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Electromagnetic tomography of spin-$\frac{3}{2}$ hidden-charm strange pentaquarks

Understanding how quarks are spatially arranged inside exotic pentaquarks remains one of the key open problems in contemporary hadron spectroscopy. The electromagnetic multipole moments of hadrons provide a direct probe of their internal quark--gluon geometry and spatial charge distributions. Motivated by this, we employ QCD light-cone sum rules to compute the magnetic dipole, electric quadrupole, and magnetic octupole moments of the $J^P = 3/2^-$ pentaquark with strangeness $S = -1$. Five distinct diquark--diquark--antiquark interpolating currents are constructed to explore possible internal configurations. The resulting electromagnetic moments exhibit pronounced sensitivity to the underlying quark arrangement: magnetic dipole moments range from $-2.28μ_N$ to $+3.36μ_N$, establishing this observable as a key discriminator among configurations with identical quantum numbers. Nonzero electric quadrupole and magnetic octupole moments indicate clear deviations from spherical symmetry, while a detailed decomposition shows that light quarks dominate the magnetic response and the charm quark drives quadrupole deformation. These findings position electromagnetic multipole moments as quantitative and discriminating probes of exotic hadron structure, providing concrete benchmarks for forthcoming LHCb, Belle II, and lattice QCD studies.