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.