Analysis of the isospin eigenstate D c, D^* c, and D 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 P₂ (4312) P c (4312), P₂ (4380) P c (4380), and P₂ (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 D^* c D ¯ ∗ Σ c and D c^* D ¯ Σ c ∗ pentaquarks, indicating a non-spherical charge distribution.