π N →η N and η N →η N partial-wave T matrices in a coupled, three-channel model

The \ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\eta}N and \ensuremath{\eta}N\ensuremath{\rightarrow}\ensuremath{\eta}N partial-wave T matrices for the eight lowest partial waves have been obtained in a three-coupled-channel model with unitarity manifestly imposed. The two physical channels are \ensuremath{\pi}N and \ensuremath{\eta}N, and the third channel, \ensuremath{\pi}\ensuremath{\pi}N is an effective, but unphysical two-body channel which represents all remaining processes. The \ensuremath{\pi}N elastic phase shifts and the weighted data base of the \ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\eta}N total and differential cross sections are chosen as the input for the fitting procedure. A model containing a single resonance in each of the three partial waves that dominates the \ensuremath{\eta} production at lower energies is compared with previous analyses, based on similar assumptions. A multiresonance coupled-channel model is introduced which significantly improves the agreement with all input data. Our results are compared with a complementary multiresonance coupled-channel analysis that is constrained with elastic and continuum production channels. The inclusion of the fourth ${\mathit{P}}_{11}$ resonance in the 1440\char21{}2200 MeV region further improves the agreement between the analysis and the data.