Analysis of the isospin eigenstate D̄ Σ c, D̄* Σ c, and D̄ Σ 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 Pc(4312) P c ( 4312 ) , Pc(4380) P c ( 4380 ) , and Pc(4440) P c ( 4440 ) pentaquarks by considering them as the molecular picture with spin-parity JP= 1/2⁻ J P = 1 2 - , JP= 3/2⁻ J P = 3 2 - , and JP= 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 D̄* Σ c D ¯ ∗ Σ c and D̄ Σ c* D ¯ Σ c ∗ pentaquarks, indicating a non-spherical charge distribution.