Analysis of the isospin eigenstate $\bar D \Sigma_c$, $\bar D^{*} \Sigma_c$, and $\bar D \Sigma_c^{*}$ pentaquarks by their electromagnetic properties

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 $\mathrm{P_{c}(4312)}$, $\mathrm{P_{c}(4380)}$, and $\mathrm{P_{c}(4440)}$ pentaquarks by considering them as the molecular picture with spin-parity $\mathrm{J^P= \frac{1}{2}^-}$, $\mathrm{J^P= \frac{3}{2}^-}$, and $\mathrm{J^P= \frac{3}{2}^-}$, 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 $\bar D^{*} \Sigma_c$ and $\bar D \Sigma_c^{*}$ pentaquarks, indicating a non-spherical charge distribution.