Invariant Amplitudes for Studying the Parity Content of Duality

Kinematic-singularity-free parity-conserving helicity amplitudes are used to obtain a new set of amplitudes. These new amplitudes can be approximated in any dynamical theory; they have the advantage that resonances with definite parity frequently decouple from certain amplitudes. This simplifies study of the parity content of duality. We give the new amplitudes for the reactions $N\overline{N}\to N\overline{N}$ and $\rho \pi \to \pi \rho$. Using these amplitudes, we formulate a Veneziano-like model for these reactions with the additional requirement that each trajectory have unique quantum numbers -i.e., no conspiracies are allowed. In $N\overline{N}$, we find that no $\pi$-like trajectories can participate in such a bootstrap. Results for $\rho \pi$ scattering are less striking, but the reduction of number of terms due to parity requirements is easily demonstrated.