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Analytic electromagnetic signatures of compact pentaquark structure: A multicurrent QCD light-cone sum rules analysis of the $P_{ψ s}^{Λ}$ states

Health Services Vocational School of Higher Education, Istanbul Aydin University, Sefakoy-Kucukcekmece, 34295 Istanbul, Türkiye

^*Contact author: ulasozdem@aydin.edu.tr

Phys. Rev. D 114, 014050 – Published 23 July, 2026

DOI: https://doi.org/10.1103/8p4m-zbpb

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 that go beyond mass spectroscopy. We argue that multicurrent QCD light-cone sum rules provide a diagnostic framework for this problem, not only through the expected sensitivity of the magnetic moment to the internal spin structure but, more importantly, through exact analytic relations among the flavor-sector contributions that are enforced by the algebra of the interpolating currents themselves. We identify two such signatures that emerge from our analysis of compact diquark-diquark-antiquark configurations: (i) for any of the four currents considered the light-quark contributions satisfy the exact ratio $μ_{u} / μ_{d} = e_{u} / e_{d} = - 2$ , reflecting a common Lorentz-color kernel that couples $u$ and $d$ only through their electric charges; and (ii) for the $J_{3} (x)$ current the charm-quark contribution vanishes identically, $μ_{c} = 0$ , arising not from the pseudoscalar embedding of the charm diquark alone—since the same embedding occurs in $J_{1} (x)$ , which yields a nonzero $μ_{c}$ —but from the specific Dirac structure associated with the anticharm coupling in the global current, which produces an analytic cancellation in the operator product expansion. We illustrate these signatures through explicit calculations using four independent diquark-diquark-antiquark interpolating currents $J_{1} (x) - J_{4} (x)$ , assumed to carry $J^{P} = {\frac{1}{2}}^{-}$ , and obtain $μ_{J_{1}} = - 1.3 5_{- 0.28}^{+ 0.35} μ_{N}$ , $μ_{J_{2}} = 3.1 4_{- 0.50}^{+ 0.65} μ_{N}$ , $μ_{J_{3}} = 1.0 1_{- 0.20}^{+ 0.25} μ_{N}$ , and $μ_{J_{4}} = - 1.7 9_{- 0.34}^{+ 0.41} μ_{N}$ . These four predictions are then assigned to the observed $P_{ψ s}^{Λ} (4338)$ and $P_{ψ s}^{Λ} (4459)$ resonances on the basis of the mass predictions of recent QCD sum rule analyses; we emphasize, however, that the corresponding $\pm 0.11 GeV$ mass uncertainties accommodate either state within $1 σ$ of all four currents, so this current-to-state mapping is adopted only as an auxiliary phenomenological choice. The predicted magnitudes $| μ | \sim 1 - 3 μ_{N}$ lie systematically above quark-model and heavy pentaquark chiral perturbation theory expectations ( $| μ | ≲ 0.5 μ_{N}$ ). Applying the same flavor-decomposition procedure to two previous molecular LCSR analyses of the same states yields $μ_{u} / μ_{d} = - 1 / 2$ rather than $- 2$ , providing an LCSR-internal contrast that operates at the flavor-decomposed level even when total magnitudes are comparable. Crucially, the two analytic signatures identified here are immune to the ambiguity of the state-to-current pairing and therefore offer falsifiable tests of the compact picture that survive the unavoidable phenomenological assumptions of mass-based assignments.

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Phys. Rev. D 114, 014050– Published 23 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 7 May 2026
Accepted 23 June 2026

DOI: https://doi.org/10.1103/8p4m-zbpb

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Analytic electromagnetic signatures of compact pentaquark structure: A multicurrent QCD light-cone sum rules analysis of the $P_{ψ s}^{Λ}$ states

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Analytic electromagnetic signatures of compact pentaquark structure: A multicurrent QCD light-cone sum rules analysis of the PψsΛ states

Abstract

Physics Subject Headings (PhySH)

Article Text

References (74)

Analytic electromagnetic signatures of compact pentaquark structure: A multicurrent QCD light-cone sum rules analysis of the $P_{ψ s}^{Λ}$ states