Pith. sign in

REVIEW 4 major objections 6 minor 45 references

$\Xi_c(2790)^{+/0}$ and $\Xi_c(2815)^{+/0}$ radiative decays

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that exact evaluation of the convective term in the electromagnetic Hamiltonian, with no free parameters, reproduces the measured Xi_c(2790) and Xi_c(2815) radiative decay widths.

desk verdict A technically sound exact convective-term calculation that overstates what the Belle data actually discriminate. read the letter →

arxiv 2501.08798 v2 pith:VBS2FEHH submitted 2025-01-15 hep-ph

H. García-Tecocoatzi , A. Ramirez-Morales , A. Rivero-Acosta , E. Santopinto , C. A. Vaquera-Araujo This is my paper · ORCID
classification hep-ph
keywords electromagneticdecayssinglycharmedbaryonsconstituentquarkmodelradiativedecaywidthsXi_cconvectivetermladderoperatorsP-wavestates
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 aims to show that the radiative decay widths of the P-wave charmed baryons $\Xi_c(2790)^{+/0}$ and $\Xi_c(2815)^{+/0}$ to their ground states can be computed exactly, with no free parameters, and that the resulting values agree with the Belle measurements. It keeps every term of the nonrelativistic electromagnetic Hamiltonian through order $m_j^{-1}$ and evaluates the convective term analytically with ladder operators, instead of using the usual dimensional substitutions such as $p_j/m_j\approx i k r_j$. The four widths come out as 335, 28, 380, and 20 keV for the neutral and charged 2790 and 2815 states, compatible with Belle's values and upper limits. If this is right, the exact treatment of the convective term, not the wave-function choice, is what decides whether constituent-quark models reproduce these transitions.

What carries the argument

The load-bearing object is the nonrelativistic electromagnetic Hamiltonian of Eq. (4), written as a sum over quarks of a magnetic spin-flip term proportional to $\hat{U}_j=e^{-i k r_j}$ and a convective orbit-flip term $\hat{T}_{j,-}=p_{j,-}\hat{U}_j+\hat{U}_j p_{j,-}$. The paper's new move is to evaluate $\hat{T}_{j,-}$ exactly rather than through the Close-Copley dimensional substitution $p_j/m_j\approx i k r_j$. In momentum space the quark momenta $p_{\rho,\pm}$ and $p_{\lambda,\pm}$ act as rank-1 irreducible tensor operators on harmonic-oscillator wave functions, so every convective matrix element can be re-expressed as a linear combination of $\hat{U}_j$ matrix elements with coefficients $C_\alpha$ and $C_\beta$ that come from SU(2) angular-momentum algebra. This ladder-operator treatment is what carries the argument: it converts the previously approximate convective term into an analytic, parameter-free calculation.

What would settle it

A future precise measurement of $\Gamma(\Xi_c(2790)^+\to\Xi_c^+\gamma)$ that excludes the 20-50 keV range, for instance finding a width near the 250-265 keV values of earlier models, would falsify the claim that the exact convective term is what produces the agreement; equivalently, measuring $\Gamma(\Xi_c(2815)^+\to\Xi_c^+\gamma)$ well above the predicted $\sim20$ keV while exceeding the current 80 keV upper limit would do the same.

Watch

Extended reading notes

Core claim

The central claim is that the exact evaluation of the convective term in the electromagnetic interaction Hamiltonian is the ingredient that produces agreement with experiment for $\Xi_c(2790)^{+/0}\to\Xi_c^{+/0}\gamma$ and $\Xi_c(2815)^{+/0}\to\Xi_c^{+/0}\gamma$. Using harmonic-oscillator wave functions and the masses and state assignments from the authors' constituent quark model [43], and without adding any parameters, the paper obtains decay widths of $335^{+23}_{-22}$, $28^{+17}_{-16}$, $380^{+24}_{-23}$, and $20^{+15}_{-13}$ keV for the four channels. It compares these with the Belle results: $\sim800\pm320$ keV (neutral 2790), $<350$ keV (charged 2790), $320\pm45^{+45}_{-80}$ keV (neutral 2815), and $<80$ keV (charged 2815). The paper characterizes the overall agreement as significant, while noting that the neutral 2790 width slightly underestimates the experimental value. Previous calculations that approximated the convective term by substituting $p_j/m_j\approx i k r_j$ or $p_{\lambda}\approx i m_{\lambda} k_{0\lambda}$ are shown to differ from the exact results by factors up to about ten.

Load-bearing premise

The load-bearing premise is that $\Xi_c(2790)$ and $\Xi_c(2815)$ are exactly the pure $P_\lambda$ harmonic-oscillator states $|1,0,0,0\rangle$ with the oscillator scales fitted in the authors' quark model [43]; any $P_\rho$ admixture or error in those scales changes the computed widths, with the charged channels most affected.

Editorial extensions

If this is right

  • The paper's predicted widths, 335, 28, 380, and 20 keV for the four channels, are ready-made targets for Belle II, BABAR, and LHC measurements of singly charmed baryon radiative decays.
  • For transitions that change orbital angular momentum ($\Delta L\neq 0$), the convective term dominates, and the paper's comparison shows that simpler dimensional substitutes can underestimate the width by up to an order of magnitude, for example $\Xi_c(2977)^+\to\Xi_c^{\prime+}\gamma$: 16 keV here versus 0.75 keV in Ref. [35].
  • The paper concludes that the correct evaluation of the convective term, not the choice of wave functions, is responsible for the agreement; this redirects future quark-model studies of radiative baryon decays toward exact treatment of this term.
  • Because the method is fully algebraic, the same ladder-operator reduction applies to other P-wave singly heavy baryon electromagnetic transitions without new approximations.

Reading between the lines

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

  • An extension the paper leaves implicit is that the exact convective term will matter most in channels where the orbital flip dominates, so its effect should be tested on other $P_\rho$-wave states such as $\Xi_c(2935)$ and $\Xi_c(2977)$, where older models differ from each other and from this calculation by large factors.
  • A sharp discriminating observable the paper does not single out is the ratio of neutral to charged widths: this work gives $\Gamma(2790^0)/\Gamma(2790^+)\approx 12$ and $\Gamma(2815^0)/\Gamma(2815^+)\approx 19$, while earlier harmonic-oscillator models give ratios of roughly 44-56 and 120, so a precise charged-width measurement would separate the two treatments.
  • If confirmed, the same exact ladder-operator evaluation could be turned into a general analytic formula for harmonic-oscillator baryon radiative transition amplitudes, allowing model comparisons without repeating the algebra for each channel.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript computes the radiative decay widths of the P-wave charmed baryons Ξ_c(2790)^{+/0} and Ξ_c(2815)^{+/0} to ground-state Ξ_c baryons in a nonrelativistic constituent quark model. The authors retain the full spin and convective terms of the electromagnetic Hamiltonian of Eq. (4) and evaluate the transition matrix elements analytically by using ladder operators in momentum space (Appendix A), instead of using the Close-Copley substitution or the p≈imk replacements adopted in earlier NRQM studies. Using masses, wave functions, and state assignments from their earlier quark-model fit (Ref. [43]), they predict Γ(Ξ_c(2790)^0→Ξ_c^0 γ)=335^{+23}_{-22} keV, Γ(Ξ_c(2790)^+→Ξ_c^+ γ)=28^{+17}_{-16} keV, Γ(Ξ_c(2815)^0→Ξ_c^0 γ)=380^{+24}_{-23} keV, and Γ(Ξ_c(2815)^+→Ξ_c^+ γ)=20^{+15}_{-13} keV. These are compared with the Belle estimates ∼800±320 keV, <350 keV, 320^{+90}_{-125} keV, and <80 keV, and the paper concludes that the agreement with experiment is due to the exact evaluation of the convective term.

Significance. If the calculation is correct, this is a useful contribution. The algebraic ladder-operator method provides an alternative to the uncontrolled substitutions used in earlier quark-model calculations, the model introduces no new free parameters for the radiative widths, and the paper gives a full set of predictions for the four Ξ_c(2790) and Ξ_c(2815) channels plus additional P-wave channels in Table 1. These predictions are falsifiable by future Belle II, LHCb, and BESIII measurements. The main caveats are that the analytic derivation is not fully self-contained, the quoted experimental support is weaker than claimed for two of the four channels, and the central causal claim about the convective term is not actually tested by the available data. The paper is therefore significant primarily as a methodological advance and as a source of new predictions, rather than as a decisive confirmation of the exact-treatment prescription.

major comments (4)
  1. [Appendix A, Eq. (A.5)] The central derivation is incomplete. The coefficients C_alpha and C_beta introduced in Eq. (A.5) are never displayed, and the examples in Appendix A.1 cover only a few actions of p_rho on low-lying states. Because the headline claim is that the convective term is evaluated exactly without further approximation, the full set of C_alpha and C_beta coefficients, or an explicit recurrence relation that generates them, is required for the calculation to be checked and reproduced for all states used in Table 1. Please include the complete algebraic reduction.
  2. [Abstract and Section 4] The data do not discriminate between the exact evaluation and the earlier approximations, so the statement that the agreement is 'due to' the exact convective term is not supported. For Ξ_c(2815)^0, the prior NRQM results (243–345 keV from Refs. [28,31,35]) and the exact result (380 keV) are all consistent with the Belle value 320^{+90}_{-125} keV. For Ξ_c(2790)^0, all NRQM predictions (218–335 keV) lie below the Belle estimate ∼800±320 keV by roughly 1.3–1.9σ, so the exact treatment does not remove the tension. The charged channels are only upper limits and cannot discriminate. The paper should be reframed to claim consistency with experiment and to state explicitly that the exact treatment changes the predicted values in a way that future data could test.
  3. [Section 3.1 and Table 2] The abstract's phrase 'significant agreement' overstates the comparison for Ξ_c(2790)^0. The predicted width 335^{+23}_{-22} keV is approximately 1.5σ below the Belle estimate of ∼800±320 keV when the quoted uncertainties are combined in quadrature. The text in §3.1 calls this a 'slight underestimate', which is misleading. The conclusions should report this discrepancy explicitly rather than presenting both neutral channels as being in good agreement.
  4. [Sections 3.1–3.4 and Table 1] The analysis relies on the assignment of Ξ_c(2790) and Ξ_c(2815) as pure P_lambda harmonic-oscillator excitations with quantum numbers |1,0,0,0>, taken from Ref. [43]. The paper itself notes in Section 3 that electromagnetic amplitudes are sensitive to the wave functions, for example the factor-of-about-three difference between Refs. [31] and [35]. No estimate is given of the effect of a possible P_rho admixture or of the uncertainty in the oscillator scales alpha_rho and alpha_lambda on the computed widths. Since the charged-state widths change by an order of magnitude between the approximate and exact treatments, this wave-function sensitivity should be quantified before the predictions can be considered robust.
minor comments (6)
  1. [Global] The unit 'KeV' should be 'keV' throughout, and 'Pλ-wave' should be written consistently as 'P_λ-wave' or 'P-lambda-wave'.
  2. [References] Reference [42] contains the typo 'Private comunication'; it should be 'Private communication'.
  3. [Table 1] The first table header 'F=¯3F' appears to be a typographical artifact for the SU(3) flavor representation; please correct or clarify the notation.
  4. [Section 2] The symbols k_0λ and k_0ρ are introduced without definition; please define them at their first use in the discussion of the substitutions used in Refs. [28,33].
  5. [Appendix A.1] Equation (A.6) uses two superficially similar notations for spherical and solid harmonics without defining them; please distinguish the two objects explicitly.
  6. [Abstract and Section 1] The claim 'for the first time' is difficult to verify and is not substantiated by a systematic literature search; consider softening it to 'we present an exact algebraic evaluation'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the radiative widths are new observables computed from an external mass fit, not from the Belle widths they are compared with.

full rationale

The derivation chain is self-contained in the relevant sense: the radiative widths are computed from the fixed nonrelativistic electromagnetic Hamiltonian of Eq. (4) and from wave functions, masses, and P-wave assignments imported from the authors' earlier quark-model fit, Ref. [43]. That fit was made to charmed-baryon masses from the PDG, not to the Belle radiative widths of Ref. [4], so the self-citation supplies independent model inputs rather than the target observables. No parameter in this paper is adjusted to reproduce the widths, and no equation defines the output in terms of itself: Eq. (7) is the standard phase-space-times-amplitude formula, and Appendix A evaluates the Hamiltonian matrix elements algebraically using harmonic-oscillator states. The paper's causal claim that the agreement is "due to" the exact evaluation of the convective term is stronger than the data can support, since previous approximate treatments [28,31,35] also fall within or near the Belle values and two of the four channels are only upper limits, but that is an interpretation/correctness concern rather than circularity. The self-citations to Refs. [43] and [37] are load-bearing, yet they are not circular because the radiative observables were not used in the fits that produced the model parameters.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central calculation is not self-contained: it imports the full quark-model Hamiltonian, wave functions, masses, and state assignments from the authors' earlier papers [43,44]. Those parameters were fitted to the charmed baryon mass spectrum, so the radiative widths are genuine predictions relative to the fitted observables. However, the phrase 'without the introduction of any additional parameters' should be read as 'no parameters beyond those already fitted to masses,' not as a first-principles derivation. No invented entities are introduced.

free parameters (3)
  • Constituent quark masses m_u, m_d, m_s, m_c = not stated in this paper; from Ref. [43]
    Enter the magnetic moments mu_j = e_j/(2m_j) and the oscillator frequencies through alpha_rho,lambda^2 = omega_rho,lambda m_rho,lambda. They were fitted to charmed baryon masses in the authors' prior model [43].
  • Oscillator frequencies omega_rho and omega_lambda (or scales alpha_rho, alpha_lambda) = not stated in this paper; from Ref. [43]
    Set the size of the harmonic-oscillator wave functions, which controls all spatial matrix elements including the convective term.
  • Hamiltonian parameters of the quark model of Ref. [43] = not stated here; fitted to PDG charmed baryon masses in [43]
    Determines the mass spectrum and the state assignments used for the initial and final baryons.
assumptions (4)
  • domain assumption Nonrelativistic reduction of the one-photon electromagnetic Hamiltonian truncated at order m_j^{-1}
    Used from Eq. (2) to Eq. (3). The expansion parameter for the light u/d quarks may not be small at the photon energies of these decays (k roughly 100 to 300 MeV), so neglected higher-order terms could affect the widths.
  • domain assumption Constituent quark model with three quarks and harmonic-oscillator spatial wave functions from Ref. [43]
    The states |k_rho,l_rho,m_lrho,k_lambda,l_lambda,m_llambda> in Appendix A diagonalize the harmonic oscillator Hamiltonian of [43,44]. No configuration mixing between P_lambda and P_rho modes is included.
  • domain assumption Quark magnetic moments are mu_j = e_j/(2m_j), with no anomalous magnetic moments
    Used in Eq. (4) for the spin-flip magnetic term. Constituent quarks may carry anomalous moments, which would change the magnetic contributions.
  • domain assumption The states Xi_c(2790) and Xi_c(2815) are pure P_lambda excitations with l_lambda = 1, l_rho = 0
    Taken from Ref. [43] and used throughout Sections 3.1 to 3.4 and Table 1. This assignment is load-bearing for the computed widths.

how reviews work

0 comments
Cite this review

Pith. "Pith review of $\Xi_c(2790)^{+/0}$ and $\Xi_c(2815)^{+/0}$ radiative decays." pith.science (2026). https://pith.science/paper/VBS2FEHH

@misc{pith2026250108798,
  author       = {Pith},
  title        = {Pith review of: $\Xi_c(2790)^+/0$ and $\Xi_c(2815)^+/0$ radiative decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VBS2FEHH}},
  note         = {Machine review of arXiv:2501.08798}
}
abstract

In this work, we study the $\Xi_c$ baryon electromagnetic decay widths within the constituent quark model formalism through an analysis of the transitions from $P-$wave states to ground states. We use the non-relativistic limit of the Hamiltonian of the electromagnetic interaction on keeping all the terms up to the order $m_j^{-1}$. We calculate the electromagnetic decay widths analytically, for the first time, without any further approximation. Specifically, our theoretical results for the $\Xi_c(2790)^{+/0}$ and $\Xi_c(2815)^{+/0}$ radiative decay widths, without the introduction of any additional parameters, display a significant agreement with the recent experimental values obtained by the Belle experiment. The agreement is due to the fact that we have not introduced further approximation to simplify the calculation of the difficult convective term, unlike what was done in previous studies. Our predictions may be useful for future experiments at the Belle, BABAR, and LHC experiments.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 17 canonical work pages

  1. [43]

    Garcia-Tecocoatzi, A

    H. Garcia-Tecocoatzi, A. Giachino, J. Li, A. Ramirez- Morales, E. Santopinto, Phys. Rev. D 107 (3) (2023) 034031.doi:10.1103/PhysRevD.107.034031

    doi:10.1103/physrevd.107.034031 2023

  2. [31]

    Wang, Y .-X

    K.-L. Wang, Y .-X. Yao, X.-H. Zhong, Q. Zhao, Phys. Rev. D 96 (11) (2017) 116016.doi:10.1103/PhysRevD.96. 116016

    doi:10.1103/physrevd.96 2017

  3. [35]

    Peng, S.-Q

    Y .-X. Peng, S.-Q. Luo, X. Liu, Refining radiative decay studies in singly heavy baryons, Phys. Rev. D 110 (7) (2024) 074034.arXiv:2405.12812,doi:10.1103/ PhysRevD.110.074034

    arXiv 2024

  4. [1]

    C. P. Jessop, et al., Phys. Rev. Lett. 82 (1999) 492–496. doi:10.1103/PhysRevLett.82.492

    doi:10.1103/physrevlett.82.492 1999

  5. [2]

    Aubert, et al., Phys

    B. Aubert, et al., Phys. Rev. Lett. 97 (2006) 232001.doi: 10.1103/PhysRevLett.97.232001

    doi:10.1103/physrevlett.97.232001 2006

  6. [3]

    Solovieva, et al., Phys

    E. Solovieva, et al., Phys. Lett. B 672 (2009) 1–5.doi: 10.1016/j.physletb.2008.12.062

    work page doi:10.1016/j.physletb.2008.12.062 2009

  7. [4]

    Yelton, et al., Phys

    J. Yelton, et al., Phys. Rev. D 102 (7) (2020) 071103.doi: 10.1103/PhysRevD.102.071103

    doi:10.1103/physrevd.102.071103 2020

  8. [5]

    Yelton, et al., Phys

    J. Yelton, et al., Phys. Rev. D 94 (5) (2016) 052011.doi: 10.1103/PhysRevD.94.052011

    work page doi:10.1103/physrevd.94.052011 2016

Show all 45 references
  1. [6]

    Cheng, C.-Y

    H.-Y . Cheng, C.-Y . Cheung, G.-L. Lin, Y . C. Lin, T.-M. Yan, H.-L. Yu, Phys. Rev. D 47 (1993) 1030–1042.doi: 10.1103/PhysRevD.47.1030

    1993 doi

  2. [7]

    Wang, The European Physical Journal A 44 (1) (2010) 105–117.doi:10.1140/epja/i2010-10952-8

    Z.-G. Wang, The European Physical Journal A 44 (1) (2010) 105–117.doi:10.1140/epja/i2010-10952-8

    2010 doi

  3. [8]

    Wang, Phys

    Z.-G. Wang, Phys. Rev. D 81 (2010) 036002.doi:10. 1103/PhysRevD.81.036002

    2010

  4. [9]

    Jiang, X.-L

    N. Jiang, X.-L. Chen, S.-L. Zhu, Phys. Rev. D 92 (2015) 054017.doi:10.1103/PhysRevD.92.054017

    2015 doi

  5. [10]

    J. Dey, M. Dey, V . Shevchenko, P. V olkovitsky, Physics Letters B 337 (1) (1994) 185–188.doi:https://doi. org/10.1016/0370-2693(94)91466-4

    1994 doi

  6. [11]

    Bernotas, V

    A. Bernotas, V . Šimonis, Phys. Rev. D 87 (2013) 074016. doi:10.1103/PhysRevD.87.074016

    2013 doi

  7. [12]

    T. M. Aliev, K. Azizi, H. Sundu, Eur. Phys. J. C 75 (1) (2015) 14.doi:10.1140/epjc/s10052-014-3229-0

    2015 doi

  8. [13]

    T. M. Aliev, K. Azizi, A. Ozpineci, Phys. Rev. D 79 (2009) 056005.doi:10.1103/PhysRevD.79.056005

    2009 doi

  9. [14]

    T. M. Aliev, T. Barakat, M. Savc ı, Phys. Rev. D 93 (2016) 056007.doi:10.1103/PhysRevD.93.056007

    2016 doi

  10. [15]

    T. M. Aliev, M. Savcı and V . S. Zamiralov, Modern Physics Letters A 27 (11) (2012) 1250054.doi:10. 1142/S021773231250054X

    2012

  11. [16]

    Chow, Phys

    C.-K. Chow, Phys. Rev. D 54 (1996) 3374–3376.doi: 10.1103/PhysRevD.54.3374

    1996 doi

  12. [17]

    Bahtiyar, K

    H. Bahtiyar, K. U. Can, G. Erkol, M. Oka, T. T. Taka- hashi, Phys. Lett. B 772 (2017) 121–126.doi:10.1016/ j.physletb.2017.06.022

    2017

  13. [18]

    Bahtiyar, K

    H. Bahtiyar, K. U. Can, G. Erkol, M. Oka, Phys. Lett. B 747 (2015) 281–286.doi:10.1016/j.physletb. 2015.06.006

    2015 doi

  14. [19]

    Ivanov, J

    M. Ivanov, J. Körner, V . Lyubovitskij, Physics Letters B 448 (1) (1999) 143–151.doi:https://doi.org/10. 1016/S0370-2693(99)00029-5

    1999

  15. [20]

    M. J. Savage, Phys. Lett. B 345 (1995) 61–66.doi:10. 1016/0370-2693(94)01597-6

    1995

  16. [21]

    Bañuls, M. C. and Pich, A. and Scimemi, I., Phys. Rev. D 61 (2000) 094009.doi:10.1103/PhysRevD.61. 094009

    2000 doi

  17. [22]

    P. L. Cho, Phys. Rev. D 50 (1994) 3295–3302.doi:10. 1103/PhysRevD.50.3295

    1994

  18. [23]

    G.-J. Wang, L. Meng, S.-L. Zhu, Phys. Rev. D 99 (3) (2019) 034021.doi:10.1103/PhysRevD.99.034021

    2019 doi

  19. [24]

    Cheng, Phys

    H.-Y . Cheng, Phys. Lett. B 399 (1997) 281–286.doi: 10.1016/S0370-2693(97)00305-5

    1997 doi

  20. [25]

    Simonis (3 2018).arXiv:1803.01809

    V . Simonis (3 2018).arXiv:1803.01809

    2018 arXiv

  21. [26]

    Majethiya, B

    A. Majethiya, B. Patel, P. C. Vinodkumar, Eur. Phys. J. A 42 (2009) 213–218.doi:10.1140/epja/ i2009-10880-8

    2009 doi

  22. [27]

    Hazra, S

    A. Hazra, S. Rakshit, R. Dhir, Phys. Rev. D 104 (5) (2021) 053002.doi:10.1103/PhysRevD.104.053002

    2021 doi

  23. [28]

    Bijker, H

    R. Bijker, H. García-Tecocoatzi, A. Giachino, E. Ortiz- Pacheco, E. Santopinto, Phys. Rev. D 105 (7) (2022) 074029.doi:10.1103/PhysRevD.105.074029

    2022 doi

  24. [29]

    Tawfiq, J

    S. Tawfiq, J. G. Körner, P. J. O’Donnell, Phys. Rev. D 63 (2001) 034005.doi:10.1103/PhysRevD.63.034005

    2001 doi

  25. [30]

    M. A. Ivanov, J. G. Körner, V . E. Lyubovitskij, A. G. Rusetsky, Phys. Rev. D 60 (1999) 094002.doi:10. 1103/PhysRevD.60.094002

    1999

  26. [32]

    Gamermann, C

    D. Gamermann, C. E. Jiménez-Tejero, A. Ramos, Phys. Rev. D 83 (2011) 074018.doi:10.1103/PhysRevD.83. 074018

    2011 doi

  27. [33]

    Ortiz-Pacheco, R

    E. Ortiz-Pacheco, R. Bijker, Phys. Rev. D 108 (2023) 054014.doi:10.1103/PhysRevD.108.054014

    2023 doi

  28. [34]

    T. M. Aliev, T. Barakat, M. Savcı, Eur. Phys. J. C 79 (5) (2019) 437.doi:10.1140/epjc/ s10052-019-6947-5

    2019 doi

  29. [36]

    F. E. Close, L. A. Copley, Nucl. Phys. B 19 (1970) 477– 500.doi:10.1016/0550-3213(70)90362-7

    1970 doi

  30. [37]

    García-Tecocoatzi, A

    H. García-Tecocoatzi, A. Giachino, A. Ramirez-Morales, A. Rivero-Acosta, E. Santopinto, C. A. Vaquera-Araujo, Phys. Rev. D 110 (11) (2024) 114005.doi:10.1103/ PhysRevD.110.114005. 7

    2024

  31. [38]

    Iachello, D

    F. Iachello, D. Kusnezov, Phys. Rev. D 45 (1992) 4156– 4177.doi:10.1103/PhysRevD.45.4156

    1992 doi

  32. [39]

    Li, H.-x

    Z.-p. Li, H.-x. Ye, M.-h. Lu, Phys. Rev. C 56 (1997) 1099– 1113.doi:10.1103/PhysRevC.56.1099

    1997 doi

  33. [40]

    Q. Zhao, J. S. Al-Khalili, Z. P. Li, R. L. Workman, Phys. Rev. C 65 (2002) 065204.doi:10.1103/PhysRevC.65. 065204

    2002 doi

  34. [41]

    W.-J. Deng, H. Liu, L.-C. Gui, X.-H. Zhong, Phys. Rev. D 95 (7) (2017) 074002.doi:10.1103/PhysRevD.95. 074002

    2017 doi

  35. [42]

    Bijker, Private comunication

    R. Bijker, Private comunication

  36. [44]

    Santopinto, A

    E. Santopinto, A. Giachino, J. Ferretti, H. García- Tecocoatzi, M. A. Bedolla, R. Bijker, E. Ortiz-Pacheco, Eur. Phys. J. C 79 (12) (2019) 1012.doi:10.1140/ epjc/s10052-019-7527-4

    2019

  37. [45]

    R. L. Workman, et al., Review of Particle Physics, PTEP 2022 (2022) 083C01.doi:10.1093/ptep/ptac097. 8

    2022 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.