Pith. sign in

REVIEW 4 major objections 5 minor 2 cited by

Experimental Determination of BSM Triple Higgs Couplings at the HL-LHC with Neural Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The paper claims that a small neural network can read the product of a heavy Higgs boson's top-Yukawa coupling and its trilinear coupling to two light Higgses from the HL-LHC di-Higgs mass spectrum, reaching 10--20% precision with…

desk verdict A solid simulation-based sensitivity study showing a small NN beats a grid MLE for extracting a BSM triple-Higgs coupling, but the title's 'experimental determination' overstates what a statistical-only projection can support. read the letter →

arxiv 2506.18981 v1 pith:DOEN2AYI submitted 2025-06-23 hep-ph

Markus Frank , Sven Heinemeyer , Margarete Mühlleitner , Kateryna Radchenko This is my paper · ORCID
classification hep-ph
keywords Higgspairproductiontrilinearcouplingtwo-Higgs-doubletmodelneuralnetworkHL-LHCinvariantmassdistributionmaximumlikelihoodestimationbeyond-Standard-Modelsector
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 claims that the product of the top-Yukawa coupling of a heavy CP-even Higgs boson and its trilinear coupling to two 125 GeV Higgs bosons, $\xi_H^t \times \lambda_{hhH}$, can be extracted from the invariant-mass spectrum of Higgs pairs at the HL-LHC using a small neural network. This product controls the resonant $H$ contribution to gluon-fusion di-Higgs production, where it creates a dip-peak or peak-dip interference structure around $m_H$ that ordinary fits struggle to read. Training on 16-bin histograms that include 15% mass smearing, 50 GeV binning, and Poisson fluctuations, the network predicts the coupling product more accurately than maximum-likelihood estimation, including its sign. Assuming the $b\bar b\, b\bar b$ final state, $3\,\text{ab}^{-1}$ of data, and improved detector efficiencies, the paper projects a determination at the 10--20% level by the end of the HL-LHC. The result matters because it is the first machine-learning sensitivity study for a beyond-Standard-Model trilinear Higgs coupling, a quantity tied to the shape of the Higgs potential.

What carries the argument

The machinery is the resonant interference structure in the di-Higgs invariant-mass distribution $m_{hh}$: the $s$-channel exchange of a heavy CP-even scalar $H$ interferes with the continuum box and light-Higgs diagrams, producing a dip-peak or peak-dip feature at $m_{hh}\approx m_H$ whose orientation encodes the sign of $\xi_H^t\times\lambda_{hhH}$. The paper converts that shape into a regression problem for a small neural network: batch normalization, one hidden layer of 64 ReLU neurons, a linear output, Adam optimization, and mean-squared-error loss, trained on 16-bin histograms (50 GeV bins) after 15% Gaussian smearing in $m_{hh}$ and Poisson resampling of event counts. The 95% confidence interval of the absolute error, $AE_{95}$, is the metric used to compare methods and training sets. This construction is what lets the network learn the coupling product from the spectrum, including the sign, without bin aggregation.

What would settle it

Compute the network's $AE_{95}$ on pseudo-experiments generated with a full detector simulation that adds correlated per-bin systematic shifts of a few percent to the $b\bar b\, b\bar b$ event counts at 3000 fb$^{-1}$; if the 95% confidence interval for $\xi_H^t\times\lambda_{hhH}$ widens beyond roughly 0.045 for the $1\sigma$-trained network, or beyond the reported 10--20% at improved efficiencies, the central projection is contradicted.

Watch

Extended reading notes

Core claim

The central claim is that a deliberately simple one-hidden-layer neural network can infer $\xi_H^t \times \lambda_{hhH}$ from the shape of the $m_{hh}$ distribution in $gg\to hh$ production, in a Type I 2HDM benchmark with $m_H=450$ GeV that satisfies theoretical and experimental constraints. The network takes as input the 16 bins of a smeared and binned $m_{hh}$ histogram and outputs the coupling product; during training each input is re-sampled with Poisson noise matching the expected event counts in the $b\bar b\, b\bar b$ channel at 3000 fb$^{-1}$. Compared with maximum-likelihood estimation, the NN gives smaller 95% CL errors, resolves the sign of the product, and can serve simultaneously for hypothesis testing and parameter estimation. The paper reports sensitivity ranges of about $0.045$ for the NN versus about $0.076$--$0.080$ for MLE, and finds that training on additional Poisson smearing of about $2\sigma$ improves robustness. With a hypothetical factor-of-four improvement in experimental efficiencies, the projected precision reaches 10--20%; only statistical uncertainties are included, with systematics left out as beyond the scope.

Load-bearing premise

The load-bearing premise is that systematic uncertainties in the measured invariant-mass spectrum are smaller than the statistical fluctuations; the analysis includes only Poisson statistics and explicitly leaves systematics out because they are harder to estimate, so if real systematics are comparable the 10--20% claim does not follow.

Editorial extensions

If this is right

  • If the projection holds, $\xi_H^t\times\lambda_{hhH}$ becomes a measurable target of HL-LHC Higgs-pair programs, not just a model parameter, with 10--20% precision when efficiencies improve by a factor of four.
  • The neural network outperforms maximum-likelihood estimation for parameter estimation and matches the classical $p$-value test for hypothesis testing, so a single trained network can replace both steps.
  • Uncertainties in $m_H$ and $m_{12}^2$ can be absorbed by training: including $m_H$ values spanning twice the expected measurement uncertainty keeps the prediction accurate, and freeing $m_{12}^2$ can even improve performance.
  • The method transfers to any model with a heavy CP-even scalar resonance in $gg\to hh$, since the trained quantity and the mass shape are defined model-independently once the resonance is present.
  • Training on data smeared to about $2\sigma$ Poisson fluctuations yields better predictions at 95% CL than training at $1\sigma$, indicating a dedicated noise-augmentation strategy improves the extraction.

Reading between the lines

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

  • A multi-channel extension the paper leaves implicit would feed NN inputs from $b\bar b\gamma\gamma$ and $b\bar b\tau^+\tau^-$ alongside $b\bar b\, b\bar b$; the per-channel statistical dilution suggests a combined network could reach the low end of the 10--20% band or better.
  • Because the network resolves the sign of the coupling product, the same regression could be adapted to measure the CP properties of the heavy scalar, since a CP-violating admixture would reshape the interference pattern in $m_{hh}$ in a way a binned likelihood fit would miss.
  • A testable generalization is to regress jointly on $m_H$ and $\xi_H^t\times\lambda_{hhH}$ rather than fixing $m_H=450$ GeV, letting the position of the dip-peak structure and its distortion be learned together; this would turn the method into a resonance search and parameter measurement in one step.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript presents a machine-learning-based sensitivity study for extracting the product of the heavy-Higgs top-Yukawa coupling modifier and the BSM trilinear coupling, ξ_H^t × λ_hhH, from the invariant mass distribution of gg→hh at the HL-LHC. The study is set in the Type I 2HDM with m_H = 450 GeV, using HPAIR predictions, with 15% Gaussian smearing and 50 GeV binning, and Poisson fluctuations derived from expected b bbar b bbar event counts with ATLAS efficiencies at 3000 fb^-1. A single-hidden-layer neural network is trained on simulated m_hh histograms and compared with maximum-likelihood template estimation and a likelihood-ratio goodness-of-fit test. The authors report that the NN outperforms the classical methods and claim that a 10-20% determination of the coupling product may be achievable by the end of the HL-LHC if efficiencies improve.

Significance. The paper is a useful proof-of-principle: it gives a fully specified benchmark plane with public tools, cross-validated interpolation checks, an explicit comparison metric (AE95), and appendices quantifying grid-size and architecture effects. It is, however, an idealized simulation study rather than a validated experimental projection. The central quantitative claim depends on assumptions—statistical-only uncertainties, specific efficiencies, known m_H, and a single underlying model—that are not tested against independent data. The main value is in demonstrating that a small NN can perform regression on binned m_hh spectra more precisely than a discrete template maximum-likelihood fit, provided the training and test data are generated from the same model.

major comments (4)
  1. [Sec. 2.6 and Sec. 6] The headline claim of a 10-20% 'experimental determination' is conditional on an uncertainty model that includes only Poisson statistics. Section 2.6 explicitly defers theoretical and systematic uncertainties ('harder to estimate', 'optimistic scenario'), and Section 6 repeats that systematics are beyond scope. The manuscript does not quantify b-tagging efficiency uncertainties, m_hh scale/calibration uncertainties, background contamination, or theory uncertainties on the m_hh template. The precision in Sec. 5.5 therefore follows only if all of these are subdominant, which is an unvalidated external assumption. The title and abstract should be revised to present this as an idealized sensitivity study with explicit caveats, or the systematics must be incorporated.
  2. [Sec. 4, Sec. 5.1, Sec. 5.3] Training and evaluation are performed on Poisson-smeared distributions generated from the same 2HDM parameter plane (e.g., the 4-fold split in Sec. 5.1 and the 256 test histograms in Sec. 5.3). This is an in-model interpolation check, not a validation against independent data. The paper acknowledges model dependence in Sec. 6, but the abstract's 'Experimental Determination' claim is much stronger than what the setup can establish. A closure test with out-of-model distributions (e.g., an EFT parameterization or a different scalar sector) or a clear statement that the result is only an internal consistency check is needed before the experimental claim can be sustained.
  3. [Sec. 5.4 and Sec. 5.5] The '10-20% level' precision is never defined quantitatively. The only precision metric, AE95, is an absolute error at 95% CL, and the quoted sensitivity ranges in Eqs. (11)-(13) are absolute thresholds on ξ_H^t × λ_hhH. No relative-error distribution or AE95 divided by |ξ_true| is shown. For the example in Sec. 5.3, the AE95 near ξ ≈ ±0.03-0.05 is comparable to the value itself, which would correspond to 60-100% relative error rather than 10-20%. The improved-efficiency results in Fig. 20 are shown only as scatter/density plots. Please state precisely which interval (e.g., 68% or 95% CL on |pred-θ|/|θ| over a specified θ range) supports the 10-20% claim and give the corresponding numbers.
  4. [Appendix A] The grid-size check in Table 2 reports deviations Δ of 12%, 8%, and 6% for three points with small ξ, yet the text concludes that the effect is at the 'few percent level'. These deviations are comparable to or larger than the claimed 10-20% precision, and the coarser grid is used throughout. Since the authors themselves interpret the grid coarseness as a source of theoretical uncertainty, this internal check actually weakens the precision claim unless the grid-induced error is included in the reported uncertainty budget.
minor comments (5)
  1. [Sec. 3, Eq. (8)] The text states that H1 is the full 2HDM prediction including the resonance, but the expression for L(H1) uses the observed counts n_i as the mean (the saturated model). Please reconcile the wording with the formula and justify the number of degrees of freedom used in the χ² approximation.
  2. [Sec. 2.6, Eq. (7)] The notation σ_i is described as the differential cross section times bin size; please make this explicit in the equation and in the units of N_i.
  3. [Sec. 3, Fig. 8] The claim that MLE 'manages to determine if ξ ≠ 0' while being unable to predict the sign is not evident from the X-shaped scatter plot; please clarify what property of the plot supports the first part of this statement.
  4. [Sec. 5.4, Fig. 18] The contours and color coding are difficult to compare; consider adding a legend that lists the AE95 thresholds for each contour line.
  5. [Throughout] There are minor typos, including 'the a χ2-distributed variable' in Sec. 3, 'T able 2' in the Appendix A header, and inconsistent spacing in reference [29].

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the NN sensitivity study is an internally validated simulation projection; self-citations are contextual and the 10-20% claim is explicitly conditional on a statistical-only uncertainty model.

full rationale

The NN-analysis chain is not circular. The m_hh templates are produced by HPAIR (external), the allowed parameter plane by thdmTools/HiggsTools (external), and the efficiencies entering Eq. (7) are taken from the ATLAS bbbb analysis [59]. The network is trained on a subset of simulated histograms labeled with xi_H^t * lambda_hhH and evaluated on held-out histograms drawn with fresh Poisson noise; the test performance thus measures the learnability/invertibility of the forward simulation, which is the standard design of a collider sensitivity projection rather than a reduction of the output to the input. The paper does not claim to have used real data, and the '10-20% determination' is explicitly conditional: Sec. 2.6 keeps only statistical uncertainties because theoretical and systematic uncertainties are 'harder to estimate' and 'in an optimistic scenario should be subdominant', and Sec. 6 repeats that systematics are beyond the scope. That is an external-validity caveat, not a circular step. The self-citations [29,35] (overlapping authors) motivate the dip-peak structure and the smearing/binning choices, but the distributions are recomputed in Figs. 3-4, the smearing/binning values are independently attributed to the LHC Higgs working group, and the efficiencies come from ATLAS; hence the self-citations are contextual rather than load-bearing. Overall, no derivation step reduces to its own input by construction, so the correct finding is no significant circularity (band 0-2). The modest score of 2 reflects the presence of minor non-load-bearing self-citations, not a circular reduction.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central result rests on the 2HDM framework, the HPAIR shape prediction, and a set of assumed detector parameters: t_beta, c_beta-alpha, m2_12, the 15% smearing, the 50 GeV binning, and the ATLAS efficiencies are all inputs. The neural network introduces no new physics entity; it is a regression fitted to theory-generated templates.

free parameters (7)
  • m_H (heavy CP-even Higgs mass) = 450 GeV
    Assumed to be measured in a different process; the NN is trained for m_H = 450 GeV, with additional planes in Models II-IV to control the uncertainty.
  • t_beta and c_beta-alpha = scanned over the allowed benchmark plane
    The two main free 2HDM parameters varied in the scan; the central claim concerns the ability to extract a function of these parameters from m_hh shapes.
  • m2_12 fixing relation = m2_12 = m_H^2 cos^2(alpha) / t_beta (Eq. 6)
    An ad hoc relation used to define the benchmark plane; it is also varied as a free parameter in dataset (2).
  • Detector smearing width = 15%
    Assumed Gaussian resolution on m_hh recommended by the LHC Higgs working group; directly affects whether the dip-peak structure remains visible after smearing.
  • Binning size = 50 GeV
    Assumed experimental bin width, yielding 16 input bins; coarser binning would further dilute the resonance shape.
  • Detector efficiencies = epsilon_TOT = 17.3%, epsilon_SR = 1%
    Taken from ATLAS [59] for the bbbb channel; the event counts and hence statistical errors scale directly with these efficiencies.
  • NN architecture and training choices = 1 hidden layer, 64 neurons, Adam lr=1e-4, 2^15 epochs
    Chosen by hand after testing; the reported performance depends on these choices, though they are not physical parameters.
assumptions (5)
  • domain assumption The CP-conserving 2HDM Type I with softly broken Z2 symmetry is the correct framework for BSM di-Higgs production at the HL-LHC.
    The entire analysis generates templates from HPAIR for this model; if nature realizes a different scalar sector, the trained NN and the extracted coupling lose their meaning.
  • domain assumption NLO QCD corrections in the heavy-top limit implemented in HPAIR are sufficiently accurate for the m_hh shape.
    The paper relies on HPAIR for theoretical predictions and explicitly does not include loop corrections to the THCs; the quoted precision is conditional on the shape prediction being reliable.
  • standard math Wilks' theorem applies to the Poisson likelihood ratio with the aggregated bins.
    Used in Sec. 3 to convert the likelihood ratio into a p-value; the paper aggregates bins to keep counts above 4, which is below the usual rule-of-thumb of 5.
  • domain assumption Event counts in each m_hh bin follow a Poisson distribution around the theory mean.
    Sec. 2.6 models statistical uncertainty as sqrt(N_i) and uses Poisson smearing in the training and test data; this is standard in particle physics but an idealization of detector counting statistics.
  • ad hoc to paper The m_hh detector resolution is a Gaussian with 15% width and the bin size is 50 GeV.
    These values are recommended by the LHC Higgs working group but are not derived from the actual ATLAS or CMS resolution functions; they directly determine how much of the resonance structure survives.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Experimental Determination of BSM Triple Higgs Couplings at the HL-LHC with Neural Networks." pith.science (2026). https://pith.science/paper/DOEN2AYI

@misc{pith2026250618981,
  author       = {Pith},
  title        = {Pith review of: Experimental Determination of BSM Triple Higgs Couplings at the HL-LHC with Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DOEN2AYI}},
  note         = {Machine review of arXiv:2506.18981}
}
abstract

The shape of the Higgs potential is modified by the presence of additional scalar fields, as predicted in many Beyond-Standard-Model (BSM) scenarios. In such cases, deviations in the Higgs self-interactions, in particular the trilinear Higgs couplings, could serve to disentangle the physics beyond the Standard Model (SM). While the SM predicts only one trilinear Higgs coupling, extended scalar sectors allow for additional self-interactions that can manifest themselves in Higgs pair production, via the $s$-channel contribution of a heavy $\mathcal{CP}$-even scalar $H$. We present the first sensitivity study to such a BSM trilinear scalar coupling using machine learning. Specifically, we train a neural network on the invariant mass distributions of Higgs pair production at the HL-LHC to extract $\xi_H^t \times \lambda_{hhH}$, i.e. the product of the resonant $H$ top-Yukawa coupling and the trilinear coupling of $H$ to the two SM-like Higgses in the final state, $hh$. Assuming a hypothetical $H$ mass of 450 GeV, we show that, depending on future experimental efficiencies and uncertainties, a determination of $\xi_H^t \times \lambda_{hhH}$ at the 10-20% level may be achievable by the end of the HL-LHC. We present a simple and more efficient alternative to classical statistical methods, proving the efficiency of neural networks for both hypothesis testing and parameter estimation, which outperforms conventional maximum likelihood methods in this context.

Figures

Figures reproduced from arXiv: 2506.18981 by the authors.

Figure 1
Figure 1. Leading-order diagrams to 2HDM SM-like Higgs pair production in the gluon fusion process at hadron colliders. For the theoretical prediction of the Higgs pair production cross section we use the code HPAIR [36, 37] adapted for the 2HDM, which also computes the invariant mass distribution of the two light Higgses hh in the final state, mhh. It allows to include next-to-leading-order QCD corrections in the heavy-top l… view at source ↗
Figure 2
Figure 2. ξ t H × λhhH in the example benchmark plane in the Type I 2HDM with mϕ = 450 GeV and m2 12 fixed via Eq. (6). Black lines are located at ξ t H × λhhH = 0, either because λhhH =0 (in the alignment limit, i.e. the vertical line, and the lower curved line on the right upper corner) or because ξ t H = 0 (the upper line on the right corner). The blue cross indicates an example point whose mhh distribution is displayed in… view at source ↗
Figure 3
Figure 3. Smearing (left) and binning (right) applied to the invariant mass distribution prediction for an example benchmark point in the 2HDM, marked in blue in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (19 more)
Figure 4
Figure 4. Figure 4: Comparison of two benchmark points yielding a positive (blue) and negative (red) value of ξ t H × λhhH with ξ t H × λhhH ≈ ±0.03. The blue (red) curve corresponds to the point marked by a blue (yellow) cross in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Example number of events in the b ¯b b¯b channel with statistical error bars (see text) for the point marked by the blue cross in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Sample distributions for the number of events with the original 50 GeV binning (left) and the aggregated bins (right). Shown are the distributions for the SM (blue), and two examples with a small value of ξ t H × λhhH = 0.0188 (orange), and with a large value, ξ t H × …
Figure 7
Figure 7. Figure 7: p-value in the example benchmark plane. The red regions shows the parameters points where the p-value is larger than 0.05, i.e. the null hypothesis cannot be rejected. The blue colored points represent the region where the null hypothesis can be tested with classical m…
Figure 8
Figure 8. Figure 8: Predicted value of ξ t H × λhhH with the classical maximum likelihood estimation method versus the theoretical value of ξ t H × λhhH [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Workflow (left) and NN architecture (right) (see text for details). It is worth to note that in our approach, the NN has been trained completely on parameter points of the 2HDM. However, we expect similar results from models where the di-Higgs production process is res…
Figure 10
Figure 10. Figure 10: Upper row: ξ t H × λhhH in the allowed region of the original benchmark plane with mH = mH± = mA = 450 GeV and m2 12 = m2 H cos α 2/tβ, projected in the three possible dimensions → planes. Lower row: same of the above → Same as upper row, but for all theoretically all…
Figure 11
Figure 11. Figure 11: Prediction of ξ t H ×λhhH in the original benchmark plane (left) and the three dimensional benchmark plane with mϕ = 450 GeV and tβ, cβ−α, and m2 12 as free parameters (right). Model I: only the example benchmark plane in [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Results of our NN analysis for ξ t H × λhhH in Model-I, -II, -III, -IV in the upper left, upper right, lower left and lower right plot, respectively. The blue (orange) points show the results for mH = 443(457) GeV (see text). The gray line is there to guide the eye an…
Figure 13
Figure 13. Figure 13: Prediction of ξ t H × λhhH for points with mH = 450 GeV with the mhh distributions statistically smeared according to their respective Poisson distributions. We show the results in a scatter plot (left) and a density plot (right), where in the latter case the color re…
Figure 14
Figure 14. Figure 14: Examples of invariant mass distributions of the point marked by a cyan cross in [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: Prediction of ξ t H × λhhH for points with mH = 450 GeV with the mhh distributions statistically smeared according to twice their respective Poisson distributions. The color coding is as in [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]
Figure 16
Figure 16. Figure 16: Predictions for statistically smeared data. Upper row for free m2 12 and lower row for mH = 443 GeV (as a test case) employing Model IV [PITH_FULL_IMAGE:figures/full_fig_p022_16.png]
Figure 17
Figure 17. Figure 17: Comparison of the AE95 with MLE (left) and NN (right) depending on the value of ξ t H × λhhH. the crossing points between the blue and gray lines in [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]
Figure 18
Figure 18. Figure 18: Comparison between the NN and the classical MLE approach. We can also use these intervals to compare the regions of the original plane that can be probed with both methods. This region is shown in [PITH_FULL_IMAGE:figures/full_fig_p023_18.png]
Figure 19
Figure 19. Figure 19: AE95 for the different datasets employed. Dataset 1 refers to the original benchmark plane, dataset 2 to the plane with m2 12 free and dataset 3 is the one with the uncertainty in the value of mH. in the NN determination of ξ t H × λhhH in the case that each of the tw…
Figure 20
Figure 20. Figure 20: Same as [PITH_FULL_IMAGE:figures/full_fig_p026_20.png]
Figure 21
Figure 21. Figure 21: NN prediction of ξ t H × λhhH for the different datasets: (1) upper, (2) middle and (3) lower row. 29 [PITH_FULL_IMAGE:figures/full_fig_p030_21.png]
Figure 22
Figure 22. Figure 22: AE95 for different NN architectures. The one employed in this project is the simplest 1-hidden layer network with 64 neurons (blue), the more complex architectures include 2- and 4-hidden layer networks with 128 neurons each, shown in green and purple, respectively. R…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. An analytic result for the $0 \to ggHHH$ amplitude

    hep-ph 2025-07 conditional novelty 7.0 of 10

    The authors present the complete leading-order one-loop amplitude for gg to HHH in closed analytic form, with full top and bottom quark mass dependence, validated against two independent numerical programs.

  2. Complementarity of gravitational wave analyses and di-Higgs production in the exploration of the Electroweak Phase Transition dynamics in the RxSM

    hep-ph 2025-10 conditional novelty 6.0 of 10

    In the real singlet extension of the SM, strong first-order electroweak phase transitions split into singlet-driven transitions (loud in gravitational waves, quiet at colliders) and doublet-driven transitions (visible...

Reference graph

Works this paper leans on

59 extracted references · 6 canonical work pages · cited by 2 Pith papers

  1. [29]

    F. Arco, S. Heinemeyer, M. M¨ uhlleitner and K. Radchenko,Sensitivity to triple Higgs couplings via di-Higgs production in the 2HDM at the (HL-)LHC,Eur. Phys. J. C83(2023) 1019 [2212.11242]

    arXiv 2023

  2. [1]

    ATLAScollaboration,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,Phys. Lett. B716(2012) 1 [1207.7214]. [2]CMScollaboration,Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,Phys. Lett. B716(2012) 30 [1207.7235]. [3]ATLAS, CMScollaboration,Measurements of t...

    arXiv 2012

  3. [4]

    de Blas et al.,Higgs Boson Studies at Future Particle Colliders,JHEP01(2020) 139 [1905.03764]

    J. de Blas et al.,Higgs Boson Studies at Future Particle Colliders,JHEP01(2020) 139 [1905.03764]

    arXiv 2020

  4. [5]

    ATLAScollaboration,A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery,Nature607(2022) 52 [2207.00092]

    arXiv 2022

  5. [6]

    CMScollaboration,A portrait of the Higgs boson by the CMS experiment ten years after the discovery., Nature607(2022) 60 [2207.00043]

    arXiv 2022

  6. [7]

    Abouabid, A

    H. Abouabid, A. Arhrib, D. Azevedo, J.E. Falaki, P.M. Ferreira, M. M¨ uhlleitner et al.,Benchmarking di-Higgs production in various extended Higgs sector models,JHEP09(2022) 011 [2112.12515]

    arXiv 2022

  7. [8]

    Cline and P.-A

    J.M. Cline and P.-A. Lemieux,Electroweak phase transition in two Higgs doublet models,Phys. Rev. D 55(1997) 3873 [hep-ph/9609240]

    arXiv 1997

  8. [9]

    Fromme, S.J

    L. Fromme, S.J. Huber and M. Seniuch,Baryogenesis in the two-Higgs doublet model,JHEP11(2006) 038 [hep-ph/0605242]

    arXiv 2006

Show all 59 references
  1. [10]

    Cline, K

    J.M. Cline, K. Kainulainen and M. Trott,Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies,JHEP11(2011) 089 [1107.3559]

    2011 arXiv

  2. [11]

    Dorsch, S.J

    G.C. Dorsch, S.J. Huber, T. Konstandin and J.M. No,A Second Higgs Doublet in the Early Universe: Baryogenesis and Gravitational Waves,JCAP05(2017) 052 [1611.05874]

    2017 arXiv

  3. [12]

    Kajantie, M

    K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov,Is there a hot electroweak phase transition atm H ≳m W ?,Phys. Rev. Lett.77(1996) 2887 [hep-ph/9605288]

    1996 arXiv

  4. [13]

    Dorsch, S.J

    G.C. Dorsch, S.J. Huber and J.M. No,A strong electroweak phase transition in the 2HDM after LHC8, JHEP10(2013) 029 [1305.6610]

    2013 arXiv

  5. [14]

    Dorsch, S.J

    G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No,Echoes of the Electroweak Phase Transition: 30 Discovering a second Higgs doublet throughA 0→ZH 0,Phys. Rev. Lett.113(2014) 211802 [1405.5537]

    2014 arXiv

  6. [15]

    Basler, M

    P. Basler, M. Krause, M. Muhlleitner, J. Wittbrodt and A. Wlotzka,Strong First Order Electroweak Phase Transition in the CP-Conserving 2HDM Revisited,JHEP02(2017) 121 [1612.04086]

    2017 arXiv

  7. [16]

    Dorsch, S.J

    G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No,The Higgs Vacuum Uplifted: Revisiting the Electroweak Phase Transition with a Second Higgs Doublet,JHEP12(2017) 086 [1705.09186]

    2017 arXiv

  8. [17]

    Basler, M

    P. Basler, M. M¨ uhlleitner and J. Wittbrodt,The CP-Violating 2HDM in Light of a Strong First Order Electroweak Phase Transition and Implications for Higgs Pair Production,JHEP03(2018) 061 [1711.04097]

    2018 arXiv

  9. [18]

    Gon¸ calves, A

    D. Gon¸ calves, A. Kaladharan and Y. Wu,Electroweak phase transition in the 2HDM: Collider and gravitational wave complementarity,Phys. Rev. D105(2022) 095041 [2108.05356]

    2022 arXiv

  10. [19]

    Biek¨ otter, S

    T. Biek¨ otter, S. Heinemeyer, J.M. No, M.O. Olea-Romacho and G. Weiglein,The trap in the early Universe: impact on the interplay between gravitational waves and LHC physics in the 2HDM,JCAP03 (2023) 031 [2208.14466]

    2023 arXiv

  11. [20]

    Caprini et al.,Science with the space-based interferometer eLISA

    C. Caprini et al.,Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions,JCAP04(2016) 001 [1512.06239]

    2016 arXiv

  12. [21]

    Caprini et al.,Detecting gravitational waves from cosmological phase transitions with LISA: an update,JCAP03(2020) 024 [1910.13125]

    C. Caprini et al.,Detecting gravitational waves from cosmological phase transitions with LISA: an update,JCAP03(2020) 024 [1910.13125]. [22]LISA Cosmology Working Groupcollaboration,Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and phy...

    2020 arXiv

  13. [23]

    Lee,A theory of spontaneous t violation,Phys

    T. Lee,A theory of spontaneous t violation,Phys. Rev. D8(1973) 1226

    1973

  14. [24]

    Gunion, H.E

    J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,The Higgs Hunter’s Guide, vol. 80 (2000)

    2000

  15. [25]

    M. Aoki, S. Kanemura, K. Tsumura and K. Yagyu,Models of Yukawa interaction in the two Higgs doublet model, and their collider phenomenology,Phys. Rev. D80(2009) 015017 [0902.4665]

    2009 arXiv

  16. [26]

    Branco, P.M

    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,Theory and phenomenology of two-Higgs-doublet models,Phys. Rept.516(2012) 1 [1106.0034]

    2012 arXiv

  17. [27]

    Plehn, A

    T. Plehn, A. Butter, B. Dillon, T. Heimel, C. Krause and R. Winterhalder,Modern Machine Learning for LHC Physicists,2211.01421

    arXiv

  18. [28]

    Feickert and B

    M. Feickert and B. Nachman,A Living Review of Machine Learning for Particle Physics, 2102.02770

    arXiv

  19. [30]

    Gunion and H.E

    J.F. Gunion and H.E. Haber,The CP conserving two Higgs doublet model: The Approach to the decoupling limit,Phys. Rev. D67(2003) 075019 [hep-ph/0207010]

    2003 arXiv

  20. [31]

    Kanemura, S

    S. Kanemura, S. Kiyoura, Y. Okada, E. Senaha and C.P. Yuan,New physics effect on the Higgs selfcoupling,Phys. Lett. B558(2003) 157 [hep-ph/0211308]

    2003 arXiv

  21. [32]

    Kanemura, Y

    S. Kanemura, Y. Okada, E. Senaha and C.P. Yuan,Higgs coupling constants as a probe of new physics, Phys. Rev. D70(2004) 115002 [hep-ph/0408364]

    2004 arXiv

  22. [33]

    Nhung, M

    D.T. Nhung, M. Muhlleitner, J. Streicher and K. Walz,Higher Order Corrections to the Trilinear Higgs Self-Couplings in the Real NMSSM,JHEP11(2013) 181 [1306.3926]

    2013 arXiv

  23. [34]

    Borschensky, T.N

    C. Borschensky, T.N. Dao, M. Gabelmann, M. M¨ uhlleitner and H. Rzehak,The trilinear Higgs self-couplings atO(α 2 t )in the CP-violating NMSSM,Eur. Phys. J. C83(2023) 118 [2210.02104]

    2023 arXiv

  24. [35]

    Heinemeyer, M

    S. Heinemeyer, M. M¨ uhlleitner, K. Radchenko and G. Weiglein,Higgs Pair Production in the 2HDM: Impact of Loop Corrections to the Trilinear Higgs Couplings and Interference Effects on Experimental Limits,2403.14776

    arXiv

  25. [36]

    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]. 31

    1996 arXiv

  26. [37]

    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

  27. [38]

    Djouadi, W

    A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas,Production of neutral Higgs boson pairs at LHC,Eur. Phys. J. C10(1999) 45 [hep-ph/9904287]

    1999 arXiv

  28. [39]

    Arhrib, R

    A. Arhrib, R. Benbrik, C.-H. Chen, R. Guedes and R. Santos,Double Neutral Higgs production in the Two-Higgs doublet model at the LHC,JHEP08(2009) 035 [0906.0387]

    2009 arXiv

  29. [40]

    Asakawa, D

    E. Asakawa, D. Harada, S. Kanemura, Y. Okada and K. Tsumura,Higgs boson pair production in new physics models at hadron, lepton, and photon colliders,Phys. Rev. D82(2010) 115002 [1009.4670]

    2010 arXiv

  30. [41]

    Grober, M

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

    2017 arXiv

  31. [42]

    Basler, S

    P. Basler, S. Dawson, C. Englert and M. M¨ uhlleitner,Di-Higgs boson peaks and top valleys: Interference effects in Higgs sector extensions,Phys. Rev. D101(2020) 015019 [1909.09987]

    2020 arXiv

  32. [43]

    Baglio, F

    J. Baglio, F. Campanario, S. Glaus, M. M¨ uhlleitner, J. Ronca and M. Spira,Full NLO QCD predictions for Higgs-pair production in the 2-Higgs-doublet model,Eur. Phys. J. C83(2023) 826 [2303.05409]

    2023 arXiv

  33. [44]

    Biek¨ otter, S

    T. Biek¨ otter, S. Heinemeyer, J.M. No, K. Radchenko, M.O.O. Romacho and G. Weiglein,First shot of the smoking gun: probing the electroweak phase transition in the 2HDM with novel searches for A→ZH inℓ +ℓ−ttandννb bfinal states,JHEP01(2024) 107 [2309.17431]

    2024 arXiv

  34. [45]

    H. Bahl, T. Biek¨ otter, S. Heinemeyer, C. Li, S. Paasch, G. Weiglein et al.,HiggsTools: BSM scalar phenomenology with new versions of HiggsBounds and HiggsSignals,Comput. Phys. Commun.291 (2023) 108803 [2210.09332]

    2023 arXiv

  35. [46]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams,HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron,Comput. Phys. Commun. 181(2010) 138 [0811.4169]

    2010 arXiv

  36. [47]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams,HiggsBounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron, Comput. Phys. Commun.182(2011) 2605 [1102.1898]

    2011 arXiv

  37. [48]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, O. St˚ al, T. Stefaniak, G. Weiglein et al.,HiggsBounds−4: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC,Eur. Phys. J. C74(2014) 2693 [1311.0055]

    2014 arXiv

  38. [49]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak and G. Weiglein,Applying Exclusion Likelihoods from LHC Searches to Extended Higgs Sectors,Eur. Phys. J. C75(2015) 421 [1507.06706]

    2015 arXiv

  39. [50]

    Bechtle, D

    P. Bechtle, D. Dercks, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein et al.,HiggsBounds-5: Testing Higgs Sectors in the LHC 13 TeV Era,Eur. Phys. J. C80(2020) 1211 [2006.06007]

    2020 arXiv

  40. [51]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. St˚ al, T. Stefaniak and G. Weiglein,HiggsSignals : Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC,Eur. Phys. J. C74(2014) 2711 [1305.1933]

    2014 arXiv

  41. [52]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. St˚ al, T. Stefaniak and G. Weiglein,Probing the Standard Model with Higgs signal rates from the Tevatron, the LHC and a future ILC,JHEP11(2014) 039 [1403.1582]

    2014 arXiv

  42. [53]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein and J. Wittbrodt,HiggsSignals-2: Probing new physics with precision Higgs measurements in the LHC 13 TeV era,Eur. Phys. J. C81 (2021) 145 [2012.09197]

    2021 arXiv

  43. [54]

    F. Arco, S. Heinemeyer and M.J. Herrero,Sensitivity and constraints to the 2HDM soft-breakingZ 2 parameterm 12,Phys. Lett. B835(2022) 137548 [2207.13501]

    2022 arXiv

  44. [55]

    Capozi and G

    M. Capozi and G. Heinrich,Exploring anomalous couplings in Higgs boson pair production through shape analysis,JHEP03(2020) 091 [1908.08923]

    2020 arXiv

  45. [56]

    F. Arco, S. Heinemeyer and M.J. Herrero,Sensitivity to triple Higgs couplings via di-Higgs production in the 2HDM ate +e− colliders,Eur. Phys. J. C81(2021) 913 [2106.11105]. 32

    2021 arXiv

  46. [57]

    F. Arco, S. Heinemeyer, M. M¨ uhlleitner, A.P. Arnay, N.R. Gonz´ alez and A.V. Schaeidt,Sensitivity to Triple Higgs Couplings via Di-Higgs Production in the RxSM at the (HL-)LHC and futuree +e− Colliders,2502.03878

    arXiv

  47. [58]

    F. Arco, S. Heinemeyer and M. M¨ uhlleitner,Large One-Loop Effects of BSM Triple Higgs Couplings on Double Higgs Production ate +e− Colliders,2505.02947

    arXiv

  48. [59]

    ATLAScollaboration,Search for resonant pair production of Higgs bosons in the b¯bb¯b final state using pp collisions at√s = 13 TeV with the ATLAS detector,Phys. Rev. D105(2022) 092002 [ 2202.07288]

    2022 arXiv

  49. [60]

    H. Bahl, A. Carnelli, F. D´ eliot, E. Fuchs, A. Kotsokechagia, T.L. Marsault et al.,CP -sensitive simplified template cross-sections fort tH,JHEP10(2024) 214 [2406.03950]

    2024 arXiv

  50. [61]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan et al.,Pytorch: An imperative style, high-performance deep learning library, 2019

    2019

  51. [62]

    Gennai, S

    S. Gennai, S. Heinemeyer, A. Kalinowski, R. Kinnunen, S. Lehti, A. Nikitenko et al.,Search for heavy neutral MSSM Higgs bosons with CMS: Reach and Higgs-mass precision,Eur. Phys. J. C52(2007) 383 [0704.0619]. 33

    2007 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.