Breaking of SU(3) Symmetry in the32+Meson-Baryon Decuplet

Breaking of SU(3) invariance is studied in the case of the meson-baryon decuplet with $J^P={\frac{3}{2}}^{+}$. In a simple theory based on single-baryon exchange, the evolution of the broken decuplet from a degenerate origin is traced in detail. Symmetry breaking is introduced by allowing initially degenerate meson and baryon masses to approach continuously their physical values, while obeying at every stage the Gell-Mann-Okubo sum rules. The following conclusions are reached: (i) The Okubo equal spacing rule for the decuplet levels follows from the validity of the Gell-Mann-Okubo rules for the meson and baryon octuplets. (ii) The main effect of the symmetry breaking may be characterized as a mixing of the 10- and 27-dimensional representations. The mixing is small enough so that the resonances can be unambiguously associated with the 10 representation, but at the same time large enough to imply coupling-constant ratios differing appreciably from the values for pure symmetry. (iii) In the approach to pure symmetry through reduction of mass differences, there are no difficulties of the type pointed out by Oakes and Yang. Resonances cross thresholds smoothly, and a degenerate decuplet of bound states is obtained in the limit.