Overview of Higgs Self Coupling

Electroweak symmetry breaking is governed by the Higgs potential, whose shape is encoded in the Higgs self-interactions. Higgs-boson pair (HH) and triple-Higgs (HHH) production provide a direct probe of the Higgs self-couplings λ₃ and λ₄. Additionally, many new physics models predict resonances that decay to two bosons, including Higgs-boson pairs, or to a Higgs boson and a new scalar S; the couplings and mixings of such states can modify λ₃ and λ₄, making these signatures important in the search for new physics. This talk surveys recent ATLAS and CMS results from LHC Run 2 and early Run 3 across multiple final states, covering non-resonant HH measurements interpreted in terms of sensitivity to the Standard Model prediction, constraints on the trilinear coupling, and limits on the quartic VVHH interaction within EFT and benchmark scenarios. We summarize searches for resonant HH and SH production, and report the current status of HHH searches and their implications for the quartic self-coupling λ₄. Where available, combined interpretations and cross-experiment comparisons are highlighted. The talk also includes prospects for the High-Luminosity LHC, outlining the expected precision and analysis advances needed for definitive tests of the Higgs potential.