Gedanken worlds without Higgs fields: QCD-induced electroweak symmetry breaking

To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy models in which no Higgs fields or other constructs are introduced to induce spontaneous symmetry breaking. Two models incorporate the standard $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(2{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_Y$ gauge symmetry and fermion content similar to that of the standard model. The first class—like the standard electroweak theory—contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromodynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion masses sufficiently small that QCD remains the dominant source of electroweak symmetry breaking and the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the hadronic scale. A third class of models is based on the left-right-symmetric $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(2{)}_{\mathrm{L}}\otimes \mathrm{SU}(2{)}_{\mathrm{R}}\otimes \mathrm{U}(1)$ gauge group. In a fourth class of models, built on $\mathrm{SU}(4{)}_{\mathrm{PS}}\otimes \mathrm{SU}(2{)}_{\mathrm{L}}\otimes \mathrm{SU}(2{)}_{\mathrm{R}}$ gauge symmetry, the lepton number is treated as a fourth color and the color gauge group is enlarged to the $\mathrm{SU}(4{)}_{\mathrm{PS}}$ of Pati and Salam (PS). Many interesting characteristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. The Higgs-free models not only provide informative contrasts to the real world, but also lead us to consider intriguing issues in the application of field theory to the real world.