Phenomenological Model of Strong and Weak Interactions in ChiralU(3)⊗U(3)

Abstract

A phenomenological model for the strong and weak interactions of an octet or nonet of pseudoscalar mesons in chiral $U\left(3\right)\mathrm{}\otimes U\left(3\right)\mathrm{}$ is constructed and discussed. In this model one can study the effect that the partially conserved axial-vector current hypothesis (PCAC) and the transformation properties of the interaction Lagrangian in chiral $U\left(3\right)\mathrm{}\otimes U\left(3\right)\mathrm{}$ have on the transition amplitudes for various meson processes. The processes considered in this paper are the leptonic and nonleptonic decays of $K$ mesons, the strong interaction decay ${\eta }^{\prime }\mathrm{}\left(959\right)\mathrm{}\to \eta \mathrm{}\left(549\right)+2\mathrm{}\pi$, the $s$- and $p$-wave scattering lengths for pion-nucleon scattering, and meson-meson scattering. Low-energy pion-pion scattering is discussed as an illustration of the fact that for processes involving more than one soft pion, PCAC and the algebra of currents are not sufficient to give unique results in general.