Pion-nucleon scattering: The P11 channel

A simple model is presented for the πN scattering in the P11 channel from the threshold to the Roper resonance N(1470). The model starts with the πBB′ coupling of the Yukawa type where B (and B') stands for N, R or Δ. A unitarized scattering amplitude is constructed from the K-matrix which is obtained perturbatively. With appropriate coupling constants and form factors for the πBB′ interactions, which conform to the quark model, the P11 scattering can be well reproduced. It is emphasized that the process πN → ππΔ → πN, which has been ignored hitherto, plays a crucial role in the energy region considered.