Eur. Phys. J. A (2025) 61: 10
https://doi.org/10.1140/epja/s10050-024-01477-2

Regular Article - Theoretical Physics

Investigation on the electromagnetic properties of the $D_{}^{(\ast )}\mathrm{\Sigma }_c^{(\ast )}$ molecules

Health Services Vocational School of Higher Education, Istanbul Aydin University, 34295, Istanbul, Türkiye

^a ulasozdem@aydin.edu.tr

Received: 25 October 2024
Accepted: 20 December 2024
Published online: 23 January 2025

Abstract

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 $D{\mathrm{\Sigma }}_c$, $D\mathrm{\Sigma }_c^{\ast }$ and $D_{}^{\ast }{\mathrm{\Sigma }}_c$ 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 $\mathrm{I}({\mathrm{J}}^{\mathrm{P}})=\frac{1}{2}({\frac{1}{2}}^{-})$, $\mathrm{I}({\mathrm{J}}^{\mathrm{P}})=\frac{1}{2}({\frac{3}{2}}^{-})$ and $\mathrm{I}({\mathrm{J}}^{\mathrm{P}})=\frac{1}{2}({\frac{3}{2}}^{-})$, for $D{\mathrm{\Sigma }}_c$, $D\mathrm{\Sigma }_c^{\ast }$ and $D_{}^{\ast }{\mathrm{\Sigma }}_c$ doubly-charmed pentaquarks, respectively. Our predictions for the magnetic dipole moment ${\mu }_{D{\mathrm{\Sigma }}_c}=2.{98}_{-0.54}^{+0.76}{\mu }_N$ for the $D{\mathrm{\Sigma }}_c$ pentaquark, ${\mu }_{D{\mathrm{\Sigma }}_c^{\ast }}=1.{65}_{-0.34}^{+0.45}{\mu }_N$ for the $D{\mathrm{\Sigma }}_c^{\ast }$ pentaquark, and ${\mu }_{D^{\ast }{\mathrm{\Sigma }}_c}=-3.{63}_{-0.60}^{+0.79}{\mu }_N$ for the $D^{\ast }{\mathrm{\Sigma }}_c$ pentaquark. Furthermore, we have also extracted the electric quadrupole and the magnetic octupole moments of the $D\mathrm{\Sigma }_c^{\ast }$ and $D_{}^{\ast }{\mathrm{\Sigma }}_c$ 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: ${\mu }_{D{\mathrm{\Sigma }}_c}=3.{78}_{-0.70}^{+0.94}{\mu }_N$, ${\mu }_{D{\mathrm{\Sigma }}_c^{\ast }}=2.{08}_{-0.43}^{+0.57}{\mu }_N$, ${\mu }_{D^{\ast }{\mathrm{\Sigma }}_c}=-4.{59}_{-0.76}^{+0.99}{\mu }_N$ for the isospin-$\frac{3}{2}$ partners $D{\mathrm{\Sigma }}_c$, $D\mathrm{\Sigma }_c^{\ast }$ and $D_{}^{\ast }{\mathrm{\Sigma }}_c$ 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.