Hadron Couplings in Broken $\mathrm{SU}\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$. II. Meson Decays

The phenomenological prescriptions outlined in the preceding paper (I) for meson-baryon couplings in a quark model of broken $\mathrm{SU}\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$ are employed for the construction of meson couplings in an almost identical spirit in respect of relativistic generalization as well as the inclusion of the recoil contribution. The multiplying form factor for a supermultiplet transition from an initial $Q\overline{Q}$ state (mass $M$) to a final $Q\overline{Q}$ state (mass $m$) is assumed to have the analogous structure $f_L\left(k^2\right)={\overline{g}}_L{\mu }^{-L-1\mathrm{}}{\left(\frac{\mu }{m_{\pi }}\right)}^{\frac{1}{2}}{\left(\frac{\mu }{{\omega }_k}\right)}^{L\pm 1}\mathrm{}\left(2M\right)\mathrm{}$, where ${\overline{g}}_L$ is a free parameter different from $g_L$ for all cases except $L=0\mathrm{}$ (when both are equal to the $\overline{Q}\mathrm{QP}$ coupling constant $f_q$). The agreement of this meson coupling scheme with experiment is found to be extremely good for a large number and variety of decays from $L^P=0^{-}, 1^{+}, \mathrm{and} 2^{-}$ supermultiplets. These results not only provide a sensitive test of the (rapidly varying) structure of the form factor, but also serve to emphasize the essential unity of description of both meson and baryon couplings through a common set of assumptions. A more sensitive test of this model is provided by its polarization predictions for $B\to \omega \pi$ and $A_1\to \rho \pi$ decays which are appreciably different from, and in somewhat better experimental accord than, those of the simple quark model.