SU(3)Multiplet Mixing and Unitarity

Abstract

A purely $S$-matrix approach to $\mathrm{SU}(3)$ multiplet mixing is given. Particular attention is devoted to the role of strong mixing in the basis states of the $S$ matrix itself and to the role of the inelastic channels in calculating mixed representations. The dependence of the mixed wave functions on the energy separation between resonances and on the magnitude of symmetry-violating vertices is considered. The analysis is applied to the single-octet mixing of the ${\frac{3}{2}}^{\ensuremath{-}}$ baryon system in terms of a multichannel model involving the states ${B}_{8}{P}_{8}$, ${B}_{8}{V}_{8}$, and ${B}_{8}{V}_{1}$. The effects of $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\omega}$ mixing in the basis states are included in the calculation and a dramatic improvement between the experimental and theoretical values of the branching ratios for the decays of $\ensuremath{\Lambda}(1520)$ and ${\ensuremath{\Lambda}}^{\ensuremath{'}}(1700)$ into $\overline{K}N$ and $\ensuremath{\pi}\ensuremath{\Sigma}$ is obtained.