Charting doubly strange hidden-charm pentaquarks: An electromagnetic mapping of spin-$\frac{1}{2}$ and $\frac{3}{2}$ states

Abstract

We calculate the magnetic dipole moments of doubly strange hidden-charm pentaquark states with spin-parity $J^P = 1/2^-$ and $3/2^-$ using QCD light-cone sum rules (LCSR), presenting the first systematic LCSR investigation of the electromagnetic multipole structure in the $S = -2$ sector. To assess the model dependence, we employ independent interpolating currents in diquark-diquark-antiquark form, which probe different assumptions about the internal color-spin correlations. For the spin-$3/2$ states, we also compute the electric quadrupole and magnetic octupole moments. The magnetic dipole moments exhibit a considerable spread across currents, ranging from $-2.15\,μ_N$ to $5.74\,μ_N$ for spin-$1/2$ pentaquarks and from $-4.25\,μ_N$ to $-0.43\,μ_N$ for spin-$3/2$ states, reflecting the sensitivity of magnetic moments to the internal wave function. A quark-level decomposition reveals that the charm quark dominates in most configurations, while strange quarks play a decisive role only in currents favoring axial-vector diquark structures. The electric quadrupole moments lie between $-2.01\times10^{-2}$ fm$^2$ and $5.55\times10^{-2}$ fm$^2$, and the magnetic octupole moments are typically an order of magnitude smaller. The current dependence of the magnetic dipole moments provides a quantitative measure of the theoretical uncertainty arising from the choice of interpolating operator. The pronounced isospin sensitivity of $J^3_μ(x)$ across all three multipole moments arises from its axial-vector diquark structure, which isolates the light quark from spin averaging and allows the charge asymmetry $e_u/e_d = -2$ to propagate directly into the electromagnetic moments; the ratio $μ_u/μ_d = -2.00$ confirms this mechanism exactly. Our predictions offer benchmarks for future experiments and lattice QCD calculations, and may help discriminate among competing structural models.