Symmetry Breaking and Spin-Zero Mass Spectrum

We discuss the mass spectrum in a very general chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ model of pseudoscalar and scalar mesons. The case of an exactly symmetric Lagrangian and spontaneous breakdown is covered, as well as the more realistic case when there is also some intrinsic symmetry breaking in the Lagrangian. Our treatment is facilitated by the derivation of a mass formula which holds for all situations. In the realistic case the structure of the theory forces the mass of the ninth pseudoscalar meson to come out right and leaves us with the freedom to choose the masses of all scalar mesons (except the $\kappa$) as high as we like. The structure of the intrinsic symmetry breaking term is predicted. We also include some discussion of the baryons in this model and estimate the corrections to the Cabibbo theory of semileptonic hyperon decay.