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The massive neutral and charged gauge bosons,

W^{\pm}

and

Z

, are linear combinations of the underlying

SU(2)_L

and

U(1)_Y

fields (

W^3_{\mu}

and

B_{\mu}

). Their masses are derived from the vacuum expectation value (VEV) of the Higgs field,

\langle \phi \rangle = v / \sqrt{2}

. The mass matrices yield the physical masses: \nM_W = \frac{1}{2} g v \quad \text{and} \nM_Z = \frac{1}{2} \sqrt{g^2 + g'^2} v$$ \nThese masses confirm that the $W$ and $Z$ bosons are massive force carriers, unlike the massless photon $\gamma$.

W and Z Bosons

The statement of the theorem