Formation reaction of $\eta'(958)$-mesic nuclei and $U_A(1)$ anomaly at finite density in NJL model

The huge mass of the $\eta'(958)$ meson is believed to have close connection with the breaking of the axial $U(1)$ symmetry at the quantum level referred as {\it the $U_A(1)$ anomaly}. There are many theoretical studies for the effects of the $U_A(1)$ anomaly on the $\eta'$ meson, not only in vacuum, but also at finite temperature and finite density, which suggest the possible character changes of $\eta'$ at finite temperature and/or finite density. At the present time, however, there exists no experimental information on the property and behavior of the $U_A(1)$ anomaly at finite density. In this presentation, we propose the formation reaction of the $\eta'$-mesic nuclei in order to investigate the $\eta'$ properties, especially its mass shift, at finite density. We apply the NJL model to describe $\eta'$ properties in nuclear medium, and show the clear relations between NJL parameters and expected reaction spectra, which should be the first step to get deeper insights on $U_A(1)$ anomaly at finite density from experimental data. The $\eta'$ mass in the medium should provide us important information on the properties of the $U_A(1)$ anomaly in the nuclear medium.