Possible existence of a dibaryon candidate $NΔ$ ($D_{21}$)
Inspired by the experimental report by WASA-at-COSY Collaboration, we investigate the possibile existence of the dibaryon candidate $NΔ$ with quantum numbers $IJ^P=21^+$ ($D_{21}$). The dynamical calculation shows that we cannot obtain the bound $D_{21}$ state in the models which can obtain the experimental $d^{*}$. %although the $D_{21}$ state can bound in the range of parameters in quark models. The low-energy scattering phase shifts of the $N-Δ$ scattering give the same conclusion. Besides, the mass calculation by using the Gursey-Radicati mass formula and the analysis of the matrix elements of the color magnetic interaction show that the mass of $D_{21}$ is larger than that of $D_{12}$ ($NΔ$ with $IJ^P=12^+$), which indicate that it is less possible for the $D_{21}$ than the $D_{12}$ to form bound state.