The $\phi p$ bound state in the unitary coupled-channel approximation

The attractive interaction of the $\phi$ meson and the proton is reported by ALICE Collaboration, and the corresponding scattering length $f_0$ is given as $Re(f_0)=0.85\pm0.34(stat)\pm0.14(syst)$ fm and $Im(f_0)=0.16\pm0.10(stat)\pm0.09(syst)$ fm. The fact that the real part is significant in contrast to the imaginary part indicates a dominate role of the elastic scattering, whereas the inelastic process is less important. In this work, such scattering processes are inspected based on a unitary coupled-channel approximation inspired by the Bethe-Salpeter equation. The $\phi p$ scattering length is calculated, and it is found that the experimental value of the $\phi p$ scattering length can be obtained only if the attractive interaction of the $\phi$ meson and the proton is taken into account. A significant outcome of such attractive interaction is a two-pole structure in the scattering amplitude. One of the pole, locating at $1969-i283$ MeV, might be a resonance state of $\phi N$, while the other one, locating at $1949-i3$ MeV, should be a $\phi N$ bound state. Both of these two states have no counterparts in the data of Particle Data Group(PDG).