The equivalence of the top quark condensate and the elementary Higgs field

Abstract

Several recent works suggested to replace the fundamental Higgs boson by a top quark condensate in analogy with the Nambu-Jona-Lasinio (NJL) mechanism. We show that the field theoretically correct replacement is a generalized NJL model with the minimal choice of three independent interaction terms in the lagrangian. We demonstrate in the large- N color limit that the physics of this model is fully equivalent to the corresponding simplified Standard Model where the Higgs boson is represented by an elementary scalar field with the usual Yukawa- and self-interactions. The generalized NJL mechanism does not lead to new physical predictions or constraints and the complete parameter range of the simplified Standard Model is recovered. Since there exists a simple mapping between the couplings of these two models, it is difficult to give physical significance to notions like composite versus fundamental, or dynamical symmetry breaking in this scheme. We also present some new numerical results on the relevant phase diagrams.