The possible $K^{\ast }\hat{I}{\pounds }^{\ast }$ molecular state

Abstract

Within the framework of the one-boson-exchange model, we systematically investigate the interaction between the vector meson $K^{\ast }$ and the baryon $\hat{I}{\pounds }^{\ast }$ with the aim of exploring the possibility of forming hadronic molecular states. The $K^{\ast }\hat{I}{\pounds }^{\ast }$ interaction potential is constructed from $\ddot{I}$, $\ddot{I}‰$, and $\ddot{I}€$ meson exchanges, and the nonrelativistic Schrödinger equation is solved using the Gaussian expansion method. The binding energies are calculated for different total angular momenta $J^P$ and isospin channels $I=1/2$ and $I=3/2$. Our results show that $S$--$D$ wave mixed $K^{\ast }\hat{I}{\pounds }^{\ast }$ molecular states with $J^P=1/2^{-}$ can be formed only in the $I=3/2$ channel, while no bound state appears in the $I=1/2$ channel. In addition, the $S$--$D$ wave mixed states with $J^P=3/2^{-}$ and $J^P=5/2^{-}$ are also found to support bound-state solutions. For higher partial-wave states in our study, the binding mechanism mainly arises from the interplay between partial-wave mixing and non-central interactions. In particular, the $J^P=1/2^{+}$ channel does not support a bound state, as the meson-exchange interaction is predominantly repulsive. Our analysis further supports the interpretation of the experimentally observed $N(2250)$ and $\hat{I}”(2200)$ states as $K^{\ast }\hat{I}{\pounds }^{\ast }$ molecular candidates, corresponding to $I=1/2,J^P=9/2^{-}$ and $I=3/2,J^P=7/2^{-}$, respectively.