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

A new form of parametrization is proposed for meson-baryon couplings in a phenomenological quark ($Q$) model of broken $\mathrm{SU}\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$ for the decays of baryons (mass $M$) belonging to the representations (56, $2l^{+}$) or [70, ${\mathrm{}(2l+1)\mathrm{}}^{-}$] to baryons (mass $m$) belonging to 56, together with the emission of pseudoscalar ($P$) mesons (mass $\mu$). The starting point is the use of the direct term in $\overline{Q}\mathrm{QP}$ coupling for the evaluation of the meson-baryon coupling structures which are reexpressed in terms of nonrelativistic Rarita-Schwinger fields together with multiple derivative structures in the meson field. A relativistic generalization of the latter is then proposed through a simple extension of the index structures in the ($L+1\mathrm{}$) partial-wave coupling terms. For the ($L-1\mathrm{}$)-wave coupling terms, which appear with an extra multiplying factor ${\mathbf{k}}^2$ in the meson three-momentum k, an additional ansatz ${\mathrm{k}}^2\to k_{\mu }{k}_{\mu } (\equiv -{\mu }^2)$ is used in order to include the contributions of the recoil terms for ($L-1\mathrm{}$)-wave transitions in a certain special combination, so as to incorporate the experimental feature of enhanced heavy-meson decays in the $s$ wave. Finally, all these coupling terms are assumed to be multiplied by the following form factor, the plausibility of whose structure is defended on physical grounds: $f_L\left(k^2\right)=g_L{\mu }^{-L-1\mathrm{}}{\left(\frac{\mu }{m_{\pi }}\right)}^{\frac{1}{2}}{\left(\frac{\mu }{w_k}\right)}^{L\pm 1}{\left(\frac{M}{m}\right)}^{\frac{1}{2}}$, where the exponents ($L\pm 1$) are used for emissions in the corresponding waves, and $g_L$ is a single free parameter governing the entire supermultiplet transition. The scheme, which is subjected to a detailed experimental test in respect to a large number of baryonic transitions from (70, $1^{-}$) and (56, $2^{+}$) states involving a wide range of masses and momenta, is found to provide an impressive number and quality of agreements with experiment. It is also shown to yield almost equal values of the coupling constants $g_L$ in respect to the couplings of several Regge recurrences of the $\Delta$ resonances, in conformity with the general expectation of a universal coupling for the Regge trajectory of a given particle.