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In their 1964 paper, François Englert and Robert Brout showed that gauge bosons associated with generators that rotate the chosen vacuum acquire masses while gauge invariance is maintained. Their discussion included both scalar and fermionic models.^[ref]

Independently, Peter Higgs exhibited a massive vector and a surviving massive scalar field by linearizing a simple gauge theory. His paper explicitly distinguishes this classical calculation from a proof for the full quantized theory. These 1964 mechanisms supplied an ingredient for the later electroweak interaction, rather than the complete Standard Model.^[ref]

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.

Peter Higgs explained how coupling a broken-symmetry scalar theory to gauge fields changes the physical particle spectrum. In his 1964 model, a massless scalar degree of freedom supplies the longitudinal mode of a massive gauge boson; another scalar excitation remains. Thus the massless-particle conclusion of the Goldstone theorem does not apply unchanged to the gauged system. This Higgs mechanism connects the vacuum's field configuration with measurable particle masses and an additional scalar particle.^[ref]

A physicist who investigated the Higgs mechanism.^[ref]