Extracting Higgs Self-Coupling Constraints through Triple Higgs Boson Production at Future Hadron Colliders

Abstract: We present a systematic study of triple Higgs boson production at future high-energy hadron colliders, using the six-$b$-jet final state as a probe of the Higgs self-interactions. We conduct, under realistic detector smearing assumptions, both a traditional cut-based analysis, and a multivariate one using gradient boosting. The multivariate strategy is found to enhance sensitivity to beyond the Standard Model effects on the Higgs boson's self-couplings, while preserving large signal event yields, thus enabling more robust statistical inference. This allows us to assess the impact of detector effects, systematic uncertainties, background normalisation, as well as different truncation choices in an effective-field-theory description of the new physics effects possibly affecting the Higgs boson's self-interactions. Our results demonstrate that statistically-meaningful and perturbative-unitarity-compatible constraints on the trilinear and quartic Higgs boson self-couplings can be achieved, provided that systematic uncertainties are controlled at the few-percent level. Finally, we extrapolate our results to various collider energies and luminosities, demonstrating in particular that an 85 TeV proton-proton collider performs comparably to a 100 TeV machine. Altogether, our findings therefore establish the six-$b$ channel as a viable probe of the Higgs self-interactions at most future hadron collider options currently being examined by the high-energy physics community.