Deciphering the nature of $P_{\psi s}^{\Sigma }$ pentaquarks in the light of their electromagnetic multipole moments

Abstract

We calculate electromagnetic multipole moments of $\Sigma$-type strange hidden-charm pentaquarks $P_{\psi s}^{\Sigma }$ (isospin triplet ${\Sigma }^{+},{\Sigma }^0,{\Sigma }^{-}$) using QCD light-cone sum rules, with six (spin-1/2) and seven (spin-3/2) interpolating currents built from diquark-diquark-antiquark operators. We compute magnetic dipole $\mu$ for all channels and, for spin-3/2, electric quadrupole $\mathcal{Q}$ and magnetic octupole $\mathcal{O}$ moments (first computation), and give the first quark-flavor decomposition. Scalar diquark currents yield charm-dominated, flavor-insensitive moments ($\mu \in [-1.92,-1.21]{\mu }_N$ for spin-1/2, $|\mu |\lesssim 1.2{\mu }_N$ for spin-3/2), consistent with heavy-quark spin symmetry. Axial-vector diquark currents produce larger, flavor-sensitive moments with sign reversals governed by $e_u/e_d=-2$. For $\mathcal{Q}$, scalar-diquark currents give oblate deformations ($Q_0\approx -2.0\times 10^{-2}{\mathrm{fm}}^2$) dominated by charm, while two-axial-vector-diquark currents predict prolate values up to $Q_0=+8.0\times 10^{-2}{\mathrm{fm}}^2$, with sign reversal for $[su][uc]\bar{c}$ in two currents. Currents with scalar antiquark coupling yield a topology-independent octupole $\mathcal{O}\approx -0.25\times 10^{-3}{\mathrm{fm}}^3$, a lattice QCD benchmark. Comparison with constituent quark models identifies four discriminants: $|\mu |\gtrsim 3{\mu }_N$ in spin-1/2; sign of $\mu$ for $[su][uc]\bar{c}$ in spin-3/2; non-zero $\mathcal{Q}$ (vanishes in $S$-wave molecules); and the $\mathcal{Q}$-$\mathcal{O}$ sign correlation, probing $1/m_q$ weighting.

Comments: 35 pages, 9 tables and 5 figures. Version accepted for publication in JHEP