Gauge boson/Higgs boson unification: The Higgs bosons as superpartners of massive gauge bosons

Abstract

We show how one can use massive gauge superfields to describe, simultaneously, gauge bosons (W ±, Z,…) and Higgs bosons (w ±,z,…) together with their spin- 1 2 partners (pairs of winos, zinos,…), despite their different electroweak properties. This provides a manifestly supersymmetric formulation of spontaneously broken supersymmetric gauge theories, and makes explicit the relations between massive gauge bosons and Higgs bosons. It raises, however, the following question: if the gauge bosons W ± and Z and the Higgs bosons w ± and z are related by supersymmetry, how is it possible that the former couple to leptons and quarks proportionately to g or g′, and the latter proportionately to G F 1 2 m (fermions)? The paradox is solved as follows: when the Higgs bosons are described by massive gauge superfields, the lagrangian density is non-polynomial and field redefinitions have to be performed, in particular: lepton or quark field → lepton or quark field + (∼ G F 1 2 Higgs field) (lepton or quark field). They automatically regenerate, from the lepton and quark supersymmetric mass terms, the correct Yukawa couplings of Higgs bosons proportional to fermion masses. We also apply this method to the case in which an extra U(1) group is gauged, the standard Higgs boson h 0 being then the superpartner of the new neutral gauge boson U.