Breakdown of Unitary Octet Symmetry in a Nonlinear Spinor Model of Elementary-Particle Theory

We consider the spontaneous breakdown of unitary octet symmetry in a nonlinear spinor model of elementary-particle theory. Our model is an adaptation to unitary octet symmetry of a model originated by Nambu and Jona-Lasinio and contains SU₃U₃ symmetry in the same way that their model contained SU₂U₂ symmetry. We derive an exact formula for the physical baryon mass that reduces to the usual superconductor-type formula in the lowest order approximation. Nonperturbative solutions that leave the physical and masses degenerate are obtained. We confirm the presence in our nonperturbative solutions of massless pseudoscalar and scalar mesons transforming as components of F-type octets as predicted by the Goldstone theorem. We also find massless pseudoscalar and scalar mesons that transform as components of unitary spin decimets. We explain that only the F octets are Goldstone mesons associated with the spontaneous breakdown of octet symmetry in our model, whereas the massless decimets are associated with the invariance of a restricted part of our Lagrangian under a larger group and their masslessness is not a consequence of symmetry breakdown in our solutions.