Off-shell model for threshold pionicηproduction on a nucleon and forηNscattering

An off-shell isobar model for πN→πN, πN→ηN, and ηN→ηN t matrices is presented. The πN, ηN, and πΔ+(ππN) channels are treated in a coupled-channel formalism. We are able to determine various vertex functions of the model by using only πN (complex) phase shifts in $S_{11}$, $P_{11}$, $D_{13}$, and $P_{33}$ partial waves. The model gives good predictions for ${\pi }^{\mathrm{-}}$p→ηn cross sections. It also predicts an attractive S-wave ηN interaction.