Decay width of $d^{\ast }(2380)\to NN\pi \pi$ processes

Abstract

The decay widths of four-body double-pion decays $\text{ds}\to pn{\pi }^0{\pi }^0$, $\text{ds}\to pn{\pi }^{+}{\pi }^{-}$, and iso-scalar parts of $\text{ds}\to pp{\pi }^0{\pi }^{-}$ and $\text{ds}\to nn{\pi }^{+}{\pi }^0$ are explicitly calculated with the help of the $d^{\ast }$ wave function obtained in a chiral SU(3) quark model calculation. The effect of the dynamical structure on $\text{ds}$'s width is analyzed both in the single $\Delta \Delta$ channel and coupled $\Delta \Delta$ and $CC$ channel approximations. It is found that in the coupled-channel approximation, the obtained partial decay widths of $\text{ds}\to pn{\pi }^0{\pi }^0$, $\text{ds}\to pn{\pi }^{+}{\pi }^{-}$, and those of $d^{\ast }$ to the iso-scalar parts of $pp{\pi }^0{\pi }^{-}$ and $nn{\pi }^{+}{\pi }^0$ are about $7.4$MeV, $16.4$MeV, $3.5$MeV and $3.5$MeV, respectively As a consequence, the total width is about $64.5$MeV. These widths are consistent with those estimated by using the corresponding cross section data in our previous investigation and also the observed data. But in the single $\Delta \Delta$ channel approximation, the widths are still almost 2-times larger than the measured values. Apparently, the explicitly calculated width together with the evaluated mass of $d^{\ast }$ in the coupled $\Delta \Delta$ and $CC$ channel approximation can well explain the observed data, which again supports our assertion that the $\text{ds}$ resonance is a six-quark dominated exotic state.

Comments: 6 pages, 1 figure, 1 table