Higgs Mechanism

Scalar Potential

A simple symmetry-breaking potential has the form

$$V(\phi)=\mu^2|\phi|^2+\lambda|\phi|^4, \qquad \lambda>0,\quad \mu^2<0.$$

The minimum occurs at nonzero field value.

Physical Role

In the electroweak theory, the Higgs field’s nonzero vacuum expectation value breaks

$$SU(2)_L\times U(1)_Y \to U(1)_{\rm EM}.$$

The $W^\pm$ and $Z$ bosons become massive, while the photon remains massless.