pith. sign in

arxiv: 2604.12533 · v2 · pith:KGJN7CANnew · submitted 2026-04-14 · ✦ hep-ph · hep-ex· hep-lat

Deciphering the nature of P^(Sigma)_(psi s) pentaquarks in the light of their electromagnetic multipole moments

Ula\c{s} \"Ozdem This is my paper

Pith reviewed 2026-05-25 06:13 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-lat
keywords pentaquarkshidden-charmelectromagnetic momentslight-cone sum rulesQCD sum rulesexotic hadronsmultipole momentsdiquark structure
0
0 comments X

The pith

Electromagnetic multipole moments of hidden-charm pentaquarks distinguish their diquark configurations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper computes the magnetic dipole moments of spin-1/2 and spin-3/2 strange hidden-charm pentaquarks, along with electric quadrupole and magnetic octupole moments for the spin-3/2 states, using QCD light-cone sum rules with diquark-diquark-antiquark interpolating currents. Different current choices produce contrasting results: scalar diquarks yield small, charm-dominated moments while axial-vector diquarks yield larger moments that depend on light-quark flavor and charge. These predictions are compared against constituent quark models to extract four concrete discriminants involving the size and sign of the magnetic moment, the presence of a quadrupole moment, and the quadrupole-octupole sign correlation. A sympathetic reader would care because the moments supply potential experimental observables that can probe whether these pentaquarks are dominated by compact multiquark configurations or by molecular structures.

Core claim

The electromagnetic multipole moments calculated for various diquark-diquark-antiquark currents show that scalar diquark configurations produce charm-dominated, flavor-insensitive moments consistent with heavy-quark spin symmetry, while axial-vector configurations yield larger, flavor-sensitive moments with sign reversals governed by quark charges. For spin-3/2 states the electric quadrupole moment is non-zero for most currents, vanishing only in S-wave molecular pictures, and the octupole moment is largely topology-independent for scalar antiquark couplings. Comparison with models yields four discriminants: |μ| ≳ 3 μ_N for spin-1/2 states, the sign of μ for the [su][uc]c-bar channel in spin

What carries the argument

QCD light-cone sum rules applied to six spin-1/2 and seven spin-3/2 diquark-diquark-antiquark interpolating currents to extract electromagnetic multipole moments.

If this is right

  • Scalar diquark currents produce magnetic moments in [-1.92, -1.21] μ_N for spin-1/2 states and |μ| ≲ 1.2 μ_N for spin-3/2 states.
  • Axial-vector diquark currents produce larger moments whose signs reverse according to the ratio of up- and down-quark charges.
  • Electric quadrupole moments range from oblate values near -2.0×10^{-2} fm² to prolate values up to +8.0×10^{-2} fm² depending on current choice.
  • Magnetic octupole moments are approximately -0.25×10^{-3} fm³ whenever the antiquark coupling is scalar.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The four discriminants supply independent handles that future experiments can use to test whether observed pentaquarks match compact or molecular pictures.
  • The flavor sensitivity of the axial-vector results implies that the three isospin states within each multiplet may exhibit measurable differences in their moments.
  • The octupole value obtained for scalar antiquark couplings offers a concrete benchmark that lattice QCD calculations could target independently of the sum-rule approach.

Load-bearing premise

The chosen diquark-diquark-antiquark interpolating currents accurately represent the dominant Fock components of the physical pentaquark states.

What would settle it

A measurement of the magnetic dipole moment of any spin-1/2 P^Σ_ψs pentaquark with magnitude larger than 3 nuclear magnetons would indicate dominance of axial-vector diquark components.

Figures

Figures reproduced from arXiv: 2604.12533 by Ula\c{s} \"Ozdem.

Figure 1
Figure 1. Figure 1: FIG. 1. Sum-rule analysis for the currents [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Electric quadrupole moment analysis of the [PITH_FULL_IMAGE:figures/full_fig_p023_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Magnetic octupole moment analysis of the [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript calculates electromagnetic multipole moments of Σ-type strange hidden-charm pentaquarks P^Σ_ψs using QCD light-cone sum rules. Six (spin-1/2) and seven (spin-3/2) diquark-diquark-antiquark interpolating currents are employed to compute magnetic dipole moments μ for all channels, plus electric quadrupole Q and magnetic octupole O for spin-3/2 (first such computation), together with quark-flavor decompositions. Scalar-diquark currents yield charm-dominated, flavor-insensitive values while axial-vector currents produce larger, sign-reversing results; these are compared to constituent quark models to identify four discriminants: |μ| ≳ 3 μ_N (spin-1/2), sign of μ for [su][uc]c-bar (spin-3/2), non-zero Q (vs. S-wave molecules), and Q-O sign correlation.

Significance. If the numerical LCSR results prove robust, the work supplies the first Q and O moments and explicit flavor decompositions for these states, furnishing concrete, testable discriminants against alternative pictures. The reported consistency with heavy-quark spin symmetry for scalar currents and the lattice-QCD benchmark value for O constitute clear strengths of the calculation.

major comments (2)
  1. [Numerical results] Results for spin-1/2 states: magnetic moments are quoted only as intervals (e.g., μ ∈ [-1.92, -1.21] μ_N) with no propagated uncertainties from Borel-mass or continuum-threshold variations, nor any demonstration that the values remain above the |μ| ≳ 3 μ_N discriminant threshold under reasonable parameter shifts.
  2. [Numerical results] Spin-3/2 results: the sign of μ for the [su][uc]c-bar channel and the Q-O sign correlation are presented as discriminants, yet the manuscript provides no explicit stability windows or higher-twist error estimates that would confirm these signs are not artifacts of the chosen auxiliary parameters.
minor comments (1)
  1. [Method] The definition of the continuum threshold s0 and the precise Borel window boundaries should be tabulated for each current to allow reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments on numerical robustness below. Both points identify areas where additional explicit documentation will strengthen the presentation, and we will incorporate the requested material in the revised version.

read point-by-point responses

  1. Referee: Results for spin-1/2 states: magnetic moments are quoted only as intervals (e.g., μ ∈ [-1.92, -1.21] μ_N) with no propagated uncertainties from Borel-mass or continuum-threshold variations, nor any demonstration that the values remain above the |μ| ≳ 3 μ_N discriminant threshold under reasonable parameter shifts.

    Authors: The quoted intervals are generated by scanning the Borel mass M² and continuum threshold s₀ inside the windows where the sum-rule stability criteria (pole dominance and OPE convergence) are satisfied. We agree, however, that the manuscript does not display the individual variations or propagate them into explicit uncertainties, nor does it tabulate the minimum |μ| obtained at the edges of those windows. In the revision we will add a table (or supplementary figure) showing the separate contributions from M² and s₀ variations for each current, together with a direct check that |μ| remains ≳ 3 μ_N throughout the allowed parameter space. revision: yes

  2. Referee: Spin-3/2 results: the sign of μ for the [su][uc]c-bar channel and the Q-O sign correlation are presented as discriminants, yet the manuscript provides no explicit stability windows or higher-twist error estimates that would confirm these signs are not artifacts of the chosen auxiliary parameters.

    Authors: The reported signs are obtained inside the Borel windows already fixed by the requirement that the ground-state contribution exceeds 50 % and that higher-dimensional condensates remain under control. Nevertheless, the manuscript does not display the explicit dependence of the signs on M² and s₀, nor does it quantify the size of higher-twist corrections for the spin-3/2 channels. We will therefore add (i) plots or tables demonstrating that the sign of μ([su][uc]c-bar) and the Q–O correlation remain unchanged across the full working windows and (ii) an estimate of the leading higher-twist uncertainty for these observables. revision: yes

Circularity Check

0 steps flagged

LCSR derivation of multipole moments is self-contained with no reduction to inputs

full rationale

The paper derives electromagnetic multipole moments via standard QCD light-cone sum rules applied to explicitly constructed diquark-diquark-antiquark interpolating currents, performing the OPE, Borel transform, and continuum subtraction to extract μ, Q, and O. These steps produce numerical values that are not equivalent by construction to the chosen currents or auxiliary parameters; the discriminants (e.g., |μ| ≳ 3 μ_N) emerge from the computed ranges rather than being presupposed. No load-bearing self-citation chain, ansatz smuggling, or fitted-input-as-prediction is exhibited in the provided text, and the octupole result is cross-referenced to an external lattice benchmark. The method therefore remains independent of its inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The calculation rests on standard QCD sum-rule assumptions plus the specific choice of six/seven interpolating currents; no new particles are postulated beyond the pentaquarks under study.

free parameters (2)
  • Borel mass parameter
    Standard auxiliary parameter in light-cone sum rules chosen for stability window; value not given in abstract.
  • Continuum threshold s0
    Fitted or chosen to suppress higher states; affects extracted moments.
axioms (2)
  • domain assumption Light-cone sum rules with diquark-diquark-antiquark currents capture the dominant contribution to the pentaquark correlators
    Invoked throughout the construction of the six and seven currents.
  • domain assumption Higher-twist and radiative corrections are under control within the chosen working windows
    Implicit in any light-cone sum-rule extraction of moments.

pith-pipeline@v0.9.0 · 5944 in / 1481 out tokens · 36899 ms · 2026-05-25T06:13:58.540743+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    hep-ph 2026-06 unverdicted novelty 6.0

    LCSR analysis of compact pentaquarks yields μ_u/μ_d = -2 for all currents and μ_c = 0 for one current, with numerical moments of order 1-3 μ_N that differ in flavor decomposition from molecular calculations.

Reference graph

Works this paper leans on

82 extracted references · 82 canonical work pages · cited by 1 Pith paper · 34 internal anchors

  1. [1]

    17 CurrentsJ 1 µ(x),J 2 µ(x),J 3 µ(x), andJ 5 µ(x)couple the diquark system to the charm sector viaΓ 3 =C, a scalar coupling

    Magnetic dipole moments The spin-3/2magnetic moments are uniformly negative and reproduce the same diquark-spin dependence estab- lished in the spin-1/2sector. 17 CurrentsJ 1 µ(x),J 2 µ(x),J 3 µ(x), andJ 5 µ(x)couple the diquark system to the charm sector viaΓ 3 =C, a scalar coupling. Their moments are small (|µ|≲1.2µN), charm-dominated, and flavor-insens...

    work page

  2. [2]

    Electric quadrupole moments and intrinsic deformation The electric quadrupole moments are the most structurally informative observable in this work and, to our knowl- edge, constitute the first systematic predictions of this quantity forPΣ∗ ψspentaquarks. No counterpart predictions exist in the molecular or constituent quark model approaches: in the simpl...

    work page

  3. [3]

    pert” and “DA

    Magnetic octupole moments The magnetic octupole momentsOare an order of magnitude smaller than the quadrupole moments, as expected from the multipole hierarchy, and constitute new predictions with no molecular or quark model counterpart. They range from−1.42×10−3fm3 (J4 µ(x),[sd][dc]¯c) to+0.56×10−3fm3 (J4 µ(x),[su][uc]¯c). The numerical results of Table ...

    work page

  4. [4]

    S. K. Choi, et al., Observation of a narrow charmonium-like state in exclusiveB± →K±π+π−J/ψdecays, Phys. Rev. Lett. 91 (2003) 262001.arXiv:hep-ex/0309032,doi:10.1103/PhysRevLett.91.262001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.91.262001 2003

  5. [5]

    Four-Quark Hadrons: an Updated Review

    A. Esposito, A. L. Guerrieri, F. Piccinini, A. Pilloni, A. D. Polosa, Four-Quark Hadrons: an Updated Review, Int. J. Mod. Phys. A 30 (2015) 1530002.arXiv:1411.5997,doi:10.1142/S0217751X15300021

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x15300021 2015

  6. [6]

    Multiquark Resonances

    A. Esposito, A. Pilloni, A. D. Polosa, Multiquark Resonances, Phys. Rept. 668 (2017) 1–97.arXiv:1611.07920,doi: 10.1016/j.physrep.2016.11.002

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2016.11.002 2017

  7. [7]

    S. L. Olsen, T. Skwarnicki, D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90 (1) (2018) 015003.arXiv:1708.04012,doi:10.1103/RevModPhys.90.015003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.90.015003 2018

  8. [8]

    R. F. Lebed, R. E. Mitchell, E. S. Swanson, Heavy-Quark QCD Exotica, Prog. Part. Nucl. Phys. 93 (2017) 143–194. arXiv:1610.04528,doi:10.1016/j.ppnp.2016.11.003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.ppnp.2016.11.003 2017

  9. [9]

    New Charmonium States in QCD Sum Rules: a Concise Review

    M. Nielsen, F. S. Navarra, S. H. Lee, New Charmonium States in QCD Sum Rules: A Concise Review, Phys. Rept. 497 (2010) 41–83.arXiv:0911.1958,doi:10.1016/j.physrep.2010.07.005

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2010.07.005 2010

  10. [11]

    Agaev, K

    S. Agaev, K. Azizi, H. Sundu, Four-quark exotic mesons, Turk. J. Phys. 44 (2) (2020) 95–173.arXiv:2004.12079, doi:10.3906/fiz-2003-15

    work page doi:10.3906/fiz-2003-15 2020

  11. [12]

    H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rept. 639 (2016) 1–121.arXiv:1601.02092,doi:10.1016/j.physrep.2016.05.004

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2016.05.004 2016

  12. [13]

    A. Ali, J. S. Lange, S. Stone, Exotics: Heavy Pentaquarks and Tetraquarks, Prog. Part. Nucl. Phys. 97 (2017) 123–198. arXiv:1706.00610,doi:10.1016/j.ppnp.2017.08.003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.ppnp.2017.08.003 2017

  13. [14]

    F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90 (1) (2018) 015004, [Erratum: Rev.Mod.Phys. 94, 029901 (2022)].arXiv:1705.00141,doi:10.1103/RevModPhys.90.015004

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.90.015004 2018

  14. [15]

    Pentaquark and Tetraquark states

    Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, Pentaquark and Tetraquark states, Prog. Part. Nucl. Phys. 107 (2019) 237–320.arXiv:1903.11976,doi:10.1016/j.ppnp.2019.04.003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.ppnp.2019.04.003 2019

  15. [16]

    G. Yang, J. Ping, J. Segovia, Tetra- and penta-quark structures in the constituent quark model, Symmetry 12 (11) (2020) 1869.arXiv:2009.00238,doi:10.3390/sym12111869

    work page doi:10.3390/sym12111869 2020

  16. [17]

    Dong, F.-K

    X.-K. Dong, F.-K. Guo, B.-S. Zou, A survey of heavy-antiheavy hadronic molecules, Progr. Phys. 41 (2021) 65–93.arXiv: 2101.01021,doi:10.13725/j.cnki.pip.2021.02.001

    work page doi:10.13725/j.cnki.pip.2021.02.001 2021

  17. [18]

    Dong, F.-K

    X.-K. Dong, F.-K. Guo, B.-S. Zou, A survey of heavy–heavy hadronic molecules, Commun. Theor. Phys. 73 (12) (2021) 125201.arXiv:2108.02673,doi:10.1088/1572-9494/ac27a2

    work page doi:10.1088/1572-9494/ac27a2 2021

  18. [19]

    H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, S.-L. Zhu, An updated review of the new hadron states, Rept. Prog. Phys. 86 (2) (2023) 026201.arXiv:2204.02649,doi:10.1088/1361-6633/aca3b6

    work page doi:10.1088/1361-6633/aca3b6 2023

  19. [20]

    L. Meng, B. Wang, G.-J. Wang, S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rept. 1019 (2023) 1–149.arXiv:2204.08716,doi:10.1016/j.physrep.2023.04.003

    work page doi:10.1016/j.physrep.2023.04.003 2023

  20. [21]

    Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda_b^0\to J/\psi K^-p}$ decays

    R. Aaij, et al., Observation ofJ/ψpResonances Consistent with Pentaquark States inΛ0 b→J/ψK−pDecays, Phys. Rev. Lett. 115 (2015) 072001.arXiv:1507.03414,doi:10.1103/PhysRevLett.115.072001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.115.072001 2015

  21. [22]

    Observation of a narrow pentaquark state, $P_c(4312)^+$, and of two-peak structure of the $P_c(4450)^+$

    R. Aaij, et al., Observation of a narrow pentaquark state,Pc(4312)+, and of two-peak structure of thePc(4450)+, Phys. Rev. Lett. 122 (22) (2019) 222001.arXiv:1904.03947,doi:10.1103/PhysRevLett.122.222001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.222001 2019

  22. [23]

    Aaij, et al., Evidence of aJ/ψΛstructure and observation of excitedΞ− states in theΞ− b →J/ψΛK− decay, Sci

    R. Aaij, et al., Evidence of aJ/ψΛstructure and observation of excitedΞ− states in theΞ− b →J/ψΛK− decay, Sci. Bull. 66 (2021) 1278–1287.arXiv:2012.10380,doi:10.1016/j.scib.2021.02.030

    work page doi:10.1016/j.scib.2021.02.030 2021

  23. [24]

    Aaij, et al., Observation of a J/ψΛResonance Consistent with a Strange Pentaquark Candidate in B-→J/ψΛp¯Decays, Phys

    R. Aaij, et al., Observation of a J/ψΛResonance Consistent with a Strange Pentaquark Candidate in B-→J/ψΛp¯Decays, Phys. Rev. Lett. 131 (3) (2023) 031901.arXiv:2210.10346,doi:10.1103/PhysRevLett.131.031901

    work page doi:10.1103/physrevlett.131.031901 2023

  24. [25]

    Adachi, et al., Search for Pcs(4459) and Pcs(4338) in Upsilon(1S,2S) inclusive decays at Belle, Phys

    I. Adachi, et al., Search for Pcs(4459) and Pcs(4338) in Upsilon(1S,2S) inclusive decays at Belle, Phys. Rev. Lett. 135 (4) (2025) 041901.arXiv:2502.09951,doi:10.1103/pf8m-6j69

    work page doi:10.1103/pf8m-6j69 2025

  25. [26]

    Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era

    R. Aaij, et al., Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era (8 2018).arXiv:1808.08865

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [27]

    Özdem, Electromagnetic tomography of spin-3 2 hidden-charm strange pentaquarks, JHEP 02 (2026) 207.arXiv: 2510.26893,doi:10.1007/JHEP02(2026)207

    U. Özdem, Electromagnetic tomography of spin-3 2 hidden-charm strange pentaquarks, JHEP 02 (2026) 207.arXiv: 2510.26893,doi:10.1007/JHEP02(2026)207

    work page doi:10.1007/jhep02(2026)207 2026

  27. [28]

    Özdem, Shedding light on the nature of the Pcs(4459) pentaquark state, Phys

    U. Özdem, Shedding light on the nature of the Pcs(4459) pentaquark state, Phys. Rev. D 111 (7) (2025) 074038.arXiv: 2411.11442,doi:10.1103/PhysRevD.111.074038

    work page doi:10.1103/physrevd.111.074038 2025

  28. [29]

    Özdem, Elucidating the nature of hidden-charm pentaquark states with spin-32 through their electromagnetic form factors, Phys

    U. Özdem, Elucidating the nature of hidden-charm pentaquark states with spin-32 through their electromagnetic form factors, Phys. Lett. B 851 (2024) 138551.arXiv:2402.03802,doi:10.1016/j.physletb.2024.138551

    work page doi:10.1016/j.physletb.2024.138551 2024

  29. [30]

    Özdem, Electromagnetic properties of D¯(∗)Ξc’, D¯(∗)Λc, D¯s(∗)Λc and D¯s(∗)Ξc pentaquarks, Phys

    U. Özdem, Electromagnetic properties of D¯(∗)Ξc’, D¯(∗)Λc, D¯s(∗)Λc and D¯s(∗)Ξc pentaquarks, Phys. Lett. B 846 (2023) 138267.arXiv:2303.10649,doi:10.1016/j.physletb.2023.138267. 32

    work page doi:10.1016/j.physletb.2023.138267 2023

  30. [31]

    Özdem, Investigation of magnetic moment of Pcs(4338) and Pcs(4459) pentaquark states, Phys

    U. Özdem, Investigation of magnetic moment of Pcs(4338) and Pcs(4459) pentaquark states, Phys. Lett. B 836 (2023) 137635.arXiv:2208.07684,doi:10.1016/j.physletb.2022.137635

    work page doi:10.1016/j.physletb.2022.137635 2023

  31. [32]

    G.-J. Wang, R. Chen, L. Ma, X. Liu, S.-L. Zhu, Magnetic moments of the hidden-charm pentaquark states, Phys. Rev. D 94 (9) (2016) 094018.arXiv:1605.01337,doi:10.1103/PhysRevD.94.094018

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.94.094018 2016

  32. [33]

    Hidden charm pentaquarks: mass spectrum, magnetic moments, and photocouplings

    E. Ortiz-Pacheco, R. Bijker, C. Fernández-Ramírez, Hidden charm pentaquarks: mass spectrum, magnetic moments, and photocouplings, J. Phys. G 46 (6) (2019) 065104.arXiv:1808.10512,doi:10.1088/1361-6471/ab096d

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1361-6471/ab096d 2019

  33. [34]

    Xu, Y.-L

    Y.-J. Xu, Y.-L. Liu, M.-Q. Huang, The magnetic moment ofPc(4312)as a ¯DΣc molecular state, Eur. Phys. J. C 81 (5) (2021) 421.arXiv:2008.07937,doi:10.1140/epjc/s10052-021-09211-8

    work page doi:10.1140/epjc/s10052-021-09211-8 2021

  34. [35]

    Electromagnetic multipole moments of the $P_c^+(4380)$ pentaquark in light-cone QCD

    U. Özdem, K. Azizi, Electromagnetic multipole moments of theP+ c (4380)pentaquark in light-cone QCD, Eur. Phys. J. C 78 (5) (2018) 379.arXiv:1803.06831,doi:10.1140/epjc/s10052-018-5873-2

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-018-5873-2 2018

  35. [36]

    Özdem, Magnetic dipole moments of the hidden-charm pentaquark states:Pc(4440),P c(4457)andP cs(4459), Eur

    U. Özdem, Magnetic dipole moments of the hidden-charm pentaquark states:Pc(4440),P c(4457)andP cs(4459), Eur. Phys. J. C 81 (4) (2021) 277.arXiv:2102.01996,doi:10.1140/epjc/s10052-021-09070-3

    work page doi:10.1140/epjc/s10052-021-09070-3 2021

  36. [37]

    Li, Z.-W

    M.-W. Li, Z.-W. Liu, Z.-F. Sun, R. Chen, Magnetic moments and transition magnetic moments of Pc and Pcs states, Phys. Rev. D 104 (5) (2021) 054016.arXiv:2106.15053,doi:10.1103/PhysRevD.104.054016

    work page doi:10.1103/physrevd.104.054016 2021

  37. [38]

    Gao, H.-S

    F. Gao, H.-S. Li, Magnetic moments of hidden-charm strange pentaquark states*, Chin. Phys. C 46 (12) (2022) 123111. arXiv:2112.01823,doi:10.1088/1674-1137/ac8651

    work page doi:10.1088/1674-1137/ac8651 2022

  38. [39]

    Guo, H.-S

    F. Guo, H.-S. Li, Analysis of the hidden-charm pentaquark states based on magnetic moment and transition magnetic moment, Eur. Phys. J. C 84 (4) (2024) 392.arXiv:2304.10981,doi:10.1140/epjc/s10052-024-12699-5

    work page doi:10.1140/epjc/s10052-024-12699-5 2024

  39. [40]

    Wang, S.-Q

    F.-L. Wang, S.-Q. Luo, H.-Y. Zhou, Z.-W. Liu, X. Liu, Exploring the electromagnetic properties of theΞc(’,*)D¯s* and Ωc(*)D¯s*molecularstates, Phys.Rev.D108(3)(2023)034006.arXiv:2210.02809,doi:10.1103/PhysRevD.108.034006

    work page doi:10.1103/physrevd.108.034006 2023

  40. [41]

    Wang, H.-Y

    F.-L. Wang, H.-Y. Zhou, Z.-W. Liu, X. Liu, What can we learn from the electromagnetic properties of hidden-charm molecular pentaquarks with single strangeness?, Phys. Rev. D 106 (5) (2022) 054020.arXiv:2208.10756,doi:10.1103/ PhysRevD.106.054020

    work page arXiv 2022

  41. [42]

    Özdem, Analysis of the isospin eigenstate¯DΣc, ¯D∗Σc, and ¯DΣ ∗ c pentaquarks by their electromagnetic properties, Eur

    U. Özdem, Analysis of the isospin eigenstate¯DΣc, ¯D∗Σc, and ¯DΣ ∗ c pentaquarks by their electromagnetic properties, Eur. Phys. J. C 84 (8) (2024) 769.arXiv:2401.12678,doi:10.1140/epjc/s10052-024-13124-7

    work page doi:10.1140/epjc/s10052-024-13124-7 2024

  42. [43]

    H.-S. Li, F. Guo, Y.-D. Lei, F. Gao, Magnetic moments and axial charges of the octet hidden-charm molecular pentaquark family, Phys. Rev. D 109 (9) (2024) 094027.arXiv:2401.14767,doi:10.1103/PhysRevD.109.094027

    work page doi:10.1103/physrevd.109.094027 2024

  43. [44]

    Li, Molecular pentaquark magnetic moments in heavy pentaquark chiral perturbation theory, Phys

    H.-S. Li, Molecular pentaquark magnetic moments in heavy pentaquark chiral perturbation theory, Phys. Rev. D 109 (11) (2024) 114039.arXiv:2401.14759,doi:10.1103/PhysRevD.109.114039

    work page doi:10.1103/physrevd.109.114039 2024

  44. [45]

    Mutuk, X.-W

    H. Mutuk, X.-W. Kang, Unveiling the structure of hidden-bottom strange pentaquarks via magnetic moments, Phys. Lett. B 855 (2024) 138772.arXiv:2405.07066,doi:10.1016/j.physletb.2024.138772

    work page doi:10.1016/j.physletb.2024.138772 2024

  45. [46]

    Mutuk, Magnetic moments of hidden-bottom pentaquark states, Eur

    H. Mutuk, Magnetic moments of hidden-bottom pentaquark states, Eur. Phys. J. C 84 (8) (2024) 874.arXiv:2403.16616, doi:10.1140/epjc/s10052-024-13263-x

    work page doi:10.1140/epjc/s10052-024-13263-x 2024

  46. [47]

    Mutuk, Magnetic moments of hidden-charm pentaquarks in the diquark–diquark–antiquark scheme, Chin

    H. Mutuk, Magnetic moments of hidden-charm pentaquarks in the diquark–diquark–antiquark scheme, Chin. J. Phys. 97 (2025) 1406–1414.arXiv:2411.16486,doi:10.1016/j.cjph.2025.07.030

    work page doi:10.1016/j.cjph.2025.07.030 2025

  47. [48]

    Özdem, Insight into the nature of thePc(4457)and related pentaquarks, Eur

    U. Özdem, Insight into the nature of thePc(4457)and related pentaquarks, Eur. Phys. J. C 85 (6) (2025) 624.arXiv: 2409.09449,doi:10.1140/epjc/s10052-025-14323-6

    work page doi:10.1140/epjc/s10052-025-14323-6 2025

  48. [49]

    Quasi-local photon surfaces in general spherically symmetric spacetimes.Eur

    U. Özdem, Probing the electromagnetic structure of thePc(4337)+ pentaquark: insights from a diquark–diquark–antiquark picture forJ P = 1 2 − and 3 2 − states, Eur. Phys. J. C 85 (6) (2025) 704.arXiv:2506.04345,doi:10.1140/epjc/ s10052-025-14439-9

    work page doi:10.1140/epjc/ 2025

  49. [50]

    S.-H.Zhu, F.-L.Wang, X.Liu, ElectromagneticcharacteristicsasprobesintotheinnerstructuresofthepredictedΞ (′,∗) c D(∗) s molecular states (10 2025).arXiv:2510.18492

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  50. [51]

    Özdem, Hidden-charm pentaquarks: electromagnetic structure in a diquark–diquark–antiquark model, Eur

    U. Özdem, Hidden-charm pentaquarks: electromagnetic structure in a diquark–diquark–antiquark model, Eur. Phys. J. C 86 (4) (2026) 359.arXiv:2603.19151,doi:10.1140/epjc/s10052-026-15591-6

    work page doi:10.1140/epjc/s10052-026-15591-6 2026

  51. [52]

    Özdem, Electromagnetic form factors: A window into theDΛc,D ∗Λc, andDΛ ∗ c molecular structure (11 2025).arXiv: 2511.16052

    U. Özdem, Electromagnetic form factors: A window into theDΛc,D ∗Λc, andDΛ ∗ c molecular structure (11 2025).arXiv: 2511.16052

    work page internal anchor Pith review arXiv 2025

  52. [53]

    Mutuk, X.-W

    H. Mutuk, X.-W. Kang, Magnetic moments of open bottom–charm molecular pentaquark octets (3 2026).arXiv:2603. 27657

    work page 2026

  53. [54]

    Li, Axial charges and magnetic moments of the decuplet pentaquark family, Phys

    H.-S. Li, Axial charges and magnetic moments of the decuplet pentaquark family, Phys. Rev. D 113 (5) (2026) 056017. arXiv:2511.12858,doi:10.1103/32n9-j3pp

    work page doi:10.1103/32n9-j3pp 2026

  54. [55]

    V. L. Chernyak, I. R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137–172.doi: 10.1016/0550-3213(90)90612-H

    work page doi:10.1016/0550-3213(90)90612-h 1990

  55. [56]

    V. M. Braun, I. E. Filyanov, QCD Sum Rules in Exclusive Kinematics and Pion Wave Function, Z. Phys. C 44 (1989) 157. doi:10.1007/BF01548594

    work page doi:10.1007/bf01548594 1989

  56. [57]

    I. I. Balitsky, V. M. Braun, A. V. Kolesnichenko, Radiative Decay Sigma+ —>p gamma in Quantum Chromodynamics, Nucl. Phys. B 312 (1989) 509–550.doi:10.1016/0550-3213(89)90570-1

    work page doi:10.1016/0550-3213(89)90570-1 1989

  57. [58]

    Analysis of the scalar and axial-vector heavy diquark states with QCD sum rules

    Z.-G. Wang, Analysis of the scalar and axial-vector heavy diquark states with QCD sum rules, Eur. Phys. J. C 71 (2011) 1524.arXiv:1008.4449,doi:10.1140/epjc/s10052-010-1524-y

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-010-1524-y 2011

  58. [59]

    R. T. Kleiv, T. G. Steele, A. Zhang, I. Blokland, Heavy-light diquark masses from QCD sum rules and constituent diquark models of tetraquarks, Phys. Rev. D 87 (12) (2013) 125018.arXiv:1304.7816,doi:10.1103/PhysRevD.87.125018

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.87.125018 2013

  59. [60]

    P. Ball, V. M. Braun, N. Kivel, Photon distribution amplitudes in QCD, Nucl. Phys. B 649 (2003) 263–296.arXiv: hep-ph/0207307,doi:10.1016/S0550-3213(02)01017-9

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(02)01017-9 2003

  60. [61]

    V. A. Novikov, M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, Calculations in External Fields in Quantum Chromody- 33 namics. Technical Review, Fortsch. Phys. 32 (1984) 585

    work page 1984

  61. [62]

    B. L. Ioffe, A. V. Smilga, Nucleon Magnetic Moments and Magnetic Properties of Vacuum in QCD, Nucl. Phys. B 232 (1984) 109–142.doi:10.1016/0550-3213(84)90364-X

    work page doi:10.1016/0550-3213(84)90364-x 1984

  62. [63]

    I. I. Balitsky, V. M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541–584.doi: 10.1016/0550-3213(89)90168-5

    work page doi:10.1016/0550-3213(89)90168-5 1989

  63. [64]

    V. M. Belyaev, B. Y. Blok, CHARMED BARYONS IN QUANTUM CHROMODYNAMICS, Z. Phys. C 30 (1986) 151. doi:10.1007/BF01560689

    work page doi:10.1007/bf01560689 1986

  64. [65]

    D. B. Leinweber, R. M. Woloshyn, T. Draper, Electromagnetic structure of octet baryons, Phys. Rev. D 43 (1991) 1659– 1678.doi:10.1103/PhysRevD.43.1659

    work page doi:10.1103/physrevd.43.1659 1991

  65. [66]

    Z.-G. Wang, Y. Liu, Analysis of the hidden-charm pentaquark candidates in theJ/ψΣmass spectrum via the QCD sum rules (3 2026).arXiv:2603.10774

    work page internal anchor Pith review arXiv 2026

  66. [67]

    Nozawa, D

    S. Nozawa, D. B. Leinweber, Electromagnetic form-factors of spin 3/2 baryons, Phys. Rev. D 42 (1990) 3567–3571. doi:10.1103/PhysRevD.42.3567

    work page doi:10.1103/physrevd.42.3567 1990

  67. [68]

    Electromagnetic excitation of the Delta(1232)-resonance

    V. Pascalutsa, M. Vanderhaeghen, S. N. Yang, Electromagnetic excitation of the Delta(1232)-resonance, Phys. Rept. 437 (2007) 125–232.arXiv:hep-ph/0609004,doi:10.1016/j.physrep.2006.09.006

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2006.09.006 2007

  68. [69]

    Electric quadrupole and magnetic octupole moments of the Delta

    G. Ramalho, M. T. Pena, F. Gross, Electric quadrupole and magnetic octupole moments of the Delta, Phys. Lett. B 678 (2009) 355–358.arXiv:0902.4212,doi:10.1016/j.physletb.2009.06.052

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2009.06.052 2009

  69. [70]

    V. M. Belyaev, B. L. Ioffe, Determination of the baryon mass and baryon resonances from the quantum-chromodynamics sum rule. Strange baryons, Sov. Phys. JETP 57 (1983) 716–721

    work page 1983

  70. [71]

    V. M. Belyaev, Delta - isobar magnetic form-factor in QCD (1 1993).arXiv:hep-ph/9301257

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  71. [72]

    Navaset al.[Particle Data Group], Phys

    S. Navas, et al., Review of particle physics, Phys. Rev. D 110 (3) (2024) 030001.doi:10.1103/PhysRevD.110.030001

    work page doi:10.1103/physrevd.110.030001 2024

  72. [73]

    B. L. Ioffe, QCD at low energies, Prog. Part. Nucl. Phys. 56 (2006) 232–277.arXiv:hep-ph/0502148,doi:10.1016/j. ppnp.2005.05.001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j 2006

  73. [74]

    Narison, mc,b, < αsG2 >andα s from Heavy Quarkonia, Nucl

    S. Narison, mc,b, < αsG2 >andα s from Heavy Quarkonia, Nucl. Part. Phys. Proc. 300-302 (2018) 153–164.doi: 10.1016/j.nuclphysbps.2018.12.026

    work page doi:10.1016/j.nuclphysbps.2018.12.026 2018

  74. [75]

    J. Rohrwild, Determination of the magnetic susceptibility of the quark condensate using radiative heavy meson decays, JHEP 09 (2007) 073.arXiv:0708.1405,doi:10.1088/1126-6708/2007/09/073

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2007/09/073 2007

  75. [76]

    A. J. Buchmann, E. M. Henley, Intrinsic quadrupole moment of the nucleon, Phys. Rev. C 63 (2001) 015202.arXiv: hep-ph/0101027,doi:10.1103/PhysRevC.63.015202

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.63.015202 2001

  76. [77]

    Electromagnetic form factors and structure of the $T_{bb}$ tetraquark from lattice QCD

    I. Vujmilovic, S. Collins, L. Leskovec, S. Prelovsek, Electromagnetic form factors and structure of theTbb tetraquark from lattice QCD (10 2025).arXiv:2510.17549

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  77. [78]

    V. I. Zakharov, L. A. Kondratyuk, L. A. Ponomarev, Bremsstrahlung and determination of electromagnetic parameters of particles, Yad. Fiz. 8 (1968) 783–792

    work page 1968

  78. [79]

    Magnetic moment of the Delta(1232)-resonance in chiral effective field theory

    V. Pascalutsa, M. Vanderhaeghen, Magnetic moment of the Delta(1232)-resonance in chiral effective field theory, Phys. Rev. Lett. 94 (2005) 102003.arXiv:nucl-th/0412113,doi:10.1103/PhysRevLett.94.102003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.94.102003 2005

  79. [80]

    Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon

    V. Pascalutsa, M. Vanderhaeghen, Chiral effective-field theory in the Delta(1232) region: I. Pion electroproduction on the nucleon, Phys. Rev. D 73 (2006) 034003.arXiv:hep-ph/0512244,doi:10.1103/PhysRevD.73.034003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.73.034003 2006

  80. [81]

    Chiral effective-field theory in the Delta(1232) region: II. radiative pion photoproduction

    V. Pascalutsa, M. Vanderhaeghen, Chiral effective-field theory in the Delta(1232) region. II. Radiative pion photoproduc- tion, Phys. Rev. D 77 (2008) 014027.arXiv:0709.4583,doi:10.1103/PhysRevD.77.014027

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.77.014027 2008

Showing first 80 references.