QQQ̅ model of meson-baryon processes

Abstract

A QQQ̅ model of beson-baryon scattering and production of both positive- and negative-parity mesons is developed as a generalization of the "elementary meson" model proposed earlier by the authors. The model is based on the assumption that mesons are tighter structures than baryons, which allows the former to "see through" the latter, but not vice versa. The formalism allows the full inclusion of multiple-scattering effects within the meson-quark system via the QQQ̅ structure, and leaves scope for the inclusion of similar effects between the meson and the quarks in the baryon, as a second-stage process. The model is more restricted than the usual quark models (based on additivity), which in general enable correlations of meson-baryon, baryon-baryon, and baryon-antibaryon amplitudes. The model makes little use of dynamics, except for the method of "spectator functions" to calculate the amplitudes for the various processes in terms of residues at the appropriate poles of the relevant spectator functions. However, the possible uses of simple dynamical considerations are indicated, by which the larger amplitudes could be distinguished from the smaller ones. The amplitudes are evaluated in a two-stage process, the first step indicating the "SU(3) level" of predictions, involving only one spin-parity type at a time, while the second step gives SU(6)-type predictions which in principle connect mesons of different spin-parity assignments. For the negative-parity mesons (0^- and 1^-), the results are similar to those obtained by previous authors. However, the model provides, with no extra physical assumptions but considerably more algebraic manipulations, amplitude relations for the production of positive-parity mesons (0⁺, 1⁺, and 2⁺) which, according to the quark picture, are structures of the form ¹P₁ and ³P_0,1,2, and are expected to simulate mesons of the type B, A₁, and A₂ (and perhaps also the scalar mesons). No attempt is made in this paper to confront the predictions with experiment, which will be the subject of a subsequent communication.