The possible $K^{*}\Sigma^{*}$ molecular state

Abstract

Within the framework of the one-boson-exchange model, we systematically investigate the interaction between the vector meson $K^{*}$ and the baryon $\Sigma^{*}$ with the aim of exploring the possibility of forming hadronic molecular states. The $K^{*}\Sigma^{*}$ interaction potential is constructed from $\rho$, $\omega$, and $\pi$ meson exchanges, and the nonrelativistic Schr\"odinger 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 $K^{*}\Sigma^{*}$ 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 due to destructive interference of the interaction potentials in isospin space. 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, the binding mechanism is governed by the interplay of partial-wave mixing, tensor forces, and spin--orbit interactions. In particular, the $J^{P}=1/2^{+}$ channel does not support a bound state because the meson-exchange interaction is predominantly repulsive. Our analysis further supports the interpretation of the experimentally observed $N(2250)$ and $\Delta(2200)$ states as $K^{*}\Sigma^{*}$ molecular states, corresponding to $I=1/2,\ J^{P}=9/2^{-}$ and $I=3/2,\ J^{P}=7/2^{-}$, respectively.