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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

Received:
19
May
2024

Accepted:
15
July
2024

Published online:
2
August
2024

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.

*© The Author(s) 2024*

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Funded by SCOAP^{3}.