On the form factors of $d^*(2380)$

In order to explore the possible physical quantities for judging different structures of the newly observed resonance $d^*(2380)$, we study its electromagnetic form factors. In addition to the electric charge monopole $C0$, we calculate its electric quadrupole $E2$, magnetic dipole $M1$, and six-pole $M3$ form factors on the base of the realistic coupled $\Delta\Delta+CC$ channel $d^*$ wave function with both the $S$- and $D$-partial waves. The results show that the magnetic dipole moment and electric quadrupole deformation of $d^*$ are 7.602 and $2.53\times 10^{-2}~\rm{fm}^2$, respectively. The calculated magnetic dipole moment in the naive constituent quark model is also compared with the result of $D_{12}\pi$ picture. By comparing with partial results where the $d^*$ state is considered with a single $\Delta\Delta$ and with a $D_{12}\pi$ structures, we find that in addition to the charge distribution of $d^*(2380)$, the magnetic dipole moment and magnetic radius can be used to discriminate different structures of $d^*$. Moreover, a quite small electric quadrupole deformation indicates that $d^*$ is more inclined to an slightly oblate shape due to our compact hexaquark dominated structure of $d^*(2380)$.