Analysis of the low-energy ηNN-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 (Jπ;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.