Model of Spontaneous Breakdown ofSU(3)⊗SU(3)Symmetry. I

Strong interactions of spin-zero and spin-one mesons are studied in a model in which the Lagrangian is approximately invariant under coordinate-dependent $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ gauge transformations. The scalar and pseudoscalar nonets are assigned to the (3,3*) ⊕ (3*,3) representation, whereas the vector and axial-vector octets are introduced as gauge fields belonging to the (1,8) ⊕ (8,1) representation. Spontaneous symmetry breaking to the isospin-hypercharge level is introduced by giving nonzero vacuum expectation values to some scalar fields. The effective Lagrangian obtained after considering field mixings and renormalizations is used in a phenomenological manner to study the masses and couplings of various particles. With some of the experimental meson masses as input, the predicted masses of remaining observed mesons are in reasonable agreement with experiment. Some scalar-meson masses are also predicted (${\mu }_{S_K}=527\mathrm{}$ MeV and ${\mu }_{S_{\pi }}=771\mathrm{}$ MeV). The widths for $V\to \mathrm{PP}$ and $A\to \mathrm{VP}$ decays are calculated and compare well with experiment. The axial-vector currents and the strangeness-changing vector currents satisfy partial conservation equations. Decay constants for spin-zero mesons are calculated. We get $\frac{F_K}{F_{\pi }}=1.17\mathrm{}$ and $\frac{F_{S_K}}{F_{\pi }}=-0.59\mathrm{}$. The $K_{l3\mathrm{}}$ form factors are calculated, the effect of the scalar kaon being included; we get $f_{+}\mathrm{}\left(0\right)=0.86\mathrm{}$, $\xi =-0.197\mathrm{}$, ${\lambda }_{+}=0.023\mathrm{}$, and ${\lambda }_{-}=0.013\mathrm{}$.