The Higgs field sits in a Mexican-hat potential, and the shape of that hat is set by how strongly the Higgs interacts with itself.
The only direct way to measure it is to catch the LHC making two Higgs bosons at once, more than a thousand times rarer than making one.
Drag κλ (1 = the Standard Model) and watch what changes.
1.00 × Standard Model self-coupling
allowed by LHC data
The shape of the potential
Solid: your κλ. Dashed: Standard Model.
Horizontal axis: distance of the Higgs field from today's vacuum, in GeV. Cartoon: only the h³ term is scaled, h⁴ kept at its SM value. A real model that shifts κλ also brings new physics, so read the shape, not the numbers.
How often the LHC makes two Higgs
σ(gg → HH), 13 TeV
30.8 fb
vs Standard Model
1.00×
pairs made in Run 2 (140 fb⁻¹)
≈ 4,310
Two diagrams make a Higgs pair: a box (top-quark loop, no self-coupling) and a triangle (one Higgs splits into two, ∝ κλ). They interfere destructively, so the rate bottoms out near κλ ≈ 2.3 instead of at 0. Shaded: excluded by the 2026 ATLAS+CMS combination.
Where the evidence stands (ATLAS + CMS, full Run 2)
Double-Higgs production has not been observed yet: 1.1σ is far from the 5σ discovery standard. The High-Luminosity LHC, with about 20 times more collisions, is where that race gets decided.
The curve behind those limits
The −0.71 … 6.1 above is where this curve crosses the 95% line. Lower means the data like that κλ better. Every point below is the collaborations’ own published scan, not a redrawing.
Vertical axis: −2 ln Λ, the profile-likelihood test statistic, zero at the best fit. For one parameter, 1 and 3.84 mark the 68% and 95% CL intervals (1σ and ≈2σ). Only κλ is scanned: the table states that all other Higgs couplings are fixed to their Standard Model values. Expected: the curve from an idealised Standard-Model dataset (the Asimov dataset), i.e. what a typical SM outcome would give. The published scan stops near −2 ln Λ ≈ 5. Crossings are linear interpolation between neighbouring table points, 0.005 apart in κλ.
What the pairs turn into
Each Higgs decays almost instantly, so experiments hunt its products. The big channels are common but messy; the rare ones are clean.
final state
share of HH
why it's hard or useful
Questions this page can't answer (ask a physicist)
Why does the interference hide the triangle best near κλ ≈ 2.3, and does that make positive or negative deviations easier to catch?
If double-Higgs is out of reach, how much can single-Higgs measurements tell us about κλ through loop corrections?
Is our vacuum really metastable, and how does the self-coupling enter that argument alongside the top-quark mass?
What does a bbγγ event actually look like in the detector, and why can a tiny rate there beat the huge bbbb rate?
Could the self-coupling have mattered for how the electroweak phase transition happened in the early universe?