Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 305 / 2 / c / Solution

Defineand rotate the neutral fields byThe quadratic mass terms from $|D_{\mu }⟨H⟩{|}^2$ are diagonal in this basis and giveThe scalar mass isThe unbroken generator is $Q=T^3+Y$, and $A_{\mu }$ is its gauge field. Its exact masslessness and coupling $e=g\sin {\theta }_W=g^{\prime }\cos {\theta }_W$ identify it as the photon.