Coupled-channels study of theπ−p→ηnprocess

The reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ is investigated within a dynamical coupled-channels model of meson production reactions in the nucleon resonance region. The meson baryon channels included are $\ensuremath{\pi}N,\ensuremath{\eta}N,\ensuremath{\pi}\ensuremath{\Delta},\ensuremath{\sigma}N$, and $\ensuremath{\rho}N$. The nonresonant meson-baryon interactions of the model are derived from a set of Lagrangians by using a unitary transformation method. One or two excited nucleon states in each of $S,P,D$, and $F$ partial waves are included to generate the resonant amplitudes. Data of the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ reaction from threshold up to a total center-of-mass energy of about 2 GeV are satisfactorily reproduced and the roles played by the following nine nucleon resonances are investigated: ${S}_{11}(1535),{S}_{11}(1650),{P}_{11}(1440),{P}_{11}(1710),{P}_{13}(1720),{D}_{13}(1520),{D}_{13}(1700),{D}_{15}(1675)$, and ${F}_{15}(1680)$. The reaction mechanism and the predicted $\ensuremath{\eta}N$ scattering length are discussed.