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

TL;DR

This work analyzes the internal structure of hidden-charm strange pentaquarks with $J^P=\tfrac{3}{2}^{-}$ by computing their electromagnetic multipole moments via QCD light-cone sum rules across five diquark–diquark–antiquark interpolating currents. The authors derive hadronic and QCD representations of a photon-coupled correlation function, obtain sum rules for the magnetic dipole, electric quadrupole, and magnetic octupole moments, and perform a detailed numerical analysis including twist-4 photon distribution amplitudes. They find strong current-dependence of the moments, with $\mu$ in the interval $[-2.28, +3.36]$ $\mu_N$, nonzero $Q$ and $O$ indicating non-spherical geometry, and a flavour decomposition showing light quarks dominate the magnetic response while the charm quark drives quadrupole deformation. The results provide structure-sensitive benchmarks for upcoming LHCb, Belle II, and lattice QCD studies, enabling discrimination among competing internal configurations and guiding future experimental searches.

Abstract

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.

Figures (4)

• Figure 1: Illustrates the charge distributions corresponding to intrinsic quadrupole moments ($\mathcal{Q}$): spherical ($\mathcal{Q}=0$), positive (prolate, $\mathcal{Q}>0$), and negative (oblate, $\mathcal{Q}<0$). Similarly, a structural asymmetry is observed for the octupole moment ($\mathcal{O}$).
• Figure 2: CVG analysis (left panels), PC (middle panels), and total value (right panels) for the magnetic dipole moments of the $P^{\Lambda}_{\psi s}$ pentaquarks versus $\rm{M^2}$ at fixed $\rm{s_0}$ values. The adopted Borel window is illustrated by the vertical lines in the middle and right panels, whereas the horizontal line in the middle panel marks the minimum PC value obtained within this region.
• Figure 3: Analysis of the electric quadrupole moment for the $P^{\Lambda}_{\psi s}$ pentaquark states. Left: three-dimensional charge density distribution $\rho$ (e/fm$^3$); Middle: isosurface visualization at 15% of maximum density showing deformation patterns; Right: individual quark contributions to the quadrupole moment (fm$^2$). The plots reveal distinct prolate/oblate deformations characteristic of each pentaquark configuration, with color coding indicating density intensity. All spatial axes are in femtometers (fm).
• Figure 4: Analysis of the magnetic octupole moment for the $P^{\Lambda}_{\psi s}$ pentaquark states. Left: three-dimensional charge density distribution $\rho$ (e/fm$^3$) exhibiting octupole deformation patterns; Middle left: isosurface visualization at 15% of maximum density, clearly displaying the characteristic peanut shape (positive octupole) or butterfly shape (negative octupole); Middle right: angular distribution of charge density showing the $Y_{30} \propto (5\cos^3\theta - 3\cos\theta)$ spherical harmonic dependence; Right: quark-sector decomposition of octupole moment components ($\times 10^{-2}$ fm$^3$). Positive octupole moments indicate axial charge accumulation (peanut shape), while negative moments show equatorial charge concentration with polar depletion (butterfly shape). The angular distributions reveal the underlying octupole symmetry. All spatial axes are in femtometers (fm).