Hidden-strange molecular states and the $Nϕ$ bound state via a QCD van der Waals force

Abstract

In this work, we study the hidden-strange molecular states composed of a baryon and a vector meson in a coupled-channel $Nρ-Nω-Nϕ-ΛK^*-ΣK^*$ interaction. With the help of the effective Lagrangians which coupling constants are determined by the SU(3) symmetry, the interaction is constructed and inserted into the quasipotential Bethe-Salpeter equation to search for poles in the complex plane, which correspond to molecular states. Two poles are found with a spin parity $3/2^-$ near the $Nρ$ and the $ΣK^*$ thresholds, which can be related to the $N(1700)$ and the $N(2100)$, respectively. No pole near the $Nϕ$ threshold can be found if direct interaction between a nucleon and $ϕ$ meson is neglected according to the OZI rule. After introducing the QCD van der Waals force between a nucleon and $ϕ$ meson, a narrow state can be produced near the $Nϕ$ threshold. Inclusion of the QCD van der Waals force changes the line shape of the invariant mass spectrum in the $Nϕ$ channel leading to a worse agreement with the present low-precision data. Future experiments at BelleII, JLab, and other facilities will be very helpful to clarify the existence of these possible hidden-strange molecular states.