A dynamical model for the meson spectrum

Abstract

A model for the meson spectrum is constructed under the following dynamical assumptions: (A) dominance of processes with low thresholds; (B) dominance of one-particle-exchange forces; (C) SU 3 symmetry; (D) dominance of quasi-two-particle states in production processes. A bootstrap system is sought which satisfies the following conditions: (i) “consistency” in that all exchanged particles are bound as poles in the appropriate direct channels; (ii) “closure” in that no further low-lying states are bound other than those whose exchange contributes to the forces; (iii) “completeness” in that all “low” energy processes involving any of the particles in the spectrum are taken into account. Starting from the 0 − octet (π, K, η) and the 1 − octet (ϱ, K ∗ , φ), these consistency considerations lead to the meson supermultiplets listed in Table I. Interesting regularities in the predicted spectrum are noted. In particular one sees that apart from “Regge” recurrences, the spectrum happens to coincide with that contained in the (6 ∗, 6)−(6, 6 ∗) representation of the recently proposed U 6 × U 6 supersymmetry. A tentative assignment is attempted of known meson states into the scheme. Apart from the K +− π +− π 0 enhancement at 1270 MeV, all reasonably well-established resonances to date fit comfortably into the spectrum. Further empirical regularities are noted in the assignment, which include one in the Bronzan-Low quantum number A. Wherever feasible, the dynamical parameters (masses, coupling constants) are computed by requiring numerical “bootstrap” consistency using a method proposed by Zachariasen and Zemach. These values are listed in Table II, where it is seen that qualitative agreement is obtained for all parameters so far calculated.