Dynamical Generation of Linear σ model SU(3) Lagrangian and Meson Nonet Mixing

This paper is the SU(3) extension of the dynamically generated SU(2) linear $\sigma$ model Lagrangian worked out previously using dimensional regularization. After discussing the quark-level Goldberger-Treiman relations for SU(3) and the related gap equations, we dynamically generate the meson cubic and quartic couplings. This also constrains the meson-quark coupling constant to $g=2\pi/\sqrt3$ and determines the SU(3) scalar meson masses in a Nambu-Jona-Lasinio fashion. Finally we dynamically induce the U(3) pseudoscalar and scalar mixing angles in a manner compatible with data.