Quark Model for Meson-Baryon Processes

An $\mathrm{SU}\left(3\right)\mathrm{}$-invariant model of the elastic quark ($Q$) meason (pseudoscalar) scattering amplitude is proposed in the spirit of an impulse approximation, for the description of meson-baryon scattering and production processes involving both the positive- and negative-parity baryons looked upon as $3Q$ composites. The mesons are looked upon as "elementary" particles, rather than $Q\overline{Q}$ composites. The positive-parity baryons are assumed to belong to the 56 representation of $\mathrm{SU}\left(6\right)\mathrm{}$, and the negative parity ones to the (70,3) representation of $\mathrm{SU}\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$. The results for the scattering and production amplitudes are expressed in the form of sum rules connecting physically interesting processes. We obtain several sum rules for the elastic scattering amplitudes which agree with the Johnson-Treiman and Lipkin relations. For production processes within the 56 of baryons, some of our results, which do not agree with $\mathrm{SU}\left(6\right)\mathrm{}$ or $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$, are at least not disfavored by experiment compared with the latter. A number of relations among amplitudes connecting production of negative-parity baryonic states are also obtained, but these cannot be tested experimentally at this stage. A slight variant of the model, in which the initial meson is replaced by a spurion octet, reproduces in a natural way all the known sum rules for nonleptonic decays of $\Sigma$, $\Lambda$, and $\Xi$. For the ${\Omega }^{-}$ decay to $\Xi \pi$ and ${\Xi }^{*}\pi$ systems, the predictions of the model are, however, different from those of $\mathrm{SU}\left(6\right)\mathrm{}$ or of partially conserved axial-vector current with equal-time commutators.