Unveiling the electromagnetic structure and intrinsic dynamics of spin-$\frac{3}{2}$ hidden-charm pentaquarks: A comprehensive QCD analysis

Understanding the internal structure of hadrons remains a fundamental challenge in experimental and theoretical hadron physics. This pursuit is crucial for advancing our comprehension of QCD and for refining the models that describe the strong interaction. The discovery of exotic states, such as hidden-charm pentaquarks, has further emphasized the complexity of hadronic systems and the need to uncover the fundamental mechanisms governing their formation and behavior. Addressing these challenges not only deepens our understanding of QCD but also tests the limits of existing theoretical frameworks, paving the way for new insights into the nature of matter. Motivated by these challenges, the present study investigates the electromagnetic properties$-$ specifically, the magnetic dipole, electric quadrupole, and magnetic octupole moments$-$ of six hidden-charm pentaquark states: $[u u][d c] \bar c$, $[dd][u c] \bar c$, $[u u][s c] \bar c$, $[dd] [s c] \bar c$, $[s s][u c] \bar c$, and $[s s][d c] \bar c$. Employing the framework of QCD light-cone sum rules and utilizing two distinct diquark-diquark-antiquark interpolating currents, we focus on pentaquark configurations with spin-parity quantum numbers $\mathrm{J^P =\frac{3}{2}^-}$. From the numerical results, we observe significant deviations between the magnetic dipole moment predictions obtained using different diquark-diquark-antidiquark structures. These results suggest that multiple pentaquark states with identical quantum numbers and quark constituents may exhibit distinct magnetic dipole moments, depending on their internal quark configurations. The obtained electromagnetic moments, particularly the variations in magnetic dipole moments, may provide insights into the internal structure of hidden-charm pentaquark states.