Explore the Mexican hat potential and how particles acquire mass
A perfectly symmetric potential can still have a lopsided resting place. That small fact is how the Higgs field gives particles their mass.
Adjust μ and λ to change the shape of the hat, and press Reset Marble to watch it roll from the unstable top into the valley of broken symmetry.
The Higgs mechanism is one of the most profound ideas in physics. Through spontaneous symmetry breaking, the Higgs field gives mass to the W and Z bosons and to all fundamental fermions. The key is the "Mexican hat" potential — a potential with a symmetric shape but an asymmetric minimum.
The Higgs potential V(φ) = −μ²|φ|² + λ|φ|⁴ looks like a Mexican hat. The top is an unstable equilibrium. The marble rolls to the circular valley — the vacuum expectation value (VEV). This breaks the symmetry and gives mass to particles.
Slide the VEV from zero to its full value and watch the W and Z gain mass. Notice that the photon stays massless.
Before electroweak symmetry breaking, all particles are massless and travel at the speed of light. After the Higgs field settles into its VEV (246 GeV), the W and Z bosons acquire mass, while the photon remains massless. Slide between the two states.
Adjust μ and λ and compare the two wiggles. The blue Goldstone mode runs around the valley for free; the rose Higgs mode climbs the wall and costs energy.
Excitations along the valley floor (angular direction) cost no energy — these are the massless Goldstone bosons, which get "eaten" by the W and Z to give them mass. Excitations up the valley walls (radial direction) cost energy — this is the massive Higgs boson discovered at CERN in 2012.
Press Play and watch the universe cool as the forces split apart one by one. Pause to read about the current epoch.
Symmetry breaking happened at specific moments in the early universe as it cooled. The forces separated one by one, from the GUT scale down to the QCD phase transition.
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