$\phi$ meson self-energy in nuclear matter from $\phi N$ resonant interactions

The $\phi$-meson properties in cold nuclear matter are investigated by implementing resonant $\phi N$ interactions as described in effective approaches including the unitarization of scattering amplitudes. Several $N^*$-like states are dynamically generated in these models around $2$ GeV, in the vicinity of the $\phi N$ threshold. We find that both these states and the non-resonant part of the amplitude contribute sizably to the $\phi$ collisional self-energy at finite nuclear density. These contributions are of a similar strength as the widely studied medium effects from the $\bar K K$ cloud. Depending on model details (position of the resonances and strength of the coupling to $\phi N$) we report a $\phi$ broadening up to about $40$-$50$ MeV, to be added to the $\phi\to\bar K K$ in-medium decay width, and an attractive optical potential at threshold up to about $35$ MeV at normal matter density. The $\phi$ spectral function develops a double peak structure as a consequence of the mixing of resonance-hole modes with the $\phi$ quasi-particle peak. The former results point in the direction of making up for missing absorption as reported in $\phi$ nuclear production experiments.