Spontaneous symmetry breaking in gauge theories via Bose-Einstein condensation

Abstract

We propose a mechanism leading naturally to spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a nonzero chemical potential with one of the globally conserved charges commuting with all the gauge transformations. This induces a negative mass squared for the Higgs field, triggering the spontaneous symmetry breaking of the global and local symmetries. The mechanism is general and we test the idea for the electroweak theory in which the Higgs sector is extended to possess an extra global Abelian symmetry. With this symmetry we associate a nonzero chemical potential. The Bose-Einstein condensation of the Higgs bosons leads, at the tree level, to modified dispersion relations for the Higgs field, while the dispersion relations of the gauge bosons and fermions remain undisturbed. The latter are modified through higher order corrections. We have computed some corrections to the vacuum polarizations of the gauge bosons and fermions. To quantify the corrections to the gauge boson vacuum polarizations with respect to the standard model we considered the effects on the T parameter. We finally derive the one loop modified fermion dispersion relations.