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

Abstract

We calculate electromagnetic multipole moments of $\Sigma$-type strange hidden-charm pentaquarks $P^{\Sigma}_{\psi s}$ (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 ${\cal Q}$ and magnetic octupole ${\cal O}$ 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, $|\mu|\lesssim1.2\mu_N$ 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 ${\cal Q}$, scalar-diquark currents give oblate deformations ($Q_0\approx-2.0\times10^{-2}{\rm fm}^2$) dominated by charm, while two-axial-vector-diquark currents predict prolate values up to $Q_0=+8.0\times10^{-2}{\rm fm}^2$, with sign reversal for $[su][uc]\bar{c}$ in two currents. Currents with scalar antiquark coupling yield a topology-independent octupole ${\cal O}\approx-0.25\times10^{-3}{\rm fm}^3$, a lattice QCD benchmark. Comparison with constituent quark models identifies four discriminants: $|\mu|\gtrsim3\mu_N$ in spin-1/2; sign of $\mu$ for $[su][uc]\bar{c}$ in spin-3/2; non-zero ${\cal Q}$ (vanishes in $S$-wave molecules); and the ${\cal Q}$-${\cal O}$ sign correlation, probing $1/m_q$ weighting.