Understanding the structure of $d^*(2380)$ in chiral quark model
The structure and decay properties of $d^*$ have been detailedly investigated in both the chiral SU(3) quark model and the extended chiral SU(3) quark model that describe the energies of baryon ground states and the nucleon-nucleon (NN) scattering data satisfactorily. By performing a dynamical coupled-channels study of the system of $\Delta\Delta$ and hidden-color channel (CC) with quantum numbers $I(J^P)=0(3^+)$ in the framework of the resonating group method (RGM), we find that the $d^*$ has a mass of about $2.38-2.42$ GeV and a root-mean-square radius (RMS) of about $0.76-0.88$ fm. The channel wave function is extracted by a projection of the RGM wave function onto the physical basis, and the fraction of CC component in the $d^*$ is found to be about $66\%-68\%$, which indicates that the $d^*$ is a hexaquark-dominated exotic state. Based on this scenario the partial decay widths of $d^*\to d \pi^0 \pi^0$ and $d^*\to d \pi^+\pi^-$ are further explicitly evaluated and the total width is then obtained by use of the branching ratios extracted from the measured cross sections of other possible decay channels. Both the mass and the decay width of $d^*$ calculated in this work are compatible with the data ($M\approx 2380$ MeV, $\Gamma\approx 70$ MeV) reported by WASA-at-COSY Collaboration.