The ${\eta }^{\prime }N$ interaction from a chiral effective model and ${\eta }^{\prime }$-$N$ bound state

Abstract

The ${\eta }^{\prime }$ mass reduction in the nuclear medium is expected from the degeneracy of the pseudoscalar-singlet and octet mesons when chiral symmetry is manifest. In this study, we investigate the ${\eta }^{\prime }N$ 2body interaction which is the foundation of the in-medium ${\eta }^{\prime }$ properties using the linear sigma model as a chiral effective model. The ${\eta }^{\prime }N$ interaction in the linear sigma model comes from the scalar meson exchange with U${}_A$(1) symmetry effect and is found to be fairly strong attraction. Moreover, the $\eta N$ transition is included in our calculation, and is important for the imaginary part of the ${\eta }^{\prime }$-optical potential. The transition amplitude of ${\eta }^{\prime }N$ to the $\eta N$ channel is relatively small compared to that of elastic channel. From the analysis of the ${\eta }^{\prime }N$ 2body system, we find a ${\eta }^{\prime }N$ bound state with the binding energy $12.3-3.3i$MeV. We expect that this strongly attractive two body interaction leads to a deep and attractive optical potential.

Comments: 6 pages, 2 figures, Contribution to the proceedings of International Conference on Exotic Atoms and Related Topics - EXA2014, September 15-19, 2014, Wien, Austria