In-medium \eta' mass and \eta'N interaction in vacuum in the linear sigma model

Abstract

We investigate the \eta'N two-body interaction in the context of the \eta' meson mass modification in the nuclear medium. It has been argued in several articles that the masses of \eta' and the other pseudoscalar mesons (\pi, K, \eta) should degenerate in the chiral-symmetric phase. It is expected that the reduction of the mass difference between eta and eta' would take place in the nuclear matter if one assumes that the decrease of the quark condensate at the normal nuclear density occurs with partial restoration of chiral symmetry. At low density, the in-medium self-energy giving the mass modification by the medium effect can be obtained by the \eta'N two-body T matrix. Thus, we also estimate the \eta'N interaction strength in vacuum with the linear sigma model which involves the effect of partial restoration of chiral symmetry. In the view of the linear sigma model, we find that the \eta'N interaction is attractive and generated through the sigma meson exchange.We expect that the interaction is enough strong and for the existence of a bound state of the \eta'N system.