Baryon Mass Splittings in anSU(6)×O(3)Quark Model

Abstract

The positive- and negative-parity baryon mass shifts are investigated under the assumption that these particles belong, respectively, to the representations (56,1) and (70,3) of the group $\mathrm{SU}(6)\ifmmode\times\else\texttimes\fi{}O(3)$, which are dynamically realizable from a 3-quark model with totally symmetric ($S$) functions, as found earlier by one of the authors. Two different types of $\mathrm{SU}(2)$-invariant central forces ${V}^{(1)}$ and ${V}^{(2)}$, each of which is shown to be in conformity with the usual mass relations for the 56 states, are employed. One of these forces (${V}^{(2)}$) is, however, found to violate the Gell-Mann-Okubo formula for certain negative-parity octets. It is also found that appreciable mixtures of both ${V}^{(1)}$ and ${V}^{(2)}$ are necessary even for a qualitative representation of the experimental masses. The effect of an $\mathrm{SU}(2)$-invariant spin-orbit force of the type ${\ensuremath{\tau}}_{1}\ensuremath{-}{\ensuremath{\tau}}_{2}$ of modest strength (\ensuremath{\sim}25 MeV) is found to be very helpful in producing a reasonably good fit to the actual masses of the negative-parity baryons. Such a force has, however, no first-order effect on the 56 masses, on the assumption of orbital $S$ functions, which can be constructed only with $S$-wave $Q\ensuremath{-}Q$ pairs. The significance of this result is briefly discussed in connection with the question of quark statistics.