Exchange‐degenerate and Exotic Trajectories in a Multiperipheral Model with VENEZIANO‐type Production Amplitudes

Abstract

The implications of duality and absence of exotics are investigated in a multiperipheral model of pseudoscalar meson-meson scattering. An exchange-degenerate leading trajectory is obtained besides low lying ones in exotic and non-exotic channels.The absence of resonances with exotic quantum numbers and the requirement of duality lead t o exchange degeneracy between trajectories of different signature and internal quantum numbers. These principles have been used by LOVELACE [l] to construct a simple model for nn-scattering with the degenerate ef-trajectory. The generalization t o production amplitudes has been given by PATON and CHAN 121 for SU (2) and SU (3) symmetry and by BARDAKCI, HAL-PERN, KLEIN and SHAPIRO 131 for higher symmetries. In this note we use such VENEZIANO-type production amplitudes as an input for a multiperipheral model of pseudoscalar meson-meson scattering in order to investigate the implications of duality and absence of exotics. We are particularly interested in the exotic channels of the elastic amplitude, where we find that unitarity corrections produce low lying trajectories appearing also in the non-exotic channels. w e leading trajectory, however, which only contributes to the non-exotic channels, is found to have the same exchange degeneracy properties as the input trajectory.Simple calculations can be performed if we approximate the production amplitude T, by the planar VENEZIANO (n + 2)-point function with cyclic and anticyclic symmetry l )The dependence on the SU(3)-quantum numbers is given by the trace of I-matrices which may be regarded as the coupling matrices of the external 1 l ) In the following we use the abbreviation <A> =tr(A). 2 K. J. BIEBL, et al. : Exchange-degenerate and Exotic Trajectories