Self-Consistent Sets of Mesons in a Bootstrap Model

Consideration is given to the possibility that the self-consistency requirements of some dispersion-theoretic bootstrap model may specify uniquely the set of strongly-interacting particles found in nature. The discussion is based on a particular, approximate model of the P (pseudoscalar) and V (vector) mesons. In this model the V exchange forces in the $P+P$ states produce the V mesons, and the V exchange forces in the $P+V$ states produce the P mesons. Attention is limited to systems in which the particles arising in a particular way are degenerate or nearly degenerate, and are represented by a small number of irreducible representations of a simple Lie group of first, second, or third rank. Three plausible self-consistency requirements are postulated. The smallest meson set that satisfies all three postulates corresponds to the group SU₃. The predicted particles in this scheme are a P-meson octet, a V octet, a V singlet, and a singlet particle of spin and parity 2^-. One of the self-consistency postulates is concerned with deviations from degeneracy, and leads to the Gell-Mann-Okubo sum rule for the SU₃ scheme. The double-septet scheme of the group G₂ does not satisfy any of the postulates.