Pith. sign in

REVIEW 2 major objections 4 minor 107 references

Effective field theory and scalar extensions of the top quark sector

T0 review · 2 major / 4 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 NLO-matched effective field theory reproduces a top-philic scalar model down to scalar masses near LHC energies, while the leading-order EFT overestimates the high-mass tails.

desk verdict A solid NLO matching case study showing that naive LO EFT overestimates top-pair tails; the main soft spot is unquantified matching-scale dependence, but that is a fixable weakness, not a fatal flaw. read the letter →

arxiv 1908.05588 v2 pith:VT3UID7A submitted 2019-08-15 hep-ph hep-ex

Christoph Englert , Peter Galler , Chris D. White This is my paper · ORCID
classification hep-phhep-ex
keywords effectivefieldtheorytopquarksimplifiedmodelnext-to-leadingordermatchingpairproductionfourdimension-sixoperatorsLHCconstraints
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 asks when effective field theory (EFT) can stand in for a concrete new-physics model at the Large Hadron Collider. It studies a minimal extension in which a new heavy scalar couples only to top quarks, derives the two dimension-six operators generated at low energy, and matches them to the full model at next-to-leading order. The central finding is that the matched EFT reproduces the full model's top-antitop invariant-mass distribution almost exactly even when the scalar mass is only slightly above LHC energies, whereas a naive leading-order EFT fit overestimates the high-mass tail. This matters because LHC searches increasingly set EFT constraints; if those constraints are computed at leading order, they could be over-optimistic by a large margin. The paper also projects HL-LHC sensitivities and finds that four-top and top-pair production have comparable exclusion power, with constraints for large scalar masses drifting into a non-perturbative region where matching the EFT to the full model is no longer possible.

What carries the argument

The load-bearing object is the NLO-matched pair of dimension-six operators generated by the scalar: $O_{tt} = (\bar t t)^2$ (or the scalar-propagator expansion at low momentum) and $O_{tG} = v\,\bar t_L T^a \sigma^{\mu\nu} t_R\, G^a_{\mu\nu}$. The four-fermion operator is tree-induced and fixes the coefficient $c_{tt}$ through $t\bar t\to t\bar t$ scattering; the dipole operator is loop-induced, and its Wilson coefficient is fixed by matching the one-loop full-theory amplitude to the one-loop EFT amplitude at $\mu_M = m_S/2$. A one-loop insertion of $O_{tt}$ generates a UV divergence that is absorbed by a counterterm for $O_{tG}$, and that operator mixing is what restores agreement with the full theory. Dropping the $O_{tt}$ contribution, as a naive LO fit does, removes the balance and produces the overestimate of the tail.

What would settle it

Measure the unfolded $m_{t\bar t}$ distribution at the HL-LHC with per-bin uncertainties below 3% in the 1–3 TeV range; if the high-mass tail falls below the NLO-matched EFT prediction or tracks the leading-order EFT shape, the claimed validity of NLO matching for $m_S\simeq 2$ TeV is falsified.

Watch

Extended reading notes

Core claim

In the simplified model of a new heavy scalar $S$ that couples only to top quarks, $\mathcal{L}_{\rm BSM} = \tfrac12 \partial_\mu S\,\partial^\mu S - \tfrac12 m_S^2 S^2 - (c_S\,\bar t_L t_R S + \mathrm{h.c.})$, integrating out $S$ generates two dimension-six operators: a four-top contact operator $O_{tt}$ that enters at tree level, and a gluon-top dipole operator $O_{tG}$ that is loop-induced. The paper matches the EFT to the full theory at next-to-leading order in $c_S$, renormalising the one-loop $O_{tt}$ insertion in the $\overline{\rm MS}$ scheme and fixing $O_{tG}$ at a matching scale $\mu_M = m_S/2$. The central discovery is that the NLO-matched EFT reproduces the full model's $m_{t\bar t}$ distribution to within a few percent for scalar masses as low as about 2 TeV, essentially down to LHC energies, whereas a naive leading-order EFT that fits only $O_{tG}$ severely overestimates the high-mass tail and would yield over-optimistic bounds on new physics. Using projected HL-LHC uncertainties, the paper further finds that four-top production has comparable exclusion power to top-pair production at low scalar masses, while for larger masses the projected constraints enter a regime where the full model is non-perturbative and cannot be matched to the EFT.

Load-bearing premise

The projected exclusion curves rest on assumed future measurement uncertainties—a flat 3% uncertainty on the unfolded top-pair invariant-mass distribution, an 18% uncertainty on the four-top cross section, and an approximate K factor of 2.5—not on established data, and if those assumptions are wrong the claimed constraints shift.

Editorial extensions

If this is right

  • Top-pair EFT fits at the LHC are reliable for a top-philic scalar down to $m_S\simeq 1.5$–$2$ TeV only if next-to-leading-order matching and operator mixing are included.
  • A leading-order EFT that floats only $O_{tG}$ overestimates the high-mass tail, so published constraints derived that way are too strong for this class of models.
  • Four-top final states contribute constraints comparable to top-pair production at low scalar masses and should be included in global top-sector EFT fits.
  • For scalar masses above roughly $2$–$3$ TeV, projected HL-LHC uncertainties push allowed couplings into the non-perturbative regime, so the full and EFT descriptions cannot be perturbatively matched there.
  • Improving the theoretical uncertainty of Standard Model top final states is the prerequisite for pushing LHC constraints into the perturbatively matchable region.

Reading between the lines

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

  • Inference: the same failure mode—a tree-induced operator mixing into a loop-induced one—is likely to distort LO EFT fits in other top-philic scenarios beyond a single scalar, so the LO-overestimation lesson generalises.
  • Inference: the paper demonstrates the point with the $m_{t\bar t}$ distribution, but the mechanism suggests other tail-sensitive observables, such as the top $p_T$ distribution, should show the same NLO-versus-LO discrepancy.
  • Inference: because the four-top comparison is leading order in the full model, higher-order corrections there could shift the mass at which the full model loses sensitivity; a full NLO four-top calculation would be a direct test.
  • Inference: if actual HL-LHC unfolded top-pair uncertainties are larger than the assumed 3%, the constraints enter the non-perturbative region at even lower scalar masses, strengthening the paper's caution.
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.

Referee Report

2 major / 4 minor

Summary. The paper studies a simplified model in which a heavy scalar S couples to top quarks via cS * tbar_L t_R S + h.c. It computes the O(cS^2) corrections to top pair production in the full theory (gluon fusion and quark-antiquark annihilation) with on-shell renormalization and explicit UV-finiteness checks, derives the low-energy dimension-six EFT consisting of the chromomagnetic operator OtG and the four-top operator Ott, and matches the EFT to the full theory at NLO in the simplified-model coupling. It then compares the full theory with the NLO-matched EFT and with a naive bottom-up LO EFT fit as functions of mS and the t-tbar invariant mass, finding excellent NLO-EFT agreement for scalar masses down to a few TeV while the naive LO approach overestimates the high-mass tail. Finally, it projects HL-LHC constraints from t-tbar and four-top production on the (mS, cS) plane, concluding that four-top production is competitive with t-tbar for low masses and that estimated systematic uncertainties push constraints into the non-perturbative regime of the full model for larger masses.

Significance. If the claims hold, this is a useful and concrete case study of when NLO matching is mandatory in EFT analyses of top-quark sectors, and it quantifies the danger of naive LO EFT constraints. The paper's strengths include an explicit one-loop calculation with on-shell renormalization and UV-finiteness checks, a transparent matching relation in Appendix A, and direct EFT-to-full-theory comparisons in Figs. 6-8 that provide a falsifiable, quantitative statement about the range of EFT validity. The demonstration that the NLO-matched EFT reproduces the full model while the LO EFT overestimates kinematic distributions is a genuinely informative result for LHC phenomenology. The main caveat is the residual matching-scale and scheme dependence, which is acknowledged in the text but not quantified; this affects the central 'excellent validity' claim and needs to be addressed before the conclusion can be fully trusted.

major comments (2)
  1. [Section II / Appendix A, Eqs. (A6)-(A8), Fig. 5] The central validity comparison in Figs. 6-8 is performed at a single matching scale mu_M = mS/2. Fig. 5 shows that the matched coefficient ctG varies substantially with mu_M (roughly a factor of 2-3 at mS = 5 TeV between mu_M = 1 TeV and mu_M = mS), and Appendix A notes that Eq. (A6) fixes only the sum of the loop-inserted ctt and the tree-level ctG, so finite terms can be moved between the two coefficients. Because the NLO EFT result is a cancellation between a tree-level OtG insertion with this scale-dependent coefficient and a one-loop Ott insertion, the good agreement with the full theory in Figs. 6-8 could be specific to the chosen scheme. Please quantify the residual scheme dependence, for example by repeating the validity analysis for mu_M = mS/4 and mu_M = mS and showing that the mmax(tbar-t) lines in Fig. 8 shift by less than the quoted tolerance, or by giving a reasoned argument for why the chosen scheme is the preferred one.
  2. [Section III, Figs. 6-7] The 'naive effective' curves, which are the basis for the claim that a bottom-up LO fit overestimates the high-mass tail, are not reproducible as presented. The text says only that ctG was treated as a free parameter and fitted to Monte Carlo data generated with the full theory; the fitted observable, binning, and fit range are not given. Since the amount of overestimation (and hence the 'over-optimistic constraints' statement in Section IV) depends on where in the m_tt distribution the coefficient is normalized, please specify the fitting procedure or, alternatively, show the result of the fit for two different normalization choices to demonstrate that the qualitative conclusion is robust.
minor comments (4)
  1. [Section IV, Fig. 9] The assumptions behind Fig. 9 (flat 3% uncertainty for the unfolded m_tt distribution, 18% accuracy for the tttt cross section, and an approximate K factor of 2.5 for the squared s-channel contribution) are stated, but a small sensitivity scan would help the reader judge how robust the 'constraints enter the non-perturbative regime' conclusion is.
  2. [Figs. 6-7] The axis label 'ratio wrst full' is ambiguous; please replace it with something like '|EFT - full| / |full|' or 'ratio w.r.t. full'.
  3. [Fig. 9 caption] The red curves for four-top production are LO only, as stated in the text and Footnote 2, but the figure caption does not say so; please add 'LO' to the caption to avoid confusion with the NLO t-tbar curves.
  4. [Abstract] The phrase 'excellent validity' is quantified in Fig. 8 only for cS = 1 and a specified percentage tolerance; the abstract could state this qualification (for example, 'within 10-20% for m_tt up to ...').

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the NLO EFT is matched to, then compared with, an independently computed full model, and the only fitted quantity in the paper is explicitly criticized as the wrong approach.

full rationale

The paper's derivation chain is not circular. The Wilson coefficient ctG is fixed by matching the full theory to the EFT at a chosen scale (Eq. A6-A8), and the full-theory amplitudes are computed independently in Vbfnlo with on-shell renormalization. The subsequent comparison of NLO EFT and full-model distributions (Figs. 6-8) is a validity test of the operator expansion, not a fit of the target observable: the matching fixes a short-distance coefficient at one scale, while the invariant-mass distributions are evaluated over a range of scales. The paper explicitly constructs a 'naive effective' LO EFT in which ctG is fitted to full-theory Monte Carlo data and shows that this bottom-up fit fails to reproduce the distributions; this is the opposite of presenting a fitted input as a prediction. The projected LHC constraints in Sec. IV rest on clearly stated assumed uncertainties (3% for the ttbar distribution, 18% for four-top, an approximate K factor of 2.5), which are inputs to the projection rather than outputs disguised as predictions. The acknowledged matching-scale dependence and the statement in Appendix A that 'only the sum of loop-inserted ctt and tree-level ctG is defined' indicate scheme freedom, but this is a systematic uncertainty in the EFT comparison, not a reduction of a predicted quantity to an input by construction. Self-citations appear in the bibliography, but no load-bearing argument reduces to a self-cited uniqueness theorem or ansatz. Accordingly, no specific circular step can be exhibited, and the circularity score is minimal.

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The paper's quantitative claims depend on assumed experimental uncertainties and an approximate K factor rather than on measured data, and on the choice of a simplified scalar model. These are transparently stated, but they are the inputs that shape the exclusion contours.

free parameters (4)
  • Assumed flat 3% uncertainty on unfolded mtt distribution = 3%
    Sets the normalization of the ttbar exclusion contours in Fig. 9; called 'optimistic' by the authors.
  • Assumed 18% uncertainty on unfolded tttt cross section = 18%
    Used for the four-top projection; slightly worse than the ATLAS extrapolation.
  • Approximate K factor for squared resonance contribution = 2.5
    Applied to the s-channel scalar contribution in the full-model ttbar exclusion; authors note it significantly impacts the result.
  • Matching scale mu_M = mS/2 (default)
    Scheme choice for extracting ctG; residual dependence shown in Fig. 5.
assumptions (6)
  • domain assumption The simplified model with a gauge-singlet scalar S coupling only to the top quark is representative of generic top-philic new physics.
    Motivated in Sec. I as covering singlet mixing and multi-Higgs doublet scenarios, but not proven to generalize.
  • domain assumption Only two dimension-six operators (OtG and Ott) contribute at the considered order.
    Argued in Sec. II based on the model's couplings and loop structure.
  • standard math Perturbative unitarity of ttbar scattering in the full model limits cS^2 to about 8pi.
    Used in Sec. IV to define the non-perturbative region; derived from partial wave projection.
  • standard math The on-shell and MS renormalization schemes provide a consistent definition of the matching.
    Standard EFT practice; UV finiteness is verified.
  • domain assumption Assumed LHC systematic uncertainties of 3% (ttbar) and 18% (tttt) are valid extrapolations.
    These numbers drive the quantitative constraint curves; the authors flag 3% as optimistic.
  • domain assumption NLO QCD corrections to the scalar resonance can be approximated by a constant K factor of 2.5.
    Used in the full-model exclusion; taken from heavy-Higgs QCD corrections.
invented entities (1)
  • Heavy scalar S with top-philic Yukawa coupling cS
    purpose: Simplified UV model used as a test case for EFT matching and LHC constraints.
    Postulated as a toy extension; no experimental anomaly motivates it, and it provides no falsifiable signature beyond the studied top-pair and four-top collider signals.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Effective field theory and scalar extensions of the top quark sector." pith.science (2026). https://pith.science/paper/VT3UID7A

@misc{pith2026190805588,
  author       = {Pith},
  title        = {Pith review of: Effective field theory and scalar extensions of the top quark sector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VT3UID7A}},
  note         = {Machine review of arXiv:1908.05588}
}
read the original abstract

Effective field theory (EFT) approaches are widely used at the LHC, such that it is important to study their validity, and ease of matching to specific new physics models. In this paper, we consider an extension of the SM in which a top quark couples to a new heavy scalar. We find the dimension six operators generated by this theory at low energy, and match the EFT to the full theory up to NLO precision in the simplified model coupling. We then examine the range of validity of the EFT description in top pair production, finding excellent validity even if the scalar mass is only slightly above LHC energies, provided NLO corrections are included. In the absence of the latter, the LO EFT overestimates kinematic distributions, such that over-optimistic constraints on BSM contributions are obtained. We next examine the constraints on the EFT and full models that are expected to be obtained from both top pair and four top production at the LHC, finding for low scalar masses that both processes show similar exclusion power. However, for larger masses, estimated LHC uncertainties push constraints into the non-perturbative regime, where the full model is difficult to analyse, and thus not perturbatively matchable to the EFT. This highlights the necessity to improve uncertainties of SM hypotheses in top final states.

Figures

Figures reproduced from arXiv: 1908.05588 by the authors.

Figure 1
Figure 1. FIG. 1: Representative one-loop Feynman diagram contributions to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Representative counter term contributions to [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a), (b) tree-level graph in the theory of eq.( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5: Matched value of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: BSM interference contribution as a function of the invariant [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Like fig [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Validity within percentage of the EFT computa [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: 95% confidence level exclusion contours for the sim [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

107 extracted references · 18 canonical work pages

  1. [1]

    Kr¨ oninger, A

    K. Kr¨ oninger, A. B. Meyer, and P. Uwer, in The Large Hadron Collider: Harvest of Run 1 , edited by T. Sch¨ orner-Sadenius (2015), pp. 259–300, 1506.02800

    arXiv 2015

  2. [2]

    Weinberg, Physica A96, 327 (1979)

    S. Weinberg, Physica A96, 327 (1979)

    1979

  3. [3]

    Buchmuller and D

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

    1986

  4. [4]

    C. J. C. Burges and H. J. Schnitzer, Nucl. Phys. B228, 464 (1983)

    1983

  5. [5]

    C. N. Leung, S. T. Love, and S. Rao, Z. Phys. C31, 433 (1986)

    1986

  6. [6]

    Hagiwara, R

    K. Hagiwara, R. D. Peccei, D. Zeppenfeld, and K. Hikasa, Nucl. Phys. B282, 253 (1987)

    1987

  7. [7]

    Grzadkowski, M

    B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, JHEP 10, 085 (2010), 1008.4884

    arXiv 2010

  8. [8]

    Dedes, W

    A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek, and K. Suxho, JHEP 06, 143 (2017), 1704.03888

    arXiv 2017

Show all 107 references
  1. [9]

    Brivio and M

    I. Brivio and M. Trott, Phys. Rept. 793, 1 (2019), 1706.08945

    2019 arXiv

  2. [10]

    Alwall, P

    J. Alwall, P. Schuster, and N. Toro, Phys. Rev. D79, 075020 (2009), 0810.3921

    2009 arXiv

  3. [11]

    Alves (LHC New Physics Working Group), J

    D. Alves (LHC New Physics Working Group), J. Phys. G39, 105005 (2012), 1105.2838

    2012 arXiv

  4. [12]

    Abdallah et al., Phys

    J. Abdallah et al., Phys. Dark Univ. 9-10, 8 (2015), 1506.03116

    2015 arXiv

  5. [13]

    Buckley, C

    A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Russell, and C. D. White, Phys. Rev. D92, 091501 (2015), 1506.08845

    2015 arXiv

  6. [14]

    M. P. Rosello and M. Vos, Eur. Phys. J. C76, 200 (2016), 1512.07542

    2016 arXiv

  7. [15]

    Buckley, C

    A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Russell, and C. D. White, JHEP 04, 015 (2016), 1512.03360

    2016 arXiv

  8. [16]

    Zhang, Phys

    C. Zhang, Phys. Rev. Lett. 116, 162002 (2016), 1601.06163

    2016 arXiv

  9. [17]

    Bessidskaia Bylund, F

    O. Bessidskaia Bylund, F. Maltoni, I. Tsinikos, E. Vryonidou, and C. Zhang, JHEP 05, 052 (2016), 1601.08193

    2016 arXiv

  10. [18]

    Castro, J

    N. Castro, J. Erdmann, C. Grunwald, K. Kr¨ oninger, and N.-A. Rosien, Eur. Phys. J. C76, 432 (2016), 1605.05585

    2016 arXiv

  11. [19]

    Barducci, M

    D. Barducci, M. Fabbrichesi, and A. Tonero, Phys. Rev. D96, 075022 (2017), 1704.05478

    2017 arXiv

  12. [20]

    Englert and M

    C. Englert and M. Russell, Eur. Phys. J. C77, 535 (2017), 1704.01782

    2017 arXiv

  13. [21]

    Schulze and Y

    M. Schulze and Y. Soreq, Eur. Phys. J.C76, 466 (2016), 1603.08911

    2016 arXiv

  14. [22]

    J. L. Birman, F. D´ eliot, M. C. N. Fiolhais, A. Onofre, and C. M. Pease, Phys. Rev. D93, 113021 (2016), 1605.02679

    2016 arXiv

  15. [23]

    Cirigliano, W

    V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Phys. Rev. D94, 034031 (2016), 1605.04311

    2016 arXiv

  16. [24]

    Englert, L

    C. Englert, L. Moore, K. Nordstr¨ om, and M. Russell, Phys. Lett. B763, 9 (2016), 1607.04304

    2016 arXiv

  17. [25]

    Maltoni, E

    F. Maltoni, E. Vryonidou, and C. Zhang, JHEP 10, 123 (2016), 1607.05330

    2016 arXiv

  18. [26]

    Zhang, Chin

    C. Zhang, Chin. Phys. C42, 023104 (2018), 1708.05928

    2018 arXiv

  19. [27]

    S. M. Etesami, S. Khatibi, and M. Mohammadi Na- jafabadi, Phys. Rev. D97, 075023 (2018), 1712.07184

    2018 arXiv

  20. [28]

    Barducci et al

    D. Barducci et al. (2018), 1802.07237

    2018 arXiv

  21. [29]

    Malekhosseini, M

    M. Malekhosseini, M. Ghominejad, H. Khanpour, and M. Mohammadi Najafabadi, Phys. Rev. D98, 095001 (2018), 1804.05598

    2018 arXiv

  22. [30]

    Degrande, F

    C. Degrande, F. Maltoni, K. Mimasu, E. Vryonidou, 11 and C. Zhang, JHEP 10, 005 (2018), 1804.07773

    2018 arXiv

  23. [31]

    Jueid, Phys

    A. Jueid, Phys. Rev. D98, 053006 (2018), 1805.07763

    2018 arXiv

  24. [32]

    D’Hondt, A

    J. D’Hondt, A. Mariotti, K. Mimasu, S. Moortgat, and C. Zhang, JHEP 11, 131 (2018), 1807.02130

    2018 arXiv

  25. [33]

    Durieux, M

    G. Durieux, M. Perell´ o, M. Vos, and C. Zhang, JHEP 10, 168 (2018), 1807.02121

    2018 arXiv

  26. [34]

    de Beurs, E

    M. de Beurs, E. Laenen, M. Vreeswijk, and E. Vry- onidou, Eur. Phys. J. C78, 919 (2018), 1807.03576

    2018 arXiv

  27. [35]

    Englert, M

    C. Englert, M. Russell, and C. D. White, Phys. Rev. D99, 035019 (2019), 1809.09744

    2019 arXiv

  28. [36]

    Chala, J

    M. Chala, J. Santiago, and M. Spannowsky, JHEP 04, 014 (2019), 1809.09624

    2019 arXiv

  29. [37]

    N. P. Hartland, F. Maltoni, E. R. Nocera, J. Rojo, E. Slade, E. Vryonidou, and C. Zhang, JHEP 04, 100 (2019), 1901.05965

    2019 arXiv

  30. [38]

    Durieux, A

    G. Durieux, A. Irles, V. Miralles, A. Pe˜ nuelas, R. P¨ oschl, M. Perell´ o, and M. Vos (2019), 1907.10619

    2019 arXiv

  31. [39]

    R. P. Moutafis, Master’s thesis, Orsay, LAL (2019), 1905.03616

    2019 arXiv

  32. [40]

    Liu and H

    W. Liu and H. Sun, Phys. Rev. D100, 015011 (2019), 1906.04884

    2019 arXiv

  33. [41]

    Boughezal, C.-Y

    R. Boughezal, C.-Y. Chen, F. Petriello, and D. Wiegand (2019), 1907.00997

    2019 arXiv

  34. [42]

    Neumann and Z

    T. Neumann and Z. E. Sullivan, JHEP 06, 022 (2019), 1903.11023

    2019 arXiv

  35. [43]

    del Aguila, Z

    F. del Aguila, Z. Kunszt, and J. Santiago, Eur. Phys. J. C76, 244 (2016), 1602.00126

    2016 arXiv

  36. [44]

    Zhang, JHEP 05, 152 (2017), 1610.00710

    Z. Zhang, JHEP 05, 152 (2017), 1610.00710

    2017 arXiv

  37. [45]

    S. A. R. Ellis, J. Quevillon, T. You, and Z. Zhang, Phys. Lett. B762, 166 (2016), 1604.02445

    2016 arXiv

  38. [46]

    Henning, X

    B. Henning, X. Lu, and H. Murayama, JHEP 01, 123 (2018), 1604.01019

    2018 arXiv

  39. [47]

    S. A. R. Ellis, J. Quevillon, T. You, and Z. Zhang, JHEP 08, 054 (2017), 1706.07765

    2017 arXiv

  40. [48]

    Summ and A

    B. Summ and A. Voigt, JHEP 08, 026 (2018), 1806.05171

    2018 arXiv

  41. [49]

    Kr¨ amer, B

    M. Kr¨ amer, B. Summ, and A. Voigt (2019), 1908.04798

    2019 arXiv

  42. [50]

    Cao, S.-L

    Q.-H. Cao, S.-L. Chen, and Y. Liu, Phys. Rev. D95, 053004 (2017), 1602.01934

    2017 arXiv

  43. [51]

    Englert, G

    C. Englert, G. F. Giudice, A. Greljo, and M. Mccullough (2019), 1903.07725

    2019 arXiv

  44. [52]

    Aaboud et al

    M. Aaboud et al. (ATLAS), Phys. Rev. D99, 052009 (2019), 1811.02305

    2019 arXiv

  45. [53]

    A. M. Sirunyan et al. (CMS), Eur. Phys. J. C78, 140 (2018), 1710.10614

    2018 arXiv

  46. [54]

    A. M. Sirunyan et al. (CMS) (2019), 1906.02805

    2019 arXiv

  47. [55]

    A. M. Sirunyan et al. (CMS) (2018), CMS-PAS-FTR- 18-031

    2018

  48. [56]

    Aaboud et al

    M. Aaboud et al. (ATLAS Collaboration), Tech. Rep. ATL-PHYS-PUB-2018-047, CERN, Geneva (2018), URL http://cds.cern.ch/record/2651870

    2018

  49. [57]

    Azzi et al

    P. Azzi et al. (HL-LHC, HE-LHC Working Group) (2019), 1902.04070

    2019 arXiv

  50. [58]

    Arina et al., JHEP 11, 111 (2016), 1605.09242

    C. Arina et al., JHEP 11, 111 (2016), 1605.09242

    2016 arXiv

  51. [59]

    Banerjee, M

    S. Banerjee, M. Chala, and M. Spannowsky, Eur. Phys. J. C78, 683 (2018), 1806.02836

    2018 arXiv

  52. [60]

    Czakon, D

    M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos, and M. Zaro, JHEP 10, 186 (2017), 1705.04105

    2017 arXiv

  53. [61]

    Vryonidou and C

    E. Vryonidou and C. Zhang, JHEP 08, 036 (2018), 1804.09766

    2018 arXiv

  54. [62]

    Maltoni, L

    F. Maltoni, L. Mantani, and K. Mimasu (2019), 1904.05637

    2019 arXiv

  55. [63]

    Anastasiou, C

    C. Anastasiou, C. Duhr, F. Dulat, F. Herzog, and B. Mistlberger, Phys. Rev. Lett. 114, 212001 (2015), 1503.06056

    2015 arXiv

  56. [64]

    Anastasiou, C

    C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog, A. Lazopoulos, and B. Mistl- berger, JHEP 05, 058 (2016), 1602.00695

    2016 arXiv

  57. [65]

    K. J. F. Gaemers and F. Hoogeveen, Phys. Lett. 146B, 347 (1984)

    1984

  58. [66]

    Dicus, A

    D. Dicus, A. Stange, and S. Willenbrock, Phys. Lett. B333, 126 (1994), hep-ph/9404359

    1994 arXiv

  59. [67]

    Bernreuther, A

    W. Bernreuther, A. Brandenburg, and M. Flesch (1998), hep-ph/9812387

    1998 arXiv

  60. [68]

    Frederix and F

    R. Frederix and F. Maltoni, JHEP 01, 047 (2009), 0712.2355

    2009 arXiv

  61. [69]

    Barger, T

    V. Barger, T. Han, and D. G. E. Walker, Phys. Rev. Lett. 100, 031801 (2008), hep-ph/0612016

    2008 arXiv

  62. [70]

    Craig, F

    N. Craig, F. D’Eramo, P. Draper, S. Thomas, and H. Zhang, JHEP 06, 137 (2015), 1504.04630

    2015 arXiv

  63. [71]

    Bernreuther, P

    W. Bernreuther, P. Galler, C. Mellein, Z. G. Si, and P. Uwer, Phys. Rev. D93, 034032 (2016), 1511.05584

    2016 arXiv

  64. [72]

    Hespel, F

    B. Hespel, F. Maltoni, and E. Vryonidou, JHEP 10, 016 (2016), 1606.04149

    2016 arXiv

  65. [73]

    Carena and Z

    M. Carena and Z. Liu, JHEP 11, 159 (2016), 1608.07282

    2016 arXiv

  66. [74]

    Buarque Franzosi, F

    D. Buarque Franzosi, F. Fabbri, and S. Schumann, JHEP 03, 022 (2018), 1711.00102

    2018 arXiv

  67. [75]

    Basler, S

    P. Basler, S. Dawson, C. Englert, and M. M¨ uhlleitner, Phys. Rev. D99, 055048 (2019), 1812.03542

    2019 arXiv

  68. [76]

    Djouadi, J

    A. Djouadi, J. Ellis, A. Popov, and J. Quevillon, JHEP 03, 119 (2019), 1901.03417

    2019 arXiv

  69. [77]

    Kauer, A

    N. Kauer, A. Lind, P. Maierh¨ ofer, and W. Song, JHEP 07, 108 (2019), 1905.03296

    2019 arXiv

  70. [78]

    Brehmer, A

    J. Brehmer, A. Freitas, D. Lopez-Val, and T. Plehn, Phys. Rev. D93, 075014 (2016), 1510.03443

    2016 arXiv

  71. [79]

    Buarque Franzosi and C

    D. Buarque Franzosi and C. Zhang, Phys. Rev. D91, 114010 (2015), 1503.08841

    2015 arXiv

  72. [80]

    Freitas, D

    A. Freitas, D. L´ opez-Val, and T. Plehn, Phys. Rev. D94, 095007 (2016), 1607.08251

    2016 arXiv

  73. [81]

    Buarque Franzosi, E

    D. Buarque Franzosi, E. Vryonidou, and C. Zhang, JHEP 10, 096 (2017), 1707.06760

    2017 arXiv

  74. [82]

    Arnold et al., Comput

    K. Arnold et al., Comput. Phys. Commun. 180, 1661 (2009), 0811.4559

    2009 arXiv

  75. [83]

    Baglio et al

    J. Baglio et al. (2011), 1107.4038

    2011 arXiv

  76. [84]

    Arnold et al

    K. Arnold et al. (2012), 1207.4975

    2012 arXiv

  77. [85]

    Baglio et al

    J. Baglio et al. (2014), 1404.3940

    2014 arXiv

  78. [86]

    Hahn, Acta Phys

    T. Hahn, Acta Phys. Polon. B30, 3469 (1999), hep- ph/9910227

    1999

  79. [87]

    Hahn and C

    T. Hahn and C. Schappacher, Comput. Phys. Commun. 143, 54 (2002), hep-ph/0105349

    2002 arXiv

  80. [88]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Mal- toni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, JHEP 07, 079 (2014), 1405.0301

    2014 arXiv

  81. [89]

    Nowakowski and A

    M. Nowakowski and A. Pilaftsis, Z. Phys. C60, 121 (1993), hep-ph/9305321

    1993 arXiv

  82. [90]

    M. H. Seymour, Phys. Lett. B354, 409 (1995), hep- ph/9505211

    1995

  83. [91]

    Passarino, C

    G. Passarino, C. Sturm, and S. Uccirati, Nucl. Phys. B834, 77 (2010), 1001.3360

    2010 arXiv

  84. [92]

    Kauer and C

    N. Kauer and C. O’Brien, Eur. Phys. J. C75, 374 (2015), 1502.04113

    2015 arXiv

  85. [93]

    Englert, I

    C. Englert, I. Low, and M. Spannowsky, Phys. Rev. D91, 074029 (2015), 1502.04678

    2015 arXiv

  86. [94]

    Goria, G

    S. Goria, G. Passarino, and D. Rosco, Nucl. Phys. B864, 530 (2012), 1112.5517

    2012 arXiv

  87. [95]

    Contino, A

    R. Contino, A. Falkowski, F. Goertz, C. Grojean, and 12 F. Riva, JHEP 07, 144 (2016), 1604.06444

    2016 arXiv

  88. [96]

    Brivio, S

    I. Brivio, S. Bruggisser, F. Maltoni, R. Moutafis, T. Plehn, E. Vryonidou, S. Westhoff, and C. Zhang (2019), 1910.03606

    2019 arXiv

  89. [97]

    Czakon, P

    M. Czakon, P. Fiedler, and A. Mitov, Phys. Rev. Lett. 110, 252004 (2013), 1303.6254

    2013 arXiv

  90. [98]

    Czakon, D

    M. Czakon, D. Heymes, and A. Mitov, Phys. Rev. Lett. 116, 082003 (2016), 1511.00549

    2016 arXiv

  91. [99]

    Czakon, A

    M. Czakon, A. Ferroglia, D. Heymes, A. Mitov, B. D. Pecjak, D. J. Scott, X. Wang, and L. L. Yang, JHEP 05, 149 (2018), 1803.07623

    2018 arXiv

  92. [100]

    Bevilacqua and M

    G. Bevilacqua and M. Worek, JHEP 07, 111 (2012), 1206.3064

    2012 arXiv

  93. [101]

    Frederix, D

    R. Frederix, D. Pagani, and M. Zaro, JHEP 02, 031 (2018), 1711.02116

    2018 arXiv

  94. [102]

    Greiner, K

    N. Greiner, K. Kong, J.-C. Park, S. C. Park, and J.-C. Winter, JHEP 04, 029 (2015), 1410.6099

    2015 arXiv

  95. [103]

    S. Baek, P. Ko, and P. Wu, JHEP 10, 117 (2016), 1606.00072

    2016 arXiv

  96. [104]

    P. J. Fox, I. Low, and Y. Zhang, JHEP 03, 074 (2018), 1801.03505

    2018 arXiv

  97. [105]

    Buchalla, A

    G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996), hep-ph/9512380

    1996 arXiv

  98. [106]

    Denner and S

    A. Denner and S. Dittmaier, Nucl. Phys. Proc. Suppl. 157, 53 (2006), [,53(2006)], hep-ph/0601085

    2006 arXiv

  99. [107]

    Passarino and M

    G. Passarino and M. J. G. Veltman, Nucl. Phys. B160, 151 (1979)

    1979

Pith tools

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