Update of the pi N --> eta N and eta N --> eta N partial-wave amplitudes

Abstract

A three-channel, multi-resonance, unitary model developed in 1995 is used to determine the $πN \rightarrow ηN$ and $ηN \rightarrow ηN$ amplitudes using as input the latest data for the dominant $S_{11}$ $πN$ elastic scattering partial wave following suggestions of Prof. G. Höhler. The sign error in the numerical evaluation of the dispersion integral in the original publication is eliminated. The remaining weighted data set for the $πN \rightarrow ηN$ total and differential cross sections is used as in the original publication. The correction of the numerical error influences the $ηN$ cusp effect and improves the quality of the fit to the input data. However, our new result for the $ηN$ scattering length, $a_{ηN }= (0.717 \pm 0.030) + i (0.263 \pm 0.025)$ fm, is a sole consequence of the correction of the $S_{11}$ input and suggests that the $ηd$ system is unbound or loosely bound.