ChiralSU(3)⊗SU(3)Mass Spectra and the Generalized "ωρπ" Interaction

We discuss the interaction between a pseudoscalar and two vector mesons within the context of chiral $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ symmetry. Assuming that the interaction transforms like a combination of zeroth and eighth components of a (3, 3*) ⊕ (3*, 3) representation, we are able, in a phenomenological Lagranigan treatment, to reproduce a previous $\mathrm{SU}\left(3\right)\mathrm{}$ parametrization of the related meson decay rates. In addition we obtain interaction terms for the decays of the $X^0$ meson. We study also the mass spectrum of the vector, axial-vector, and pseudoscalar mesons when these last belong to a nonlinear representation and when they are part of a linear representation which includes scalar mesons. In the latter case we find that the $\kappa -K^{*}$ mixing is negligible.