The $η'N$ interaction from a chiral effective model and $η'$-$N$ bound state

The $η'$ 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 $η'N$ 2body interaction which is the foundation of the in-medium $η'$ properties using the linear sigma model as a chiral effective model. The $η'N$ 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 $ηN$ transition is included in our calculation, and is important for the imaginary part of the $η'$-optical potential. The transition amplitude of $η'N$ to the $ηN$ channel is relatively small compared to that of elastic channel. From the analysis of the $η'N$ 2body system, we find a $η'N$ 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.

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