Analysis of the low-energy $η$NN-dynamics within a three-body formalism

Abstract

The interaction of an $η$-meson with two nucleons is studied within a three-body approach. The major features of the $ηNN$-system in the low-energy region are accounted for by using a s-wave separable ansatz for the two-body $ηN$- and $NN$-amplitudes. The calculation is confined to the $(J^π;T)=(0^-;1)$ and $(1^-;0)$ configurations which are assumed to be the most promising candidates for virtual or resonant $ηNN$-states. The eigenvalue three-body equation is continued analytically into the nonphysical sheets by contour deformation. The position of the poles of the three-body scattering matrix as a function of the $ηN$-interaction strength is investigated. The corresponding trajectory, starting on the physical sheet, moves around the $ηNN$ three-body threshold and continues away from the physical area giving rise to virtual $ηNN$-states. The search for poles on the nonphysical sheets adjacent directly to the upper rim of the real energy axis gives a negative result. Thus no low-lying s-wave $ηNN$-resonances were found. The possible influence of virtual poles on the low-energy $ηNN$-scattering is discussed.