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

Abstract

The strong attractive interaction of the $\varphi$ meson and the proton is reported by ALICE collaboration recently. The corresponding scattering length $f_0$ is given as $Re(f_0)=0.85\pm 0.34(stat)\pm 0.14(syst)$fm and $Im(f_0)=0.16\pm 0.10(stat)\pm 0.09(syst)$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 $\varphi p$ scattering length is calculated based on this approach, and it is found that the experimental value of the $\varphi p$ scattering length can be obtained only if the attractive interaction of the $\varphi$ meson and the proton is taken into account. A significant outcome of such attractive interaction is a two-pole structure in the $\varphi p$ 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 $\varphi N$ bound state, which has no counterpart in the PDG data.

9 pages, 2 figures and 4 tables. To be published in Communications in Theoretical Physics

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Cited by in corpus (4)

• Indication of a p-$\varphi$ bound state from a correlation function analysis
• Examination of the $\varphi -NN$ bound-state problem with lattice QCD $N-\varphi$ potentials
• Dynamically generated states from the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems within the fixed-center approximation
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram