Partial-Wave Analysis ofπ−+p→η+n

It is shown that by using the nucleon pole and a sum of direct-channel resonances, a reasonable fit to both the differential and total cross sections, for the process ${\pi }^{-}+p\to \eta +n$, is obtained for incident-pion laboratory kinetic energies ($T_{\pi }$) between threshold and 1.3 GeV. Inelastic branching ratios for the $\eta n$ channel are predicted with results consistent with experiment. The $\eta$-nucleon coupling constant is found to be $\frac{{g_{\pi \mathrm{NN}}}^2}{4\pi }\lesssim {10}^{-4\mathrm{}}$. By assuming the spin and parity of the $N\left(2650\right)\mathrm{}$ to be $J^P={\frac{11}{2}}^{-}$, agreement with the polarization data near the $N\left(2650\right)\mathrm{}$ is obtained. However, this model can not give a good fit to the differential cross-section data at $T_{\pi }=2.41\mathrm{} \mathrm{and} 2.93$ GeV.