Minimal Bootstrap in Meson-Baryon Systems

We consider two-particle scattering systems for which the crossing matrices give a good estimate of the nature of forces. We define a bootstrap state to be an eigenvector of the total crossing matrix. It is shown that bootstrap schemes are generally not unique. We conjecture that the physical particles manifest themselves in a state of minimal bootstrap, that is, a scheme involving the participation of the least number of particles. By studying meson-baryon scattering in the $\mathrm{SU}\left(2\right)\mathrm{}$ and $\mathrm{SU}\left(3\right)\mathrm{}$ symmetries, we find substantial evidence in support of this conjecture. The results are not only that the minimal boostrap vectors accommodate the observed particles in the usual way, but also that the ratio of the coupling strengths of particles in different representations and the mixing parameter ($\frac{D}{F}$ ratio) of the Yukawa-type octet coupling both turn out to agree with experiments.