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 $S{U}_3\otimes S{U}_3$ symmetry in the same way that their model contained $S{U}_2\otimes S{U}_2$ 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 $\Lambda$ and $\Sigma$ 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.