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

TL;DR

This paper investigates the $\,\phi p$ interaction using a unitary coupled-channel approach, predicting a possible $\,\phi N$ bound state and explaining recent experimental scattering data.

Contribution

It introduces a unitary coupled-channel model inspired by Bethe-Salpeter equations to analyze the $\,\phi p$ interaction and predicts a novel $\,\phi N$ bound state.

Findings

The model reproduces experimental scattering lengths.

Identifies a two-pole structure in the $\,\phi p$ amplitude.

Predicts a $\,\phi N$ bound state at 1949-i3 MeV.

Abstract

The strong attractive interaction of the $\phi$ meson and the proton is reported by ALICE collaboration recently. 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 approach inspired by Bethe-Salpeter equation. The $\phi p$ scattering length is calculated based on this approach, 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 $\phi p$ scattering amplitude. One of the pole, locating at $(1969-i283)$~MeV might correspond to $N(1895)1/2^-$ or $N(1875)3/2^-$ listed in the review of the Particle Data Group(PDG). The other one, locating at ${1949-i3}$~MeV should be a $\phi N$ bound state, which has no counterpart in the PDG data.