Schulze, JHEP07, 091 (2014), [Erratum: JHEP09, 132 (2015)], arXiv:1404.1005 [hep-ph]

2014 arXiv
[57]

Khachatryanet al.(CMS), JHEP01, 096 (2016), arXiv:1510.01131 [hep-ex]

V. Khachatryanet al.(CMS), JHEP01, 096 (2016), arXiv:1510.01131 [hep-ex]

2016 arXiv
[58]

Bessidskaia Bylund, F

O. Bessidskaia Bylund, F. Maltoni, I. Tsinikos, E. Vryonidou, and C. Zhang, JHEP05, 052 (2016), arXiv:1601.08193 [hep-ph]

2016 arXiv
[59]

Degrande, F

C. Degrande, F. Maltoni, K. Mimasu, E. Vryonidou, and C. Zhang, JHEP10, 005 (2018), arXiv:1804.07773 [hep-ph]

2018 arXiv
[60]

A. M. Sirunyanet al.(CMS), JHEP03, 056 (2020), arXiv:1907.11270 [hep-ex]

2020 arXiv
[61]

Ravina, E

B. Ravina, E. Simpson, and J. Howarth, Eur. Phys. J. C81, 809 (2021), arXiv:2106.09690 [hep-ph]

2021 arXiv
[62]

H. E. Faham, F. Maltoni, K. Mimasu, and M. Zaro, JHEP01, 100 (2022), arXiv:2111.03080 [hep-ph]

2022 arXiv
[63]

Mammen Abraham and D

R. Mammen Abraham and D. Gonçalves, Eur. Phys. J. C83, 965 (2023), arXiv:2208.05986 [hep-ph]

2023 arXiv
[64]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C85, 1434 (2025), arXiv:2504.05919 [hep-ex]

2025 arXiv
[65]

Cornet-Gomez, V

F. Cornet-Gomez, V. Miralles, M. Miralles López, M. Moreno Llácer, and M. Vos, JHEP 10, 156 (2025), arXiv:2503.11518 [hep-ph]

2025
[66]

Durieux, A

G. Durieux, A. Irles, V. Miralles, A. Peñuelas, R. Pöschl, M. Perelló, and M. Vos, JHEP 12, 98 (2019), [Erratum: JHEP01, 195 (2021)], arXiv:1907.10619 [hep-ph]

2019 arXiv
[67]

Aoude, T

R. Aoude, T. Hurth, S. Renner, and W. Shepherd, JHEP12, 113 (2020), arXiv:2003.05432 [hep-ph]

2020 arXiv
[68]

Bißmann, C

S. Bißmann, C. Grunwald, G. Hiller, and K. Kröninger, JHEP06, 010 (2021), arXiv:2012.10456 [hep-ph]

2021 arXiv
[69]

Bruggisser, D

S. Bruggisser, D. van Dyk, and S. Westhoff, JHEP02, 225 (2023), arXiv:2212.02532 [hep-ph]

2023 arXiv
[70]

Grunwald, G

C. Grunwald, G. Hiller, K. Kröninger, and L. Nollen, JHEP11, 110 (2023), arXiv:2304.12837 [hep-ph]. – 57 –

2023 arXiv
[71]

Garosi, D

F. Garosi, D. Marzocca, A. R. Sánchez, and A. Stanzione, JHEP12, 129 (2023), arXiv:2310.00047 [hep-ph]

2023 arXiv
[72]

Allwicher, G

L. Allwicher, G. Isidori, J. M. Lizana, N. Selimovic, and B. A. Stefanek, JHEP05, 179 (2023), arXiv:2302.11584 [hep-ph]

2023 arXiv
[73]

Allwicher, C

L. Allwicher, C. Cornella, G. Isidori, and B. A. Stefanek, JHEP03, 049 (2024), arXiv:2311.00020 [hep-ph]

2024 arXiv
[74]

Haisch, J

U. Haisch, J. Linder, G. Pelliccioli, E. Re, and G. Zanderighi, JHEP11, 080 (2025), arXiv:2507.21768 [hep-ph]

2025
[75]

Dedes, M

A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho, and L. Trifyllis, JHEP08, 103 (2018), arXiv:1805.00302 [hep-ph]

2018 arXiv
[76]

Ellis, M

J. Ellis, M. Madigan, K. Mimasu, V. Sanz, and T. You, JHEP04, 279 (2021), arXiv:2012.02779 [hep-ph]

2021 arXiv
[77]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C81, 163 (2021), arXiv:2006.15458 [hep-ex]

2021 arXiv
[78]

J. J. Ethier, R. Gomez-Ambrosio, G. Magni, and J. Rojo, Eur. Phys. J. C81, 560 (2021), arXiv:2101.03180 [hep-ph]

2021 arXiv
[79]

Tumasyanet al.(CMS), Phys

A. Tumasyanet al.(CMS), Phys. Rev. D105, 052003 (2022), arXiv:2111.13948 [hep-ex]

2022 arXiv
[80]

Celada, T

E. Celada, T. Giani, J. ter Hoeve, L. Mantani, J. Rojo, A. N. Rossia, M. O. A. Thomas, and E. Vryonidou, JHEP09, 091 (2024), arXiv:2404.12809 [hep-ph]

2024 arXiv
[81]

Hayrapetyanet al.(CMS), JHEP12, 068 (2023), arXiv:2307.15761 [hep-ex]

A. Hayrapetyanet al.(CMS), JHEP12, 068 (2023), arXiv:2307.15761 [hep-ex]

2023 arXiv
[82]

Allwicher, D

L. Allwicher, D. A. Faroughy, F. Jaffredo, O. Sumensari, and F. Wilsch, JHEP03, 064 (2023), arXiv:2207.10714 [hep-ph]

2023 arXiv
[83]

de Blas, M

J. de Blas, M. Chala, and J. Santiago, JHEP09, 189 (2015), arXiv:1507.00757 [hep-ph]

2015 arXiv
[84]

Greljo, H

A. Greljo, H. Tiblom, and A. Valenti, SciPost Phys.18, 152 (2025), arXiv:2411.02485 [hep-ph]

2025 arXiv
[85]

Jiang, Y

X.-H. Jiang, Y. Liu, and B. Yan, Phys. Rev. D112, L111303 (2025), arXiv:2507.21477 [hep-ph]

2025
[86]

Cao and F

H. Cao and F. Petriello, Phys. Rev. D113, 035033 (2026), arXiv:2511.01994 [hep-ph]

2026
[87]

Allwicher, C

L. Allwicher, C. Grojean, and L. Tabatt, (2025), arXiv:2512.06916 [hep-ph]

2025 arXiv
[88]

Allwicher, G

L. Allwicher, G. Isidori, and M. Pesut, Eur. Phys. J. C85, 631 (2025), arXiv:2503.17019 [hep-ph]

2025 arXiv
[89]

Bellafronte, S

L. Bellafronte, S. Dawson, P. P. Giardino, and H. Liu, Phys. Rev. Lett.135, 251801 (2025), arXiv:2507.02039 [hep-ph]

2025
[90]

Schulze and Y

M. Schulze and Y. Soreq, Eur. Phys. J. C76, 466 (2016), arXiv:1603.08911 [hep-ph]

2016 arXiv
[91]

Brivio, S

I. Brivio, S. Bruggisser, F. Maltoni, R. Moutafis, T. Plehn, E. Vryonidou, S. Westhoff, and C. Zhang, JHEP02, 131 (2020), arXiv:1910.03606 [hep-ph]

2020 arXiv
[92]

J. J. Ethier, G. Magni, F. Maltoni, L. Mantani, E. R. Nocera, J. Rojo, E. Slade, E. Vryonidou, and C. Zhang (SMEFiT), JHEP11, 089 (2021), arXiv:2105.00006 [hep-ph]

2021 arXiv
[93]

Aoude, H

R. Aoude, H. El Faham, F. Maltoni, and E. Vryonidou, JHEP10, 163 (2022), arXiv:2208.04962 [hep-ph]. – 58 –

2022 arXiv
[94]

de Blas, A

J. de Blas, A. Goncalves, V. Miralles, L. Reina, L. Silvestrini, and M. Valli, (2025), arXiv:2512.02256 [hep-ph]

2025 arXiv
[95]

Greiner, S

N. Greiner, S. Willenbrock, and C. Zhang, Phys. Lett. B704, 218 (2011), arXiv:1104.3122 [hep-ph]

2011 arXiv
[96]

Hartmann and M

C. Hartmann and M. Trott, JHEP07, 151 (2015), arXiv:1505.02646 [hep-ph]

2015 arXiv
[97]

Hartmann and M

C. Hartmann and M. Trott, Phys. Rev. Lett.115, 191801 (2015), arXiv:1507.03568 [hep-ph]

2015 arXiv
[98]

Bißmann, J

S. Bißmann, J. Erdmann, C. Grunwald, G. Hiller, and K. Kröninger, Eur. Phys. J. C80, 136 (2020), arXiv:1909.13632 [hep-ph]

2020 arXiv
[99]

Bruggisser, R

S. Bruggisser, R. Schäfer, D. van Dyk, and S. Westhoff, JHEP05, 257 (2021), arXiv:2101.07273 [hep-ph]

2021 arXiv
[100]

N. P. Hartland, F. Maltoni, E. R. Nocera, J. Rojo, E. Slade, E. Vryonidou, and C. Zhang, JHEP04, 100 (2019), arXiv:1901.05965 [hep-ph]

2019 arXiv
[101]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C83, 496 (2023), [Erratum: Eur. Phys. J. C84, 156 (2024)], arXiv:2303.15061 [hep-ex]

2023 arXiv
[102]

Hayrapetyanet al.(CMS), Phys

A. Hayrapetyanet al.(CMS), Phys. Lett. B847, 138290 (2023), arXiv:2305.13439 [hep-ex]

2023 arXiv
[103]

Degrande, R

C. Degrande, R. Rosenfeld, and A. Vasquez, JHEP07, 114 (2024), arXiv:2402.06528 [hep-ph]

2024 arXiv
[104]

Aaboudet al.(ATLAS), JHEP04, 046 (2019), arXiv:1811.12113 [hep-ex]

M. Aaboudet al.(ATLAS), JHEP04, 046 (2019), arXiv:1811.12113 [hep-ex]

2019 arXiv
[105]

A. M. Sirunyanet al.(CMS), Eur. Phys. J. C80, 75 (2020), arXiv:1908.06463 [hep-ex]

2020 arXiv
[106]

A. M. Sirunyanet al.(CMS), Phys. Lett. B803, 135285 (2020), arXiv:1909.05306 [hep-ex]

2020 arXiv
[107]

Aadet al.(ATLAS), Eur

G. Aadet al.(ATLAS), Eur. Phys. J. C80, 1085 (2020), arXiv:2007.14858 [hep-ex]

2020 arXiv
[108]

Banelli, E

G. Banelli, E. Salvioni, J. Serra, T. Theil, and A. Weiler, JHEP02, 043 (2021), arXiv:2010.05915 [hep-ph]

2021 arXiv
[109]

Aadet al.(ATLAS), JHEP11, 118 (2021), arXiv:2106.11683 [hep-ex]

G. Aadet al.(ATLAS), JHEP11, 118 (2021), arXiv:2106.11683 [hep-ex]

2021 arXiv
[110]

Tumasyanet al.(CMS), Phys

A. Tumasyanet al.(CMS), Phys. Lett. B844, 138076 (2023), arXiv:2303.03864 [hep-ex]

2023 arXiv
[111]

CMS,Search for physics beyond the standard model in four and three top quark production events using proton-proton collisions at√s= 13 TeV, CERN, Geneva, 2025

2025
[112]

Chekhovskyet al.(CMS), Eur

V. Chekhovskyet al.(CMS), Eur. Phys. J. C86, 331 (2026), arXiv:2504.02958 [hep-ex]

2026 arXiv
[113]

Subba and S

A. Subba and S. Ganguly, (2026), arXiv:2605.18382 [hep-ph]

2026 arXiv
[114]

Gauld, B

R. Gauld, B. D. Pecjak, and D. J. Scott, JHEP05, 080 (2016), arXiv:1512.02508 [hep-ph]

2016 arXiv
[115]

Hartmann, W

C. Hartmann, W. Shepherd, and M. Trott, JHEP03, 060 (2017), arXiv:1611.09879 [hep-ph]

2017 arXiv
[116]

Boughezal, C.-Y

R. Boughezal, C.-Y. Chen, F. Petriello, and D. Wiegand, Phys. Rev. D100, 056023 (2019), arXiv:1907.00997 [hep-ph]

2019 arXiv
[117]

Degrande, G

C. Degrande, G. Durieux, F. Maltoni, K. Mimasu, E. Vryonidou, and C. Zhang, Phys. Rev. D103, 096024 (2021), arXiv:2008.11743 [hep-ph]

2021 arXiv
[118]

Heinrich and J

G. Heinrich and J. Lang, JHEP05, 121 (2024), arXiv:2311.15004 [hep-ph]

2024 arXiv
[119]

Freiheit and U

M. Freiheit and U. Haisch, JHEP04, 045 (2026), arXiv:2512.05857 [hep-ph]. – 59 –

2026
[120]

D. B. Kaplan, Nucl. Phys. B365, 259 (1991)

1991
[121]

G. F. Giudice, C. Grojean, A. Pomarol, and R. Rattazzi, JHEP06, 045 (2007), arXiv:hep-ph/0703164

2007 arXiv
[122]

Pomarol and J

A. Pomarol and J. Serra, Phys. Rev. D78, 074026 (2008), arXiv:0806.3247 [hep-ph]

2008 arXiv
[123]

Agashe, G

K. Agashe, G. Perez, and A. Soni, Phys. Rev. D75, 015002 (2007), arXiv:hep-ph/0606293

2007 arXiv
[124]

Casagrande, F

S. Casagrande, F. Goertz, U. Haisch, M. Neubert, and T. Pfoh, JHEP10, 094 (2008), arXiv:0807.4937 [hep-ph]

2008 arXiv
[125]

A. J. Buras and M. Jung, JHEP06, 067 (2018), arXiv:1804.05852 [hep-ph]

2018 arXiv
[126]

Hisano, K

J. Hisano, K. Tsumura, and M. J. S. Yang, Phys. Lett. B713, 473 (2012), arXiv:1205.2212 [hep-ph]

2012 arXiv
[127]

J. Brod, U. Haisch, and J. Zupan, JHEP11, 180 (2013), arXiv:1310.1385 [hep-ph]

2013 arXiv
[128]

Cirigliano, W

V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Phys. Rev. D94, 016002 (2016), arXiv:1603.03049 [hep-ph]

2016 arXiv
[129]

Cirigliano, W

V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Phys. Rev. D94, 034031 (2016), arXiv:1605.04311 [hep-ph]

2016 arXiv
[130]

Panico, A

G. Panico, A. Pomarol, and M. Riembau, JHEP04, 090 (2019), arXiv:1810.09413 [hep-ph]

2019 arXiv
[131]

Brod and E

J. Brod and E. Stamou, JHEP07, 080 (2021), arXiv:1810.12303 [hep-ph]

2021 arXiv
[132]

Bauer, M

M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, JHEP04, 063 (2021), arXiv:2012.12272 [hep-ph]

2021 arXiv
[133]

Ardu and S

M. Ardu and S. Davidson, JHEP08, 002 (2021), arXiv:2103.07212 [hep-ph]

2021 arXiv
[134]

J. Brod, Z. Polonsky, and E. Stamou, JHEP06, 091 (2024), arXiv:2306.12478 [hep-ph]

2024 arXiv
[135]

Biekötter, J

A. Biekötter, J. Fuentes-Martín, A. M. Galda, and M. Neubert, JHEP09, 120 (2023), arXiv:2307.10372 [hep-ph]

2023 arXiv
[136]

Zhang and S

C. Zhang and S. Willenbrock, Phys. Rev. D83, 034006 (2011), arXiv:1008.3869 [hep-ph]

2011 arXiv
[137]

Degrande, J.-M

C. Degrande, J.-M. Gerard, C. Grojean, F. Maltoni, and G. Servant, JHEP03, 125 (2011), arXiv:1010.6304 [hep-ph]

2011 arXiv
[138]

Buarque Franzosi and C

D. Buarque Franzosi and C. Zhang, Phys. Rev. D91, 114010 (2015), arXiv:1503.08841 [hep-ph]

2015 arXiv
[139]

Deutschmann, C

N. Deutschmann, C. Duhr, F. Maltoni, and E. Vryonidou, JHEP12, 063 (2017), [Erratum: JHEP02, 159 (2018)], arXiv:1708.00460 [hep-ph]

2017 arXiv
[140]

Grazzini, A

M. Grazzini, A. Ilnicka, and M. Spira, Eur. Phys. J. C78, 808 (2018), arXiv:1806.08832 [hep-ph]

2018 arXiv
[141]

Battaglia, M

M. Battaglia, M. Grazzini, M. Spira, and M. Wiesemann, JHEP11, 173 (2021), arXiv:2109.02987 [hep-ph]

2021 arXiv
[142]

Di Noi and R

S. Di Noi and R. Gröber, Eur. Phys. J. C84, 403 (2024), arXiv:2312.11327 [hep-ph]

2024 arXiv
[143]

Maltoni, G

F. Maltoni, G. Ventura, and E. Vryonidou, JHEP12, 183 (2024), arXiv:2406.06670 [hep-ph]

2024 arXiv
[144]

Campillo Aveleira, G

B. Campillo Aveleira, G. Heinrich, M. Kerner, and L. Kunz, JHEP04, 060 (2025), arXiv:2409.05728 [hep-ph]. – 60 –

2025 arXiv
[145]

Ghosh and M

D. Ghosh and M. Wiebusch, Phys. Rev. D91, 031701 (2015), arXiv:1411.2029 [hep-ph]

2015 arXiv
[146]

Krauss, S

F. Krauss, S. Kuttimalai, and T. Plehn, Phys. Rev. D95, 035024 (2017), arXiv:1611.00767 [hep-ph]

2017 arXiv
[147]

Hirschi, F

V. Hirschi, F. Maltoni, I. Tsinikos, and E. Vryonidou, JHEP07, 093 (2018), arXiv:1806.04696 [hep-ph]

2018 arXiv
[148]

Goldouzian and M

R. Goldouzian and M. D. Hildreth, Phys. Lett. B811, 135889 (2020), arXiv:2001.02736 [hep-ph]

2020 arXiv
[149]

Bardhan, D

D. Bardhan, D. Ghosh, P. Jain, and A. M. Thalapillil, Phys. Rev. D103, 115003 (2021), arXiv:2010.13402 [hep-ph]

2021 arXiv
[150]

Bartocci, A

R. Bartocci, A. Biekötter, and T. Hurth, JHEP05, 074 (2024), arXiv:2311.04963 [hep-ph]

2024 arXiv
[151]

Bevilacqua, M

G. Bevilacqua, M. Reinartz, and M. Worek, (2026), arXiv:2605.11747 [hep-ph]

2026 arXiv
[152]

Azatov and A

A. Azatov and A. Paul, JHEP01, 014 (2014), arXiv:1309.5273 [hep-ph]

2014 arXiv
[153]

Grojean, E

C. Grojean, E. Salvioni, M. Schlaffer, and A. Weiler, JHEP05, 022 (2014), arXiv:1312.3317 [hep-ph]

2014 arXiv
[154]

Azatov, C

A. Azatov, C. Grojean, A. Paul, and E. Salvioni, Zh. Eksp. Teor. Fiz.147, 410 (2015), arXiv:1406.6338 [hep-ph]

2015 arXiv
[155]

Buschmann, D

M. Buschmann, D. Goncalves, S. Kuttimalai, M. Schonherr, F. Krauss, and T. Plehn, JHEP02, 038 (2015), arXiv:1410.5806 [hep-ph]

2015 arXiv
[156]

ATLAS,Effective field theory interpretation of the measurement of off-shell Higgs boson production fromZZ→4ℓandZZ→2ℓ2νdecay channels with the ATLAS detector, CERN, Geneva, 2023

2023
[157]

Ghosh, M

A. Ghosh, M. Griese, U. Haisch, and T. H. Park, Eur. Phys. J. C86, 415 (2026), arXiv:2507.02032 [hep-ph]

2026 arXiv
[158]

Gauld, B

R. Gauld, B. D. Pecjak, and D. J. Scott, Phys. Rev. D94, 074045 (2016), arXiv:1607.06354 [hep-ph]

2016 arXiv
[159]

Capozi and G

M. Capozi and G. Heinrich, JHEP03, 091 (2020), arXiv:1908.08923 [hep-ph]

2020 arXiv
[160]

Heinrich, J

G. Heinrich, J. Lang, and L. Scyboz, JHEP08, 079 (2022), [Erratum: JHEP10, 086 (2023)], arXiv:2204.13045 [hep-ph]

2022 arXiv
[161]

Brivio, R

I. Brivio, R. Gröber, and K. Schmid, JHEP05, 031 (2026), arXiv:2511.23411 [hep-ph]

2026 arXiv
[162]

Carvalho, M

A. Carvalho, M. Dall’Osso, T. Dorigo, F. Goertz, C. A. Gottardo, and M. Tosi, JHEP04, 126 (2016), arXiv:1507.02245 [hep-ph]

2016 arXiv
[163]

Bizoń, U

W. Bizoń, U. Haisch, and L. Rottoli, JHEP10, 267 (2019), arXiv:1810.04665 [hep-ph]

2019 arXiv
[164]

Borowka, C

S. Borowka, C. Duhr, F. Maltoni, D. Pagani, A. Shivaji, and X. Zhao, JHEP04, 016 (2019), arXiv:1811.12366 [hep-ph]

2019 arXiv
[165]

Heinrich, S

G. Heinrich, S. P. Jones, M. Kerner, G. Luisoni, and L. Scyboz, JHEP06, 066 (2019), arXiv:1903.08137 [hep-ph]

2019 arXiv
[166]

Bagnaschi, G

E. Bagnaschi, G. Degrassi, and R. Gröber, Eur. Phys. J. C83, 1054 (2023), arXiv:2309.10525 [hep-ph]

2023 arXiv
[167]

Bizoń, U

W. Bizoń, U. Haisch, L. Rottoli, Z. Gillis, B. Moser, and P. Windischhofer, JHEP02, 170 (2024), arXiv:2402.03463 [hep-ph]. – 61 –

2024 arXiv
[168]

H. T. Li, Z.-G. Si, J. Wang, X. Zhang, and D. Zhao, Chin. Phys. C49, 023107 (2025), arXiv:2407.14716 [hep-ph]

2025 arXiv
[169]

Aadet al.(CMS, ATLAS), (2026), arXiv:2602.23991 [hep-ex]

G. Aadet al.(CMS, ATLAS), (2026), arXiv:2602.23991 [hep-ex]

2026
[170]

Degrassi, P

G. Degrassi, P. P. Giardino, F. Maltoni, and D. Pagani, JHEP12, 080 (2016), arXiv:1607.04251 [hep-ph]

2016 arXiv
[171]

Bizon, M

W. Bizon, M. Gorbahn, U. Haisch, and G. Zanderighi, JHEP07, 083 (2017), arXiv:1610.05771 [hep-ph]

2017 arXiv
[172]

Maltoni, D

F. Maltoni, D. Pagani, A. Shivaji, and X. Zhao, Eur. Phys. J. C77, 887 (2017), arXiv:1709.08649 [hep-ph]

2017 arXiv
[173]

Gorbahn and U

M. Gorbahn and U. Haisch, JHEP04, 062 (2019), arXiv:1902.05480 [hep-ph]

2019 arXiv
[174]

Haisch and G

U. Haisch and G. Koole, JHEP02, 030 (2022), arXiv:2111.12589 [hep-ph]

2022 arXiv
[175]

Gao, X.-M

J. Gao, X.-M. Shen, G. Wang, L. L. Yang, and B. Zhou, Phys. Rev. D107, 115017 (2023), arXiv:2302.04160 [hep-ph]

2023 arXiv
[176]

Haisch and M

U. Haisch and M. Niggetiedt, JHEP10, 236 (2024), arXiv:2408.13186 [hep-ph]

2024 arXiv
[177]

McCullough, Phys

M. McCullough, Phys. Rev. D90, 015001 (2014), [Erratum: Phys. Rev. D92, 039903 (2015)], arXiv:1312.3322 [hep-ph]

2014 arXiv
[178]

Di Vita, G

S. Di Vita, G. Durieux, C. Grojean, J. Gu, Z. Liu, G. Panico, M. Riembau, and T. Vantalon, JHEP02, 178 (2018), arXiv:1711.03978 [hep-ph]

2018 arXiv
[179]

Maltoni, D

F. Maltoni, D. Pagani, and X. Zhao, JHEP07, 087 (2018), arXiv:1802.07616 [hep-ph]

2018 arXiv
[180]

S. D. Rindani and B. Singh, Int. J. Mod. Phys. A35, 2050011 (2020), arXiv:1805.03417 [hep-ph]

2020 arXiv
[181]

K. Rao, S. D. Rindani, P. Sarmah, and B. Singh, Nucl. Phys. B975, 115649 (2022), arXiv:2109.11134 [hep-ph]

2022 arXiv
[182]

M. E. Peskin and T. Takeuchi, Phys. Rev. D46, 381 (1992)

1992
[183]

Degrassi, M

G. Degrassi, M. Fedele, and P. P. Giardino, JHEP04, 155 (2017), arXiv:1702.01737 [hep-ph]

2017 arXiv
[184]

G. D. Kribs, A. Maier, H. Rzehak, M. Spannowsky, and P. Waite, Phys. Rev. D95, 093004 (2017), arXiv:1702.07678 [hep-ph]

2017 arXiv
[185]

Navaset al.(Particle Data Group), Phys

S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

2024
[186]

Greljo, B

A. Greljo, B. A. Stefanek, and A. Valenti, Phys. Lett. B871, 140009 (2025), arXiv:2507.03073 [hep-ph]

2025 arXiv
[187]

Bozzi and M

G. Bozzi and M. Schott, (2025), arXiv:2506.01887 [hep-ph]

2025 arXiv
[188]

Awramik, M

M. Awramik, M. Czakon, A. Freitas, and G. Weiglein, Phys. Rev. D69, 053006 (2004), arXiv:hep-ph/0311148

2004 arXiv
[189]

Theory uncertainties, PPG EW WG,

A. Freitas, “Theory uncertainties, PPG EW WG,” Talk presented at the EW Physics Preparatory Group,https://indico.cern.ch/event/1551879/contributions/6540716/ (2025)

2025
[190]

Benediktet al.(FCC), Eur

M. Benediktet al.(FCC), Eur. Phys. J. C85, 1468 (2025), arXiv:2505.00272 [hep-ex]

2025 arXiv
[191]

Agashe, A

K. Agashe, A. Delgado, M. J. May, and R. Sundrum, JHEP08, 050 (2003), arXiv:hep-ph/0308036. – 62 –

2003 arXiv
[192]

Randall and R

L. Randall and R. Sundrum, Phys. Rev. Lett.83, 3370 (1999), arXiv:hep-ph/9905221

1999 arXiv
[193]

Agashe, R

K. Agashe, R. Contino, L. Da Rold, and A. Pomarol, Phys. Lett. B641, 62 (2006), arXiv:hep-ph/0605341

2006 arXiv
[194]

Blanke, A

M. Blanke, A. J. Buras, B. Duling, S. Gori, and A. Weiler, JHEP03, 001 (2009), arXiv:0809.1073 [hep-ph]

2009 arXiv
[195]

Bauer, S

M. Bauer, S. Casagrande, U. Haisch, and M. Neubert, JHEP09, 017 (2010), arXiv:0912.1625 [hep-ph]

2010 arXiv
[196]

Casagrande, F

S. Casagrande, F. Goertz, U. Haisch, M. Neubert, and T. Pfoh, JHEP09, 014 (2010), arXiv:1005.4315 [hep-ph]

2010 arXiv
[197]

Grossman and M

Y. Grossman and M. Neubert, Phys. Lett. B474, 361 (2000), arXiv:hep-ph/9912408

2000 arXiv
[198]

Gherghetta and A

T. Gherghetta and A. Pomarol, Nucl. Phys. B586, 141 (2000), arXiv:hep-ph/0003129

2000 arXiv
[199]

Azatov, M

A. Azatov, M. Toharia, and L. Zhu, Phys. Rev. D82, 056004 (2010), arXiv:1006.5939 [hep-ph]

2010 arXiv
[200]

Goertz, U

F. Goertz, U. Haisch, and M. Neubert, Phys. Lett. B713, 23 (2012), arXiv:1112.5099 [hep-ph]

2012 arXiv
[201]

Carena, S

M. Carena, S. Casagrande, F. Goertz, U. Haisch, and M. Neubert, JHEP08, 156 (2012), arXiv:1204.0008 [hep-ph]

2012 arXiv
[202]

Frank, N

M. Frank, N. Pourtolami, and M. Toharia, Phys. Rev. D87, 096003 (2013), arXiv:1301.7692 [hep-ph]

2013 arXiv
[203]

R. Malm, M. Neubert, K. Novotny, and C. Schmell, JHEP01, 173 (2014), arXiv:1303.5702 [hep-ph]

2014 arXiv
[204]

J. Hahn, C. Hörner, R. Malm, M. Neubert, K. Novotny, and C. Schmell, Eur. Phys. J. C 74, 2857 (2014), arXiv:1312.5731 [hep-ph]

2014 arXiv
[205]

R. Malm, M. Neubert, and C. Schmell, JHEP02, 008 (2015), arXiv:1408.4456 [hep-ph]

2015 arXiv
[206]

P. R. Archer, M. Carena, A. Carmona, and M. Neubert, JHEP01, 060 (2015), arXiv:1408.5406 [hep-ph]

2015 arXiv
[207]

I. Low, R. Rattazzi, and A. Vichi, JHEP04, 126 (2010), arXiv:0907.5413 [hep-ph]

2010 arXiv
[208]

Agashe, R

K. Agashe, R. Contino, and A. Pomarol, Nucl. Phys. B719, 165 (2005), arXiv:hep-ph/0412089

2005 arXiv
[209]

Agashe and R

K. Agashe and R. Contino, Nucl. Phys. B742, 59 (2006), arXiv:hep-ph/0510164

2006 arXiv
[210]

Contino, T

R. Contino, T. Kramer, M. Son, and R. Sundrum, JHEP05, 074 (2007), arXiv:hep-ph/0612180

2007 arXiv
[211]

Panico and A

G. Panico and A. Wulzer,The Composite Nambu-Goldstone Higgs, Vol. 913 (Springer,
[212]

J. M. Maldacena, Adv. Theor. Math. Phys.2, 231 (1998), arXiv:hep-th/9711200

1998 arXiv
[213]

S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B428, 105 (1998), arXiv:hep-th/9802109

1998 arXiv
[214]

Witten, Adv

E. Witten, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150

1998 arXiv
[215]

Davoudiasl, G

H. Davoudiasl, G. Perez, and A. Soni, Phys. Lett. B665, 67 (2008), arXiv:0802.0203 [hep-ph]. – 63 –

2008 arXiv
[216]

Bauer, S

M. Bauer, S. Casagrande, L. Grunder, U. Haisch, and M. Neubert, Phys. Rev. D79, 076001 (2009), arXiv:0811.3678 [hep-ph]

2009 arXiv
[217]

S. R. Coleman, J. Wess, and B. Zumino, Phys. Rev.177, 2239 (1969)

1969
[218]

C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zumino, Phys. Rev.177, 2247 (1969)

1969
[219]

Bando, T

M. Bando, T. Kugo, S. Uehara, K. Yamawaki, and T. Yanagida, Phys. Rev. Lett.54, 1215 (1985)

1985
[220]

Bando, T

M. Bando, T. Kugo, and K. Yamawaki, Phys. Rept.164, 217 (1988)

1988
[221]

Low and A

I. Low and A. Vichi, Phys. Rev. D84, 045019 (2011), arXiv:1010.2753 [hep-ph]

2011 arXiv
[222]

Gillioz, R

M. Gillioz, R. Gröber, C. Grojean, M. Mühlleitner, and E. Salvioni, JHEP10, 004 (2012), arXiv:1206.7120 [hep-ph]

2012 arXiv
[223]

Glioti, R

A. Glioti, R. Rattazzi, L. Ricci, and L. Vecchi, SciPost Phys.18, 201 (2025), arXiv:2402.09503 [hep-ph]

2025 arXiv
[224]

Bellazzini, C

B. Bellazzini, C. Csáki, and J. Serra, Eur. Phys. J. C74, 2766 (2014), arXiv:1401.2457 [hep-ph]

2014 arXiv
[225]

Fuentes-Martin, G

J. Fuentes-Martin, G. Isidori, J. M. Lizana, N. Selimovic, and B. A. Stefanek, Phys. Lett. B834, 137382 (2022), arXiv:2203.01952 [hep-ph]

2022 arXiv
[226]

Alloul, N

A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, Comput. Phys. Commun.185, 2250 (2014), arXiv:1310.1921 [hep-ph]

2014 arXiv
[227]

Hahn, Comput

T. Hahn, Comput. Phys. Commun.140, 418 (2001), arXiv:hep-ph/0012260

2001 arXiv
[228]

T. Hahn, S. Paßehr, and C. Schappacher, PoSLL2016, 068 (2016), arXiv:1604.04611 [hep-ph]

2016 arXiv
[229]

H. H. Patel, Comput. Phys. Commun.197, 276 (2015), arXiv:1503.01469 [hep-ph]

2015 arXiv
[230]

R. D. Ballet al.(NNPDF), Eur. Phys. J. C77, 663 (2017), arXiv:1706.00428 [hep-ph]

2017 arXiv
[231]

D. B. Clark, E. Godat, and F. I. Olness, Comput. Phys. Commun.216, 126 (2017), arXiv:1605.08012 [hep-ph]

2017 arXiv
[232]

Fuentes-Martin, P

J. Fuentes-Martin, P. Ruiz-Femenia, A. Vicente, and J. Virto, Eur. Phys. J. C81, 167 (2021), arXiv:2010.16341 [hep-ph]

2021 arXiv
[233]

Catani, S

S. Catani, S. Devoto, M. Grazzini, S. Kallweit, J. Mazzitelli, and H. Sargsyan, Phys. Rev. D99, 051501 (2019), arXiv:1901.04005 [hep-ph]

2019 arXiv
[234]

Catani, S

S. Catani, S. Devoto, M. Grazzini, S. Kallweit, and J. Mazzitelli, JHEP07, 100 (2019), arXiv:1906.06535 [hep-ph]

2019 arXiv
[235]

Czakon and A

M. Czakon and A. Mitov, Comput. Phys. Commun.185, 2930 (2014), arXiv:1112.5675 [hep-ph]

2014 arXiv
[236]

Alwall, R

J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, JHEP07, 079 (2014), arXiv:1405.0301 [hep-ph]

2014 arXiv
[237]

van Beekveld, A

M. van Beekveld, A. Kulesza, and L. M. Valero, Phys. Rev. Lett.131, 211901 (2023), arXiv:2212.03259 [hep-ph]

2023 arXiv
[238]

Tumasyanet al.(CMS), Phys

A. Tumasyanet al.(CMS), Phys. Rev. D104, 092013 (2021), arXiv:2108.02803 [hep-ex]

2021 arXiv
[239]

Falkowski and D

A. Falkowski and D. Straub, JHEP04, 066 (2020), arXiv:1911.07866 [hep-ph]. – 64 –

2020 arXiv
[240]

Giani, G

T. Giani, G. Magni, and J. Rojo, Eur. Phys. J. C83, 393 (2023), arXiv:2302.06660 [hep-ph]

2023 arXiv
[241]

ATLAS,Combined measurements of Higgs boson production and decay at√s= 13 TeV using up to 140 fb−1 of data collected by the ATLAS Experiment, CERN, Geneva, 2025

2025
[242]

Hayrapetyanet al.(CMS), (2026), arXiv:2602.18611 [hep-ex]

A. Hayrapetyanet al.(CMS), (2026), arXiv:2602.18611 [hep-ex]

2026 arXiv
[243]

Cepedaet al., CERN Yellow Rep

M. Cepedaet al., CERN Yellow Rep. Monogr.7, 221 (2019), arXiv:1902.00134 [hep-ph]

2019 arXiv
[244]

Aadet al.(ATLAS, CMS), (2025), arXiv:2504.00672 [hep-ex]

G. Aadet al.(ATLAS, CMS), (2025), arXiv:2504.00672 [hep-ex]. – 65 –

2025 arXiv
[2016]

arXiv:1506.01961 [hep-ph]

arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [20]

L. Born, J. Fuentes-Martín, and A. E. Thomsen, (2026), arXiv:2601.19974 [hep-ph]. – 55 –

arXiv 2026

[2] [1]

Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys

S. Schaelet al.(ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys. Rept.427, 257 (2006), arXiv:hep-ex/0509008

arXiv 2006

[3] [2]

Abadaet al.(FCC), Eur

A. Abadaet al.(FCC), Eur. Phys. J. ST228, 261 (2019)

2019

[4] [3]

Donget al.(CEPC Study Group), (2018), arXiv:1811.10545 [hep-ex]

M. Donget al.(CEPC Study Group), (2018), arXiv:1811.10545 [hep-ex]

arXiv 2018

[5] [4]

Buchmüller and D

W. Buchmüller and D. Wyler, Nucl. Phys. B268, 621 (1986)

1986

[6] [5]

Grzadkowski, M

B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, JHEP10, 085 (2010), arXiv:1008.4884 [hep-ph]

arXiv 2010

[7] [6]

Brivio and M

I. Brivio and M. Trott, Phys. Rept.793, 1 (2019), arXiv:1706.08945 [hep-ph]

arXiv 2019

[8] [7]

Isidori, F

G. Isidori, F. Wilsch, and D. Wyler, Rev. Mod. Phys.96, 015006 (2024), arXiv:2303.16922 [hep-ph]

arXiv 2024