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

Abstract

The width of three-body single-pion decay process $d^{\ast }\to NN{\pi }^{0,\pm }$ is calculated by using the $d^{\ast }$ wave function obtained from our chiral SU(3) constituent quark model calculation. The effect of the dynamical structure on the width of $d^{\ast }$ 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 $d^{\ast }\to NN\pi$ is about several hundred $\mathrm{KeV}$, while in the single $\Delta \Delta$ channel it is just about $2\sim 3\mathrm{MeV}$. We, therefore, conclude that the partial width in the single-pion decay process of $d^{\ast }$ is much smaller than the widths in its double-pion decay processes. Our prediction may provide a criterion for judging different interpretations of the $d^{\ast }$ structure, as different pictures for the $d^{\ast }$ may result quite different partial decay width.

Comments: 6 pages, 1 figure, and 1 table, typos corrected