Dynamical symmetry breaking with four-superfield interactions

Abstract

We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu-Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part.A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference.Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.

Supersymmetric NJL-Type Model for a Real Superfield Composite

“…In a re-examination of the supersymmetric Nambu-Jona-Lasinio (SNJL) model, in general, our group found many interesting features in variants of the model in the alternative supersymmetrization. The new holomorphic model has a dimension-five four-chiral-superfield interaction in the superpotential [14,17,21]. The interaction gives rise to a chiral superfield as a composite of two chiral superfields, with the scalar being a bi-scalar composite.…”

“…The interaction gives rise to a chiral superfield as a composite of two chiral superfields, with the scalar being a bi-scalar composite. A model with two such composite chiral superfields bearing symmetry breaking VEVs can give a supersymmetric Standard Model with both Higgs doublets being (different) squark composites [17,21]. Nevertheless, input soft supersymmetry breaking masses are needed.…”

“…In Ref. [21], we introduced the powerful analysis of formulating the quantum effective action as a superfield functional with parameters like constant superfields, having explicit supersymmetric and Grassmann number dependent supersymmetry breaking parts. A superfield diagram, like the proper self-energy diagram in the gap equation, therefore also including the supersymmetry breaking parts.…”

“…It is our opinion that complete formulations of various superfield theories along the basic theme should be of great interest. The formulation plays a key role in our earlier works [21,22] as well as here.…”

Possible Approach to Dynamical Supersymmetry Breaking via Nambu-Jona-Lasinio Model

“…II, we present the model and the supergraph derivation of the superfield gap equation, elaborating the extension of our framework of analysis [12,13]. In Sec.…”