Analysis of the isospin eigenstate $$\bar{D} \Sigma _c$$ D ¯ Σ c , $$\bar{D}^{} \Sigma _c$$ D ¯ ∗ Σ c , and $$\bar{D} \Sigma _c^{}$$ D ¯ Σ c ∗ pentaquarks by their electromagnetic properties

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