 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 conventionThe 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.^[ref] Using tree-level Feynman diagrams,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.