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Register a new userDynamical Symmetry Breaking in Supersymmetric Extensions of Nambu-Jona-Lasinio Model
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In this paper we discuss Nambu-Jona-Lasinio model as a classical model for dynamical mass generation and symmetry breaking. In addition we discuss the possible supersymmetric extensions of this model resulting from interaction terms with four chiral superfields that may be regarded as a supersymmetric generalization of the four-fermion interactions of the Nambu-Jona-Lasinio model. A four-superfield interaction terms can be constructed as either dimension 6 or dimension 5 operators. Through analyzing solutions to the gap equations, we discuss 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.
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This is a report on our newly proposed model of dynamical supersymmetry breaking with some details of the analysis involved. The model in the simplest version has only a chiral superfield (multiplet), with a strong four-superfield interaction in the Kahler potential that induces a real two-superfield composite with vacuum condensate. The latter has supersymmetry breaking parts, which we show to bear nontrivial solution following basically a standard nonperturbative analysis for a Nambu--Jona-Lasinio type model on a superfield setting. The real composite superfield has a spin one component but is otherwise quite unconventional. We discuss also the parallel analysis for the effective theory with the composite. Plausible vacuum solutions are illustrated and analyzed. The supersymmetry breaking solutions have generated soft mass(es) for the scalar avoiding the vanishing supertrace condition for the squared-masses of the superfield components. We also present some analysis of the resulted low energy effective theory with components of the composite become dynamical. The determinant of the fermionic modes is shown to be zero illustrating the presence of the expected Goldstino. The model gives the possibility of constructing a supersymmetric standard model with all (super)symmetry breaking masses generated dynamically and directly without the necessity of complicated hidden or mediating sectors.
Based on our idea of an alternative supersymmetrization of the Nambu--Jona-Lasinio model for dynamical symmetry breaking, we analyze the resulted new model with a holomorphic dimension-five operator in the superpotential. The approach provides a new direction for modeling dynamical symmetry breaking in a supersymmetric setting. In particular, we adopt the idea to formulate a model that gives rise to the Minimal Supersymmetric Standard Model as the low energy effective theory with both Higgs superfields as composites. A renormalization group analysis is performed to establish the phenomenological viability of the scenario, with admissible background scale that could go down to the TeV scale. We give the Higgs mass range predicted.
A recently proposed new mechanism of D-term triggered dynamical supersymmetry breaking is reviewed. Supersymmetry is dynamically broken by nonvanishing D-term vacuum expectation value, which is realized as a nontrivial solution of the gap equation in the self-consistent approximation as in the case of Nambu-Jona-Lasinio model and BCS superconductivity.
It is recently shown that in 4D $SU(N)$ Nambu--Jona-Lasinio (NJL) type models, the $SU(N)$ symmetry breaking into its special subgroups is not special but much more common than that into the regular subgroups, where the fermions belong to complex representations of $SU(N)$. We perform the same analysis for $SO(N)$ NJL model for various $N$ with fermions belonging to an irreducible spinor representation of $SO(N)$. We find that the symmetry breaking into special or regular subgroups has some correlation with the type of fermion representations; i.e., complex, real, pseudo-real representations.
We study the theoretical features in relation to dynamical mass generation and symmetry breaking for the recently proposed holomorphic supersymmetric Nambu--Jona-Lasinio model. The basic model has two different chiral superfields (multiplets) with a strongly coupled dimension five four-superfield interaction. In addition to the possibility of generation of Dirac mass between the pair established earlier, we show here the new option of generation of Majorana masses for each chiral superfield. We also give a first look at what condition may prefer Dirac over Majorana mass, illustrating that a split in the soft supersymmetry breaking masses is crucial. In particular, in the limit where one of the soft masses vanish, we show that generation of the Majorana mass is no longer an option, while the Dirac mass generation survives well. The latter is sensitive mostly to the average of the two soft masses. The result has positive implication on the application of the model framework towards dynamical electroweak symmetry breaking with Higgs superfields as composites.
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