= Solution
A bare <gauge boson> mass would spoil the electroweak gauge structure. In the <Standard Model> a complex <Higgs doublet> instead has a symmetry-breaking potential. Choose the convention
$$
V=-\mu^2\Phi^\dagger\Phi+\lambda(\Phi^\dagger\Phi)^2,\qquad
\Phi=\frac1{\sqrt2}\binom{0}{v+h},\qquad v^2=\mu^2/\lambda.
$$
The <Higgs mechanism> rearranges three scalar components into the <longitudinal polarizations> of the massive <W bosons> and <Z bosons>; the unbroken <electromagnetic gauge symmetry> leaves the <photon> massless. One physical scalar excitation, the <Higgs boson> $h$, remains.<Broken Symmetries and the Masses of Gauge Bosons by Peter Higgs>[pp. 508–509, gauge-field mass generation in a symmetry-breaking scalar model]{ref} Using <tree-level Feynman diagrams>,
$$
\boxed{m_W=gv/2,\quad m_Z=\sqrt{g^2+g'^2}\,v/2,\quad m_h^2=2\lambda v^2,\quad m_f=y_fv/\sqrt2}.
$$
These equations use <natural units>. <Yukawa interactions> generate charged-fermion masses and Higgs couplings proportional to those masses; the minimal model does not account for observed <neutrino masses>. The gauge kinetic term supplies Higgs couplings to W and Z pairs. The physical Higgs exchange also cancels the otherwise excessive high-energy growth of longitudinal vector-boson scattering. The mechanism does not fix the <Yukawa couplings> or the Higgs self-coupling, and most <proton> mass arises from strong-interaction dynamics rather than directly from the light-quark Higgs masses.
The mass-generation mechanism is a statement about the field and its <vacuum expectation value>; the observable boson is the excitation about that vacuum.
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