Direct-Channel Resonances in Antiproton-Proton Elastic Scattering

The effect of a direct-channel resonance on antiproton-proton elastic scattering is investigated. The differential cross section has a nonresonant term, a pure resonant term, and an interference term. It is not possible to say much about the interference term. The angular shape of the pure resonant term depends upon the resonance quantum numbers $C$ and $P$, as well as the spin $J$, but in general resembles the square of the Legendre polynomial $P_J\left(\theta \right)$. The possibility of a background amplitude in the resonant partial waves affects the enhancements in the total elastic and total cross sections.