= Solution
After <electroweak symmetry breaking>, the <Higgs field> has vacuum expectation value $\langle H\rangle=(0,v/\sqrt2)^T$. A <Yukawa interaction> $-y_f\bar f_LHf_R+\mathrm{h.c.}$ then becomes a fermion mass with $m_f=y_fv/\sqrt2$. The Higgs <gauge-covariant kinetic term> $|D_\mu H|^2$ gives
$$
m_W=\frac{gv}{2},
\qquad
m_Z=\frac{v}{2}\sqrt{g^2+g'^2},
$$
while the radial fluctuation is the massive <Higgs boson>. The <photon> and all eight <gluons> correspond to unbroken gauge generators and remain massless. In the minimal renormalizable Standard Model, which has no right-handed neutrinos, the neutrinos also remain massless; adding right-handed neutrinos permits Higgs-generated Dirac masses.
Back to article page
