Decay width of $d^*(2380) \to NN \pi$ process in a chiral constituent quark model

The width of three-body single-pion decay process $d^*\to NN\pi^{0,\pm}$ is calculated by using the $d^*$ wave function obtained from our chiral SU(3) constituent quark model calculation. The effect of the dynamical structure on the width of $d^*$ is taken into account in both the single $\Delta\Delta$ channel and coupled $\Delta\Delta+CC$ two-channel approximations. Our numerical result shows that in the coupled-channel approximation, namely, the hidden-color configuration being considered, the obtained partial decay width of $d^*\to NN\pi$ is about several hundred $\rm {KeV}$, while in the single $\Delta\Delta$ channel it is just about $2\sim 3~\rm{MeV}$. We, therefore, conclude that the partial width in the single-pion decay process of $d^*$ is much smaller than the widths in its double-pion decay processes. Our prediction may provide a criterion for judging different interpretations of the $d^*$ structure, as different pictures for the $d^*$ may result quite different partial decay width.