A New Dynamical Model for Meson States

Abstract

Reasons are advanced for considering the effect of inelastic coupling to the vector-vector state on the meson states occurring in pseudoscalar-pseudoscalar scattering. A model based on the angular-momentum properties of the box graph containing 2 vector mesons in the intermediate state is developed. In the dynamics of the model the "elementary" vector-meson octet disappears, and a vector-octet Regge trajectory is generated. A Pomeranchuk trajectory is generated in the singlet amplitude. The slopes of the trajectories are in quite reasonable agreement with experimental indications. The model predicts a $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ coupling constant a factor of 2 or 3 above the experimental value and about the same as the value predicted by bootstrap models. The model shares with bootstrap models the feature that $S{U}_{3}$ symmetry is "predicted" as a consequence of dynamical self-consistency. The basic effect is expected to be important in more conventional dynamical schemes, and suggestions are made for further work.