Baryon mass splittings in an SU(6) × O(3) quark model

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 SU(6)×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 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 SU(2)-invariant spin-orbit force of the type τ1-τ2 of modest strength (∼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-Q pairs. The significance of this result is briefly discussed in connection with the question of quark statistics