Eur. Phys. J. C (2024) 84: 769
https://doi.org/10.1140/epjc/s10052-024-13124-7

Regular Article - Theoretical Physics

Analysis of the isospin eigenstate $\overline{D}{\mathrm{\Sigma }}_c$, ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c$, and $\overline{D}\mathrm{\Sigma }_c^{\ast }$ pentaquarks by their electromagnetic properties

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

^a ulasozdem@aydin.edu.tr

Received: 19 May 2024
Accepted: 15 July 2024
Published online: 2 August 2024

Abstract

To shed light on the nature of the controversial and not yet fully understood exotic states, we are carrying out a systematic study of their electromagnetic properties. The magnetic moment of a hadron state is as fundamental a dynamical quantity as its mass and contains valuable information on the deep underlying structure. In this study, we use the QCD light-cone sum rule to extract the magnetic moments of the ${\mathrm{P}}_{\mathrm{c}}(4312)$, ${\mathrm{P}}_{\mathrm{c}}(4380)$, and ${\mathrm{P}}_{\mathrm{c}}(4440)$ pentaquarks by considering them as the molecular picture with spin-parity ${\mathrm{J}}^{\mathrm{P}}={\frac{1}{2}}^{-}$, ${\mathrm{J}}^{\mathrm{P}}={\frac{3}{2}}^{-}$, and ${\mathrm{J}}^{\mathrm{P}}={\frac{3}{2}}^{-}$, respectively. We define the isospin of the interpolating currents of these states, which is the key to solving the puzzle of the hidden-charm pentaquark states, to make these analyses more precise and reliable. We have compared our results with other theoretical predictions that could be a useful complementary tool for the interpretation of the hidden-charm pentaquark sector, and we observe that they are not in mutual agreement with each other. We have also calculated higher multipole moments for spin-3/2 ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c$ and $\overline{D}\mathrm{\Sigma }_c^{\ast }$ pentaquarks, indicating a non-spherical charge distribution.