Possible molecular states from the $N\Delta$ interaction

Recently, a hint for dibaryon $N\Delta(D_{21})$ was observed at WASA-AT-COSY with a mass about $30\pm10$ MeV below the $N\Delta$ threshold. It has a relatively small binding energy compared with the $d^*(2380)$ and a width close to the width of the $\Delta$ baryon, which suggests that it may be a dibaryon in a molecular state picture. In this work, we study the possible $S$-wave molecular states from the $N\Delta$ interaction within the quasipotential Bethe-Salpeter equation approach. The interaction is described by exchanging $\pi$, $\rho$, and $\omega$ mesons. With reasonable parameters, a $D_{21}$ bound state can be produced from the interaction. The results also suggest that there may exist two more possible $D_{12}$ and $D_{22}$ states with smaller binding energies. The $\pi$ exchange is found to play the most important role to bind two baryons to form the molecular states. An experimental search for possible $N\Delta(D_{12})$ and $N\Delta(D_{22})$ states will be helpful for understanding the hint of the dibaryon $N\Delta(D_{21})$.