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High energy probes of Higgs self-coupling via $W$ boson fusion at future lepton colliders

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Amir Subba, Hrishikesh Deka, Subhaditya Bhattacharya, Abhik Sarkar

High Energy Physics - Phenomenology · Submitted 5 Aug 2026 · 42 references

Pith's verdict: The GNN design and the HEFT/SMEFT split are worth reading, but the headline Z≈20 does not survive arithmetic on the paper's own table; the current version needs major correction before any coupling projection can be trusted.

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arXiv ID2608.05096 (version 1)
Pith IDALMKMVPN, Pith's permanent record of this paper and its review
CitationAbhik Sarkar, Amir Subba, Hrishikesh Deka, Subhaditya Bhattacharya. "High energy probes of Higgs self-coupling via $W$ boson fusion at future lepton colliders." arXiv:2608.05096 (2026). https://pith.science/paper/ALMKMVPN
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The paper

The paper claims

This paper claims that W-boson fusion di-Higgs production at a 3 TeV lepton collider, analyzed with a graph neural network, can reach 20σ significance and constrain the Higgs self-coupling modifier to roughly 30% precision at 95%…

The reading

This paper aims to show that the Higgs self-coupling can be measured precisely at a future high-energy lepton collider, specifically the 3 TeV CLIC, using W-boson fusion di-Higgs production in the four-bottom-quark plus missing-energy final state. It argues that a graph neural network classifier, which treats each event as a graph of jets and uses attention-based message passing, can separate the small signal from much larger backgrounds well enough to reach a signal significance of about 20σ at 5 $ab^{-1}$. If that holds, CLIC would constrain the Higgs self-coupling modifier κλ to about [0.76,1.31] and the double Higgs-gauge coupling modifier κ2V to about [0.95,1.05] at 95% confidence, well beyond projected HL-LHC sensitivity. The same measurement would also distinguish linearly realized electroweak symmetry breaking from non-linearly realized frameworks because the two scenarios predict different correlations between κV and κ2V.

What carries the argument

The central object is a heterogeneous graph neural network classifier. Each reconstructed jet is a node with a 14-component feature vector (transverse momentum, angles, mass, particle multiplicities, energy ratios, b-tag and flavour information, time of flight, and jet-shape variables), a missing-energy node carries the MET information, and directed edges connect jets within angular distance ΔR≤1.5. Three GATv2 attention layers perform message passing, then pooled jet and MET embeddings feed a small multilayer perceptron that assigns each event a probability of being signal. This classifier is the machine that pulls the hhννbar signal out of single-Higgs and top-quark backgrounds; the coupling reach is then set by a binned profile likelihood over the reconstructed di-Higgs kinematic observables m_hh, Δη_hh, and Δφ_hh, using the cross-section parameterization σ = $κ_λ^{2}$ $κ_V^{2}$ C_11 + $κ_2V^{2}$ C_22 + $κ_V^{4}$ C_33 plus interference terms.

Extended reading notes

Core claim

The central claim is that WBF di-Higgs production at a 3 TeV e+e− collider, with each Higgs decaying to bbbar, is a discovery-level and precision-level probe of the Higgs potential. For the Standard Model benchmark, the paper's GNN classifier yields a micro-averaged AUC of 0.95 and post-classification signal and background efficiencies of about 2×$10^{-2}$ and 6×$10^{-4}$, translating to Z≈8, 15, and 20 at integrated luminosities of 1, 3, and 5 $ab^{-1}$. A binned profile-likelihood fit over reconstructed di-Higgs mass, rapidity separation, and azimuthal separation then gives, at 5 $ab^{-1}$ and 95% CL, κλ∈[0.76,1.31] and κ2V∈[0.95,1.05] when κV=1, and κ2V∈[0.90,1.10] when the SMEFT-like relation κV=κ2V is imposed. The author's conclusion is that high-energy lepton colliders combined with graph-based machine learning provide a powerful, discriminating probe of new physics in the electroweak sector.

Load-bearing premise

The projection rests on the assumption that the GNN's simulated separation power—about 2% signal efficiency and 0.06% background efficiency at the chosen working point—will hold in the real CLIC detector, since the analysis uses fast simulation and propagates only a single global 10% normalization systematic, not shape systematics in the classifier score, b-tagging, or jet energy scale.

Editorial extensions

If this is right

  • At 5 ab^-1, a 3 TeV CLIC run would make WBF di-Higgs production a discovery channel with Z≈20 for the Standard Model, and already Z≈8 at 1 ab^-1.
  • The trilinear Higgs coupling would be measured to about ±30% at 95% CL, a direct test of the shape of the Higgs potential.
  • The double Higgs-gauge coupling κ2V would be pinned to roughly ±5% in the HEFT-like scenario, offering a sharper test of the hhVV vertex than the LHC.
  • Comparing the two scenarios would give an indirect discriminator between SMEFT and HEFT: the allowed region in the κλ–κ2V plane changes shape and orientation depending on whether κV=κ2V.
  • The same analysis strategy, applied at a muon collider with similar center-of-mass energy, would likely deliver comparable sensitivity.

Reading between the lines

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

  • Because only one global normalization systematic is included, the quoted intervals would likely widen once shape systematics in the GNN score distribution, b-tagging efficiency, and jet energy scale are propagated in a full detector simulation.
  • The 4b final state is only one of several hh decay channels; combining bbWW and bbττ in the same graph framework would probably tighten the κλ constraint beyond the reported values.
  • The strong κλ–κ2V correlation visible in the 2D contours suggests that a global simultaneous fit, rather than separate 1D intervals, is the right way to interpret a future measurement; a shift in one coupling could masquerade as a shift in the other.
  • If the GNN score calibration is validated in data control regions, the same classifier could be reused as a model-independent search for anomalous couplings, not just the two benchmark scenarios.
Original abstract

We investigate the sensitivity to the Higgs self-coupling through $W$ boson fusion di-Higgs production at CLIC with a center-of-mass energy of $\sqrt{s}=3$ TeV. We study the interplay between the Higgs self-coupling modifier ($\kappa_{\lambda}$) and Higgs-gauge coupling modifiers ($\kappa_{V}$ and $\kappa_{2V}$) within the $\kappa$ framework. To enhance the separation between signal and background, we develop a graph neural network (GNN) based classifier that achieves a signal significance of $\mathscr{Z}\approx 20~\sigma$ at $5~\mathrm{ab}^{-1}$, substantially exceeding projected HL-LHC sensitivity. Our results demonstrate that high-energy lepton colliders, combined with graph-based machine learning, provide excellent sensitivity to the Higgs self-coupling and offer a powerful probe of new physics in the electroweak sector, disentangling linearly and non-linearly realized electroweak symmetry breaking.

Figures
Figure 1. FIG. 1. Di-Higgs production cross sections as a function of
Figure 2. FIG. 2. Feynman diagrams contributing to di-Higgs production via WBF.
Figure 3. FIG. 3. WBF di-Higgs production cross sections in different parameter planes:
Figure 4. FIG. 4. Left: One-vs-rest ROC curves for the three-class GATv2 classifier. Right: Profile-likelihood significance
Figure 5. FIG. 5. Signal significance in different parameter planes:
Figure 6. FIG. 6. 95% C.L. 2D sensitivity contours at
Figure 7. FIG. 7. 95% C.L. 2D sensitivity contours at

Figures reproduced from arXiv:2608.05096 by the authors.

References

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 9 sentences without a confident label

Uses the method or tool of 4 papers
Uses data or values from 2 papers
Cites as background 9 papers
  • The nature of the underlying new physics (NP) that modifies these interactions determines whether deviations in $κ_V$ and $κ_2V$ are correlated, as in SMEFT [ref] , or independent, as in HEFT [ref] .

    Strong Double Higgs Production at the LHC · Introduction · 0.95

  • The nature of the underlying new physics (NP) that modifies these interactions determines whether deviations in $κ_V$ and $κ_2V$ are correlated, as in SMEFT [ref] , or independent, as in HEFT [ref] .

    Dimension-Six Terms in the Standard Model Lagrangian · Introduction · 0.95

  • The nature of the underlying new physics (NP) that modifies these interactions determines whether deviations in $κ_V$ and $κ_2V$ are correlated, as in SMEFT [ref] , or independent, as in HEFT [ref] .

    Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO · Introduction · 0.95

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