Two-Channel Model ofP11 π−NPartial-Wave Amplitude

A simple two-channel model of the $P_{11} \pi -N$ channel and a phenomenological second channel, the $\sigma -N$, is constructed. It is shown that this model reproduces the detailed structure of the $\pi -N$ phase shift and produces the nucleon pole as a dynamical bound state with the proper residue. On the basis of this model it is argued that the forces required in the second channel are comparable to those in the $\pi -N$ channel, and a significant portion of the binding of the nucleon is produced by the $\sigma -N$ channel. Finally, it is observed that the Roper resonance (600 MeV) corresponds to a pole in the $S$ matrix, and should be fitted into an ${\mathrm{SU}}_3$ multiplet.