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

The decay widths of four-body double-pion decays $d^{*}\to pn{\pi }^0{\pi }^0,d^{*}\to pn{\pi }^{+}{\pi }^{-}$, and isoscalar parts of $d^{*}\to pp{\pi }^0{\pi }^{-}$ and $d^{*}\to nn{\pi }^{+}{\pi }^0$ are explicitly calculated with the help of the $d^{*}$ wave function obtained in a chiral SU(3) quark model calculation. The effect of the dynamical structure on $d^{*}$'s width is analyzed both in the single $\mathrm{\Delta }\mathrm{\Delta }$ channel and the $\mathrm{\Delta }\mathrm{\Delta }+CC$ coupled-channel approximations. It is found that in the latter case, the obtained partial decay widths of $d^{*}\to pn{\pi }^0{\pi }^0,d^{*}\to pn{\pi }^{+}{\pi }^{-}$, and those of $d^{*}$ to the isoscalar parts of $pp{\pi }^0{\pi }^{-}$ and $nn{\pi }^{+}{\pi }^0$ are about $9.6\mathrm{MeV},20.6\mathrm{MeV},3.5\mathrm{MeV}$ and $3.5\mathrm{MeV}$, respectively. As a consequence, the total width is about $71.9\mathrm{MeV}$. These widths are consistent with our previous estimation by using cross section data and observed width. Apparently, the resultant mass and width in the $\mathrm{\Delta }\mathrm{\Delta }+CC$ coupled-channel calculation again support our assertion that the $d^{*}$ resonance is a six-quark dominated exotic state.

Figure 1

Four possible emission ways in the decay of the $d^{*}$ resonance composed of the $\mathrm{\Delta }\mathrm{\Delta }$ structure only. Two pions with momenta of ${\vec{k}}_{1,2}$ are emitted from one of the three quarks in $2 \mathrm{\Delta }\mathrm{s}$, respectively.