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This paper asks how well a future high-energy lepton collider could measure the Higgs boson’s self-coupling. The authors study di-Higgs production through W boson fusion at the 3 teraelectronvolt (TeV) stage of the Compact Linear Collider (CLIC). They work in a simple “κ” framework that describes small deviations from the Standard Model by modifiers: κλ for the Higgs trilinear (self) coupling, κV for the Higgs coupling to one pair of electroweak gauge bosons, and κ2V for the coupling to two gauge bosons.
The study focuses on the process e+e− → hh νν̄ with both Higgs bosons decaying to b-quark pairs (hh → 4b) plus missing energy. At center-of-mass energies above about 1 TeV, W boson fusion (WBF) is the dominant way to produce two Higgs bosons, and the three leading production diagrams depend differently on κλ and κ2V. The authors simulate signal and background events with MG5_aMC@NLO, hadronize with Pythia8, and run a fast detector simulation with Delphes3. Main backgrounds considered include single-Higgs production with b-quarks, multi-b production, and top-quark processes.
To separate the small di-Higgs signal from the backgrounds, the team uses a two-stage strategy of selection cuts followed by a graph neural network (GNN) classifier. Collider events are represented as graphs where jets are nodes and proximity gives edges. Their GNN has about 2.6×10^5 trainable parameters and reaches a micro-averaged area-under-curve of 0.95. For the Standard Model benchmark (κλ=κV=κ2V=1) they report signal and background efficiencies after classification of about 2.0×10^−2 and 6×10^−4, respectively, and a profile-likelihood signal significance Z ≈ 20 at an integrated luminosity of 5 ab^−1. The authors quote discovery-level sensitivity within the nominal CLIC program.
From a binned likelihood fit using observables built from the reconstructed Higgs pair (invariant mass and angular variables), they derive projected constraints at 95% confidence level. For a benchmark where κV is fixed to 1 (motivated by non-linear Higgs frameworks), they obtain κλ in [0.76, 1.31] and κ2V in [0.95, 1.05]. If κV and κ2V are forced to be equal (a relation that follows in Standard Model Effective Field Theory, SMEFT), the constraint on κ2V weakens to about [0.90, 1.10]. These results include only statistical uncertainties.
Important caveats remain. The quoted sensitivities are driven by simulation and statistical uncertainties; the paper notes that systematic uncertainties are assessed only in supplementary material and could affect the final limits. The analysis also relies on assumptions about detector performance, event reconstruction, and the specific κ-framework choices (for example neglecting the highly suppressed quartic self-coupling modifier). Finally, the difference between the two coupling scenarios reflects genuine model dependence: assumptions about how Higgs and gauge interactions are modified change the interference between diagrams and therefore the final sensitivity. The study nonetheless shows that high-energy lepton colliders, when paired with graph-based machine learning, can provide a powerful and relatively clean probe of the Higgs self-interaction and of how electroweak symmetry breaking might be realized.