Field-Current Identity, Partially Conserved Currents, and the Veneziano Model

Hard-meson partial conservation of axial-vector current and partial conservation of vector current are imposed upon the Veneziano amplitudes. It is seen that these determine inelastic amplitudes (e.g., $\pi \pi \to \pi A_1$, etc.) in terms of corresponding elastic amplitudes (e.g., $\pi \pi \to \pi \pi$). Mass formulas for the $\kappa$ and $\delta$ meson, equality of many trajectory slopes of either normality, and $\pi K$ scattering lengths are obtained, in good agreement with experiment.