= Electroweak doublet gauge-boson mass matrix
{title2=$m_W^2=g^2v^2/4$}
For a <Higgs doublet> with <hypercharge> $1/2$ and <vacuum expectation value> $(0,v/\sqrt2)^T$, its <gauge-covariant kinetic term> gives the neutral <gauge-boson mass matrix>
$$
M_{\mathrm{neutral}}^2=\frac{v^2}{4}\begin{pmatrix}g^2&-gg'\\-gg'&g'^2\end{pmatrix}
$$
in the $(W^3,B)$ basis. Its <eigenvalues> are zero and $(g^2+g'^2)v^2/4$, and the <Weinberg angle> rotation gives the <photon> and Z boson. The two charged <electroweak gauge bosons> have $m_W^2=g^2v^2/4$. The zero <eigenvalue> expresses the unbroken electric-charge <gauge symmetry>.
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