ANALYTIC SOLUTION OF LINEAR-TRAJECTORY BOOTSTRAP

The quark-model bootstrap previously proposed is extended to include the lower trajectories. The extension is obtained by showing that the factorization properties of the multiparticle Veneziano amplitude can be generalized to the resonances on the lower trajectories. All trajectories other than the leading trajectory are degenerate, and the degeneracy increases rapidly as we go downward. Apart from the fundamental narrow-resonance approximation, the solution of the bootstrap model is exact. If we make a hypothesis regarding the simplicity of the spectrum of the lower trajectories, then the solution appears to be unique to within a finite number of constants. The inconsistency associated with negative widths remains, and any improvement in this respect will probably require going beyond the narrow-resonance approximation. © 1969 The American Physical Society.