Total widths of resonances: a criterion for the formulation of hadronic interactions

Abstract

The structure of relativistic hadron couplings in the harmonic-oscillator model is studied in terms of a criterion which demands a less-than-exponential increase of total widths of resonances with their excitation quantum numbers. The implementation of this program in turn requires a model for the evaluation of total widths which is formulated within the framework of the harmonic-oscillator model with the help of a physically plausible inclusiveness ansatz. For the coupling structures, two available alternatives are examined:A) the unsymmetrical radiation quantum (RQ) hypothesis for one of the mesons and B) the more symmetrical quark pair creation (QPC) hypothesis consistent with duality diagrams. For their relativistic formulations, a comparison is made between a) the 4-dimensional covariant theory of the Lipes-Kim-Noz type and b) a 3-dimensional noncovariant approach due to Licht and Pagnamenta. Model calculations are performed mostly for M→MM transitions, by involving radial and orbital excitations, but by ignoring the spin and SU₃ degrees of freedom. It is found that the 4-dimensional covariant formulation, with either of the RQ and QPC hypotheses, gives rise to exponentially increasing total widths, and hence is incompatible with the stated criterion. The noncovariant relativistic version, on the other hand, satisfies the criterion only under QPC, but not under RQ. It is therefore concluded that, of the four alternatives studied, only one, the 3-dimensional relativistic formulation with the QPC hypothesis, is favored by the chosen criterion which is defended on other grounds as well.