Inspect the Higgs potential V(Φ)=μ2Φ†Φ+λ(Φ†Φ)2, watch the vacuum move to a nonzero value v=−μ2/λ when μ2<0, and connect this to mass generation for the W and Z bosons.
Research
Equipment
3D projection canvas of the field and potential (rotatable)
Slider “Cường độ” (intensity of the field coupling)
Slider “Thang năng lượng” (energy scale)
“Tạm dừng” and “Đặt lại góc nhìn” buttons
Procedure
Read the potential shape
Rotate the 3D view and inspect the potential: with μ2>0 it has a single minimum at the origin, but for μ2<0 it becomes a “Mexican hat” whose minima form a ring at v=−μ2/λ≈246 GeV.
Sweep the parameters
Move the intensity and energy-scale sliders and watch the vacuum expectation value and boson masses respond: mW=21gv and mZ=21g2+g′2v grow with v while the photon stays massless.
Interpret the excitation
Pause the model and distinguish the two modes living on the ring potential: oscillations along the ring cost no energy (the massless Goldstone modes absorbed by W and Z), while radial oscillations have a mass — that radial excitation is the Higgs boson, with mh≈125 GeV.
Simulation
Experiment history
In 1964 three groups — François Englert and Robert Brout, Peter Higgs, and Gerald Guralnik, Carl Hagen and Tom Kibble — independently showed how spontaneous symmetry breaking could give mass to gauge bosons without destroying gauge invariance. Steven Weinberg and Abdus Salam folded the mechanism into the electroweak theory in 1967, which predicted the W and Z masses measured at CERN in 1983.
On 4 July 2012, the ATLAS and CMS collaborations at the Large Hadron Collider announced a new boson at about 125 GeV whose properties matched the Higgs; Englert and Higgs received the 2013 Nobel Prize (Brout having died in 2011). Precision study of the boson's couplings — including to itself — remains an active LHC program.