Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_{c})\times U(N_{f})_{L}\times U(N_{f})_{R}$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model

Details Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_{c})\times U(N_{f})_{L}\times U(N_{f})_{R}$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model Dynamical Chiral Symmetry Breaking, Color Superconductivity, and Bose-Einstein Condensation in an $SU(N_{c})\times U(N_{f})_{L}\times U(N_{f})_{R}$-invariant Supersymmetric Nambu$-$Jona-Lasinio Model

2006-01-02

arxiv.org/abs/hep-ph/0601009v4

Nucl.Phys.B803:299-322,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, 9 figures, submitted to Nuclear Physics B

Scientific paper

10.1016/j.nuclphysb.2008.05.021

We investigate the phenomena of the dynamical chiral symmetry breaking (DCSB), color superconductivity (CSC), and Bose-Einstein condensation (BEC) in an ${\cal N}=1$ four-dimensional generalized SUSY Nambu$-$Jona-Lasinio model at finite temperature and density. Both the ${\cal N}=1$ four-dimensional and ${\cal N}=2$ three-dimensional cases are considered. The ${\cal N}=2$ three-dimensional theory is obtained by a simple dimensional reduction scheme of the four-dimensional counterpart. In order to realize the DCSB and BCS-type CSC in this model, we introduce a SUSY soft mass term. After adopting the method of SUSY auxiliary fields with the Fierz transformation in color and flavor spaces, we discuss several possible breaking schemes of the global symmetries of the model. The integrations of the auxiliary fields of composites in the effective potential are performed by using the steepest descent approximation. The roles of both the boson and fermion sectors in the BEC, DCSB and CSC are examined by the quasiparticle excitation spectra and the gap equations. The physical properties of the DCSB and the CSC are studied in detail, while that of the BEC is beyond scope of this paper. It is found that the BEC, DCSB and CSC can coexist under a condition of model parameters.

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