Model of the Baryon Ground State

Abstract

We construct a bootstrap description of the lowest-mass states with baryon number one. A fundamental consideration in this approach is the selection of the most important two-particle channels coupled to these ground-state baryons. We suggest that $S$- and $P$-wave couplings to meson-baryon composites dominate, and that existing evidence from decays of resonant states supports our idea. A theoretical description which fits in naturally with this observation is the $\mathrm{SU}(6)$-multiplet classification of baryon states first formulated by Capps and by Belinfante and Cutkosky. This symmetry of $S$- and $P$-wave baryon-interaction vertices may be viewed as an extension of the original Chew-Low static interaction. The dynamical basis for our model is a set of bootstrap equations implied by the Bethe-Salpeter equation. We assign positive- and negative-parity baryons to ${56}^{+}$ and ${70}^{\ensuremath{-}}$, respectively, and determine the ${70}^{\ensuremath{-}}$-${56}^{+}$ mass difference, as well as the ${56}^{+}$${56}^{+}$${35}^{\ensuremath{-}}$, $70_{F}^{}{}_{}{}^{\ensuremath{-}}{70}^{\ensuremath{-}}{35}^{\ensuremath{-}}$, and $70_{D}^{}{}_{}{}^{\ensuremath{-}}{70}^{\ensuremath{-}}{35}^{\ensuremath{-}}$ $P$-wave and the ${70}^{\ensuremath{-}}$${56}^{+}$${35}^{\ensuremath{-}}$ $S$-wave coupling constants. We calculate a ${70}^{\ensuremath{-}}$-${56}^{+}$ mass difference of 230 MeV, and a ${70}^{\ensuremath{-}}$ $\frac{F}{D}$ ratio of - 1.1. The relation of the model to $\ensuremath{\rho}$-universality and also to the parity-doublet conjecture for baryons is discussed.