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 $-2.15{\mu }_N$ to $5.74{\mu }_N$ for spin-$1/2$ pentaquarks and from $-4.25{\mu }_N$ to $-0.43{\mu }_N$ 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 $-2.01\times 10^{-2}$ fm${}^2$ and $5.55\times 10^{-2}$ 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 $J_{\mu }^3(x)$ 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 ${\mu }_u/{\mu }_d=-2.00$ confirms this mechanism exactly. Our predictions offer benchmarks for future experiments and lattice QCD calculations, and may help discriminate among competing structural models.

22 pages, 2 figures, 4 tables. Version accepted for publication in Chinese Journal of Physics

References in corpus (2)

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• Analysis of the hidden-charm pentaquark candidates in the $J/\ddot{I}ˆ\hat{I}ž$ mass spectrum via the QCD sum rules