Analytic electromagnetic signatures of compact pentaquark structure: A multi-current QCD light-cone sum rules analysis of the $P_{\psi s}^{\Lambda}$ states

Abstract

Probing the internal organization of hidden-charm pentaquarks -- including the spin-color correlations that distinguish compact diquark-diquark-antiquark configurations from loosely bound hadronic molecules -- requires observables beyond mass spectroscopy. We argue that multi-current QCD light-cone sum rules (LCSR) provide a diagnostic framework through exact analytic relations among flavor-sector contributions enforced by the algebra of the interpolating currents. We identify two such signatures: (i) the light-quark contributions satisfy $\mu_{u}/\mu_{d}=e_{u}/e_{d}=-2$ in all four currents considered, reflecting a common Lorentz-color kernel; and (ii) for the $J_{3}(x)$ current the charm contribution vanishes identically, $\mu_{c}=0$, from the Dirac structure of the anti-charm coupling rather than the pseudoscalar charm-diquark embedding alone. Using four diquark-diquark-antiquark currents $J_{1}(x)$-$J_{4}(x)$ with $J^{P}=\tfrac{1}{2}^{-}$, we obtain $\mu_{J_{1}}=-1.35^{+0.35}_{-0.28}\,\mu_{N}$, $\mu_{J_{2}}=3.14^{+0.65}_{-0.50}\,\mu_{N}$, $\mu_{J_{3}}=1.01^{+0.25}_{-0.20}\,\mu_{N}$, $\mu_{J_{4}}=-1.79^{+0.41}_{-0.34}\,\mu_{N}$. These predictions are paired with the $P_{\psi s}^{\Lambda}(4338)$ and $P_{\psi s}^{\Lambda}(4459)$ on mass grounds as a working hypothesis, since the $\pm 0.11~\text{GeV}$ uncertainties accommodate either state within $1\sigma$ of all four currents. The magnitudes $|\mu|\sim 1$-$3\,\mu_{N}$ lie above quark-model and heavy pentaquark chiral perturbation theory expectations ($|\mu|\lesssim 0.5\,\mu_{N}$). Applying the same procedure to two previous molecular LCSR analyses yields $\mu_{u}/\mu_{d}=-1/2$ rather than $-2$, providing an LCSR-internal contrast at the flavor-decomposed level even when total magnitudes are comparable. The two signatures are immune to the state-to-current pairing and offer falsifiable tests of the compact picture.