Pith. sign in

REVIEW 2 major objections 5 minor 3 cited by

Exploring anomalous couplings in Higgs boson pair production through shape analysis

T0 review · 2 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 Unsupervised learning resolves seven shape classes in Higgs pair mass spectra that hand-defined types blur.

desk verdict A useful NLO shape taxonomy with honest limits; the 2D-slice sampling is the main caveat, not the ML. read the letter →

arxiv 1908.08923 v2 pith:A5J4CVLH submitted 2019-08-23 hep-ph

Matteo Capozi , Gudrun Heinrich This is my paper · ORCID
classification hep-ph
keywords Higgspairproductionshapeanalysisanomalouscouplingsnon-linearEFTautoencoderKMeansclusteringbenchmarkpointsnext-to-leadingorderQCD
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the shape of the Higgs boson pair invariant mass distribution is a sharp diagnostic of anomalous Higgs couplings, and that an unsupervised classifier extracts that information more faithfully than a small set of human-defined shapes. Working at NLO with full top-quark mass dependence in a five-coupling non-linear EFT, it maps which regions of coupling space produce which $m_{hh}$ shapes. It claims the unsupervised approach resolves features such as an enhanced tail, a shoulder, and close-by double peaks that predefined categories blur, and yields seven cluster centers usable as benchmark points. If right, experimental searches can use these shapes and benchmark points to constrain couplings, especially $c_{hhh}$ and $c_{tt}$, beyond what total cross-section limits alone provide.

What carries the argument

The load-bearing object is the factorization of the NLO differential cross section into a sum over coupling monomials times bin-wise coefficient functions $A_i$ (Eq. 2.5), which allows a dense scan of the five-dimensional coupling space. On top of this sits an autoencoder that compresses each normalised 30-bin $m_{hh}$ histogram into a four-dimensional latent vector, followed by a standard K-means clustering algorithm into a chosen number of shape clusters. Ten differently initialised encoder models are trained, and a majority vote assigns each parameter point its final cluster label. The cluster centers act as shape prototypes, and a distance-based procedure converts them into concrete benchmark points in coupling space.

What would settle it

Evaluate $m_{hh}$ shapes at parameter points where $c_{hhh}$, $c_{tt}$, and $c_{gghh}$ are all shifted from their SM values, using the published coefficient tables; if such points produce shapes outside the regions predicted by the two-coupling maps, the maps are not representative of the full five-dimensional space.

Watch

Extended reading notes

Core claim

The central claim is that an autoencoder followed by K-means clustering on normalised NLO $m_{hh}$ distributions identifies seven reproducible shape classes whose cluster centers are stable across ten encoder models, and that the parameter-space maps built from these clusters are more discriminating than the four predefined shape types. In particular, the paper claims that small deviations of $c_{tt}$ from zero are very likely to produce a doubly peaked $m_{hh}$ structure, while SM-like shapes reappear as $c_{tt}$ moves further away from zero. It also claims that shapes with an enhanced tail or a shoulder are likely to be produced by nonzero values of $c_{gghh}$, and that shape variation is dominated by $c_{hhh}$ and $c_{tt}$. The paper derives seven NLO benchmark points from the cluster centers, each satisfying the current combined LHC upper bound of 6.9 times the Standard Model cross section.

Load-bearing premise

The paper's maps and conclusions assume that two-dimensional slices with the other three couplings at their Standard Model values represent the full five-dimensional coupling space, so shapes caused by simultaneous deviations of three or more couplings could be missed.

Editorial extensions

If this is right

  • The seven cluster centers give experimentalists concrete NLO benchmark points, each within the current combined LHC cross-section limit, for profile-likelihood or template fits.
  • The claim that small $c_{tt}$ deviations produce a doubly peaked $m_{hh}$ structure offers a direct target: search for that shape to constrain $c_{tt}$, which single-Higgs measurements constrain only weakly.
  • Shapes with an enhanced tail or a shoulder are tied to nonzero $c_{gghh}$, so shape analyses can probe the effective gluon-Higgs couplings that total cross sections alone do not resolve.
  • Because $m_{hh}$ is more shape-sensitive than $p_{T,h}$, differential $m_{hh}$ measurements should be prioritized in future di-Higgs analyses; the method itself transfers to other observables and other processes.
  • In the SMEFT limit, where $c_{ggh}$ and $c_{gghh}$ are related and $c_{tt}$ is suppressed relative to $c_t$, the shape maps reduce to a three-dimensional parameter space that can be visualised directly and used for more model-dependent projections.

Reading between the lines

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

  • A natural extension is to treat the cluster centers as a continuous latent space and interpolate between them, which could give smooth parameter-shape maps rather than discrete labels; the paper only provides discrete clusters and benchmark points.
  • Since the coefficient tables are published for 13, 14, and 27 TeV, the same clustering pipeline could be rerun at 14 and 27 TeV; the paper's benchmark points are quoted only for 13 TeV.
  • If small $c_{tt}$ deviations really do imprint a double peak, that shape may be one of the cleanest new-physics signatures in di-Higgs data, provided background and parton-shower modeling retain the feature.
  • The autoencoder's latent dimension of four limits the resolution of the shape manifold; a larger latent space might separate additional features such as the exact peak separation, which could be tested before applying the method to data.
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 / 5 minor

Summary. This manuscript classifies shapes of the NLO gg->HH invariant mass distribution computed with full top-quark mass dependence in a five-coupling HEFT parameterization. It first defines four pre-defined shape types and maps them onto ten 2D coupling slices, then applies an autoencoder plus KMeans clustering to identify four or seven shape clusters and derives seven benchmark points from the cluster centers. The paper claims that the unsupervised method captures subtle shape features, such as enhanced tails and shoulders, better than the predefined taxonomy, and concludes that small deviations of ctt from zero tend to produce doubly peaked mhh distributions while chhh drives the low-mass enhancement.

Significance. If the claims hold, the seven-cluster taxonomy and the NLO benchmark points are a useful contribution: they extend the LO cluster-analysis benchmarks of Ref. [62] to full NLO with top-mass dependence, and they demonstrate a transparent unsupervised pipeline based on public coefficient tables. The classification logic is simple and reproducible, and the paper is honest about the arbitrariness of the pre-defined shapes. However, the mapping to the five-dimensional parameter space and the 'very well' performance claim are not yet quantitatively established because of the 2D-slice sampling and the absence of cluster-quality metrics.

major comments (2)
  1. [§2.3, §3.2, §3.3] The paper's central claim that the analysis maps shape classes onto the five-dimensional coupling space is not supported by the sampling described. Section 2.3 states that all two-coupling scans set the remaining three couplings to their SM values, and the cluster maps in Section 3.2 are drawn on the same ten 2D planes. Because Eq. (2.5) contains terms involving three or more couplings (e.g., A9 ctt cggh chhh, A17 ct ctt cggh, A18 ct cggh^2 chhh), simultaneous deviations can produce mhh shapes that never appear in any 2D slice with the remaining couplings SM-valued. The benchmark selection in Section 3.3 searches the same input grids, which makes the multiple non-SM benchmark points in Table 2 (e.g., point 1 with ct=0.94, chhh=3.94, ctt=-1/3, cggh=0.5, cgghh=1/3 as rendered in the manuscript) difficult to reconcile with a purely 2D-slice input set. The authors should either generate and scan a genuine 5D grid (or a structured sampling of the full space) and re-derive the cluster maps and benchmarks, or explicitly restrict the scope of the conclusions to the 2D-slice families.
  2. [§3.1] The choice of seven clusters and the claim that the unsupervised procedure 'captures shape features very well' are not quantitatively validated. Section 3.1 reports that seven clusters 'seemed to be the optimal number' based on visual inspection of the cluster centers, and the comparison in Section 3.2 is made against the authors' own four predefined shapes. No objective cluster-quality metric (e.g., silhouette score, Davies-Bouldin index, reconstruction error as a function of latent dimension, or stability across the ten encoder models) is provided. Since the central claim is the superiority of the unsupervised taxonomy, this omission is load-bearing; a quantitative validation would also make the seven-cluster choice reproducible.
minor comments (5)
  1. [§1, §3.1, §3.2] There are several typos: 'definine' in Section 1, 'gobal' in Section 3.1, and 'disribution' in Section 3.2.
  2. [§3.3 and Fig. 19 caption] The text and the caption refer to 'Table 3.3' when the benchmark points are in Table 2; please fix the cross-reference.
  3. [Eq. (2.5)] The term 'A10cttccgghh' appears to be a typesetting error for A10 ctt cgghh; please correct it.
  4. [Fig. 12] Figure 12 is never discussed in the body of the paper; either refer to it explicitly in Section 3.2 or remove it.
  5. [Table 2] The benchmark table is difficult to read because the fractional entries are split across lines; please use consistent decimal or fraction notation for all couplings.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper transparently maps input NLO spectra through pre-defined and unsupervised classifiers, and its cluster benchmarks are selections, not fitted predictions.

full rationale

The derivation chain is self-contained once the input NLO distributions are supplied. The m_hh spectra are generated from Eq. (2.5) using the coefficients A_i from Ref. [71]; Ref. [71] is an independent NLO computation that is used as an input, not as evidence for the paper's shape-classification claims. The pre-defined shape types in Section 2.2 are explicit slope-based criteria, and the parameter-space maps in Figs. 2-6 simply record which coupling regions produce each shape class; no shape class is defined in terms of the couplings it is later said to explain. The unsupervised part in Section 3.1 trains an autoencoder and KMeans on the same generated distributions without target labels, so there is no fitted quantity that is later renamed a prediction. The seven benchmark points in Section 3.3 are selected as grid points closest to the cluster centers, subject to cross-section limits; this is a selection procedure, not a fit to external data. The only author-overlap citation is Ref. [71], which provides the A_i tables; this is legitimate independent support because it is a published calculation with stated assumptions that do not include the present paper's conclusions. The paper's reliance on 2D slices with the other couplings fixed at SM values is a coverage limitation of the parameter study, not a circular step: it does not fold any output back into an input. No self-definitional, fitted-input-as-prediction, self-citation-load-bearing, uniqueness-imported, ansatz-smuggled, or renaming pattern is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are methodological choices (cluster count, latent dimension, shape thresholds, and uncertainty-exclusion cuts), not fitted constants. The physics content is imported from Ref. [71], which is a legitimate external NLO computation. This is a classification study, so the circularity burden is low.

free parameters (4)
  • Number of KMeans clusters = 7
    Chosen by hand after testing 4 to 8 clusters as the number that best captures distinct shape features while avoiding local minima (Section 3.1); the central claim of detailed shape capture depends on this choice.
  • Autoencoder latent-space dimension = 4 nodes
    The compressed representation length; the paper tests network depth but not the latent dimension, and the resulting cluster structure depends indirectly on it (Section 3.1).
  • Predefined shape-type thresholds = Peak separation >100 GeV vs <100 GeV
    The boundaries between shape kinds 2 and 4 in Section 2.2 are arbitrary; the authors note that kind 4 would move to kind 1 or 3 for bin widths >= 100 GeV.
  • Statistical-uncertainty exclusion cut = Exclusion rates of about 20% (kind 4), 8% (kind 2), <5% (kinds 1 and 3)
    Points whose shape class changes under bin-wise variations of the Ai uncertainties are removed from the data set; this is a data-selection cut that reshapes the inferred parameter regions.
assumptions (6)
  • domain assumption The coefficients Ai in Eq. (2.5), taken from Ref. [71] as .csv tables, accurately reproduce the NLO differential cross section with full top quark mass dependence.
    All shape classifications in this paper are generated from this parametrization; errors in the underlying NLO calculation or interpolation tables would propagate directly into the shape maps and benchmark points.
  • domain assumption The five anomalous couplings are varied within the ranges in Eq. (2.6), and in each 2D projection the remaining three couplings are fixed to their SM values.
    This restriction defines what the plots and the derived coupling-shape associations actually show; it ignores simultaneous non-SM deviations of more than two couplings, which are not probed anywhere in the paper.
  • domain assumption Scale uncertainties are approximately uniform over the m_hh range and can be neglected in a shape analysis.
    Invoked twice (Sections 2.2 and 2.3) with reference to Refs. [42,71]; the paper does not check whether scale variations could alter local shape features such as peak positions.
  • domain assumption The median statistical uncertainty of the Ai coefficients is low enough that a shape class is meaningful once points whose class changes under those uncertainties are removed.
    The exclusion procedure in Section 2.2 removes unstable points, but the residual effect of the 20-30% uncertainties in high-m_hh bins on the remaining classifications is not quantified.
  • domain assumption The autoencoder latent space plus KMeans provides a meaningful similarity measure for m_hh shapes.
    Section 3.1 adopts this architecture and the choice of seven clusters based on visual inspection, without an external validation metric or comparison to other similarity measures.
  • domain assumption The SMEFT relations cggh = 2 cgghh and ctt = 0.05 ct are used to simulate a reduced parameter space in Fig. 18.
    These are model assumptions taken from the SMEFT literature, not derived in this paper, and they affect the interpretation of the SMEFT-like shape pattern.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exploring anomalous couplings in Higgs boson pair production through shape analysis." pith.science (2026). https://pith.science/paper/A5J4CVLH

@misc{pith2026190808923,
  author       = {Pith},
  title        = {Pith review of: Exploring anomalous couplings in Higgs boson pair production through shape analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A5J4CVLH}},
  note         = {Machine review of arXiv:1908.08923}
}
abstract

We classify shapes of Higgs boson pair invariant mass distributions $m_{hh}$, calculated at NLO with full top quark mass dependence, and visualise how distinct classes of shapes relate to the underlying coupling parameter space. Our study is based on a five-dimensional parameter space relevant for Higgs boson pair production in a non-linear Effective Field Theory framework. We use two approaches: an analysis based on predefined shape types and a classification into shape clusters based on unsupervised learning. We find that our method based on unsupervised learning is able to capture shape features very well and therefore allows a more detailed study of the impact of anomalous couplings on the $m_{hh}$ shape compared to more conventional approaches to a shape analysis.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Electroweak precision observables at NLL order in the SMEFT

    hep-ph 2026-08 accept novelty 6.0 of 10

    SMEFT electroweak precision predictions can be upgraded to NLL accuracy using two-loop renormalization-group evolution plus one-loop matching, yielding complete 210-coefficient expressions and stronger indirect new-ph...

  2. Search for nonresonant triple Higgs boson production in the final state with six bottom quarks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

    hep-ex 2026-07 accept novelty 6.0 of 10

    No excess is observed; the 95% CL upper limit on nonresonant HHH→6b is 44 fb (588×SM), with κ3 constrained to −7.4 < κ3 < 12.4 (κ4=1) and κ4 to −177 < κ4 < 185 (κ3=1).

  3. Probing the Symmetric Higgs Portal with Di-Higgs Boson Production

    hep-ph 2019-08 conditional novelty 6.0 of 10

    Di-Higgs production at a future 100 TeV hadron collider can probe Higgs portal couplings of a stable scalar of order one for masses above half the Higgs mass.

Reference graph

Works this paper leans on

109 extracted references · 5 canonical work pages · cited by 3 Pith papers

  1. [62]

    Carvalho, M

    A. Carvalho, M. Dall’Osso, T. Dorigo, F. Goertz, C. A. Gottardo and M. Tosi, Higgs Pair Production: Choosing Benchmarks With Cluster Analysis , JHEP 04 (2016) 126 [1507.02245]

    arXiv 2016

  2. [1]

    Aad et al., Combination of searches for Higgs boson pairs in pp collisions at√s =13 TeV with the ATLAS detector , Phys

    ATLAS collaboration, G. Aad et al., Combination of searches for Higgs boson pairs in pp collisions at√s =13 TeV with the ATLAS detector , Phys. Lett. B800 (2020) 135103 [1906.02025]

    arXiv 2020

  3. [2]

    CMS collaboration, A. M. Sirunyan et al., Combination of searches for Higgs boson pair production in proton-proton collisions at √s = 13 TeV, Phys. Rev. Lett. 122 (2019) 121803 [ 1811.09689]

    arXiv 2019

  4. [3]

    McCullough, An Indirect Model-Dependent Probe of the Higgs Self-Coupling , Phys

    M. McCullough, An Indirect Model-Dependent Probe of the Higgs Self-Coupling , Phys. Rev. D90 (2014) 015001 [ 1312.3322]

    arXiv 2014

  5. [4]

    Gorbahn and U

    M. Gorbahn and U. Haisch, Indirect probes of the trilinear Higgs coupling: gg→h and h→γγ, JHEP 10 (2016) 094 [ 1607.03773]

    arXiv 2016

  6. [5]

    Degrassi, P

    G. Degrassi, P. P. Giardino, F. Maltoni and D. Pagani, Probing the Higgs self coupling via single Higgs production at the LHC , JHEP 12 (2016) 080 [ 1607.04251]

    arXiv 2016

  7. [6]

    Bizon, M

    W. Bizon, M. Gorbahn, U. Haisch and G. Zanderighi, Constraints on the trilinear Higgs coupling from vector boson fusion and associated Higgs production at the LHC , JHEP 07 (2017) 083 [ 1610.05771]

    arXiv 2017

  8. [7]

    Maltoni, D

    F. Maltoni, D. Pagani, A. Shivaji and X. Zhao, Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC , Eur. Phys. J. C77 (2017) 887 [ 1709.08649]. – 27 –

    arXiv 2017

Show all 109 references
  1. [8]

    G. D. Kribs, A. Maier, H. Rzehak, M. Spannowsky and P. Waite, Electroweak oblique parameters as a probe of the trilinear Higgs boson self-interaction , Phys. Rev. D95 (2017) 093004 [ 1702.07678]

    2017 arXiv

  2. [9]

    Degrassi, M

    G. Degrassi, M. Fedele and P. P. Giardino, Constraints on the trilinear Higgs self coupling from precision observables, JHEP 04 (2017) 155 [ 1702.01737]

    2017 arXiv

  3. [10]

    Nakamura and A

    J. Nakamura and A. Shivaji, Direct measurement of the Higgs self-coupling in e+e−→ZH , Phys. Lett. B797 (2019) 134821 [ 1812.01576]

    2019 arXiv

  4. [11]

    Kilian, S

    W. Kilian, S. Sun, Q.-S. Yan, X. Zhao and Z. Zhao, Multi-Higgs Production and Unitarity in Vector-Boson Fusion at Future Hadron Colliders , 1808.05534

    arXiv

  5. [12]

    Maltoni, D

    F. Maltoni, D. Pagani and X. Zhao, Constraining the Higgs self-couplings at e +e− colliders, JHEP 07 (2018) 087 [ 1802.07616]

    2018 arXiv

  6. [13]

    Vryonidou and C

    E. Vryonidou and C. Zhang, Dimension-six electroweak top-loop effects in Higgs production and decay, JHEP 08 (2018) 036 [ 1804.09766]

    2018 arXiv

  7. [14]

    Gorbahn and U

    M. Gorbahn and U. Haisch, Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling , JHEP 04 (2019) 062 [ 1902.05480]

    2019 arXiv

  8. [15]

    ATLAS collaboration, Constraint of the Higgs boson self-coupling from Higgs boson differential production and decay measurements, Tech. Rep. ATL-PHYS-PUB-2019-009, CERN, Geneva, Mar, 2019

    2019

  9. [16]

    ATLAS collaboration, Constraints on the Higgs boson self-coupling from the combination of single-Higgs and double-Higgs production analyses performed with the ATLAS experiment, Tech. Rep. ATL-PHYS-PUB-2019-049, CERN, Geneva, Oct, 2019

    2019

  10. [17]

    Bizon, U

    W. Bizon, U. Haisch and L. Rottoli, Constraints on the quartic Higgs self-coupling from double-Higgs production at future hadron colliders , JHEP 10 (2019) 267 [1810.04665]

    2019 arXiv

  11. [18]

    Borowka, C

    S. Borowka, C. Duhr, F. Maltoni, D. Pagani, A. Shivaji and X. Zhao, Probing the scalar potential via double Higgs boson production at hadron colliders , JHEP 04 (2019) 016 [ 1811.12366]

    2019 arXiv

  12. [19]

    Falkowski and R

    A. Falkowski and R. Rattazzi, Which EFT, JHEP 10 (2019) 255 [ 1902.05936]

    2019 arXiv

  13. [20]

    Chang and M

    S. Chang and M. A. Luty, The Higgs Trilinear Coupling and the Scale of New Physics, 1902.05556

    1902 arXiv

  14. [21]

    Di Luzio, R

    L. Di Luzio, R. Gr¨ ober and M. Spannowsky, Maxi-sizing the trilinear Higgs self-coupling: how large could it be? , Eur. Phys. J. C77 (2017) 788 [ 1704.02311]

    2017 arXiv

  15. [22]

    Di Vita, C

    S. Di Vita, C. Grojean, G. Panico, M. Riembau and T. Vantalon, A global view on the Higgs self-coupling, JHEP 09 (2017) 069 [ 1704.01953]. – 28 –

    2017 arXiv

  16. [23]

    Braathen and S

    J. Braathen and S. Kanemura, On two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors , Phys. Lett. B796 (2019) 38 [ 1903.05417]

    2019 arXiv

  17. [24]

    Basler, S

    P. Basler, S. Dawson, C. Englert and M. M¨ uhlleitner, Showcasing HH production: Benchmarks for the LHC and HL-LHC , Phys. Rev. D99 (2019) 055048 [ 1812.03542]

    2019 arXiv

  18. [25]

    K. S. Babu and S. Jana, Enhanced Di-Higgs Production in the Two Higgs Doublet Model, JHEP 02 (2019) 193 [ 1812.11943]

    2019 arXiv

  19. [26]

    Adhikary, S

    A. Adhikary, S. Banerjee, R. K. Barman, B. Bhattacherjee and S. Niyogi, Revisiting the non-resonant Higgs pair production at the HL-LHC , JHEP 07 (2018) 116 [1712.05346]

    2018 arXiv

  20. [27]

    I. M. Lewis and M. Sullivan, Benchmarks for Double Higgs Production in the Singlet Extended Standard Model at the LHC , Phys. Rev. D96 (2017) 035037 [ 1701.08774]

    2017 arXiv

  21. [28]

    Dawson, C

    S. Dawson, C. Englert and T. Plehn, Higgs Physics: It ain’t over till it’s over , Phys. Rept. 816 (2019) 1 [ 1808.01324]

    2019 arXiv

  22. [29]

    Cepeda et al., Report from Working Group 2 , CERN Yellow Rep

    M. Cepeda et al., Report from Working Group 2 , CERN Yellow Rep. Monogr. 7 (2019) 221 [ 1902.00134]

    2019 arXiv

  23. [30]

    Alison et al., Higgs Boson Pair Production at Colliders: Status and Perspectives , in Double Higgs Production at Colliders Batavia, IL, USA, September 4, 2018-9, 2019 (B

    J. Alison et al., Higgs Boson Pair Production at Colliders: Status and Perspectives , in Double Higgs Production at Colliders Batavia, IL, USA, September 4, 2018-9, 2019 (B. Di Micco, M. Gouzevitch, J. Mazzitelli and C. Vernieri, eds.), 2019, 1910.00012, https://lss.fnal.gov/a...

    2018 arXiv

  24. [31]

    O. J. P. Eboli, G. C. Marques, S. F. Novaes and A. A. Natale, Twin Higgs Boson Production, Phys. Lett. B197 (1987) 269

    1987

  25. [32]

    E. W. N. Glover and J. J. van der Bij, Higgs Boson Pair Production via Gluon Fusion, Nucl. Phys. B309 (1988) 282

    1988

  26. [33]

    Plehn, M

    T. Plehn, M. Spira and P. M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys. B479 (1996) 46 [ hep-ph/9603205]

    1996 arXiv

  27. [34]

    Dawson, S

    S. Dawson, S. Dittmaier and M. Spira, Neutral Higgs boson pair production at hadron colliders: QCD corrections , Phys. Rev. D58 (1998) 115012 [ hep-ph/9805244]

    1998 arXiv

  28. [35]

    Maltoni, E

    F. Maltoni, E. Vryonidou and M. Zaro, Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO , JHEP 11 (2014) 079 [ 1408.6542]

    2014 arXiv

  29. [36]

    Borowka, N

    S. Borowka, N. Greiner, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk et al., Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence, Phys. Rev. Lett. 117 (2016) 012001 [ 1604.06447]

    2016 arXiv

  30. [37]

    Borowka, N

    S. Borowka, N. Greiner, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk et al., Full top quark mass dependence in Higgs boson pair production at NLO , JHEP 10 (2016) 107 [1608.04798]. – 29 –

    2016 arXiv

  31. [38]

    Baglio, F

    J. Baglio, F. Campanario, S. Glaus, M. M¨ uhlleitner, M. Spira and J. Streicher, Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme , Eur. Phys. J. C79 (2019) 459 [ 1811.05692]

    2019 arXiv

  32. [39]

    Baglio, F

    J. Baglio, F. Campanario, S. Glaus, M. M. M¨ uhlleitner, J. Ronca, M. Spira et al., Higgs-Pair Production via Gluon Fusion at Hadron Colliders: NLO QCD Corrections , 2003.03227

    2003 arXiv

  33. [40]

    Heinrich, S

    G. Heinrich, S. P. Jones, M. Kerner, G. Luisoni and E. Vryonidou, NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers, JHEP 08 (2017) 088 [ 1703.09252]

    2017 arXiv

  34. [41]

    Jones and S

    S. Jones and S. Kuttimalai, Parton Shower and NLO-Matching uncertainties in Higgs Boson Pair Production, JHEP 02 (2018) 176 [ 1711.03319]

    2018 arXiv

  35. [42]

    Heinrich, S

    G. Heinrich, S. P. Jones, M. Kerner, G. Luisoni and L. Scyboz, Probing the trilinear Higgs boson coupling in di-Higgs production at NLO QCD including parton shower effects, JHEP 06 (2019) 066 [ 1903.08137]

    2019 arXiv

  36. [43]

    de Florian and J

    D. de Florian and J. Mazzitelli, Two-loop virtual corrections to Higgs pair production , Phys. Lett. B724 (2013) 306 [ 1305.5206]

    2013 arXiv

  37. [44]

    de Florian and J

    D. de Florian and J. Mazzitelli, Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD , Phys. Rev. Lett. 111 (2013) 201801 [1309.6594]

    2013 arXiv

  38. [45]

    Grigo, K

    J. Grigo, K. Melnikov and M. Steinhauser, Virtual corrections to Higgs boson pair production in the large top quark mass limit , Nucl. Phys. B888 (2014) 17 [1408.2422]

    2014 arXiv

  39. [46]

    Grigo, J

    J. Grigo, J. Hoff and M. Steinhauser, Higgs boson pair production: top quark mass effects at NLO and NNLO , Nucl. Phys. B900 (2015) 412 [ 1508.00909]

    2015 arXiv

  40. [47]

    de Florian, M

    D. de Florian, M. Grazzini, C. Hanga, S. Kallweit, J. M. Lindert, P. Maierh¨ ofer et al., Differential Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD , JHEP 09 (2016) 151 [ 1606.09519]

    2016 arXiv

  41. [48]

    Grazzini, G

    M. Grazzini, G. Heinrich, S. Jones, S. Kallweit, M. Kerner, J. M. Lindert et al., Higgs boson pair production at NNLO with top quark mass effects , JHEP 05 (2018) 059 [1803.02463]

    2018 arXiv

  42. [49]

    De Florian and J

    D. De Florian and J. Mazzitelli, Soft gluon resummation for Higgs boson pair production including finite Mt effects, JHEP 08 (2018) 156 [ 1807.03704]

    2018 arXiv

  43. [50]

    Gr¨ ober, A

    R. Gr¨ ober, A. Maier and T. Rauh, Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes , JHEP 03 (2018) 020 [ 1709.07799]

    2018 arXiv

  44. [51]

    Bonciani, G

    R. Bonciani, G. Degrassi, P. P. Giardino and R. Gr¨ ober, Analytical Method for Next-to-Leading-Order QCD Corrections to Double-Higgs Production, Phys. Rev. Lett. 121 (2018) 162003 [ 1806.11564]. – 30 –

    2018 arXiv

  45. [52]

    Xu and L

    X. Xu and L. L. Yang, Towards a new approximation for pair-production and associated-production of the Higgs boson , JHEP 01 (2019) 211 [ 1810.12002]

    2019 arXiv

  46. [53]

    Davies, G

    J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double-Higgs boson production in the high-energy limit: planar master integrals , JHEP 03 (2018) 048 [1801.09696]

    2018 arXiv

  47. [54]

    Davies, F

    J. Davies, F. Herren, G. Mishima and M. Steinhauser, Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops , JHEP 05 (2019) 157 [1904.11998]

    2019 arXiv

  48. [55]

    Davies, G

    J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double Higgs boson production at NLO in the high-energy limit: complete analytic results , JHEP 01 (2019) 176 [ 1811.05489]

    2019 arXiv

  49. [56]

    Davies, G

    J. Davies, G. Heinrich, S. P. Jones, M. Kerner, G. Mishima, M. Steinhauser et al., Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion, JHEP 11 (2019) 024 [ 1907.06408]

    2019 arXiv

  50. [57]

    Contino, M

    R. Contino, M. Ghezzi, M. Moretti, G. Panico, F. Piccinini and A. Wulzer, Anomalous Couplings in Double Higgs Production , JHEP 08 (2012) 154 [ 1205.5444]

    2012 arXiv

  51. [58]

    Goertz, A

    F. Goertz, A. Papaefstathiou, L. L. Yang and J. Zurita, Higgs boson pair production in the D=6 extension of the SM , JHEP 04 (2015) 167 [ 1410.3471]

    2015 arXiv

  52. [59]

    Chen and I

    C.-R. Chen and I. Low, Double take on new physics in double Higgs boson production , Phys. Rev. D90 (2014) 013018 [ 1405.7040]

    2014 arXiv

  53. [60]

    Azatov, R

    A. Azatov, R. Contino, G. Panico and M. Son, Effective field theory analysis of double Higgs boson production via gluon fusion , Phys. Rev. D92 (2015) 035001 [1502.00539]

    2015 arXiv

  54. [61]

    Dawson, A

    S. Dawson, A. Ismail and I. Low, Whats in the loop? The anatomy of double Higgs production, Phys. Rev. D91 (2015) 115008 [ 1504.05596]

    2015 arXiv

  55. [63]

    Q.-H. Cao, B. Yan, D.-M. Zhang and H. Zhang, Resolving the Degeneracy in Single Higgs Production with Higgs Pair Production , Phys. Lett. B752 (2016) 285 [1508.06512]

    2016 arXiv

  56. [64]

    Q.-H. Cao, G. Li, B. Yan, D.-M. Zhang and H. Zhang, Double Higgs production at the 14 TeV LHC and a 100 TeV pp collider, Phys. Rev. D96 (2017) 095031 [1611.09336]

    2017 arXiv

  57. [65]

    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

  58. [66]

    Gr¨ ober, M

    R. Gr¨ ober, M. M¨ uhlleitner, M. Spira and J. Streicher,NLO QCD Corrections to – 31 – Higgs Pair Production including Dimension-6 Operators , JHEP 09 (2015) 092 [1504.06577]

    2015 arXiv

  59. [67]

    Gr¨ ober, M

    R. Gr¨ ober, M. M¨ uhlleitner and M. Spira,Signs of Composite Higgs Pair Production at Next-to-Leading Order, JHEP 06 (2016) 080 [ 1602.05851]

    2016 arXiv

  60. [68]

    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

  61. [69]

    Gr¨ ober, M

    R. Gr¨ ober, M. M¨ uhlleitner and M. Spira,Higgs Pair Production at NLO QCD for CP-violating Higgs Sectors , Nucl. Phys. B925 (2017) 1 [ 1705.05314]

    2017 arXiv

  62. [70]

    de Florian, I

    D. de Florian, I. Fabre and J. Mazzitelli, Higgs boson pair production at NNLO in QCD including dimension 6 operators , JHEP 10 (2017) 215 [ 1704.05700]

    2017 arXiv

  63. [71]

    Buchalla, M

    G. Buchalla, M. Capozi, A. Celis, G. Heinrich and L. Scyboz, Higgs boson pair production in non-linear Effective Field Theory with full mt-dependence at NLO QCD, JHEP 09 (2018) 057 [ 1806.05162]

    2018 arXiv

  64. [72]

    Carvalho, M

    A. Carvalho, M. Dall’Osso, P. De Castro Manzano, T. Dorigo, F. Goertz, M. Gouzevich et al., Analytical parametrization and shape classification of anomalous HH production in the EFT approach , 1608.06578

    arXiv

  65. [73]

    Carvalho, F

    A. Carvalho, F. Goertz, K. Mimasu, M. Gouzevitch and A. Aggarwal, On the reinterpretation of non-resonant searches for Higgs boson pairs , 1710.08261

    arXiv

  66. [74]

    https://www.scikit-learn.org

  67. [75]

    de Oliveira, M

    L. de Oliveira, M. Kagan, L. Mackey, B. Nachman and A. Schwartzman, Jet-images – deep learning edition, JHEP 07 (2016) 069 [ 1511.05190]

    2016 arXiv

  68. [76]

    Brehmer, K

    J. Brehmer, K. Cranmer, F. Kling and T. Plehn, Better Higgs boson measurements through information geometry, Phys. Rev. D95 (2017) 073002 [ 1612.05261]

    2017 arXiv

  69. [77]

    Brehmer, K

    J. Brehmer, K. Cranmer, G. Louppe and J. Pavez, Constraining Effective Field Theories with Machine Learning , Phys. Rev. Lett. 121 (2018) 111801 [ 1805.00013]

    2018 arXiv

  70. [78]

    Brehmer, K

    J. Brehmer, K. Cranmer, G. Louppe and J. Pavez, A Guide to Constraining Effective Field Theories with Machine Learning , Phys. Rev. D98 (2018) 052004 [ 1805.00020]

    2018 arXiv

  71. [79]

    Guest, J

    D. Guest, J. Collado, P. Baldi, S.-C. Hsu, G. Urban and D. Whiteson, Jet Flavor Classification in High-Energy Physics with Deep Neural Networks , Phys. Rev. D94 (2016) 112002 [ 1607.08633]

    2016 arXiv

  72. [80]

    Kasieczka, T

    G. Kasieczka, T. Plehn, M. Russell and T. Schell, Deep-learning Top Taggers or The End of QCD? , JHEP 05 (2017) 006 [ 1701.08784]

    2017 arXiv

  73. [81]

    Datta and A

    K. Datta and A. J. Larkoski, Novel Jet Observables from Machine Learning , JHEP 03 (2018) 086 [ 1710.01305]. – 32 –

    2018 arXiv

  74. [82]

    Louppe, K

    G. Louppe, K. Cho, C. Becot and K. Cranmer, QCD-Aware Recursive Neural Networks for Jet Physics , JHEP 01 (2019) 057 [ 1702.00748]

    2019 arXiv

  75. [83]

    A. J. Larkoski, I. Moult and B. Nachman, Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning , 1709.04464

    arXiv

  76. [84]

    Macaluso and D

    S. Macaluso and D. Shih, Pulling Out All the Tops with Computer Vision and Deep Learning, JHEP 10 (2018) 121 [ 1803.00107]

    2018 arXiv

  77. [85]

    Bollweg, M

    S. Bollweg, M. Haumann, G. Kasieczka, M. Luchmann, T. Plehn and J. Thompson, Deep-Learning Jets with Uncertainties and More , SciPost Phys. 8 (2020) 006 [1904.10004]

    2020 arXiv

  78. [86]

    Butter et al., The Machine Learning Landscape of Top Taggers , SciPost Phys

    A. Butter et al., The Machine Learning Landscape of Top Taggers , SciPost Phys. 7 (2019) 014 [ 1902.09914]

    2019 arXiv

  79. [87]

    Butter, T

    A. Butter, T. Plehn and R. Winterhalder, How to GAN LHC Events , SciPost Phys. 7 (2019) 075 [ 1907.03764]

    2019 arXiv

  80. [88]

    E. A. Moreno, O. Cerri, J. M. Duarte, H. B. Newman, T. Q. Nguyen, A. Periwal et al., JEDI-net: a jet identification algorithm based on interaction networks , Eur. Phys. J. C80 (2020) 58 [ 1908.05318]

    2020 arXiv

  81. [89]

    Y.-C. J. Chen, C.-W. Chiang, G. Cottin and D. Shih, BoostedW/Z Tagging with Jet Charge and Deep Learning, 1908.08256

    1908 arXiv

  82. [90]

    Chang, K

    J. Chang, K. Cheung, J. S. Lee and J. Park, Probing the trilinear Higgs boson self-coupling at the high-luminosity LHC via multivariate analysis , Phys. Rev. D101 (2020) 016004 [ 1908.00753]

    2020 arXiv

  83. [91]

    Carrazza and J

    S. Carrazza and J. Cruz-Martinez, Towards a new generation of parton densities with deep learning models, Eur. Phys. J. C79 (2019) 676 [ 1907.05075]

    2019 arXiv

  84. [92]

    Hajer, Y.-Y

    J. Hajer, Y.-Y. Li, T. Liu and H. Wang, Novelty Detection Meets Collider Physics , 1807.10261

    arXiv

  85. [93]

    De Simone and T

    A. De Simone and T. Jacques, Guiding New Physics Searches with Unsupervised Learning, Eur. Phys. J. C79 (2019) 289 [ 1807.06038]

    2019 arXiv

  86. [94]

    Andreassen, I

    A. Andreassen, I. Feige, C. Frye and M. D. Schwartz, JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics , Eur. Phys. J. C79 (2019) 102 [1804.09720]

    2019 arXiv

  87. [95]

    R. T. D’Agnolo and A. Wulzer, Learning New Physics from a Machine , Phys. Rev. D99 (2019) 015014 [ 1806.02350]

    2019 arXiv

  88. [96]

    Chang, T

    S. Chang, T. Cohen and B. Ostdiek, What is the Machine Learning? , Phys. Rev. D97 (2018) 056009 [ 1709.10106]. – 33 –

    2018 arXiv

  89. [97]

    Englert, P

    C. Englert, P. Galler, P. Harris and M. Spannowsky, Machine Learning Uncertainties with Adversarial Neural Networks , Eur. Phys. J. C79 (2019) 4 [ 1807.08763]

    2019 arXiv

  90. [98]

    Blance, M

    A. Blance, M. Spannowsky and P. Waite, Adversarially-trained autoencoders for robust unsupervised new physics searches , JHEP 10 (2019) 047 [ 1905.10384]

    2019 arXiv

  91. [99]

    Brehmer, S

    J. Brehmer, S. Dawson, S. Homiller, F. Kling and T. Plehn, Benchmarking simplified template cross sections in WH production, JHEP 11 (2019) 034 [ 1908.06980]

    2019 arXiv

  92. [100]

    F. F. Freitas, C. K. Khosa and V. Sanz, Exploring the standard model EFT in VH production with machine learning , Phys. Rev. D100 (2019) 035040 [ 1902.05803]

    2019 arXiv

  93. [101]

    Buchalla, O

    G. Buchalla, O. Cata, A. Celis and C. Krause, Note on Anomalous Higgs-Boson Couplings in Effective Field Theory , Phys. Lett. B750 (2015) 298 [ 1504.01707]

    2015 arXiv

  94. [102]

    Berthier and M

    L. Berthier and M. Trott, Towards consistent Electroweak Precision Data constraints in the SMEFT , JHEP 05 (2015) 024 [ 1502.02570]

    2015 arXiv

  95. [103]

    Brivio, Y

    I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools , JHEP 12 (2017) 070 [ 1709.06492]

    2017 arXiv

  96. [104]

    C. Arzt, M. B. Einhorn and J. Wudka, Patterns of deviation from the standard model , Nucl. Phys. B433 (1995) 41 [ hep-ph/9405214]

    1995 arXiv

  97. [105]

    Butterworth et al., PDF4LHC recommendations for LHC Run II , J

    J. Butterworth et al., PDF4LHC recommendations for LHC Run II , J. Phys. G43 (2016) 023001 [ 1510.03865]

    2016 arXiv

  98. [106]

    CMS collaboration, A. M. Sirunyan et al., Measurement and interpretation of differential cross sections for Higgs boson production at √s = 13 TeV, Phys. Lett. B792 (2019) 369 [ 1812.06504]

    2019 arXiv

  99. [108]

    https://www.tensorflow.org

  100. [109]

    D. P. Kingma and J. Ba, Adam: A Method for Stochastic Optimization , 1412.6980

    arXiv

  101. [110]

    Kullback, Information Theory and Statistics

    S. Kullback, Information Theory and Statistics . John Wiley & Sons. Republished by Dover Publications, 1978. – 34 –

    1978

Pith tools

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