= Electroweak symmetry breaking
{wiki}
Electroweak symmetry breaking is the Higgs-field breaking $SU(2)_L\times U(1)_Y\to U(1)_Q$. It gives masses to the $W$ and $Z$ bosons while leaving the photon massless.
With the <hypercharge> convention $Q=T_3+Y$, the lower component of the <Higgs doublet> has $T_3=-1/2$ and $Y=1/2$. Thus $Q\langle\phi\rangle=0$: the <vacuum expectation value> is electrically neutral. This is why one combination of the neutral <gauge fields> remains the massless <photon>, as the <electroweak doublet gauge-boson mass matrix> shows.
Continue the chosen <Higgs field potential> example with $g=3/5$ and $g'=4/5$. The <tree-level electroweak gauge-boson masses> are $m_W=72\,\mathrm{GeV}$, $m_Z=120\,\mathrm{GeV}$ and $m_A=0$. In the $(W^3,B)$ basis,
$$
M_{\rm neutral}^2=\begin{pmatrix}5184&-6912\\-6912&9216\end{pmatrix}\mathrm{GeV}^2.
$$
Its orthonormal <eigenvectors> $(4/5,3/5)^T$ and $(3/5,-4/5)^T$ have <eigenvalues> zero and $14400\,\mathrm{GeV}^2$. Thus $\cos\theta_W=3/5=m_W/m_Z$. This is an exact model check, not a fit to measured <electroweak interaction> parameters.
A diagonal charged-fermion <Yukawa coupling> expands as
$$
-\frac{y_f}{\sqrt2}(v+H)\bar f f=-m_f\bar f f-\frac{m_f}{v}H\bar f f,\qquad m_f=\frac{y_fv}{\sqrt2}.
$$
The <Yukawa coupling> remains a free parameter: the mechanism relates a <fermion> mass to its scalar interaction but does not predict the numerical mass. This example concerns charged <fermions>; the minimal <Standard Model> has no right-handed <neutrino> and does not account for <neutrino oscillations> without an extension.
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