The $φp$ bound state in the unitary coupled-channel approximation

TL;DR

This work addresses the attractive $\phi p$ interaction observed by ALICE and seeks a dynamical description that reproduces the scattering length. It combines a hidden gauge formalism for vector-meson–baryon octet interactions with a unitary coupled-channel (Bethe-Salpeter) framework, augmented by an attractive Yukawa-type $\phi N$ potential to capture elastic and inelastic channel dynamics near threshold. The analysis yields a $\phi N$ scattering length consistent with experiment and reveals a two-pole structure: a bound state at $1949-i\,3$ MeV below threshold and a resonance at $1969-i\,283$ MeV above threshold, both degenerate in $J^P=1/2^-,3/2^-$. The bound state strongly couples to $\phi N$, $K^*\Lambda$, and $K^*\Sigma$, while the resonance couples predominantly to $K^*\Lambda$ and $K^*\Sigma$, with no PDG counterparts, highlighting a novel, data-inspired two-pole structure in the $\phi N$ system.

Abstract

The attractive interaction of the $φ$ meson and the proton is reported by the 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 dominating role of the elastic scattering, whereas the inelastic process is less important. In this work, such scattering processes are inspected on the basis of a unitary coupled-channel approximation inspired by the Bethe-Salpeter equation. The $φp$ scattering length is calculated and it is found that the experimental value of the $φp$ scattering length can be obtained only if the attractive interaction of the $φ$ meson and the proton is taken into account. A significant outcome of such an attractive interaction is a two-pole structure in the scattering amplitude. One of the poles, located at $1969-i283$ MeV, might be a resonance state of $φN$, while the other pole, located at $1949-i3$ MeV, should be a bound state of $φN$. Both of these states do not have counterparts in the data of the Particle Data Group(PDG).