Analysis of the low-energy $\mth{\eta}$NN-dynamics within a three-body formalism

A. Fix; H. Arenhövel

doi:doi:10.1007/s100500070062

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Hadrons and Nuclei

Eur. Phys. J. A 9, 119-129

Analysis of the low-energy $\mathsf\eta$ NN-dynamics within a three-body formalism

A. Fix¹ - H. Arenhövel²

¹ Tomsk Polytechnic University, 634034 Tomsk, Russia
² Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany

Received: 27 June 2000
Communicated by W. Weise

Abstract
The interaction of an $\eta$ -meson with two nucleons is studied within a three-body approach. The major features of the $\eta NN$ -system in the low-energy region are accounted for by using a s-wave separable ansatz for the two-body $\eta N$ and NN amplitudes. The calculation is confined to the $(J^\pi;T)=(0^-;1)$ and (1^-;0)configurations which are assumed to be the most promising candidates for virtual or resonant $\eta NN$ -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 $\eta N$ -interaction strength is investigated. The corresponding trajectory, starting on the physical sheet, moves around the $\eta NN$ three-body threshold and continues away from the physical area giving rise to virtual $\eta NN$ -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 $\eta NN$ -resonances were found. The possible influence of virtual poles on the low-energy $\eta NN$ -scattering is discussed.