Dynamical model for baryon resonances

Abstract

We propose a nonrelativistic three-quark (Q) model of baryons and their resonances with the assumptions of (i) parastatistics which, in constrast to Fermi statistics, allows totally symmetric wave functions, and (ii) operation of Q-Q forces of the factorable type in s and p waves which facilitate an exact solution of the three-body problem. It is found that the s-wave force gives rise to a strong attraction in a spatially symmetric (S) state of L=0, but repulsion in a mixed-symmetric (M) state. This provides a natural dynamical realization of the 56 representation of SU(6) for the familiar octet and decuplet of baryons. The same s-wave force also predicts a set of negative-parity resonances but these are of much too high energy to be of any physical consequence. The p-wave force leads to a set of negative-parity L=1 resonances via strong attraction in M-type spatial states of L=1, thus making up the representation (70,3) of SU(6)×O(3). A p-wave spin-orbit Q-Q force splits these states in a manner which fits in rather well with Dalitz's recent analysis of experimental data for the negative-parity baryonic resonances. Finally, the p-wave force generates a strong attraction in a spatially antisymemtric state (A) of even parity and L=1, giving rise to the representation (20,3) of SU(6)×O(3), of which the lowest states are an octet and a singlet of J^P=1/2⁺, the central mass of each lying lower than the corresponding lowest mass multiplet of negative parity. This provides a natural explanation of the so-called "Roper" resonance (at 1450 MeV), and in addition, strongly predicts an even-parity singlet of a mass lower than the Y₀^∗(1405). The distinction between Fermi statistics and paraststistics is discussed in the context of the above results, and it is argued that while Fermi statistics could in principle generate negative-parity L=1 resonances (via M functions), it could not possibly account for the 56 of baryons, since with Q-Q forces alone,the A function of L=0 that should go with it has a strongly repulsive kernel.