Investigation on the electromagnetic properties of the \( D^{(*)} \Sigma _c^{(*)}\) molecules

We systematically explore their electromagnetic characteristics to improve our understanding of the quark-gluon dynamics underlying the complex and controversial nature of multiquark systems. In this study, the magnetic dipole moments of \( D \Sigma _c\), \( D \Sigma _c^{*}\) and \( D^{*} \Sigma _c\) doubly-charmed pentaquarks are extracted, which are directly related to the inner organization of the relevant states. The magnetic dipole moments of these pentaquarks are evaluated employing the QCD light-cone sum rules technique with isospin spin-parity \(\mathrm{I(J^P)} = \frac{1}{2}(\frac{1}{2}^-)\), \(\mathrm{I(J^P)} = \frac{1}{2}(\frac{3}{2}^-)\) and \(\mathrm{I(J^P)} = \frac{1}{2}(\frac{3}{2}^-)\), for \( D \Sigma _c\), \( D \Sigma _c^{*}\) and \( D^{*} \Sigma _c\) doubly-charmed pentaquarks, respectively. Our predictions for the magnetic dipole moment \(\mu _{D\Sigma _c} = 2.98^{+0.76}_{-0.54}~\mu _N\) for the \( D \Sigma _c\) pentaquark, \(\mu _{D\Sigma _c^*} = 1.65^{+0.45}_{-0.34}~\mu _N\) for the \(D\Sigma _c^*\) pentaquark, and \(\mu _{D^*\Sigma _c} = -3.63^{+0.79}_{-0.60}~\mu _N\) for the \(D^*\Sigma _c\) pentaquark. Furthermore, we have also extracted the electric quadrupole and the magnetic octupole moments of the \( D \Sigma _c^{*}\) and \( D^{*} \Sigma _c\) doubly-charmed pentaquarks. These values show a non-spherical charge distribution. As a by-product, the magnetic dipole moments of the isospin-\(\frac{3}{2}\) partners associated with these doubly-charmed pentaquarks have also been determined. The magnetic dipole moments are calculated as follows: \(\mu _{D\Sigma _c} = 3.78^{+0.94}_{-0.70}~\mu _N\), \( \mu _{D\Sigma _c^*} = 2.08^{+0.57}_{-0.43}~\mu _N\), \(\mu _{D^*\Sigma _c} = -4.59^{+0.99}_{-0.76}~\mu _N\) for the isospin-\(\frac{3}{2}\) partners \( D \Sigma _c\), \( D \Sigma _c^{*}\) and \( D^{*} \Sigma _c\) doubly-charmed pentaquarks, respectively. We hope that our predictions of the magnetic dipole moments of the doubly-charmed pentaquarks, in conjunction with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these intriguing pentaquarks, will prove valuable in the search for these states in future experiments and in elucidating the internal structure of these pentaquarks.