Dynamical theory for theP-wave pion-nucleon interaction

Abstract

We present a dynamical theory of low energy $P$-wave $\ensuremath{\pi}N$ interaction. The theory is an extension of the Chew-Low theory, with three additional features, namely, (1) inclusion of the full nucleon recoil effect, (2) inclusion of the $Z$ graphs, and (3) inclusion of $P11$ channel inelasticity. The second feature is new in a $P$-wave theory based on the Low expansion. We are able to fit the $P33$ and the $P11$ phase shifts in the energy region $0<{T}_{\ensuremath{\pi}}<250$ MeV quite well. In particular, we show that it is possible to explain the change of sign of the $P11$ phase shift, ${T}_{\ensuremath{\pi}}\ensuremath{\sim}150$ MeV, in terms of the strong inelasticity present in the channel. For the $P13$ and $P31$ channels, where the phase shifts are the smallest, we do reasonably well at threshold, but not so well as the energy increases. We have also examined the structure of the off-mass-shell amplitudes in the $P11$ and $P33$ channels. Only the $P33$ channel amplitude is found to be factorable. A major result of our work is that the $P33$ form factor is very hard. If one used a monopole form, the form factor mass should be $10{m}_{\ensuremath{\pi}}$ or larger.NUCLEAR REACTIONS Pion-nucleon interaction, $Z$-graph term, sigma exchange term, $P33$ resonance, form factor of $P33$ amplitude, $P11$ inelasticity, nonstatic kinematics.