π−ρScattering in the Veneziano Model

The conditions for nondegeneracy of the leading trajectory in scalar-vector scattering are derived. They are applied to the Veneziano model for the pion contribution to the $\pi -\rho$ scattering amplitude. A general class of models for the double-charge-exchange process is found, and a "minimal" model is discussed in detail. The Adler self-consistency condition and its relation to the quantization rules of Ademollo et al. is discussed. The possible existence of exotic resonances or an $I=0\mathrm{}$ trajectory degenerate with the $\pi$ trajectory is also discussed.