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

TL;DR

This study investigates hidden-strange molecular states involving baryons and vector mesons using a coupled-channel approach and QCD van der Waals forces, predicting possible bound states near the $N ho$, $ ext{K}^*$, and $N ext{phi}$ thresholds.

Contribution

It introduces the role of QCD van der Waals forces in forming $N ext{phi}$ bound states, providing a novel mechanism for hidden-strange molecular state formation.

Findings

Two poles near $N ho$ and $ ext{K}^*$ thresholds related to $N(1700)$ and $N(2100)$.

No $N ext{phi}$ pole without QCD van der Waals force.

QCD van der Waals force produces a narrow $N ext{phi}$ state, altering the invariant mass spectrum.

Abstract

In this work, we study the hidden-strange molecular states composed of a baryon and a vector meson in a coupled-channel $N\rho-N\omega-N\phi-\Lambda K^*-\Sigma K^*$ 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 $N\rho$ and the $\Sigma K^*$ thresholds, which can be related to the $N(1700)$ and the $N(2100)$, respectively. No pole near the $N\phi$ threshold can be found if direct interaction between a nucleon and $\phi$ meson is neglected according to the OZI rule. After introducing the QCD van der Waals force between a nucleon and $\phi$ meson, a narrow state can be produced near the $N\phi$ threshold. Inclusion of the QCD van der Waals force changes the line shape of the invariant mass spectrum in the $N\phi$ 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.