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REVIEW 4 major objections 4 minor 86 references

The electromagnetic form factors of $\Sigma$ and $\Sigma^0 \to \Lambda$ transition in the timelike region

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that the 2.5 GeV bump in electron-positron annihilation into Sigma hyperon pairs is the phi(3D) vector meson, and that a subthreshold rho(3D) state shapes the Lambda-Sigma0 transition.

desk verdict A solid VMD extension with real predictions and an appendix worth reading, but the 'phi(3D) is essential' claim is not supported by the fits as presented. read the letter →

arxiv 2507.01277 v1 pith:M4QOO6TC submitted 2025-07-02 hep-ph

Cheng Chen , Bing Yan , Bing-Wei Long , Ju-Jun Xie This is my paper
classification hep-ph MSC 81V1081V05 PACS 12.40.Vv13.40.Gp14.20.Jn
keywords electromagneticformfactorstimelikeregionvectormesondominancehyperonpairproductionexcitedmesonsphi(3D)resonancesigmabaryonpolarization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper extends the vector meson dominance model for the reactions $e^+e^- \to \Sigma\bar{\Sigma}$ and $e^+e^- \to \Lambda\bar{\Sigma}^0$ by adding the excited vector mesons $\rho(3D)$, $\omega(3D)$, $\phi(3D)$, and $\rho(6D)$ to the usual ground-state $\rho$, $\omega$, and $\phi$. It claims that the resulting model reproduces the measured timelike electromagnetic form factors of the $\Sigma$ triplet, including the cross sections, the ratio $|G_E/G_M|$, and the relative phase $\Delta\Phi$, and that the $\phi(3D)$ state at 2500 MeV is essential for the near-threshold enhancement of the $\Sigma$ cross section seen by BESIII around $\sqrt{s}=2.5$ GeV. For the $\Lambda\bar{\Sigma}^0$ transition, the $\rho(3D)$ state is claimed to be crucial for reproducing the threshold cross section. A sympathetic reader would care because the work ties observed bumps and oscillating form-factor ratios to specific, still-unconfirmed excited vector states, and it makes concrete predictions for angular distributions and hyperon polarization that future experiments can check.

What carries the argument

The machinery is the extended vector meson dominance model: the virtual photon couples to baryon pairs through Breit-Wigner propagators $B_R = M_R^2/(M_R^2 - q^2 - i M_R \Gamma_R)$ for each included vector meson $R$, multiplied by a dipole intrinsic form factor $g(q^2)=(1-\gamma q^2)^{-2}$ that gives the correct large-$Q^2$ falloff. The named central objects are the excited states $\rho(3D)$, $\omega(3D)$, $\phi(3D)$ (a $\phi$ meson in the $3D$ orbital excitation, mass about 2500 MeV), and $\rho(6D)$, whose poles and interferences generate the threshold enhancement, the oscillatory $|G_E/G_M|$, and the nontrivial relative phase $\Delta\Phi$. Because $\rho(3D)$ and $\omega(3D)$ share nearly the same mass, the authors split the analysis into two scenarios that swap the isospin-1 and isospin-0 contributions, and the observed cross-section ratio $\sigma(\Sigma^+):\sigma(\Sigma^0):\sigma(\Sigma^-)\approx 9.7:3.3:1$ is used to constrain the isospin decomposition.

What would settle it

A fine energy scan of $e^+e^-\to\Sigma^+\bar{\Sigma}^-$ between 2.4 and 2.6 GeV: if the bump near 2.5 GeV does not show the line shape and phase motion of a 170-MeV-wide Breit-Wigner pole, or if high-statistics polarization data at $\sqrt{s}=2.5$ GeV show no peak in $P_y$ where the $\phi(3D)$ interference predicts one, the claim would be refuted. Similarly, measuring the angular distribution of $e^+e^-\to\Lambda\bar{\Sigma}^0$ near 2.46 GeV and checking whether the parameter $\alpha$ indeed approaches $-1$ would test the $\rho(3D)$ attribution.

Watch

Extended reading notes

Core claim

The central claim is that the timelike electromagnetic form factors of the $\Sigma$ and the $\Lambda\to\bar{\Sigma}^0$ transition are governed by a small set of vector-meson poles, including excited states that lie at or above the reaction thresholds. Within the extended vector meson dominance model, adding $\rho(3D)$, $\omega(3D)$, $\phi(3D)$, and $\rho(6D)$ with masses and widths taken from theory and the PDG yields a simultaneous description of 43 cross-section data points, 6 $|G_E/G_M|$ points, and 4 relative-phase points for $e^+e^-\to\Sigma\bar{\Sigma}$ with $\chi^2/\mathrm{d.o.f.}=0.9$ (Scenario I) or 1.1 (Scenario II). The specific physical conclusion is that the $2.5$ GeV enhancement in the BESIII data is caused by $\phi(3D)$, a vector meson predicted at 2500 MeV with a width of 170 MeV and a significant $\Sigma\bar{\Sigma}$ branching ratio; the $\rho(6D)$ is responsible for the nonzero phase at 2.9 GeV; and in $e^+e^- \to \Lambda\bar{\Sigma}^0$ the subthreshold $\rho(3D)$ pole produces the threshold enhancement and a non-monotonic $|G_E/G_M|$. The paper also corrects published formulas for the polarization moment $M(\cos\theta)$, stating that two earlier experimental extractions used a sign-inconsistent definition and should be revised.

Load-bearing premise

The whole explanation rests on the theoretical masses, widths, and especially the $\Sigma\bar{\Sigma}$ branching ratio of the excited vector mesons, above all the $\phi(3D)$ state at 2500 MeV with 170 MeV width taken from Refs. [59,65]; if that state does not exist with those properties, the enhancement would need another cause.

Editorial extensions

If this is right

  • The near-threshold enhancement of $e^+e^-\to\Sigma\bar{\Sigma}$ at $\sqrt{s}\approx2.5$ GeV is identified with the $\phi(3D)$ resonance at 2500 MeV, turning a data bump into evidence for a specific predicted state.
  • The oscillating $|G_E/G_M|$ ratio of $\Sigma^+$, similar to the $\Lambda_c^+$ pattern, is produced by the interference of near-threshold vector resonances, so the same mechanism may unify the two channels.
  • The $\rho(6D)$ state, with an enlarged effective width, accounts for the nonzero relative phase at 2.9 GeV; without it the phase would vanish.
  • In $e^+e^-\to\Lambda\bar{\Sigma}^0$, the subthreshold $\rho(3D)$ pole drives the threshold cross-section rise and creates a non-monotonic $|G_E/G_M|$ with $\alpha\to -1$ near 2.46 GeV.
  • The predicted polarization $P_y$ peaks near the $\phi(3D)$ and $\rho(6D)$ energies in $\Sigma$ production and near 2.4-2.5 GeV in the $\Lambda\bar{\Sigma}^0$ channel, making the resonances testable by spin measurements.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the $\phi(3D)$ identification survives, it would be one of the first direct dynamical confirmations of a highly excited vector meson predicted by the modified Godfrey-Isgur quark model, validating that model's mass spectrum in the 2.4-3.0 GeV region.
  • The appendix's correction to the polarization-moment formula implies that previously published relative phases $\Delta\Phi$ extracted from $\Lambda$ and $\Xi$ angular distributions may carry a sign error; reanalyzing existing BESIII data with the corrected formula is a cheap, direct test.
  • Because the $\rho(6D)$ here is an effective single resonance with an artificially large width absorbing several predicted states, a finer energy scan near 2.9 GeV should resolve multiple poles; the model predicts the phase data will then split into several narrower interferences.
  • The strong isospin sensitivity of $|G_E/G_M|$ for $\Sigma^0$ and $\Sigma^-$ suggests that measuring differential cross sections for those channels, not just total rates, would sharply distinguish which of the two scenarios is realized.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper studies the electromagnetic form factors of the Σ isospin triplet and the Λ–Σ0 transition in the timelike region within an extended vector meson dominance (VMD) model. In addition to the ground-state ρ, ω, and φ mesons, the authors include excited states ρ(3D), ω(3D), φ(3D), and ρ(6D), splitting the analysis into two scenarios that differ in the isospin assignment of the 2.3 GeV excited state. Good fits to the e+e−→ΣΣbar total cross sections, |GE/GM|, and the relative phase ΔΦ are obtained (χ2/d.o.f. 0.9 and 1.1 for the two scenarios). The paper claims that φ(3D) is essential for the near-threshold enhancement in e+e−→Σ+Σ− at √s≈2.5 GeV, and that ρ(3D) is important for the e+e−→ΛΣ0bar threshold cross section. It also provides predictions for the Σ0 and Σ− form factor ratios, phases, angular asymmetries, and polarizations, and includes a lengthy appendix on polarization observables in the decay chain.

Significance. If the central claim is correct, the paper offers a natural VMD explanation for the BESIII data at √s≈2.5 GeV and produces concrete, falsifiable predictions for Σ0, Σ−, and Λ–Σ0 observables that can be tested by future experiments. The fits are good, the model is economical, and the out-of-sample predictions for the Σ0/Σ− ratios and phases and for the Λ–Σ0 transition are genuine and useful. The paper also openly acknowledges that the ρ(6D) width is phenomenological and compensates for several unconstrained states. However, the strongest claim in the abstract—that φ(3D) is essential—is not supported by a controlled test, and the paper's own text notes correlations that undermine the uniqueness of that attribution. This is the main gap between the evidence and the conclusion.

major comments (4)
  1. [Sec. III.A, Fig. 1; Abstract; Sec. IV] The claim that φ(3D) is essential to the near-threshold enhancement is not tested by a controlled exclusion. The gray dashed baseline in Fig. 1(a) is the ground-state-only model of Ref. [36], while both full scenarios (blue and orange) include φ(3D) together with ω(3D)/ρ(3D) and ρ(6D). This comparison cannot isolate the role of φ(3D). A fit with φ(3D) removed and all remaining parameters re-optimized is required, with a chi-squared comparison and a check of whether the 2.5 GeV structure persists. Without such a test, the abstract's statement that 'φ(3D) is essential' goes beyond what the reported calculations demonstrate.
  2. [Table II] The fitted φ(3D) couplings flip sign between Scenario I (β=−0.500, α=0.486) and Scenario II (β=0.375, α=−0.361), indicating strong parameter correlations with the other excited states. This is consistent with the near-threshold enhancement being produced by a combination of subthreshold resonances rather than by a unique, isolated φ(3D) contribution. A stability analysis, such as profiling the χ2 as a function of the φ(3D) couplings or excluding φ(3D) entirely, is needed to substantiate the claimed essentiality.
  3. [Table I and Sec. I] The mass and width of φ(3D) are fixed at the theoretical values 2500 MeV and 170 MeV from Refs. [59,65] and are not varied in the fits. The essentiality claim therefore depends on unvalidated resonance properties. A sensitivity study varying the φ(3D) mass and width over the ranges suggested by these references is needed to establish that the conclusion is robust to the model input.
  4. [Sec. III.B, Fig. 7] For the e+e−→ΛΣ0bar channel, the text states that the gray dashed line 'represents a fit without ρ(3D) (achieved by setting the βρ(3D) and αρ(3D) coupling constant to zero)'. It is unclear whether the remaining two parameters were re-optimized after setting those couplings to zero. If they were merely zeroed in the best-fit parameter set, the comparison is not a controlled test of ρ(3D)'s importance. The χ2 for the without-ρ(3D) case is not reported. Please clarify the procedure and, if necessary, re-fit the reduced model and report the resulting χ2.
minor comments (4)
  1. [Throughout] There are several typographical errors: 'obatined' in Sec. III.A, 'BarBar' instead of 'BaBar' in Sec. I and in the captions of Figs. 3 and 7, and 'expect' instead of 'except' in Sec. I.
  2. [Eqs. (18)-(21)] The signs in the constraints for fΣ±2 in Eq. (19) involve '∓ βρ(6D)/√2' while FΣ±1 in Eq. (13) has '± βρ(6D)/√2'. Please verify that this sign difference is intentional and not a typographical error.
  3. [Sec. II] Equation (22) is an empty numbered equation; it should be removed or given content.
  4. [Appendix] The appendix is very long relative to the main text and includes a critique of formulas in Refs. [18,27]. While the derivation is instructive, the connection to the main results could be stated more concisely, and the critique could be separated into a dedicated note.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are fit interpretations, and the paper's out-of-sample predictions are genuinely new observables.

full rationale

The paper is a standard phenomenological vector meson dominance fit. The excited-state couplings (β, α) are free parameters fitted to the e+e− → ΣΣ-bar cross-section, |GE/GM| and ΔΦ data, while the masses and widths are taken from external theoretical sources (Refs. [58,59,65,68]). The Abstract's statement that 'the ϕ(3D) resonance is essential to the near threshold enhancement' is an interpretive summary of the fitted model, but no equation in the paper makes that claim true by construction: the gray comparison line in Fig. 1(a) removes all excited states, not ϕ(3D) alone, and no re-fit without ϕ(3D) is reported. This is an evidentiary/model-selection gap, not a circular reduction. Similarly, ρ(6D) is explicitly introduced 'to account for experimental data at a center-of-mass energy of 2.9 GeV' and later used to interpret the phase at that energy; this is transparent parameterization, not a renamed prediction. The ΛΣ̄0 analysis contains a genuine removal test: 'the gray dashed line represents a fit without ρ(3D) (achieved by setting the βρ(3D) and αρ(3D) coupling constant to zero)'. The claimed predictions for |GE/GM|, ΔΦ, α and Py in channels where no data were fitted are genuine out-of-sample outputs of the fitted amplitude. The only self-citations (Refs. [34,36,78]) are used for baseline comparison or for the value γ = 0.43, which is externally supported by a ΛΛ̄ fit and by the authors' own Σ fit; none is load-bearing in a way that forces the central result. I therefore find no step in the derivation chain that reduces to its inputs by definition or by construction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 3 invented entities

The model rests on the VMD ansatz, a phenomenological dipole intrinsic form factor with a fitted slope, and the unverified existence of several excited vector meson states. The rho(6D) is effectively a free entity tuned to the data. The paper does not derive these states from QCD; it borrows them from prior theoretical predictions.

free parameters (5)
  • gamma (dipole form factor slope) = 0.4217 (Scenario I), 0.4662 (Scenario II); fixed to 0.43 for Lambda-Sigma0
    Slope of the intrinsic form factor g(q^2) = (1 - gamma q^2)^-2; fitted to cross section, ratio, and phase data for Sigma, and fixed by flavor symmetry for Lambda-Sigma0.
  • Vector meson couplings (Scenario I: beta_rho, beta_omega_phi, alpha_omega_phi, beta_omega_3D, alpha_omega_3D… = 0.9354, -0.3363, -2.8767, 0.6881, -0.7078, -0.4998, 0.4856, -0.0265, 0.0278
    Fitted to 53 data points (43 cross sections, 6 |GE/GM|, 4 phase) for e+e- -> Sigma Sigma-bar.
  • Vector meson couplings (Scenario II: beta_rho, beta_omega_phi, alpha_omega_phi, beta_rho_3D, alpha_rho_3D… = 1.4189, -0.4264, 7.9466, 0.0645, -0.0968, 0.3754, -0.3608, 0.0537, -0.050
    Alternative fit replacing omega(3D) with rho(3D) because the two states have nearly equal mass.
  • Lambda-Sigma0 couplings (beta_rho_3D, alpha_rho_3D) = 0.3784, -0.4053
    Fitted to BESIII total cross section data for e+e- -> Lambda Sigma-zero; gamma fixed at 0.43 and beta_rho fixed at 0.
  • rho(6D) mass and width = 2850 MeV, 150 MeV
    Set by hand to describe the data near 2.9 GeV; width is larger than theoretical predictions in Refs [65,68], acting as an effective lumping of several higher excited states.
assumptions (6)
  • domain assumption Vector meson dominance: the virtual photon couples to baryons through intermediate vector meson resonances
    Standard phenomenological assumption used throughout Sec. II to write F1 and F2 as sums of Breit-Wigner propagators.
  • standard math Breit-Wigner propagator form B_R = M_R^2 / (M_R^2 - q^2 - i M_R Gamma_R)
    Used in Eqs. (13)-(16) and Eqs. (24)-(25) to represent each vector meson contribution.
  • ad hoc to paper Dipole intrinsic form factor g(q^2) = (1 - gamma q^2)^-2
    Introduced in Eq. (23) as a phenomenological factor; its form is not derived, and gamma is fitted.
  • domain assumption Existence and properties of rho(3D), omega(3D), phi(3D) excited states as listed in Table I
    Masses and widths taken from theoretical predictions in Refs [58,59,65]; these states are not experimentally well established.
  • domain assumption g_Sigma-Lambda-rho = 0, hence beta_rho = 0 for Lambda-Sigma0
    Taken from current algebra (Ref [80]) and QCD sum rule (Ref [81]); used to reduce the Lambda-Sigma0 parameter set in Sec. III B.
  • domain assumption Same intrinsic form factor slope gamma for Lambda-Sigma0 as for Sigma and Lambda
    Assumed from quark model flavor structure (Sec. III B); gamma fixed at 0.43 based on Lambda and Sigma fits.
invented entities (3)
  • rho(6D) resonance
    purpose: Describes the cross section and phase data near 2.9 GeV in e+e- -> Sigma Sigma-bar
    State not observed; mass and width set by hand to match data, wider than theoretical predictions. It is effectively a fudge factor for several higher excited rho states.
  • phi(3D) resonance
    purpose: Produces the near-threshold enhancement at 2.5 GeV in e+e- -> Sigma Sigma-bar
    Predicted by Refs [59,65] but not experimentally established; its coupling is fitted, so the claimed essential role is inferred from the fit.
  • rho(3D) resonance (for Lambda-Sigma0)
    purpose: Enhances the near-threshold cross section of e+e- -> Lambda Sigma-zero
    Predicted in Ref [58] but not established; the fit requires a non-zero coupling to reproduce the BESIII threshold point.

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Cite this review

Pith. "Pith review of The electromagnetic form factors of $\Sigma$ and $\Sigma^0 \to \Lambda$ transition in the timelike region." pith.science (2026). https://pith.science/paper/M4QOO6TC

@misc{pith2026250701277,
  author       = {Pith},
  title        = {Pith review of: The electromagnetic form factors of $\Sigma$ and $\Sigma^0 \to \Lambda$ transition in the timelike region},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M4QOO6TC}},
  note         = {Machine review of arXiv:2507.01277}
}
abstract

We investigate the $e^+e^-\to \Sigma\bar{\Sigma}$ and $e^+e^-\to \Lambda\bar{\Sigma}^0$ reactions within the extended vector meson dominance model. In addition to the ground state mesons $\rho$ and $\omega$, we consider the contributions of the excited states $\rho(3D)$, $\omega(3D)$, $\phi(3D)$, and $\rho(6D)$. It is found that the current experimental data on the $\Sigma$ electromagnetic form factors in timelike region can be well reproduced. And the $\phi(3D)$ resonance is essential to the near threshold enhancement of the cross section for the $e^+e^-\to \Sigma\bar{\Sigma}$ reaction. Furthermore, in the $e^+e^-\to \Lambda\bar{\Sigma}^0$ reaction, the $\rho(3D)$ is important to get a good fit for the experimental results.

Figures

Figures reproduced from arXiv: 2507.01277 by the authors.

Figure 2
Figure 2. FIG. 2: The angular distribution parameter [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1: The obtained total cross sections, ratio [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 4
Figure 4. FIG. 4: The obtained total cross sections of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: FIG. 5: The angular distribution parameter [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: The angular distribution parameter [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The obtained total cross sections of the process [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The obtained angular distribution parameter [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Works this paper leans on

86 extracted references · 47 canonical work pages

  1. [36]

    Dai, Z.-Y

    A.-X. Dai, Z.-Y . Li, L. Chang, and J.-J. Xie, Chin. Phys. C 46, 073104 (2022), arXiv:2112.06264 [hep-ph]

    arXiv 2022

  2. [1]

    (A37) After simplifying the expressions, the final result is H µν S Lµν = sD(s) p 1 − α2 sin θ cos θ sin ∆Φ × 1 sin θ (ˆp × ˆk) · ⃗l′ 1 . (A38) For the third component H µν ¯S , its explicit form is given by H µν ¯S = Tr h (/p1 + M )Γµ(/p2 − M )γ5 /l 2 − H2 ¯Γν i = −4i|GM |2(M ερσµν (p1ρ + p2ρ)l2σ − H2ερσµν p1ρp2σ) −GM F ∗ 2 2M 4iεαβγµ p1αp2βl2γ(pν 1 − pν...

  3. [2]

    Denig and G

    A. Denig and G. Salme, Prog. Part. Nucl. Phys. 68, 113 (2013), arXiv:1210.4689 [hep-ex]

    arXiv 2013

  4. [3]

    Pacetti, R

    S. Pacetti, R. Baldini Ferroli, and E. Tomasi-Gustafsson, Phys. Rept. 550-551, 1 (2015)

    2015

  5. [4]

    Punjabi, C

    V . Punjabi, C. F. Perdrisat, M. K. Jones, E. J. Brash, and C. E. Carlson, Eur. Phys. J. A51, 79 (2015), arXiv:1503.01452 [nucl- ex]

    arXiv 2015

  6. [5]

    The first exploration of the physical Riemann surfaces of the ratio $G_E^\Lambda/G_M^\Lambda$

    A. Mangoni, S. Pacetti, and E. Tomasi-Gustafsson, Phys. Rev. D 104, 116016 (2021), arXiv:2109.03759 [hep-ph]

    work page Pith review arXiv 2021

  7. [6]

    E. A. Kuraev, E. Tomasi-Gustafsson, and A. Dbeyssi, Phys. Lett. B 712, 240 (2012), arXiv:1106.1670 [hep-ph]

    work page Pith review arXiv 2012

  8. [7]

    Aubert et al

    B. Aubert et al. (BaBar), Phys. Rev. D 76, 092006 (2007), arXiv:0709.1988 [hep-ex]

    arXiv 2007

Show all 86 references
  1. [8]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D 97, 032013 (2018), arXiv:1709.10236 [hep-ex]

    2018

  2. [9]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 124, 032002 (2020), arXiv:1910.04921 [hep-ex]

    2020

  3. [10]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 123, 122003 (2019), arXiv:1903.09421 [hep-ex]

    2019

  4. [11]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Lett. B 820, 136557 (2021), arXiv:2105.14657 [hep-ex]

    2021

  5. [12]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Lett. B 831, 137187 (2022), arXiv:2110.04510 [hep-ex]

    2022

  6. [13]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D104, L091104 (2021), arXiv:2108.02410 [hep-ex]

    2021

  7. [14]

    Gong et al

    G. Gong et al. (Belle), Phys. Rev. D 107, 072008 (2023), arXiv:2210.16761 [hep-ex]

    2023 arXiv

  8. [15]

    Ablikim et al

    M. Ablikim et al. (BESIII), JHEP 11, 228 (2023), arXiv:2309.04215 [hep-ex]

    2023

  9. [16]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D 109, 034029 (2024), arXiv:2312.12719 [hep-ex]

    2024

  10. [17]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D 109, 012002 (2024), arXiv:2308.03361 [hep-ex]

    2024

  11. [18]

    Ablikim et al

    M. Ablikim et al. (BESIII), JHEP 05, 022 (2024), arXiv:2401.09468 [hep-ex]

    2024

  12. [19]

    Ablikim et al

    M. Ablikim et al. (BESIII), Nature Phys. 15, 631 (2019), arXiv:1808.08917 [hep-ex]

    2019 arXiv

  13. [20]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D105, L011101 (2022), arXiv:2111.11742 [hep-ex]

    2022

  14. [21]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 129, 131801 (2022), arXiv:2204.11058 [hep-ex]

    2022

  15. [22]

    Ablikim et al

    M. Ablikim et al. (BESIII), JHEP 10, 081 (2023), [Erratum: JHEP 12, 080 (2023)], arXiv:2303.00271 [hep-ex]

    2023

  16. [23]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 125, 052004 (2020), arXiv:2004.07701 [hep-ex]

    2020

  17. [24]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 132, 081904 (2024), arXiv:2307.15894 [hep-ex]

    2024

  18. [25]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 133, 101902 (2024), arXiv:2406.06118 [hep-ex]

    2024

  19. [26]

    Ablikim et al

    M. Ablikim et al. (BESIII), (2024), 10.1007/JHEP12(2024)186, arXiv:2408.03205 [hep-ex]

    2024

  20. [27]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D106, L091101 (2022), arXiv:2206.10900 [hep-ex]

    2022

  21. [28]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D108, L031106 (2023), arXiv:2305.09218 [hep-ex]

    2023

  22. [29]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D108, L011101 (2023), arXiv:2302.09767 [hep-ex]

    2023

  23. [30]

    H. Liu, J. Zhang, and X. Wang, Symmetry 15, 214 (2023)

    2023

  24. [31]

    Cao, J.-P

    X. Cao, J.-P. Dai, and Y .-P. Xie, Phys. Rev. D 98, 094006 (2018), arXiv:1808.06382 [hep-ph]

    2018 arXiv

  25. [32]

    Yang, D.-Y

    Y . Yang, D.-Y . Chen, and Z. Lu, Phys. Rev. D 100, 073007 (2019), arXiv:1902.01242 [hep-ph]

    2019 arXiv

  26. [33]

    Haidenbauer, U.-G

    J. Haidenbauer, U.-G. Meißner, and L.-Y . Dai, Phys. Rev. D 103, 014028 (2021), arXiv:2011.06857 [nucl-th]

    2021 arXiv

  27. [34]

    Li and J.-J

    Z.-Y . Li and J.-J. Xie, Commun. Theor. Phys. 73, 055201 (2021), arXiv:2012.02379 [hep-ph]

    2021 arXiv

  28. [35]

    Li, A.-X

    Z.-Y . Li, A.-X. Dai, and J.-J. Xie, Chin. Phys. Lett. 39, 011201 (2022), arXiv:2107.10499 [hep-ph]

    2022 arXiv

  29. [37]

    B. Yan, C. Chen, and J.-J. Xie, Phys. Rev. D 107, 076008 (2023), arXiv:2301.00976 [hep-ph]

    2023 arXiv

  30. [38]

    Lin, H.-W

    Y .-H. Lin, H.-W. Hammer, and U.-G. Meißner, Eur. Phys. J. C 82, 1091 (2022), arXiv:2208.14802 [hep-ph]

    2022 arXiv

  31. [39]

    J.-P. Dai, X. Cao, and H. Lenske, Phys. Lett. B 846, 138192 17 (2023), arXiv:2304.04913 [hep-ph]

    2023 arXiv

  32. [40]

    Lin, F.-K

    Y .-H. Lin, F.-K. Guo, and U.-G. Meißner, Phys. Lett. B 856, 138887 (2024), arXiv:2309.07850 [hep-ph]

    2024 arXiv

  33. [41]

    Cao, Y .-T

    X. Cao, Y .-T. Liang, and R.-G. Ping, Phys. Rev. D110, 014035 (2024), arXiv:2404.00298 [hep-ph]

    2024 arXiv

  34. [42]

    Zhang, R.-G

    Z. Zhang, R.-G. Ping, T. Liu, J. J. Song, W. Yang, and Y .- j. Zhou, Phys. Rev. D 110, 034034 (2024), arXiv:2404.04787 [hep-ph]

    2024 arXiv

  35. [43]

    Zheng, A

    W. Zheng, A. Kupsc, S. Pacetti, F. Rosini, N. Salone, X. Wang, and S.-s. Fang, Chin. Phys. Lett. 42, 041201 (2025), arXiv:2501.11205 [hep-ex]

    2025 arXiv

  36. [44]

    L.-Y . Dai, J. Haidenbauer, and U.-G. Meißner, Chin. Phys. Lett. 42, 030202 (2025), arXiv:2412.07543 [hep-ph]

    2025 arXiv

  37. [45]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Lett. B 814, 136110 (2021), arXiv:2009.01404 [hep-ex]

    2021

  38. [46]

    Mangoni, SciPost Phys

    A. Mangoni, SciPost Phys. Proc. 10, 021 (2022), arXiv:2110.12475 [hep-ex]

    2022 arXiv

  39. [47]

    Irshad, D

    M. Irshad, D. Liu, X. Zhou, and G. Huang, Symmetry 14, 69 (2022)

    2022

  40. [48]

    Ramalho, M

    G. Ramalho, M. T. Pe ˜na, and K. Tsushima, Phys. Rev. D 101, 014014 (2020), arXiv:1908.04864 [hep-ph]

    2020 arXiv

  41. [49]

    Anselmino, E

    M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, and D. B. Lichtenberg, Rev. Mod. Phys. 65, 1199 (1993)

    1993

  42. [50]

    Kubis and U

    B. Kubis and U. G. Meissner, Eur. Phys. J. C 18, 747 (2001), arXiv:hep-ph/0010283

    2001 arXiv

  43. [51]

    Iachello, A

    F. Iachello, A. D. Jackson, and A. Lande, Phys. Lett. B 43, 191 (1973)

    1973

  44. [52]

    Iachello and Q

    F. Iachello and Q. Wan, Phys. Rev. C 69, 055204 (2004)

    2004

  45. [53]

    Bijker and F

    R. Bijker and F. Iachello, Phys. Rev. C 69, 068201 (2004), arXiv:nucl-th/0405028

    2004 arXiv

  46. [54]

    B. Yan, C. Chen, X. Li, and J.-J. Xie, Phys. Rev. D109, 036033 (2024), arXiv:2312.04866 [nucl-th]

    2024 arXiv

  47. [55]

    Bisello et al

    D. Bisello et al. (DM2), Z. Phys. C 48, 23 (1990)

    1990

  48. [56]

    Haidenbauer, K

    J. Haidenbauer, K. Holinde, and J. Speth, Nucl. Phys. A 562, 317 (1993)

    1993

  49. [57]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D110, 030001 (2024)

    2024

  50. [58]

    Pang, Y .-R

    C.-Q. Pang, Y .-R. Wang, J.-F. Hu, T.-J. Zhang, and X. Liu, Phys. Rev. D 101, 074022 (2020), arXiv:1910.12408 [hep-ph]

    2020 arXiv

  51. [59]

    Wang, L.-M

    J.-Z. Wang, L.-M. Wang, X. Liu, and T. Matsuki, Phys. Rev. D 104, 054045 (2021), arXiv:2106.14582 [hep-ph]

    2021 arXiv

  52. [60]

    Wang, S.-Q

    L.-M. Wang, S.-Q. Luo, and X. Liu, Phys. Rev. D 105, 034011 (2022), arXiv:2109.06617 [hep-ph]

    2022 arXiv

  53. [61]

    Feng, X.-W

    J.-C. Feng, X.-W. Kang, Q.-F. L ¨u, and F.-S. Zhang, Phys. Rev. D 104, 054027 (2021), arXiv:2104.01339 [hep-ph]

    2021 arXiv

  54. [62]

    Zhou, J.-Z

    Q.-S. Zhou, J.-Z. Wang, and X. Liu, Phys. Rev. D 106, 034010 (2022), arXiv:2207.00276 [hep-ph]

    2022 arXiv

  55. [63]

    Zhou, J.-Z

    Q.-S. Zhou, J.-Z. Wang, X. Liu, and T. Matsuki, Phys. Rev. D 105, 074035 (2022), arXiv:2201.06393 [hep-ph]

    2022 arXiv

  56. [64]

    Wang, T.-Y

    Y .-R. Wang, T.-Y . Li, Z.-Y . Fang, H. Chen, and C.-Q. Pang, Phys. Rev. D 106, 114024 (2022), arXiv:2208.10329 [hep-ph]

    2022 arXiv

  57. [65]

    Y .-r. Wang, Y . Ma, and C.-q. Pang, Int. J. Mod. Phys. A 38, 2350118 (2023), arXiv:2211.09023 [hep-ph]

    2023 arXiv

  58. [66]

    Bai, Q.-S

    Z.-Y . Bai, Q.-S. Zhou, and X. Liu, Phys. Rev. D 108, 094036 (2023), arXiv:2307.16255 [hep-ph]

    2023 arXiv

  59. [67]

    Lodha and A

    C. Lodha and A. K. Rai, Eur. Phys. J. Plus 139, 663 (2024)

    2024

  60. [68]

    Lodha and A

    C. Lodha and A. K. Rai, Few Body Syst. 65, 99 (2024), arXiv:2410.14246 [hep-ph]

    2024 arXiv

  61. [69]

    Feng, Z.-Y

    X.-C. Feng, Z.-Y . Li, D.-M. Li, Q.-T. Song, E. Wang, and W.- C. Yan, Phys. Rev. D 106, 076012 (2022), arXiv:2206.10132 [hep-ph]

    2022 arXiv

  62. [70]

    A. D. Sakharov, Zh. Eksp. Teor. Fiz. 18, 631 (1948)

    1948

  63. [71]

    F ¨aldt and A

    G. F ¨aldt and A. Kupsc, Phys. Lett. B 772, 16 (2017), arXiv:1702.07288 [hep-ph]

    2017 arXiv

  64. [72]

    Granados, S

    C. Granados, S. Leupold, and E. Perotti, Eur. Phys. J. A 53, 117 (2017), arXiv:1701.09130 [hep-ph]

    2017 arXiv

  65. [73]

    G. P. Lepage and S. J. Brodsky, Phys. Rev. Lett.43, 545 (1979), [Erratum: Phys.Rev.Lett. 43, 1625–1626 (1979)]

    1979

  66. [74]

    G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980)

    1980

  67. [75]

    A. V . Belitsky, X.-d. Ji, and F. Yuan, Phys. Rev. Lett. 91, 092003 (2003), arXiv:hep-ph/0212351

    2003 arXiv

  68. [76]

    D. B. Leinweber, R. M. Woloshyn, and T. Draper, Phys. Rev. D 43, 1659 (1991)

    1991

  69. [77]

    T. M. Aliev, A. Ozpineci, and M. Savci, Phys. Lett. B 516, 299 (2001), arXiv:hep-ph/0104204

    2001 arXiv

  70. [78]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. Lett. 131, 191901 (2023), arXiv:2307.07316 [hep-ex]

    2023

  71. [79]

    C. Chen, B. Yan, and J.-J. Xie, Chin. Phys. Lett. 41, 021302 (2024), arXiv:2312.16753 [hep-ph]

    2024 arXiv

  72. [80]

    Bijker, F

    R. Bijker, F. Iachello, and A. Leviatan, Phys. Rev. C 54, 1935 (1996), arXiv:nucl-th/9510001

    1996 arXiv

  73. [81]

    C. S. Lai, Phys. Rev. 155, 1562 (1967)

    1967

  74. [82]

    Erkol, R

    G. Erkol, R. G. E. Timmermans, and T. A. Rijken, Phys. Rev. C 74, 045201 (2006)

    2006

  75. [83]

    Xiao, X.-Z

    L.-Y . Xiao, X.-Z. Weng, X.-H. Zhong, and S.-L. Zhu, Chin. Phys. C 43, 113105 (2019), arXiv:1904.06616 [hep-ph]

    2019 arXiv

  76. [84]

    H. Czyz, A. Grzelinska, and J. H. Kuhn, Phys. Rev. D 75, 074026 (2007), arXiv:hep-ph/0702122

    2007 arXiv

  77. [85]

    F ¨aldt, Eur

    G. F ¨aldt, Eur. Phys. J. A 51, 74 (2015), arXiv:1306.0525 [nucl- th]

    2015 arXiv

  78. [86]

    F ¨aldt, Eur

    G. F ¨aldt, Eur. Phys. J. A 52, 141 (2016), arXiv:1602.02532 [nucl-th]

    2016 arXiv

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Reviewed August 6, 2026 · model on record in the stance chip above.