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

TL;DR

This paper investigates the electromagnetic form factors of the $d^*(2380)$ resonance to understand its internal structure, calculating various form factors and comparing different structural models to identify key physical characteristics.

Contribution

It provides detailed calculations of the electromagnetic form factors of $d^*(2380)$ using a coupled channel model and compares different structural hypotheses to distinguish its internal configuration.

Findings

Magnetic dipole moment of 7.602 nuclear magnetons

Electric quadrupole deformation of 2.53×10^(-2) fm^2

Small quadrupole deformation suggests a slightly oblate shape

Abstract

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 $d^*(2380)$.