Supersymmetric NJL-Type Model for a Real Superfield Composite

Abstract

The Nambu-Jona-Lasinio (NJL) model is a classic theory for the strong dynamics of composite fields and symmetry breaking. Supersymmetric versions of the NJL-type models are certainly of interest too. Particularly, the case with a composite (Higgs) chiral superfield formed by two (quark) chiral superfields has received much attention. Here, we propose a prototype model with a four-chiral-superfield interaction, giving a real superfield composite. It has a spin-one composite vector field with properties being somewhat similar to a massive gauge boson of spontaneously broken gauge symmetry. As such, it is like the first supersymmetric analog to non-supersymmetric models with spin-one composites. The key formulation developed here is the picture of quantum effective action as a superfield functional with parameters like constant superfields, having explicit supersymmetric and Grassmann number dependent supersymmetry breaking parts. Following the standard non-perturbative analysis for NJL-type models, the gap equation analysis shows plausible signature of dynamical supersymmetry breaking which is worth more serious analysis.With an extra superfield model Lagrangian included, comparison between the models and their non-supersymmetric counterparts is discussed, illustrating the notion of supersymmetrization is nontrivial in the setting.

Further Studies of the Supersymmetric NJL-Type Model for a Real Superfield Composite

“…There are more interesting possibilities in the supersymmetrization of NJL-type models. Here, we focus on a simple one giving a real two-superfield composite from a dimension-six four-chiral-superfield interaction, first reported in our earlier paper [16]. Following and extending the framework of our earlier analyses [14][15][16], we present, in the article, further interesting nontrivial solutions for the soft mass parameters of the composite, under a more general setting, and the resulting physics.…”

“…Here, we focus on a simple one giving a real two-superfield composite from a dimension-six four-chiral-superfield interaction, first reported in our earlier paper [16]. Following and extending the framework of our earlier analyses [14][15][16], we present, in the article, further interesting nontrivial solutions for the soft mass parameters of the composite, under a more general setting, and the resulting physics. This kind of model may have the chance of dynamically generating the SNJL model with soft supersymmetry breaking masses for the further dynamical electroweak symmetry breaking, though the simple NJL framework is not able to have a firmly conclusive result on the dynamical supersymmetry breaking beyond its nature of a large-N approximation.…”

“…We have suppressed any multiplet (color) indices, with basic notation being in line with that of Wess and Bagger [17]. Note the two supersymmetric mass terms in the superpotential which are absent in our previous study [16]. We present here a standard NJL gap equation analysis [11,14,15], to check for the dynamical generation of a ΦΦ composite and the related physics.…”

“…Apart from supersymmetry itself, the model Lagrangian has, independent of the multiplet content of Φ a , a U(1) R , symmetry under which Φ a has a unit charge. With vanishing m o , it has a full U(N) symmetry under which the multiplet can be considered in the fundamental representation [16]. With the condition lifted, Φ a may then be considered as an SO(N), instead of SU(N), multiplet.…”

“…Note that with Φ = A + √ 2ψθ + Fθ 2 , the four-superfield interaction after the d 4 θ integration, has the part −g 2 o AA † (ΦΦ † )| θ, θ=0 . We have also performed the calculation fully in the component field framework for cases of Reference [16], but prefer to illustrate the superfield calculation here in accordance with the formulation under the perspective discussed in Reference [14]. The soft supersymmetry breaking mass m2 as a superfield term is just the θ 2 θ2 component of the kinetic term, to which Σ ΦΦ † (p; θ 2 , θ2 ) is the quantum correction to the latter.…”