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Title: What is the Higgs trilinear self-coupling?
Plain: The Higgs interacts with itself, and the SM predicts the exact strength from the Higgs mass. Measuring it requires seeing Higgs bosons produced in pairs, an extremely rare process.
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.
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).
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
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 $1.1\sigma$.
Posed since: (empty)