Coupled-channels study of the $\pi^{-}p \to \eta n$ process

The reaction $\pi^{-}p \to \eta n$ is investigated within a dynamical coupled-channels model of meson production reactions in the nucleon resonance region. The meson baryon channels included are $\pi N$, $\eta N$, $\pi \Delta$, $\sigma N$, and $\rho N$. The non-resonant 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 $\pi^{-}p \to \eta n$ 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 as well as the predicted $\eta N$ scattering length are discussed.