The ϕ p bound state in the unitary coupled-channel approximation

Abstract

Abstract The strong attractive interaction of the ϕ meson and the proton has recently been reported by the ALICE Collaboration. The corresponding scattering length f 0 is given as Re ( f 0 ) = 0.85 ± 0.34 ( stat ) ± 0.14 ( syst ) and Im ( f 0 ) = 0.16 ± 0.10 ( stat ) ± 0.09 ( syst ) fm. The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of 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 the Bethe–Salpeter equation. The ϕ p scattering length is calculated based on this approach, and it is found that the experimental value of the ϕ p 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 attractive interaction is a two-pole structure in the ϕ p scattering amplitude. One of the poles, located at (1969 − i283) MeV might correspond to N(1895)1/2− or N(1875)3/2− as listed in the review of the Particle Data Group (PDG). The other one, located at 1949 − i3 MeV should be a ϕ N bound state, which has no counterpart in the PDG data.