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

TL;DR

This paper calculates electromagnetic multipole moments of $P^{ ext{Sigma}}_{ ext{psi s}}$ pentaquarks using QCD sum rules, providing insights into their internal structure and flavor composition.

Contribution

It presents the first computation of electric quadrupole and magnetic octupole moments for these pentaquarks, including a quark-flavor decomposition and comparison with quark models.

Findings

Scalar diquark currents produce charm-dominated, flavor-insensitive moments.

Axial-vector diquark currents yield larger, flavor-sensitive moments with sign reversals.

Scalar-antiquark coupling yields a topology-independent octupole moment.

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.