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Double Higgs Production in Vector Boson Fusion at NLO QCD in HEFT

T0 review · 1 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper establishes that the leading HEFT couplings $c_\lambda$, $c_V$, and $c_{2V}$ control both the rate and the shape of $pp\to hhjj$ at NLO QCD, and that combinations within current experimental bounds can strongly distort…

desk verdict Solid, well-validated NLO QCD prediction for VBF double-Higgs in HEFT; the completeness argument for dropping L4 operators is under-explained but does not sink the calculation. read the letter →

arxiv 2502.09132 v2 pith:U7PHR7ZS submitted 2025-02-13 hep-ph

Jens Braun , Pia Bredt , Gudrun Heinrich , Marius Höfer This is my paper · ORCID
classification hep-ph PACS 12.38.Bx13.85.Lg14.80.Bn
keywords HiggspairproductionvectorbosonfusionNLOQCDEffectiveFieldTheoryanomalouscouplingsLHCphenomenologykappaframework
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

The paper presents the full next-to-leading-order QCD prediction for Higgs-boson pair production in vector boson fusion, $pp \to hhjj$ at order $\alpha_{\rm ew}^4$, within Higgs Effective Field Theory. It keeps the three leading anomalous couplings—$c_\lambda$ for the trilinear Higgs coupling, $c_V$ for the single $hVV$ coupling, and $c_{2V}$ for the double $hhVV$ coupling—and includes non-factorisable QCD diagrams and Higgs-strahlung topologies, so it goes beyond the structure-function approximation used by earlier tools. A sympathetic reader should care because these three couplings are exactly the ones the HL-LHC can hope to constrain through double-Higgs VBF, and the paper shows that combinations of them can change not just the total rate but the shapes of $m_{hh}$, $p_T^h$, $\Delta\eta(h,h)$, and $\Delta R(h,h)$ in experimentally accessible regions.

What carries the argument

The load-bearing object is the effective Lagrangian (2.9), which parametrises the leading HEFT effects through three coupling multipliers $c_\lambda$, $c_V$, and $c_{2V}$ attached to the $h^3$, $hVV$, and $hhVV$ vertices. Around this Lagrangian the calculation is organised by chiral dimension: the paper assigns $d_\chi=0$ to gauge and scalar fields and $d_\chi=1$ to each weak coupling, derivative, and fermion bilinear, which fixes the operator counting and justifies dropping $d_\chi=4$ operators at this order. The technical carrier is an automated NLO interface between a Monte Carlo event generator and a one-loop amplitude generator using a UFO model file, which delivers real and virtual corrections including non-factorising diagrams and $s$-channel Higgs-strahlung topologies rather than factorised DIS-like structures.

What would settle it

A concrete check is to enumerate the $X^2 U h$ and $X U h D^2$ classes of the complete $d_\chi=4$ HEFT basis and test whether any operator contracts to a $q q \to q q h h$ tree topology with two electroweak emissions at $O(g_{\rm ew}^4 g_s^2)$. If such an operator exists, the restricted Lagrangian (2.9) is incomplete and the shape predictions would need revision.

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Extended reading notes

Core claim

The central claim is that the leading HEFT Lagrangian, restricted to the three custodial-symmetric operators of equation (2.9), is sufficient for a complete NLO QCD description of electroweak $hhjj$ production, and that this calculation can be done without the structure-function approximation. The authors argue that at $O(\alpha_{\rm ew}^4 \alpha_s)$ no $d_\chi=4$ HEFT operator can form the required tree topology with the correct coupling powers, so the anomalous vertices coincide with the $\kappa$-framework modifiers. Numerically, the NLO QCD $K$-factor is about $0.90$ and varies by only a few percent across the coupling parameter space, while the total cross section can range from roughly half to more than an order of magnitude above the SM value. The more distinctive result is shape-level: combinations of anomalous couplings that are individually within current experimental bounds can turn the dip in the pseudorapidity separation $\Delta\eta(h,h)$ into a peak, create a peak-dip structure in $m_{hh}$, and enhance the high-$p_T$ tails, patterns that would not appear when varying any single coupling alone.

Load-bearing premise

The calculation's HEFT interpretation rests on the claim that no higher-order effective operator can contribute to this process at $O(\alpha_{\rm ew}^4 \alpha_s)$; the paper asserts this is checkable by power counting but does not show the full enumeration.

Editorial extensions

If this is right

  • Within the stated HEFT operator set, the NLO QCD prediction for $pp\to hhjj$ is now known without the structure-function approximation, so the non-factorisable and Higgs-strahlung contributions are included at perturbative order $\alpha_{\rm ew}^4 \alpha_s$.
  • The K-factor is nearly flat and almost independent of the anomalous couplings, meaning the QCD correction factor can be treated as approximately universal across the HEFT parameter space.
  • The polynomial parametrisation of the total cross section in $c_\lambda$, $c_V$, and $c_{2V}$ gives a fast continuous interpolation that can be evaluated for arbitrary coupling values without rerunning the full simulation.
  • Coupling combinations that are individually allowed by current experimental constraints can change the shape of $\Delta\eta(h,h)$ and $m_{hh}$ in ways that a single-coupling analysis would miss.
  • The new NLO setup is usable for arbitrary user-defined processes beyond this one, so the same interface can be applied to related VBF and EFT observables.

Reading between the lines

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

  • Editorial inference: because the anomalous couplings enter only the electroweak subdiagram, the near-universal K-factor suggests the NLO QCD correction could be transferred to any $\kappa$-framework model as a process-level factor, but the paper does not claim this beyond the investigated parameter space.
  • Editorial inference: the shape flips in the central $\Delta\eta(h,h)$ region are promising discriminants for an experimental search, since they appear at moderate separations rather than only in high-energy tails, which is a testable strategy the paper leaves implicit.
  • Editorial inference: when NLO electroweak corrections are added, $d_\chi=4$ operators will introduce vertex structures beyond the $\kappa$-framework, so the simple coupling-multiplier picture of this paper is expected to break down at that order.
  • Editorial inference: the same automated chain could be used to produce NLO QCD predictions for single-Higgs VBF or for $hhjj$ in SMEFT, where the operator counting and the pattern of shape distortions would differ.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 6 minor

Summary. The paper presents the next-to-leading order QCD corrections to Higgs pair production in vector boson fusion, pp -> hhjj, within the Higgs Effective Field Theory framework. The calculation uses an automated Whizard-GoSam interface with a UFO model file containing the three leading anomalous couplings c_lambda, c_V and c_2V. It includes non-factorisable one-loop diagrams and s/u-channel Higgs-strahlung type topologies, going beyond the usual structure-function approximation. The authors validate their setup at LO against MadGraph5 and Whizard+OpenLoops, and at the amplitude level against OpenLoops over a large phase-space sample. They present total cross sections and K-factors for eleven benchmark points, a polynomial parametrisation of the total cross section in the anomalous couplings, and differential distributions for p_T(h), m_hh, Delta_eta(h,h) and Delta_R(h,h). The central phenomenological claim is that combinations of anomalous couplings that are still allowed by current constraints can produce characteristic shape distortions in these observables.

Significance. If the operator-completeness claim is secured, this is a valuable calculation: it provides the first full NLO QCD prediction for HEFT VBF double-Higgs production without the structure-function approximation, and it demonstrates that combined anomalous couplings can generate shape features that are absent when each coupling is varied individually. The technical validation is strong: amplitude-level checks over 10^6 phase-space points show relative differences of 10^-15 for Born and real amplitudes and 10^-8 for the virtual finite part, and the authors make their UFO model and example run files publicly available. The shape observables, especially the dip-to-peak change in Delta_eta(h,h), are plausible and experimentally relevant for the HL-LHC. The main reservation concerns the derivation of the 'leading HEFT operator' set, which is the basis for interpreting the results as the leading EFT effects.

major comments (1)
  1. [Sec. 2.2, Eq. (2.9)] The claim that the Lagrangian (2.9) contains the leading HEFT operators for pp -> hhjj at NLO QCD rests on the statement in Sec. 2.2 that 'one can check' that no L4 operator can be inserted in a tree topology at O(g_ew^4 g_s^2). This is not demonstrated. The subsequent discussion covers only the bosonic classes X^2 U h and X U h D^2; it does not enumerate the fermionic operators in the complete L4 bases of Refs. [38, 57, 58] (for example four-fermion contact terms with two Higgs fields, or psi^2 X h operators), nor does it show that their coefficients cannot be of comparable size under a weakly or strongly coupled UV. The coupling-power assignment that excludes gluon-Higgs operators is an assumption about UV origins rather than a consequence of HEFT chiral counting. Because the abstract and Sec. 2.2 use 'leading' to characterise the restricted operator set, this is load-bearing for the shape conclusions in Sec. 4.3 and for the polynomial (4.6). Please either provide a complete enumeration of the L4 operators and a stated power-counting assumption, or explicitly restrict the claims to the L2 Lagrangian and adjust the abstract and conclusions accordingly.
minor comments (6)
  1. [Sec. 1] There is a typo in the Introduction: 'in the in the so-calledstructure function approximation' should read 'in the so-called structure function approximation'.
  2. [Sec. 4.2, Table 2] The fitted polynomial (4.6) should give sigma/sigma_SM = 1 at c_lambda = c_V = c_2V = 1, but the central coefficients in Table 2 sum to about 1.04 at that point. Please clarify whether the SM point was included in the fit and consider constraining the parametrisation to pass through (1,1,1).
  3. [Sec. 5] The conclusions state that the NLO QCD corrections reduce the SM cross section by about 7%, but the SM row of Table 1 gives sigma_NLO/sigma_LO = 0.904(6), which is a reduction of about 9.6%. Please reconcile this statement with the tabulated result.
  4. [Sec. 3.1] The GoSam version used is described as 'to appear' [42], and the Whizard-GoSam interface details are referenced to a Master thesis [88]. Please provide version identifiers or a more detailed public documentation of the interface so that the calculation is reproducible beyond the provided example files.
  5. [Sec. 4.2] In Figures 3 and 4, the uncertainty bands are attributed to the uncertainties of the fit coefficients. Please state explicitly whether the full covariance matrix of the fit was propagated, since the coefficients in Table 2 are strongly correlated.
  6. [Sec. 4.1, Table 1] Several entries in Table 1 have a lower scale-variation error of exactly 0.000 while the upper error is non-zero. A brief comment on why the scale dependence is one-sided for those benchmark points would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: NLO hhjj cross sections and shapes are computed from the HEFT Lagrangian and validated against independent tools, while Eq. (4.6) is a post-hoc fit to those computations. Sec. 2.2's unenumerated L4 exclusion is a completeness gap, not an input-output circularity.

full rationale

The central derivation is self-contained. The NLO cross sections and differential distributions are obtained by generating Feynman diagrams from the stated effective Lagrangian (2.9) and integrating them with GoSam/Whizard; the anomalous couplings c_lambda, c_V and c_2V enter as Lagrangian parameters, not as fitted outputs of the observables being predicted. The polynomial parametrisation in Eq. (4.6) is explicitly a fit to already-computed cross sections: 'We obtain values for the coefficients Ai by fitting the parametrisation (4.6) to the cross sections of the benchmark points in table 1'. Its coefficients are therefore outputs of the calculation, not inputs that force the cross-section ratios. The validation is anchored externally: the paper reports amplitude-level agreement with OpenLoops at the level of O(10^-8) for the finite part of the virtual amplitude, and LO agreement with MadGraph5 and VBFNLO, so the physics result does not rest on the authors' own prior conclusions. Self-references [42] and [88] concern a code release and a master thesis with validation details; neither is load-bearing for the physics claim. The one passage worth flagging is Sec. 2.2, where the exclusion of all d_chi=4 operators at O(g_ew^4 g_s^2) is asserted with 'One can check that there are no operators from L4 with which we can construct tree topology diagrams...' rather than demonstrated by enumeration. That is an omitted completeness proof and a potential correctness risk for the 'leading HEFT' interpretation, but it is not circular: the calculation does not define the L4 exclusion in terms of the predicted cross sections, nor does it fit the target observables. The derivation chain from Lagrangian to predictions is therefore not an input-output equivalence, and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The three scanned coupling modifiers are the free inputs; they are not fitted here but drawn from experimental constraints. The six coefficients A0..A5 in Table 2 are outputs of the exact monomial decomposition in Eq. (4.6), so they are not counted as free parameters. The axioms are the standard HEFT power-counting and VBF setup assumptions; the L4 operator exclusion in Section 2.2 is the least explicitly demonstrated assumption. No invented physical entities are introduced; the UFO model file is a software artefact.

free parameters (3)
  • cλ (Higgs self-coupling modifier) = scanned over [-1, 6]; benchmark values in Table 1
    EFT coupling modifier for the h^3 interaction (Eq. 2.9); scanned over the range used in Table 1 and Figs. 3-6, oriented at current experimental constraints. Not fitted in this paper.
  • cV (hVV coupling modifier) = scanned over [0.9, 1.1]
    Coupling of a single Higgs to W/Z pairs (Eq. 2.9); benchmark range oriented at the constraints of Refs. [1,2].
  • c2V (hhVV coupling modifier) = scanned over [0.5, 1.5]
    Coupling of a Higgs pair to W/Z pairs (Eq. 2.9); benchmark range oriented at the constraints of Refs. [1,2].
assumptions (7)
  • standard math QCD factorisation and the FKS subtraction scheme correctly handle the IR singularities of the real and virtual contributions.
    Adopted from the Whizard NLO framework (Section 3.1); standard in the field and validated by the comparison with OpenLoops at cross-section level.
  • domain assumption The leading HEFT operators relevant for pp -> hhjj at NLO QCD are those of Eq. (2.9), i.e., the L2 Lagrangian restricted to cλ, cV, c2V with SM Lorentz structures.
    Section 2.2 asserts this after power counting; this is the standard HEFT/kappa-framework setup for this process, but the completeness against L4 operators is the paper's own argument.
  • domain assumption No dχ=4 (L4) operator can generate tree-level diagrams at O(g_ew^4 g_s^2) for pp -> hhjj.
    Section 2.2: the authors argue that gluon-Higgs and EW gauge-Higgs local interactions from L4 are one-loop-suppressed relative to the NLO QCD corrections; the full check is asserted rather than exhibited.
  • domain assumption The custodial-symmetry-breaking operator Oβ1 is loop suppressed by the T-parameter constraint, so W and Z couplings share the same cV.
    Section 2.1, based on the small experimental T-parameter [62,63]; standard in HEFT analyses.
  • domain assumption Light quarks (u,d,s,c,b) are massless and do not couple to the Higgs; the CKM matrix is diagonal and top quarks are absent from external states.
    Section 2.3; standard VBF simplification, justified because the Higgs coupling to light quarks is assumed not to be drastically enhanced.
  • domain assumption The NLO QCD renormalisation requires no new counterterms beyond the SM, because the anomalous couplings appear only in the electroweak subdiagrams.
    Section 2.3; this relies on the fact that QCD corrections act only on quark lines at this order.
  • domain assumption The electroweak input scheme {alpha, GF, mZ} with SM tree-level mW remains valid in HEFT at the order considered.
    Section 4.1: mW = 79.8244 GeV is computed from SM tree-level relations; assumed valid for this calculation.

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Cite this review

Pith. "Pith review of Double Higgs Production in Vector Boson Fusion at NLO QCD in HEFT." pith.science (2026). https://pith.science/paper/U7PHR7ZS

@misc{pith2026250209132,
  author       = {Pith},
  title        = {Pith review of: Double Higgs Production in Vector Boson Fusion at NLO QCD in HEFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U7PHR7ZS}},
  note         = {Machine review of arXiv:2502.09132}
}
read the original abstract

We present the next-to-leading order QCD corrections to Higgs boson pair production in vector boson fusion, including the leading operators in the framework of Higgs Effective Field Theory (HEFT). The corresponding calculation is based on an automated interface between the Monte Carlo event generator Whizard and the one-loop amplitude generator GoSam. The QCD corrections also include non-factorising diagrams and diagrams of Higgs-Strahlung type, thus going beyond the structure function approach. We find that some constellations of anomalous couplings, while being well within the current experimental constraints, can have a significant impact on the shape of typical observables for this process.

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Forward citations

Cited by 6 Pith papers

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  3. Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$

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    In the electroweak chiral Lagrangian, off-shell Higgs contributions to gg to Z_L Z_L at leading order reduce to two independent combinations of the anomalous couplings c_t, c_V, and c_ggh.

  4. One-Loop Calculations in Effective Field Theories with GoSam-3.0

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Reference graph

Works this paper leans on

98 extracted references · 8 canonical work pages · cited by 6 Pith papers

  1. [98]

    J¨ ager, A

    B. J¨ ager, A. Karlberg and S. Reinhardt, Precision tools for the simulation of double-Higgs production via vector-boson fusion , 2502.09112. – 26 –

    arXiv

  2. [1]

    Aad et al., Combination of Searches for Higgs Boson Pair Production in pp Collisions at √s = 13 TeV with the ATLAS Detector , Phys

    ATLAS collaboration, G. Aad et al., Combination of Searches for Higgs Boson Pair Production in pp Collisions at √s = 13 TeV with the ATLAS Detector , Phys. Rev. Lett. 133 (2024) 101801 [ 2406.09971]

    arXiv 2024

  3. [2]

    Hayrapetyan et al., Constraints on the Higgs boson self-coupling from the combination of single and double Higgs boson production in proton-proton collisions at √s = 13 TeV, Phys

    CMS collaboration, A. Hayrapetyan et al., Constraints on the Higgs boson self-coupling from the combination of single and double Higgs boson production in proton-proton collisions at √s = 13 TeV, Phys. Lett. B 861 (2025) 139210 [ 2407.13554]

    arXiv 2025

  4. [3]

    Aad et al., Search for pair production of boosted Higgs bosons via vector-boson fusion in the b¯bb¯b final state using pp collisions at √s = 13 TeV with the ATLAS detector , Phys

    ATLAS collaboration, G. Aad et al., Search for pair production of boosted Higgs bosons via vector-boson fusion in the b¯bb¯b final state using pp collisions at √s = 13 TeV with the ATLAS detector , Phys. Lett. B 858 (2024) 139007 [ 2404.17193]

    arXiv 2024

  5. [4]

    rep., CERN, Geneva, 2024

    CMS collaboration, Combination of searches for nonresonant Higgs boson pair production in proton-proton collisions at sqrt(s) = 13 TeV , tech. rep., CERN, Geneva, 2024

    2024

  6. [5]

    Figy, Next-to-leading order QCD corrections to light Higgs Pair production via vector boson fusion , Mod

    T. Figy, Next-to-leading order QCD corrections to light Higgs Pair production via vector boson fusion , Mod. Phys. Lett. A 23 (2008) 1961 [ 0806.2200]. – 19 –

    arXiv 2008

  7. [6]

    Baglio, A

    J. Baglio, A. Djouadi, R. Gr¨ ober, M. M. M¨ uhlleitner, J. Quevillon and M. Spira,The measurement of the Higgs self-coupling at the LHC: theoretical status , JHEP 04 (2013) 151 [1212.5581]

    arXiv 2013

  8. [7]

    Frederix, S

    R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, P. Torrielli et al., Higgs pair production at the LHC with NLO and parton-shower effects , Phys. Lett. B 732 (2014) 142 [ 1401.7340]

    arXiv 2014

Show all 98 references
  1. [8]

    Arnold et al., VBFNLO: A Parton level Monte Carlo for processes with electroweak bosons, Comput

    K. Arnold et al., VBFNLO: A Parton level Monte Carlo for processes with electroweak bosons, Comput. Phys. Commun. 180 (2009) 1661 [ 0811.4559]

    2009 arXiv

  2. [9]

    Baglio et al., Release note: VBFNLO 3.0 , Eur

    J. Baglio et al., Release note: VBFNLO 3.0 , Eur. Phys. J. C 84 (2024) 1003 [2405.06990]

    2024 arXiv

  3. [10]

    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

  4. [11]

    Ling, R.-Y

    L.-S. Ling, R.-Y. Zhang, W.-G. Ma, L. Guo, W.-H. Li and X.-Z. Li, NNLO QCD corrections to Higgs pair production via vector boson fusion at hadron colliders , Phys. Rev. D 89 (2014) 073001 [ 1401.7754]

    2014 arXiv

  5. [12]

    F. A. Dreyer and A. Karlberg, Fully differential Vector-Boson Fusion Higgs Pair Production at Next-to-Next-to-Leading Order, Phys. Rev. D 99 (2019) 074028 [1811.07918]

    2019 arXiv

  6. [13]

    F. A. Dreyer and A. Karlberg, Vector-Boson Fusion Higgs Pair Production at N 3LO, Phys. Rev. D 98 (2018) 114016 [ 1811.07906]

    2018 arXiv

  7. [14]

    F. A. Dreyer, A. Karlberg, J.-N. Lang and M. Pellen, Precise predictions for double-Higgs production via vector-boson fusion , Eur. Phys. J. C 80 (2020) 1037 [2005.13341]

    2020 arXiv

  8. [15]

    F. A. Dreyer, A. Karlberg and L. Tancredi, On the impact of non-factorisable corrections in VBF single and double Higgs production , JHEP 10 (2020) 131 [2005.11334]

    2020 arXiv

  9. [16]

    proVBFHH

    A. Karlberg, “proVBFHH.” https://github.com/alexanderkarlberg/proVBFH

  10. [17]

    M. J. Dolan, C. Englert, N. Greiner and M. Spannowsky, Further on up the road: hhjj production at the LHC , Phys. Rev. Lett. 112 (2014) 101802 [ 1310.1084]

    2014 arXiv

  11. [18]

    M. J. Dolan, C. Englert, N. Greiner, K. Nordstrom and M. Spannowsky, hhjj production at the LHC , Eur. Phys. J. C 75 (2015) 387 [ 1506.08008]

    2015 arXiv

  12. [19]

    Bishara, R

    F. Bishara, R. Contino and J. Rojo, Higgs pair production in vector-boson fusion at the LHC and beyond , Eur. Phys. J. C 77 (2017) 481 [ 1611.03860]

    2017 arXiv

  13. [20]

    Ling, R.-Y

    L.-S. Ling, R.-Y. Zhang, W.-G. Ma, X.-Z. Li, L. Guo and S.-M. Wang, Dimension-six – 20 – operators in Higgs boson pair production via vector-boson fusion at the LHC , Phys. Rev. D 96 (2017) 055006 [ 1708.04785]

    2017 arXiv

  14. [21]

    Arganda, C

    E. Arganda, C. Garcia-Garcia and M. J. Herrero, Probing the Higgs self-coupling through double Higgs production in vector boson scattering at the LHC , Nucl. Phys. B 945 (2019) 114687 [ 1807.09736]

    2019 arXiv

  15. [22]

    J. Y. Araz, S. Banerjee, R. S. Gupta and M. Spannowsky, Precision SMEFT bounds from the VBF Higgs at high transverse momentum , JHEP 04 (2021) 125 [2011.03555]

    2021 arXiv

  16. [23]

    Kilian, S

    W. Kilian, S. Sun, Q.-S. Yan, X. Zhao and Z. Zhao, Multi-Higgs boson production and unitarity in vector-boson fusion at future hadron colliders , Phys. Rev. D 101 (2020) 076012 [1808.05534]

    2020 arXiv

  17. [24]

    Kilian, S

    W. Kilian, S. Sun, Q.-S. Yan, X. Zhao and Z. Zhao, Highly Boosted Higgs Bosons and Unitarity in Vector-Boson Fusion at Future Hadron Colliders , JHEP 05 (2021) 198 [2101.12537]

    2021 arXiv

  18. [25]

    G´ omez-Ambrosio, F

    R. G´ omez-Ambrosio, F. J. Llanes-Estrada, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, Distinguishing electroweak EFTs with WLWL → n h, Phys. Rev. D 106 (2022) 053004 [2204.01763]

    2022 arXiv

  19. [26]

    G´ omez-Ambrosio, F

    R. G´ omez-Ambrosio, F. J. Llanes-Estrada, A. Salas-Bern´ ardez and J. J. Sanz-Cillero, SMEFT is falsifiable through multi-Higgs measurements (even in the absence of new light particles), Commun. Theor. Phys. 75 (2023) 095202 [ 2207.09848]

    2023 arXiv

  20. [27]

    M. J. Herrero and R. A. Morales, One-loop corrections for WW to HH in Higgs EFT with the electroweak chiral Lagrangian , Phys. Rev. D 106 (2022) 073008 [ 2208.05900]

    2022 arXiv

  21. [28]

    Domenech, C

    Anisha, D. Domenech, C. Englert, M. J. Herrero and R. A. Morales, Bosonic multi-Higgs correlations beyond leading order , Phys. Rev. D 110 (2024) 095016 [2405.05385]

    2024 arXiv

  22. [29]

    Domenech, C

    Anisha, D. Domenech, C. Englert, M. J. Herrero and R. A. Morales, HEFT’s appraisal of triple (versus double) Higgs weak boson fusion , 2407.20706

    arXiv

  23. [30]

    Feruglio, The Chiral approach to the electroweak interactions , Int

    F. Feruglio, The Chiral approach to the electroweak interactions , Int. J. Mod. Phys. A 8 (1993) 4937 [ hep-ph/9301281]

    1993 arXiv

  24. [31]

    Bagger, V

    J. Bagger, V. D. Barger, K.-m. Cheung, J. F. Gunion, T. Han, G. A. Ladinsky et al., The Strongly interacting W W system: Gold plated modes , Phys. Rev. D 49 (1994) 1246 [hep-ph/9306256]

    1994 arXiv

  25. [32]

    Koulovassilopoulos and R

    V. Koulovassilopoulos and R. S. Chivukula, The Phenomenology of a nonstandard Higgs boson in W(L) W(L) scattering , Phys. Rev. D 50 (1994) 3218 [hep-ph/9312317]

    1994 arXiv

  26. [33]

    C. P. Burgess, J. Matias and M. Pospelov, A Higgs or not a Higgs? What to do if you discover a new scalar particle , Int. J. Mod. Phys. A 17 (2002) 1841 [ hep-ph/9912459]. – 21 –

    2002 arXiv

  27. [34]

    Wang and Q

    L.-M. Wang and Q. Wang, Nonstandard Higgs in electroweak chiral Lagrangian , hep-ph/0605104

    arXiv

  28. [35]

    Grinstein and M

    B. Grinstein and M. Trott, A Higgs-Higgs bound state due to new physics at a TeV , Phys. Rev. D 76 (2007) 073002 [ 0704.1505]

    2007 arXiv

  29. [36]

    Alonso, M

    R. Alonso, M. B. Gavela, L. Merlo, S. Rigolin and J. Yepes, The Effective Chiral Lagrangian for a Light Dynamical ”Higgs Particle” , Phys. Lett. B 722 (2013) 330 [1212.3305]

    2013 arXiv

  30. [37]

    Buchalla and O

    G. Buchalla and O. Cata, Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO , JHEP 07 (2012) 101 [ 1203.6510]

    2012 arXiv

  31. [38]

    Buchalla, O

    G. Buchalla, O. Cat` a and C. Krause, Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO , Nucl. Phys. B 880 (2014) 552 [ 1307.5017]

    2014 arXiv

  32. [39]

    Degrande, G

    C. Degrande, G. Durieux, F. Maltoni, K. Mimasu, E. Vryonidou and C. Zhang, Automated one-loop computations in the standard model effective field theory , Phys. Rev. D 103 (2021) 096024 [ 2008.11743]

    2021 arXiv

  33. [40]

    Cullen, N

    GoSam collaboration, G. Cullen, N. Greiner, G. Heinrich, G. Luisoni, P. Mastrolia, G. Ossola et al., Automated One-Loop Calculations with GoSam , Eur. Phys. J. C 72 (2012) 1889 [ 1111.2034]

    2012 arXiv

  34. [41]

    Cullen et al., GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond , Eur

    GoSam collaboration, G. Cullen et al., GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond , Eur. Phys. J. C 74 (2014) 3001 [1404.7096]

    2014 arXiv

  35. [42]

    Braun et al., GoSam-3.0, to appear ,

    J. Braun et al., GoSam-3.0, to appear ,

  36. [43]

    Moretti, T

    M. Moretti, T. Ohl and J. Reuter, O’Mega: An Optimizing matrix element generator , hep-ph/0102195

    arXiv

  37. [44]

    Kilian, T

    W. Kilian, T. Ohl and J. Reuter, WHIZARD: Simulating Multi-Particle Processes at LHC and ILC , Eur. Phys. J. C 71 (2011) 1742 [ 0708.4233]

    2011 arXiv

  38. [45]

    Binoth et al., A Proposal for a Standard Interface between Monte Carlo Tools and One-Loop Programs, Comput

    T. Binoth et al., A Proposal for a Standard Interface between Monte Carlo Tools and One-Loop Programs, Comput. Phys. Commun. 181 (2010) 1612 [ 1001.1307]

    2010 arXiv

  39. [46]

    Alioli et al., Update of the Binoth Les Houches Accord for a standard interface between Monte Carlo tools and one-loop programs , Comput

    S. Alioli et al., Update of the Binoth Les Houches Accord for a standard interface between Monte Carlo tools and one-loop programs , Comput. Phys. Commun. 185 (2014) 560 [ 1308.3462]

    2014 arXiv

  40. [47]

    Degrande, C

    C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer and T. Reiter, UFO - The Universal FeynRules Output , Comput. Phys. Commun. 183 (2012) 1201 [ 1108.2040]

    2012 arXiv

  41. [48]

    Universal Feynman Output

    L. Darm´ e et al.,UFO 2.0: the “Universal Feynman Output” format , Eur. Phys. J. C 83 (2023) 631 [ 2304.09883]. – 22 –

    2023 arXiv

  42. [49]

    Buchm¨ uller and D

    W. Buchm¨ uller and D. Wyler,Effective Lagrangian Analysis of New Interactions and Flavor Conservation , Nucl. Phys. B 268 (1986) 621

    1986

  43. [50]

    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]

    2010 arXiv

  44. [51]

    Brivio and M

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

    2019 arXiv

  45. [52]

    Isidori, F

    G. Isidori, F. Wilsch and D. Wyler, The standard model effective field theory at work , Rev. Mod. Phys. 96 (2024) 015006 [ 2303.16922]

    2024 arXiv

  46. [53]

    C. Arzt, M. B. Einhorn and J. Wudka, Patterns of deviation from the standard model , Nucl. Phys. B 433 (1995) 41 [ hep-ph/9405214]

    1995 arXiv

  47. [54]

    Craig, M

    N. Craig, M. Jiang, Y.-Y. Li and D. Sutherland, Loops and Trees in Generic EFTs , JHEP 08 (2020) 086 [ 2001.00017]

    2020 arXiv

  48. [55]

    Buchalla, G

    G. Buchalla, G. Heinrich, C. M¨ uller-Salditt and F. Pandler, Loop counting matters in SMEFT, SciPost Phys. 15 (2023) 088 [ 2204.11808]

    2023 arXiv

  49. [56]

    Buchalla, O

    G. Buchalla, O. Cat´ a and C. Krause, On the Power Counting in Effective Field Theories, Phys. Lett. B 731 (2014) 80 [ 1312.5624]

    2014 arXiv

  50. [57]

    Sun, M.-L

    H. Sun, M.-L. Xiao and J.-H. Yu, Complete NLO operators in the Higgs effective field theory, JHEP 05 (2023) 043 [ 2206.07722]

    2023 arXiv

  51. [58]

    Gr´ af, B

    L. Gr´ af, B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series, the Higgs mechanism, and HEFT , JHEP 02 (2023) 064 [ 2211.06275]

    2023 arXiv

  52. [59]

    Alonso, K

    R. Alonso, K. Kanshin and S. Saa, Renormalization group evolution of Higgs effective field theory, Phys. Rev. D 97 (2018) 035010 [ 1710.06848]

    2018 arXiv

  53. [60]

    Buchalla, O

    G. Buchalla, O. Cata, A. Celis, M. Knecht and C. Krause, Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian, Nucl. Phys. B 928 (2018) 93 [1710.06412]

    2018 arXiv

  54. [61]

    Buchalla, O

    G. Buchalla, O. Cat` a, A. Celis, M. Knecht and C. Krause, Higgs-electroweak chiral Lagrangian: One-loop renormalization group equations , Phys. Rev. D 104 (2021) 076005 [2004.11348]

    2021 arXiv

  55. [62]

    M. E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections , Phys. Rev. D 46 (1992) 381

    1992

  56. [63]

    de Blas, M

    J. de Blas, M. Ciuchini, E. Franco, A. Goncalves, S. Mishima, M. Pierini et al., Global analysis of electroweak data in the Standard Model , Phys. Rev. D 106 (2022) 033003 [2112.07274]

    2022 arXiv

  57. [64]

    David, A

    LHC Higgs Cross Section Working Groupcollaboration, A. David, A. Denner, – 23 – M. Duehrssen, M. Grazzini, C. Grojean, G. Passarino et al., LHC HXSWG interim recommendations to explore the coupling structure of a Higgs-like particle , 1209.0040

    arXiv

  58. [65]

    LHC Higgs Cross Section Working Groupcollaboration, J. R. Andersen et al., Handbook of LHC Higgs Cross Sections: 3. Higgs Properties , 1307.1347

    arXiv

  59. [66]

    de Blas, O

    J. de Blas, O. Eberhardt and C. Krause, Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory , JHEP 07 (2018) 048 [ 1803.00939]

    2018 arXiv

  60. [67]

    Ciccolini, A

    M. Ciccolini, A. Denner and S. Dittmaier, Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC , Phys. Rev. D 77 (2008) 013002 [0710.4749]

    2008 arXiv

  61. [68]

    Bierlich et al., Robust Independent Validation of Experiment and Theory: Rivet version 3 , SciPost Phys

    C. Bierlich et al., Robust Independent Validation of Experiment and Theory: Rivet version 3 , SciPost Phys. 8 (2020) 026 [ 1912.05451]

    2020 arXiv

  62. [69]

    Bierlich, A

    C. Bierlich, A. Buckley, J. M. Butterworth, C. Gutschow, L. Lonnblad, T. Procter et al., Robust independent validation of experiment and theory: Rivet version 4 release note, SciPost Phys. Codeb. 36 (2024) 1 [ 2404.15984]

    2024 arXiv

  63. [70]

    Ohl, Vegas revisited: Adaptive Monte Carlo integration beyond factorization , Comput

    T. Ohl, Vegas revisited: Adaptive Monte Carlo integration beyond factorization , Comput. Phys. Commun. 120 (1999) 13 [ hep-ph/9806432]

    1999 arXiv

  64. [71]

    Brass, W

    S. Brass, W. Kilian and J. Reuter, Parallel Adaptive Monte Carlo Integration with the Event Generator WHIZARD , Eur. Phys. J. C 79 (2019) 344 [ 1811.09711]

    2019 arXiv

  65. [72]

    Chokouf´ e Nejad, W

    B. Chokouf´ e Nejad, W. Kilian, J. M. Lindert, S. Pozzorini, J. Reuter and C. Weiss, NLO QCD predictions for off-shell tt and ttH production and decay at a linear collider , JHEP 12 (2016) 075 [ 1609.03390]

    2016 arXiv

  66. [73]

    Stienemeier, S

    P. Stienemeier, S. Braß, P. Bredt, W. Kilian, N. Kreher, T. Ohl et al., WHIZARD 3.0: Status and News , in International Workshop on Future Linear Colliders , 4, 2021, 2104.11141

    2021 arXiv

  67. [74]

    Frixione, Z

    S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order , Nucl. Phys. B 467 (1996) 399 [ hep-ph/9512328]

    1996 arXiv

  68. [75]

    Frixione, A General approach to jet cross-sections in QCD , Nucl

    S. Frixione, A General approach to jet cross-sections in QCD , Nucl. Phys. B 507 (1997) 295 [ hep-ph/9706545]

    1997 arXiv

  69. [76]

    Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [ hep-ph/0409146]

    P. Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [ hep-ph/0409146]

    2004 arXiv

  70. [77]

    Stienemeier, Automation and Application of fixed-order and matched NLO Simulations, Ph.D

    P. Stienemeier, Automation and Application of fixed-order and matched NLO Simulations, Ph.D. thesis, Hamburg U., Hamburg, 2022. 10.3204/PUBDB-2022-07425

    2022 doi

  71. [78]

    Nogueira, Automatic Feynman Graph Generation, J

    P. Nogueira, Automatic Feynman Graph Generation, J. Comput. Phys. 105 (1993) 279

    1993

  72. [79]

    J. A. M. Vermaseren, New features of FORM , math-ph/0010025. – 24 –

    arXiv

  73. [80]

    Kuipers, T

    J. Kuipers, T. Ueda, J. A. M. Vermaseren and J. Vollinga, FORM version 4.0 , Comput. Phys. Commun. 184 (2013) 1453 [ 1203.6543]

    2013 arXiv

  74. [81]

    van Deurzen, G

    H. van Deurzen, G. Luisoni, P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro, Multi-leg One-loop Massive Amplitudes from Integrand Reduction via Laurent Expansion, JHEP 03 (2014) 115 [ 1312.6678]

    2014 arXiv

  75. [82]

    Peraro, Ninja: Automated Integrand Reduction via Laurent Expansion for One-Loop Amplitudes, Comput

    T. Peraro, Ninja: Automated Integrand Reduction via Laurent Expansion for One-Loop Amplitudes, Comput. Phys. Commun. 185 (2014) 2771 [ 1403.1229]

    2014 arXiv

  76. [83]

    van Hameren, OneLOop: For the evaluation of one-loop scalar functions , Comput

    A. van Hameren, OneLOop: For the evaluation of one-loop scalar functions , Comput. Phys. Commun. 182 (2011) 2427 [ 1007.4716]

    2011 arXiv

  77. [84]

    Maltoni, E

    F. Maltoni, E. Vryonidou and C. Zhang, Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD , JHEP 10 (2016) 123 [ 1607.05330]

    2016 arXiv

  78. [85]

    Anomalous Couplings within Standard Model Effective Field Theory in ttH Production at NLO QCD

    M. van Geest, “Anomalous Couplings within Standard Model Effective Field Theory in ttH Production at NLO QCD.” Master thesis, Karlsruhe Institute of Technology, https://www.itp.kit.edu/publications/diploma

  79. [86]

    Cascioli, P

    F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering Amplitudes with Open Loops , Phys. Rev. Lett. 108 (2012) 111601 [ 1111.5206]

    2012 arXiv

  80. [87]

    Buccioni, J.-N

    F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierh¨ ofer, S. Pozzorini, H. Zhang et al., OpenLoops 2, Eur. Phys. J. C 79 (2019) 866 [ 1907.13071]

    2019 arXiv

  81. [88]

    Higgs Boson Pair Production in Vector Boson Fusion at NLO QCD in HEFT

    J. Braun, “Higgs Boson Pair Production in Vector Boson Fusion at NLO QCD in HEFT.” Master thesis, Karlsruhe Institute of Technology, https://www.itp.kit.edu/publications/diploma

  82. [89]

    PDF4LHC Working Groupcollaboration, R. D. Ball et al., The PDF4LHC21 combination of global PDF fits for the LHC Run III , J. Phys. G 49 (2022) 080501 [2203.05506]

    2022 arXiv

  83. [90]

    Buckley, J

    A. Buckley, J. Ferrando, S. Lloyd, K. Nordstr¨ om, B. Page, M. R¨ ufenacht et al., LHAPDF6: parton density access in the LHC precision era , Eur. Phys. J. C 75 (2015) 132 [1412.7420]

    2015 arXiv

  84. [91]

    Cacciari, G

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

    2008 arXiv

  85. [92]

    Cacciari, G

    M. Cacciari, G. P. Salam and G. Soyez, FastJet User Manual , Eur. Phys. J. C 72 (2012) 1896 [ 1111.6097]

    2012 arXiv

  86. [93]

    Dembinski and P

    H. Dembinski and P. O. et al., scikit-hep/iminuit,

  87. [94]

    James and M

    F. James and M. Roos, Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations , Comput. Phys. Commun. 10 (1975) 343. – 25 –

    1975

  88. [95]

    Talk at the 21st Workshop of the LHC Higgs Working Group

    A. R. Martinez, “Talk at the 21st Workshop of the LHC Higgs Working Group.” https://indico.cern.ch/event/1389221/contributions/6195709/

  89. [96]

    Cohen, N

    T. Cohen, N. Craig, X. Lu and D. Sutherland, Unitarity violation and the geometry of Higgs EFTs , JHEP 12 (2021) 003 [ 2108.03240]

    2021 arXiv

  90. [97]

    Barducci, M

    D. Barducci, M. Nardecchia and C. Toni, Perturbative unitarity constraints on generic vector interactions, JHEP 09 (2023) 134 [ 2306.11533]

    2023 arXiv

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