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 $J^P={\frac{1}{2}}^{-}$, we obtain ${\mu }_{J_1}=-1.35_{-0.28}^{+0.35}{\mu }_N$, ${\mu }_{J_2}=3.14_{-0.50}^{+0.65}{\mu }_N$, ${\mu }_{J_3}=1.01_{-0.20}^{+0.25}{\mu }_N$, ${\mu }_{J_4}=-1.79_{-0.34}^{+0.41}{\mu }_N$. 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.

22 pages, 3 Figures, 3 Tables. Version accepted for publication in PRD

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