Application of Noninvariance Groups to Meson-Baryon Scattering

Abstract

The multiplet structure of hadrons must be related to the structure of their interactions. For multiplet structures associated with an invariance group, the interactions are to be invariant under the group; but for supermultiplet structure related to a noninvariance group the interaction structure has to be specified somewhat differently. We have shown elsewhere 1 how vertex functions may be associated with certain noninvariant generators, and shown that this leads to a variety of valid and useful predictions. We get, for example, the electromagnetic mass difference relation M(n)-M(p) = (5/ll){M(£°)-M(2 + )} which is in good agreement with experiment. In this Letter we consider the structure of scattering amplitudes within the noninvariance-group framework and deduce several relations between different amplitudes which include the Johnson-Trieman 2 relations and the Olsson 3 relation but extend their domain of validity. We establish the connection between this framework and the groups of strong-and intermediate-coupling meson theories. 4 We note that the results we obtain are independent of the specific representation to which the baryons are assigned.The characteristic noninvariance 5 group G of a system contains the invariance group K as a subgroup and is such that all states of the dynamical system constitute a single irreducible representation. We shall confine our attention to systems with baryon number unity and with K chosen to be SU(3)<8> SU J (2) (unitary symmetric pseudoscalar theory); the dynamical postulate is the identification of the meson coupling matrices A a to be the generators of G that are not conserved. The commutator of two such nonconserved generators is then a generator of the invariance group K.Let us now consider two meson-baryon scattering processes related by crossing and denote the corresponding scattering amplitudes by