Dynamics of Low-Spin Baryon States

We study baryon states of spin $<~\frac{3}{2}$ using a dynamics based on an approximation to the Bethe-Salpeter equation which includes baryon and meson-exchange forces. Considering only $S$- and $P$-wave vertices, we perform a multichannel calculation using an $\mathrm{SU}\left(6\right)\mathrm{}$ description. A solution to a ${56}^{+}$:${70}^{-}$ bootstrap model (superscript denotes parity) is found which qualitatively reproduces the experimental coupling constants and has a mass difference, $M\left(70\right)-M\left(56\right)=260\mathrm{}$ MeV. Analysis of symmetry-breaking effects in this model gives qualitative agreement with experiment. A solution to a ${56}^{+}$:${70}^{-}$:${20}^{+}$ bootstrap is found with ${56}^{+}$, ${70}^{-}$, ${20}^{+}$ approximately degenerate, thus supplying theoretical evidence for the existence of ${20}^{+}$ in nature. The multiplet ${20}^{-}$ is found to exist only with a ${56}^{+}$:${70}^{-}$:${20}^{+}$:${20}^{-}$ model. A separate study of long-range forces in pseudoscalar meson-baryon scattering predicts an effect in the isospin-zero $P_{\frac{1}{2}}$ wave of the $\mathrm{KN}$ system and possibly the occurrence of a family of $P_{\frac{1}{2}}$ resonances belonging to the $\mathrm{SU}\left(3\right)\mathrm{}$ multiplet, $\overline{10}$, but not containing the Roper effect.