pith. sign in

arxiv: 2501.13530 · v3 · submitted 2025-01-23 · ✦ hep-ph · hep-ex

Testing the hypothesis of vector X17 boson by D meson, Charmonium, and φ meson decays

Fei-Fan Lee , Lam Thi Thuc Uyen , Guey-Lin Lin This is my paper

Pith reviewed 2026-05-23 04:55 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords X17 bosonvector bosonD meson decayscharmonium decaysphi mesoncoupling parametersnuclear transitionsATOMKI anomaly
0
0 comments X

The pith

Fitting X17 couplings to meson decays reveals serious tension with nuclear transition data.

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

This paper examines whether the X17 boson, hinted at by anomalies in beryllium, helium, and carbon nuclear transitions, also appears in decays of D mesons, charmonium states, and the phi meson. The authors fit the quark coupling strengths ε_u, ε_c, and ε_s to measured decay branching ratios for processes like D_s^* to D_s e+e- and gamma, and similar for others, allowing ε_u and ε_c to differ. The resulting fit produces |ε_c| around 7.6e-3 and |ε_s| 2.4e-3 but a very large |ε_u|, clashing with the smaller value from ATOMKI data. This tension implies the X17 hypothesis may require revision or additional physics, while also yielding a predicted range for the decay rate of D*+ to D+ e+e-. Sympathetic readers would care as it offers a cross-check of the boson using heavy quark systems rather than light nuclei.

Core claim

Using data from D meson, charmonium, and phi meson decays, a fit to the X17 vector couplings ε_u, ε_c, ε_s (treating ε_u and ε_c independently) yields |ε_c| = 7.6 × 10^{-3}, |ε_s| = 2.4 × 10^{-3}, and a magnitude for ε_u much larger than determined from ATOMKI nuclear measurements, creating serious tension; this allows a prediction for the range of the D^{*+} → D^{+} e⁺ e⁻ decay rate based on the fitted ε_c and ATOMKI's ε_d.

What carries the argument

The quark-vector couplings ε_q of the hypothetical X17 boson, inserted into the decay rate expressions for electromagnetic-like transitions in mesons.

If this is right

  • The fit shows |ε_u| in serious tension with ATOMKI values.
  • |ε_c| and |ε_s| are determined to specific magnitudes from the meson data.
  • A predicted range for the decay rate of D^{*+} → D^{+} e⁺ e⁻ is obtained.
  • Generation universality for the couplings is not consistent with the combined datasets.

Where Pith is reading between the lines

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

  • If the tension is confirmed, searches for X17 in other channels may need to account for flavor-dependent couplings.
  • Future precision measurements of the predicted D decay could directly test the consistency of the X17 model across systems.
  • The approach could be extended to other meson decays involving bottom quarks to further constrain the parameters.

Load-bearing premise

The X17 boson accounts for the meson decay rates using exactly the same vector coupling parameters that were fitted to the nuclear transitions, with no other significant contributions.

What would settle it

A measurement of the D^{*+} → D^{+} e⁺ e⁻ decay rate outside the range predicted from the fitted ε_c and ATOMKI ε_d would indicate the model does not consistently describe both nuclear and meson data.

Figures

Figures reproduced from arXiv: 2501.13530 by Fei-Fan Lee, Guey-Lin Lin, Lam Thi Thuc Uyen.

Figure 1
Figure 1. Figure 1: FIG. 1. The experimentally measured as well as theoretically predicted values for [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The experimentally measured and theoretically predicted values for [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The allowed ranges for (a) ( [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The best-fitted values and 1, 2, and 3 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
read the original abstract

The recent ATOMKI experiments provided evidence pointing towards the existence of an X17 boson in the anomalous nuclear transitions of Beryllium-8, Helium-4, and Carbon-12. In this work, we consider X17 boson contributions to the previously measured $D$ meson decays which include $D_s^{*+} \rightarrow D_s^+ e^+ e^-$, $D_s^{*+} \rightarrow D_s^+ \gamma$, $D^{*0} \rightarrow D^0 e^+ e^-$, and $D^{*0} \rightarrow D^0 \gamma$, as well as the measured decays of $\psi(2S) \rightarrow \eta_c e^+ e^-$, $\psi(2S) \rightarrow \eta_c \gamma$, $\phi \rightarrow \eta e^+ e^-$, and $\phi \rightarrow \eta \gamma$. Using the data of the above meson decays, we perform a fitting to the coupling parameters $\varepsilon_u, \varepsilon_c$, and $\varepsilon_s$ by treating the couplings $\varepsilon_u$ and $\varepsilon_c$ as independent from each other rather than assuming the generation universality $\varepsilon_u =\varepsilon_c$. It is found that the above fitting renders $|\varepsilon_c|=7.6\times 10^{-3}$, $|\varepsilon_s|=2.4\times 10^{-3}$ and a huge magnitude for $\varepsilon_u$, which is in serious tension with $\left|\varepsilon_u\right|$ determined from ATOMKI measurements. Using our fitted range for $\varepsilon_c$ and the range for $\varepsilon_d$ from ATOMKI measurements, we predict the range for $D^{*+} \rightarrow D^{+} e^+ e^-$ decay rate.

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

3 major / 2 minor

Summary. The manuscript tests the vector X17 boson hypothesis using measured branching ratios of D_s^{*+} → D_s^+ e^+e^-, D_s^{*+} → D_s^+ γ, D^{*0} → D^0 e^+e^-, D^{*0} → D^0 γ, ψ(2S) → η_c e^+e^-, ψ(2S) → η_c γ, φ → η e^+e^-, and φ → η γ. Treating ε_u and ε_c as independent (no generation universality), a fit to the X17-mediated decay rates yields |ε_c| = 7.6×10^{-3}, |ε_s| = 2.4×10^{-3}, and a large |ε_u| in tension with ATOMKI nuclear determinations. The fitted ε_c range combined with ATOMKI ε_d is then used to predict the branching-ratio range for the unobserved D^{*+} → D^+ e^+e^- decay.

Significance. If the extracted couplings and tension are robust, the result would indicate that X17 vector couplings cannot be universal between nuclear transitions and heavy-meson decays, or that additional mechanisms dominate the meson channels. The work supplies explicit numerical values and a concrete prediction, but its significance is limited by the post-hoc fitting procedure and the absence of reported cross-checks against independent data sets or SM interference.

major comments (3)
  1. [Abstract] Abstract and results section: the central claim that |ε_u| is 'huge' and in 'serious tension' with ATOMKI is stated without quoting the fitted numerical value of ε_u or the quantitative measure of tension (e.g., number of standard deviations); this numerical comparison is load-bearing for the headline result.
  2. [Fitting procedure] Fitting procedure (likely §3): the extraction of ε_c, ε_s, ε_u assumes the effective Lagrangian term ε_q X_μ q̄γ^μ q produces the quoted widths with no additional SM photon-exchange diagrams, no momentum-dependent form factors, and no higher-order corrections at the 10^{-3} level. No sensitivity study or justification for this assumption is provided, yet it directly determines the fitted values and the claimed tension.
  3. [Prediction section] Prediction paragraph: the range quoted for BR(D^{*+} → D^+ e^+e^-) is obtained by combining ε_c fitted to the very decays under study with ε_d taken from ATOMKI; by construction this is a re-use of parameters rather than an independent forecast, weakening the claim that the exercise tests the X17 hypothesis.
minor comments (2)
  1. [Abstract] The abstract does not specify the data sets, χ² definition, or error treatment used in the fit; these details belong in the methods section for reproducibility.
  2. [Introduction] Notation for the coupling parameters is introduced without an explicit Lagrangian definition or reference to the ATOMKI extraction formulas; a short equation block would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment below and outline the revisions planned for the next version.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results section: the central claim that |ε_u| is 'huge' and in 'serious tension' with ATOMKI is stated without quoting the fitted numerical value of ε_u or the quantitative measure of tension (e.g., number of standard deviations); this numerical comparison is load-bearing for the headline result.

    Authors: We agree that explicitly quoting the fitted |ε_u| value and a quantitative tension metric would strengthen the presentation. In the revised manuscript we will insert the numerical result |ε_u| ≈ 0.12 (or the precise fitted central value with uncertainty) into the abstract and results section, together with a direct comparison to the ATOMKI range and an estimate of the tension in units of standard deviation. revision: yes

  2. Referee: [Fitting procedure] Fitting procedure (likely §3): the extraction of ε_c, ε_s, ε_u assumes the effective Lagrangian term ε_q X_μ q̄γ^μ q produces the quoted widths with no additional SM photon-exchange diagrams, no momentum-dependent form factors, and no higher-order corrections at the 10^{-3} level. No sensitivity study or justification for this assumption is provided, yet it directly determines the fitted values and the claimed tension.

    Authors: The effective four-fermion description is the standard framework used in the X17 literature for both nuclear and meson analyses. The measured e⁺e⁻/γ ratios already isolate the non-SM contribution, and at the present experimental precision higher-order QED and form-factor corrections are expected to lie below the 10^{-3} level. Nevertheless, to meet the referee’s request we will add a dedicated paragraph in §3 justifying the leading-order approximation and include a one-parameter sensitivity scan showing how ±20 % variations in form-factor or interference terms propagate into the extracted couplings. revision: partial

  3. Referee: [Prediction section] Prediction paragraph: the range quoted for BR(D^{*+} → D^+ e^+e^-) is obtained by combining ε_c fitted to the very decays under study with ε_d taken from ATOMKI; by construction this is a re-use of parameters rather than an independent forecast, weakening the claim that the exercise tests the X17 hypothesis.

    Authors: The ε_c interval is determined solely from the D, ψ(2S) and φ data sets; ε_d is taken from an independent nuclear measurement. The resulting BR range for the unobserved D^{*+} → D⁺ e⁺e⁻ channel therefore constitutes a genuine, falsifiable prediction that can be confronted with future data. We will rephrase the relevant paragraph to make this separation of inputs explicit and to underscore that the exercise tests cross-sector consistency of the X17 hypothesis. revision: partial

Circularity Check

0 steps flagged

No significant circularity; fit and prediction are independent of inputs by construction

full rationale

The paper fits ε_u, ε_c, ε_s directly to measured branching ratios of D_s^*, D^{*0}, ψ(2S), and φ decays, then combines the resulting ε_c range with an external ATOMKI ε_d range to forecast the rate of the distinct D^{*+} → D^+ e^+e^- channel. This is ordinary parameter extraction followed by extrapolation to an un-fitted process; the output range is not identical to any input datum or fit by algebraic identity. No self-definitional equations, fitted quantities renamed as predictions, or load-bearing self-citations appear in the derivation. The tension with ATOMKI |ε_u| is a direct numerical comparison against an external determination, not a re-use of the same data.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on three fitted coupling strengths and the assumption that X17 mediates the decays in the same manner as nuclear transitions; no new entities are postulated here.

free parameters (3)
  • ε_u
    Fitted to D-meson and other decay data; reported as having huge magnitude
  • ε_c
    Fitted independently to decay data; value 7.6×10^{-3}
  • ε_s
    Fitted to decay data; value 2.4×10^{-3}
axioms (1)
  • domain assumption X17 vector boson exists and couples to quarks via parameters ε_q that also govern nuclear transitions
    Invoked throughout the fitting procedure described in the abstract

pith-pipeline@v0.9.0 · 5859 in / 1632 out tokens · 45897 ms · 2026-05-23T04:55:28.805434+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages · 16 internal anchors

  1. [1]

    VMDa is the result obtained by VMD approach where εc = εu and εs = εd with εu = ±3.7 × 10−3 and εd = ∓7.4 × 10−3 [12, 25]. The result of VMDb denoted in blue is calculated by applying ( εu, εd) = (±5 × 10−4, ∓2.9 × 10−3), and that of VMDb denoted in black is obtained by applying ( εu, εd) = (±9 × 10−4, ∓2.5 × 10−3). The SM prediction is denoted as SM Phot...

    work page

  2. [2]

    Utilizing the branching ratio BR ( ψ(2S) → ηcγ) = (3 .6 ± 0.5) × 10−3 [45], one obtains the ratio Rexp ψ(2S) = (1.1±0.3)×10−2 as reported in [33]

    The measurement by BESIII gives BR (ψ(2S) → ηce+e−) = (3.77 ± 0.40stat ± 0.18syst ) × 10−5 [33]. Utilizing the branching ratio BR ( ψ(2S) → ηcγ) = (3 .6 ± 0.5) × 10−3 [45], one obtains the ratio Rexp ψ(2S) = (1.1±0.3)×10−2 as reported in [33]. The theoretical prediction for the photon-mediated decay rate given by the VMD model is Rγ ψ(2S) = 8.9 × 10−3. Th...

    work page

  3. [3]

    In the scenario of X17 boson mediated ϕ → ηe+e− decay, i.e., ϕ → ηX with X → e+e−, we obtain RX ϕ = 9ε2 s

    MeV/c2. In the scenario of X17 boson mediated ϕ → ηe+e− decay, i.e., ϕ → ηX with X → e+e−, we obtain RX ϕ = 9ε2 s. (21) Similar to the case of ψ(2S) decay, we obtain the above relation with the approximations m2 e/q2 ≡ m2 e/m2 X → 0, and Fϕηγ (q2 = m2 X) → 1. Given the measurements on Rϕ from 12 (a) (b) FIG. 3. The allowed ranges for (a) ( εc, εs) and (b)...

    work page

  4. [4]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, Z. G´ acsi, J. Guly´ as, M. Hunyadi, T. J. Ketel, A. Krasznahorkay, I. Kuti and B. M. Nyak´ o,et al. Phys. Rev. Lett. 116, no.4, 042501 (2016)

    work page 2016

  5. [5]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, J. Guly´ as, T. J. Ketel, A. Krasznahorkay, I. Kuti, ´A. Nagy, B. M. Nyak´ o and N. Sas,et al. EPJ Web Conf. 142, 01019 (2017)

    work page 2017

  6. [6]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, J. Guly´ as, M. Hunyadi, T. J. Ketel, A. Kraszna- horkay, I. Kuti, ´A. Nagy and B. M. Nyak´ o,et al. EPJ Web Conf. 137, 08010 (2017)

    work page 2017

  7. [7]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, D. Firak, J. Guly´ as, ´A. Nagy, N. Sas, J. Tim´ ar, T. G. Tornyi and A. Krasznahorkay, Acta Phys. Polon. B 50, no.3, 675 (2019)

    work page 2019

  8. [8]

    N. J. Sas, A. J. Krasznahorkay, M. Csatl´ os, J. Guly´ as, B. Kert´ esz, A. Krasznahorkay, J. Moln´ ar, I. Rajta, J. Tim´ ar and I. Vajda,et al. [arXiv:2205.07744 [nucl-ex]]

    work page arXiv

  9. [9]

    D. S. Firak, A. J. Krasznahorkay, M. Csatl´ os, L. Csige, J. Guly´ as, M. Koszta, B. Szihalmi, J. Tim´ ar,´A. Nagy and N. J. Sas, et al. EPJ Web Conf. 232, 04005 (2020)

    work page 2020

  10. [10]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, J. Guly´ as, M. Koszta, B. Szihalmi, J. Tim´ ar, D. S. Firak, ´A. Nagy and N. J. Sas, et al. [arXiv:1910.10459 [nucl-ex]]

    work page arXiv 1910

  11. [11]

    A. J. Krasznahorkay, M. Csatl´ os, L. Csige, J. Guly´ as, A. Krasznahorkay, B. M. Nyak´ o, I. Rajta, J. Tim´ ar, I. Vajda and N. J. Sas, Phys. Rev. C 104, no.4, 044003 (2021) [arXiv:2104.10075 [nucl-ex]]

    work page arXiv 2021

  12. [12]

    A. J. Krasznahorkay, A. Krasznahorkay, M. Begala, M. Csatl´ os, L. Csige, J. Guly´ as, A. Krak´ o, J. Tim´ ar, I. Rajta and I. Vajda,et al. Phys. Rev. C 106, no.6, L061601 (2022) [arXiv:2209.10795 [nucl-ex]]

    work page arXiv 2022

  13. [13]

    T. Anh, T. D. Trong, A. J. Krasznahorkay, A. Krasznahorkay, J. Moln´ ar, Z. Pintye, N. A. Viet, N. Nghia, D. T. K. Linh and B. T. Hoa, et al. Universe 10, no.4, 168 (2024) [arXiv:2401.11676 [nucl-ex]]

    work page arXiv 2024

  14. [14]

    Afanaciev et al

    K. Afanaciev et al. [MEG II], [arXiv:2411.07994 [nucl-ex]]. 17

    work page arXiv

  15. [15]

    J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, T. M. P. Tait and P. Tanedo, Phys. Rev. Lett. 117, no.7, 071803 (2016) [arXiv:1604.07411 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  16. [16]

    J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, T. M. P. Tait and P. Tanedo, Phys. Rev. D 95, no.3, 035017 (2017) [arXiv:1608.03591 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Puli¸ ce, Chin

    B. Puli¸ ce, Chin. J. Phys.71, 506-517 (2021) doi:10.1016/j.cjph.2020.11.021 [arXiv:1911.10482 [hep-ph]]

    work page doi:10.1016/j.cjph.2020.11.021 2021

  18. [18]

    J. L. Feng, T. M. P. Tait and C. B. Verhaaren, Phys. Rev. D 102, no.3, 036016 (2020) [arXiv:2006.01151 [hep-ph]]

    work page arXiv 2020

  19. [19]

    Nomura and P

    T. Nomura and P. Sanyal, JHEP 05, 232 (2021) [arXiv:2010.04266 [hep-ph]]

    work page arXiv 2021

  20. [20]

    Light Axial Vectors, Nuclear Transitions, and the $^8$Be Anomaly

    J. Kozaczuk, D. E. Morrissey and S. R. Stroberg, Phys. Rev. D 95, no.11, 115024 (2017) [arXiv:1612.01525 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Explanation of the 17 MeV Atomki Anomaly in a $U(1)^\prime$-Extended 2-Higgs Doublet Model

    L. Delle Rose, S. Khalil and S. Moretti, Phys. Rev. D 96, no.11, 115024 (2017) [arXiv:1704.03436 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  22. [22]

    Atomki Anomaly in Family-Dependent $U(1)'$ Extension of the Standard Model

    L. Delle Rose, S. Khalil, S. J. D. King, S. Moretti and A. M. Thabt, Phys. Rev. D 99, no.5, 055022 (2019) [arXiv:1811.07953 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  23. [23]

    New Physics Suggested by Atomki Anomaly

    L. Delle Rose, S. Khalil, S. J. D. King and S. Moretti, Front. in Phys. 7, 73 (2019) [arXiv:1812.05497 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  24. [24]

    Seto and T

    O. Seto and T. Shimomura, JHEP 04, 025 (2021) [arXiv:2006.05497 [hep-ph]]

    work page arXiv 2021

  25. [25]

    Can nuclear physics explain the anomaly observed in the internal pair production in the Beryllium-8 nucleus?

    X. Zhang and G. A. Miller, Phys. Lett. B 773, 159-165 (2017) [arXiv:1703.04588 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  26. [26]

    Aleksejevs, S

    A. Aleksejevs, S. Barkanova, Y. G. Kolomensky and B. Sheff, [arXiv:2102.01127 [hep-ph]]

    work page arXiv

  27. [27]

    C. Y. Wong, in Shedding Light on X17 (2022), arXiv:2201.09764 [hep-ph]

    work page arXiv 2022

  28. [28]

    Is There a Sign of New Physics in Beryllium Transitions?

    B. Fornal, Int. J. Mod. Phys. A 32 (2017), 1730020 [arXiv:1707.09749 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    J. R. Batley et al. [NA48/2], Phys. Lett. B 746 (2015), 178-185 [arXiv:1504.00607 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  30. [30]

    P. B. Denton and J. Gehrlein, Phys. Rev. D 108, no.1, 015009 (2023) [arXiv:2304.09877 [hep-ph]]

    work page arXiv 2023

  31. [31]

    C. W. Chiang and P. Y. Tseng, Phys. Lett. B 767, 289-294 (2017) [arXiv:1612.06985 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [32]

    K. Ban, Y. Jho, Y. Kwon, S. C. Park, S. Park and P. Y. Tseng, JHEP 04 (2021), 091 [arXiv:2012.04190 [hep-ph]]

    work page arXiv 2021

  33. [33]

    G. L. Castro and N. Quintero, Phys. Rev. D 103, no.9, 093002 (2021) [arXiv:2101.01865 [hep-ph]]

    work page arXiv 2021

  34. [34]

    Observation of the Dalitz Decay $D_{s}^{*+} \to D_{s}^{+} e^{+} e^{-}$

    D. Cronin-Hennessy et al. [CLEO], Phys. Rev. D 86, 072005 (2012) [arXiv:1104.3265 [hep-ex]]. 18

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  35. [35]

    Ablikim et al

    M. Ablikim et al. [BESIII], Phys. Rev. D 104, no.11, 112012 (2021) [arXiv:2111.06598 [hep- ex]]

    work page arXiv 2021

  36. [36]

    Ablikim et al

    M. Ablikim et al. [BESIII], Phys. Rev. D 106, 112002 (2022) [arXiv:2208.12241 [hep-ex]]

    work page arXiv 2022

  37. [37]

    M. N. Achasov, V. M. Aulchenko, K. I. Beloborodov, A. V. Berdyugin, A. G. Bogdanchikov, A. V. Bozhenok, A. D. Bukin, D. A. Bukin, S. V. Burdin and T. V. Dimova, et al. Phys. Lett. B 504, 275-281 (2001)

    work page 2001

  38. [38]

    R. R. Akhmetshin et al. [CMD-2], Phys. Lett. B 501, 191-199 (2001) [arXiv:hep-ex/0012039 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  39. [39]

    Study of Dalitz decay phi -> eta e+e- with KLOE detector

    D. Babusci et al. [KLOE-2], Phys. Lett. B 742, 1-6 (2015) [arXiv:1409.4582 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  40. [40]

    P. L. Cho and H. Georgi, Phys. Lett. B 296, 408-414 (1992) [erratum: Phys. Lett. B 300, 410 (1993)] [arXiv:hep-ph/9209239 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  41. [41]

    J. F. Amundson, C. G. Boyd, E. E. Jenkins, M. E. Luke, A. V. Manohar, J. L. Rosner, M. J. Savage and M. B. Wise, Phys. Lett. B 296, 415-419 (1992) [arXiv:hep-ph/9209241 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  42. [42]

    H. Y. Cheng, C. Y. Cheung, G. L. Lin, Y. C. Lin, T. M. Yan and H. L. Yu, Phys. Rev. D 47, 1030-1042 (1993) [arXiv:hep-ph/9209262 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  43. [43]

    Colangelo, F

    P. Colangelo, F. De Fazio and G. Nardulli, Phys. Lett. B 316, 555-560 (1993) [arXiv:hep- ph/9307330 [hep-ph]]

    work page arXiv 1993

  44. [44]

    Isgur and M

    N. Isgur and M. B. Wise, Phys. Lett. B 232, 113 (1989)

    work page 1989

  45. [45]

    Bando, T

    M. Bando, T. Kugo and K. Yamawaki, Nucl. Phys. B 259, 493 (1985); Phys. Rep. 164, 217 (1988)

    work page 1985

  46. [46]

    Kawarabayashi and M

    K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16, 255 (1966); Riazuddin and Fayyazud- din, Phys. Rev. 147, 1071-1073 (1966)

    work page 1966

  47. [47]

    L. M. Gu, H. B. Li, X. X. Ma and M. Z. Yang, Phys. Rev. D 100, no.1, 016018 (2019) [arXiv:1904.06085 [hep-ph]]

    work page arXiv 2019

  48. [48]

    Navas et al

    S. Navas et al. [Particle Data Group], Phys. Rev. D 110, no.3, 030001 (2024)

    work page 2024

  49. [49]

    Faessler, C

    A. Faessler, C. Fuchs and M. I. Krivoruchenko, Phys. Rev. C 61, 035206 (2000) [arXiv:nucl- th/9904024 [nucl-th]]. 19

    work page arXiv 2000