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 magnetic octupole $M3$ form factors on the base of the realistic coupled $\mathrm{\Delta }\mathrm{\Delta }+C_8{C}_8$ 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 $2.53\times {10}^{-2}{\mathrm{fm}}^2$, 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 $\mathrm{\Delta }\mathrm{\Delta }$ and with a $D_{12}\pi$ structures, we find that in addition to the charge distribution of $d^{*}$, 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 a slightly oblate shape due to our compact hexaquark dominated structure of $d^{*}$.

• Received 16 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.114002

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Published by the American Physical Society