Baryon mass splittings in an SU(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 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.