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Measuring it requires seeing Higgs bosons produced in pairs, an extremely rare process.","posed_since":"","precise":"Measure $\\kappa_{\\lambda} = \\lambda_3/\\lambda_3^{\\mathrm{SM}}$, where the SM gives $\\lambda_3 = m_h^2/(2 v^2) \\sim 0.13$ for the cubic term $\\lambda_3 v h^3$. An answer is $\\kappa_{\\lambda}$ with total uncertainty below about 0.3 (30 percent), sufficient to distinguish the SM from models with a strongly first-order phase transition.","problem_ref":"5cafbb5387f70f4eb4f5161950259036ebcfe9c689101d8ca10289773d61d566","references":"","settled_by":"Combined HH production at the HL-LHC (projected about 30 to 50 percent precision) and at a future collider (FCC-hh projected $\\sim 5$ percent).","status_note":"The 2026 ATLAS plus CMS Run 2 HH combination (arXiv:2602.23991) gives $-0.71 < \\kappa_{\\lambda} < 6.1$ at 95 percent CL (expected -1.3 to 6.7) and HH signal strength $0.8 +0.9/-0.7$, an observed significance of $1.1\\sigma$.","title":"What is the Higgs trilinear 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