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Relativistic effects in the strong and electromagnetic decays of ${D^*}$ meson

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that the $D^*$ meson's strong and radiative widths are controlled by relativistic partial-wave components in the Salpeter wave function, giving $\Gamma(D^{*0})=54.0$ keV and turning $D^{*0}\to D^0\gamma$ into an…

desk verdict Useful Salpeter calculation of D* decays with a testable D*0 width prediction, but the reliability of the small relativistic wave-function components that drive the results is unquantified, and the abstract contradicts the paper's own Table II. read the letter →

arxiv 2412.10775 v2 pith:JVMHZUBW submitted 2024-12-14 hep-ph

Man Jia , Wei Li , Su-Yan Pei , Xin-Yao Du , Guo-Zhu Ning , Guo-Li Wang This is my paper · ORCID
classification hep-ph
keywords D*mesonSalpeterequationrelativisticwavefunctionstrongdecayradiativeM1transitionmultipoleexpansionheavy-light
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

This paper aims to show that a fully relativistic treatment of the charmed vector meson $D^*$ changes both its strong and radiative decay pattern. Solving the complete Salpeter equation, the authors predict $\Gamma(D^{*0}\to D^0\pi^0)=34.6$ keV and $\Gamma(D^{*0}\to D^0\gamma)=19.4$ keV, for a total width around 54 keV. Their central point is that the $D^*$ and $D$ wave functions contain small relativistic P- and D-wave components, so $D^*\to D\gamma$ is not a pure M1 transition but a superposition of M1, E2, M3, and E4 multipoles, with the relativistic corrections actually dominating the rate. If right, this means the $D^*$ width is far below the current 2.1 MeV upper limit and that radiative charmed-meson decays are a sensitive test of quark-model wave functions.

What carries the argument

The central object is the complete instantaneous Salpeter equation and its positive-energy wave-function solutions for a $1^-$ vector meson and a $0^-$ pseudoscalar meson. The $1^-$ wave function is expanded in $S$-, $P$-, and $D$-wave parts; the $0^-$ wave function in $S$- and $P$-wave parts. Transition amplitudes are formed by tracing these wave functions with $\gamma_\mu\gamma_5$ for the strong decay (with a pion entering through PCAC) or with $\gamma_\mu$ for the electromagnetic decay, with quark charges $Q_1$ and $Q_2$. The numerical kernel is a linear confining potential plus a vector Coulomb potential whose parameters are fit to meson spectroscopy. This machinery lets the authors separate the naive $S\times S'$ contribution from relativistic $P$- and $D$-wave contributions and expose the interference that sets the final widths.

What would settle it

A precise measurement of the $D^{*}(2007)^0$ full width, together with the photon angular distribution in $D^{*0}\to D^0\gamma$, would settle it: a width far from 54 keV or a purely dipole photon distribution would contradict the claimed relativistic dominance.

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Extended reading notes

Core claim

The authors solve the complete Salpeter equation for the charmed mesons and use the positive-energy wave functions to compute the $D^*\to D\pi$ and $D^*\to D\gamma$ transition amplitudes. In their solutions the $D^*$ is not a pure $S$-wave state: its wave function is a mixture of $S$-, $P$-, and $D$-waves, while the $D$ meson mixes $S$- and $P$-waves. Consequently $D^*\to D\gamma$ is calculated as an M1+E2+M3+E4 transition rather than a pure M1. They report $\Gamma(D^{*0}\to D^0\pi^0)=34.6$ keV and $\Gamma(D^{*0}\to D^0\gamma)=19.4$ keV, estimating $\Gamma(D^{*0})\simeq54.0$ keV, and note that the nonrelativistic M1 piece contributes only 2.60 keV of the radiative width, so the relativistic correction dominates.

Load-bearing premise

Everything hangs on the small P- and D-wave components of the wave functions being quantitatively right, since those components provide the claimed relativistic dominance in $D^*\to D\gamma$ and the interference that lowers the strong width.

Editorial extensions

If this is right

  • The $D^{*}(2007)^0$ total width is predicted to be about 54 keV, far below the current experimental upper limit of 2.1 MeV, so a dedicated measurement is a sharp test of the calculation.
  • The predicted branching fractions, 64.1% for $D^{*0}\to D^0\pi^0$ and 35.9% for $D^{*0}\to D^0\gamma$, match the measured values within uncertainties.
  • The strong-decay width of $D^{*+}\to D^0\pi^+$ (55.8 keV) and the ratio to $D^{*+}\to D^+\pi^0$ (about 2.16) agree with experiment and with other model calculations, making these quantities a stable benchmark.
  • For $D^{*+}\to D^+\gamma$, the predicted 0.84 keV is close to the measured $1.33\pm0.4$ keV, and the large neutral-versus-charged radiative width difference is traced to quark charges adding rather than cancelling in the two photon-emission graphs.
  • In the strong decay $D^{*0}\to D^0\pi^0$, the $S\times S'$ term alone would give 91.0 keV, so relativistic $P$-wave interference is required to bring the width down to 34.6 keV.

Reading between the lines

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

  • If the small partial waves are this decisive, then using $D^*\to D\gamma$ as a clean magnetic-dipole probe of $D^*$ properties would be misleading; a photon angular-distribution measurement is a direct way to check the multipole content.
  • The interference pattern that reduces the strong width depends on the relative sign of the $S$- and $P$-wave amplitudes, so an independent lattice-QCD calculation of the $D^*\to D\pi$ matrix element could confirm or exclude the kernel's parameter choice.
  • The same relativistic components are likely to affect other heavy-light vector mesons such as $D_s^*$ and $B^*$; extending the calculation would predict radiative widths that deviate from pure-M1 estimates by comparable factors.
  • Because the $D^{*0}$ width is predicted so precisely, a future high-statistics measurement would turn the Salpeter-equation wave functions into a quantitative test of the instantaneous approximation itself.
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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 manuscript solves the complete Salpeter equation for the D and D* mesons and uses the resulting relativistic wave functions, which contain S-, P-, and D-wave components, to compute the strong decays D* → Dπ and the radiative decays D* → Dγ. The authors report Γ(D*(2007)0 → D0π0) = 34.6 keV and Γ(D*(2007)0 → D0γ) = 19.4 keV, leading to an estimated D*0 full width of 54.0 keV, and they emphasize that the radiative decay is an M1+E2+M3+E4 transition in which relativistic corrections dominate, whereas they state that in the strong decay the non-relativistic contribution dominates.

Significance. If the predictions are reliable, the paper provides useful results for the unmeasured D*0 total width and for the branching ratios of D*0, and it highlights the possible importance of relativistic partial-wave admixtures in heavy-light meson decays. The strong decay widths for D*(2010)+ agree well with experiment (55.8 vs 56.5 keV and 25.8 vs 25.6 keV), and the predicted branching ratios for D*0 agree with the PDG values; the use of ratios between decay widths also helps reduce model dependence. The main limitations are the absence of uncertainty estimates and the reliance on small P- and D-wave components that are not constrained by the meson masses used to fix the kernel parameters.

major comments (4)
  1. [Abstract, Sec. III.A, Table II, Sec. IV] The statement that in the strong decay D* → Dπ the non-relativistic contribution is dominant is contradicted by the authors' own Table II. For D*0 → D0π0 the pure S×S' term gives 91.0 keV, while the complete width is 34.6 keV; the corresponding numbers for D*+ → D0π+ in Table III are 143 keV and 55.8 keV. Thus the relativistic corrections are large and destructive rather than small, and the abstract and Sec. IV should be revised to reflect this.
  2. [Sec. III.B, Eq. (10), Eq. (12), Tables V-VI] The central prediction Γ(D*0 → D0γ) = 19.4 keV hinges on the small P- and D-wave components of the Salpeter wave functions, since the non-relativistic S×S' contribution is only 2.60 keV while the complete result is 19.4 keV. These components are not constrained by the meson masses used in the Sec. III kernel fit, and no sensitivity study or error estimate is given. Because the final width is dominated by interference among terms of different partial waves, a modest change in the magnitudes or phases of the B1, B2, B7, B8 and A3, A4 amplitudes could shift the predicted width by a factor of several. The authors should provide quantitative sensitivity information or independent constraints on these components.
  3. [Sec. II.A, Eq. (2), Sec. III] The manuscript does not report the numerical values of two parameters that enter the calculation: the decay constant fπ used in Eq. (2) and the constant V0 in the linear potential of the kernel. Since these values are needed to reproduce the results, their omission makes the calculation incomplete as presented.
  4. [Throughout, Tables I, IV-VI] No uncertainty estimates are provided for any computed decay width. Given that the theoretical inputs (quark masses, kernel parameters, and the small partial-wave amplitudes) carry uncertainties, the agreement claimed with experiment cannot be fully assessed. At minimum, the authors should quantify the sensitivity of the widths to reasonable variations of the input parameters.
minor comments (4)
  1. [Sec. III, paragraph 1] There is a typo in the sentence 'and the quark masses mu = 0.374 GeV, md = 0.38 GeV, and mc = 1.62 GeV are usde', where 'usde' should be 'used'.
  2. [Sec. IV heading] The heading 'DISSCUSSION' should be 'DISCUSSION'.
  3. [Sec. III.B, Eq. (18)] The comparison with '68±17 keV in Ref.[ ? ]' contains an unresolved citation placeholder; the reference should be filled in.
  4. [Tables II-III] The table captions use the notation 'D∗0' and 'D0π0' but do not define the prime on the final-state partial waves; a short definition would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the decay widths are predicted from Salpeter wave functions with parameters fitted to spectroscopy, not to the target observables; self-citations are methodological, not load-bearing.

full rationale

The paper's central results, Eqs. (13)-(17), are computed from transition amplitudes (3) and (5) using relativistic Salpeter wave functions obtained by solving the instantaneous Bethe-Salpeter equation. The kernel parameters and quark masses are fixed by meson spectroscopy in Sec. III, not by the decay widths being predicted. The branching ratios and the total width in Eq. (18) are then sums/ratios of the computed widths and are compared with, not fitted to, PDG data. The self-citations (e.g., Refs. [35], [37], [38], [50], [51]) provide the standard Mandelstam/Salpeter formalism and the general wave-function decomposition; they are methodological inputs and do not presuppose the numerical D* widths. The small P- and D-wave components that drive the claim of relativistic dominance are outputs of the Salpeter equation and are not separately fitted to experimental decay widths, so their reliability is a modeling uncertainty, not a circular step. One non-circular inconsistency should be flagged for the correctness pass: the Abstract and Sec. IV state that the non-relativistic contribution is dominant in D* -> D pi, whereas Sec. III.A and Table II show the S x S' term (91.0 keV) is much larger than the complete width (34.6 keV), meaning the relativistic correction is actually large and destructive; this is an internal-consistency issue, not circularity.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central predictions depend on the phenomenological kernel, its fitted parameters, and the Salpeter solution. The small P/D wave components, which drive the claimed relativistic dominance, are not tested against any independent observable within this paper.

free parameters (9)
  • V0 = not given
    Zero-point energy of the linear potential, fitted to meson spectroscopy (Sec. III).
  • lambda = 0.15 GeV^2
    String tension in the confining potential (Sec. III).
  • Lambda_QCD = 0.18 GeV
    QCD scale in the running coupling (Sec. III).
  • a = e = 2.7183
    Regulator in the running coupling (Sec. III).
  • Nf = 3
    Number of active flavors in the running coupling (Sec. III).
  • mu = 0.374 GeV
    Constituent up quark mass (Sec. III).
  • md = 0.38 GeV
    Constituent down quark mass (Sec. III).
  • mc = 1.62 GeV
    Constituent charm quark mass (Sec. III).
  • f_pi = not stated
    Pion decay constant appears in Eq. (2) but its numerical value is not given.
assumptions (5)
  • domain assumption Instantaneous approximation to the Bethe-Salpeter equation is valid for the D and D* mesons.
    Used throughout Sec. II; the Salpeter equation is derived under this approximation.
  • domain assumption PCAC and the low-energy theorem relate the pion emission amplitude to the axial current matrix element.
    Invoked in Sec. II.A, Eq. (2); reasonable because the pion is nearly at rest in this decay.
  • standard math The Mandelstam formula gives the transition amplitude in terms of the positive-energy Salpeter wave functions.
    Standard QFT result used in Eqs. (3) and (5).
  • domain assumption The Cornell-type kernel with a linear scalar potential and a vector Coulomb term describes the quark interaction.
    The interaction kernel is introduced in Sec. III with no derivation.
  • ad hoc to paper The fitted kernel parameters yield quantitatively correct small P- and D-wave components of the wave functions.
    These components are not directly constrained by the mass fit yet drive the claimed relativistic dominance.

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Pith. "Pith review of Relativistic effects in the strong and electromagnetic decays of ${D^*}$ meson." pith.science (2026). https://pith.science/paper/JVMHZUBW

@misc{pith2026241210775,
  author       = {Pith},
  title        = {Pith review of: Relativistic effects in the strong and electromagnetic decays of $D^*$ meson},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JVMHZUBW}},
  note         = {Machine review of arXiv:2412.10775}
}
abstract

In this paper, we solve the complete Salpeter equation and use the obtained relativistic wave function to calculate the strong and radiative electromagnetic decays of the ${D^*}$ meson. { We obtain the results $\Gamma(D^{*}(2007)^{0}\to D^{0}\pi^{0})=34.6~\rm{keV}$ and $\Gamma(D^{*}(2007)^{0}\rightarrow D^{0}\gamma)=19.4~\rm{keV}$, and the estimated full width is $\Gamma(D^{*}(2007)^{0})=54.0~\rm{keV}$.} The focus of this study is on the relativistic corrections. In our method, the wave function of the $D$ meson is not a pure $S$-wave, but includes both a non-relativistic $S$-wave and a relativistic $P$-wave, while the wave function of the $D^*$ meson includes a non-relativistic $S$-wave as well as both relativistic $P$-wave and $D$-wave. Therefore, in this case, the decay ${D^{*}\rightarrow{D}\gamma}$ is not a non-relativistic $M1$ transition, but rather an $M1+E2+M3+E4$ decay. We find that in a strong decay $D^{*}\rightarrow{D}{\pi}$, the non-relativistic contribution is dominant, while in an electromagnetic decay ${D^{*}\rightarrow{D}\gamma}$, the relativistic correction is dominant.

Figures

Figures reproduced from arXiv: 2412.10775 by the authors.

Figure 1
Figure 1. FIG. 1: The Feynman diagram for the two-body strong decay. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The Feynman diagram for the EM decay. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Cited by 2 Pith papers

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Reference graph

Works this paper leans on

53 extracted references · 50 canonical work pages · cited by 2 Pith papers

  1. [1]

    Peruzzi, et al ., Phys

    I. Peruzzi, et al ., Phys. Rev. Lett. 37, 569 (1976)

    work page 1976

  2. [2]

    9 ± 2 32 14

    [25] [23] [44] [45] [46] ours Ex[13] Γ( D∗(2007)0 → D0γ) 12. 9 ± 2 32 14 . 4 21.69 19 . 4 Γ( D∗(2010)+ → D+γ) 0. 23 ± 0. 1 1 . 8 1 . 5 0 . 56 0 . 271 0 . 339 0 . 84 1 . 33 ± 0. 4 As shown in Table IV, our result for decay Γ( D∗(2007)0 → D0γ) is in good agreement with the prediction in Ref. [44] and close to the results of Refs. [20, 23], b ut significantly...

    work page 2007

  3. [3]

    Goldhaber, et al ., (Mark I Collaboration), Phys

    G. Goldhaber, et al ., (Mark I Collaboration), Phys. Lett. B 69, 503 (1977)

    work page 1977

  4. [4]

    G. J. Feldman, et al ., (Mark I Collaboration), Phys. Rev. Lett. 38, 1313 (1977)

    work page 1977

  5. [5]

    Bartel et al ., (JADE Collaboration), Phys

    W. Bartel et al ., (JADE Collaboration), Phys. Lett. B 161, 197 (1985)

    work page 1985

  6. [6]

    M. W. Coles, et al ., Phys. Rev. D 26, 2190 (1982)

    work page 1982

  7. [7]

    Adler, et al ., (Mark III Collaboration), Phys

    J. Adler, et al ., (Mark III Collaboration), Phys. Lett. B 208, 152 (1988) (Phys. Lett. B 227, 501 (1989) (erratum))

    work page 1988

  8. [8]

    E. H. Low et al ., Phys. Lett. B 183, 232 (1987)

    work page 1987

Show all 53 references
  1. [9]

    Barlag et al ., (ACCMOR Collaboration), Phys

    S. Barlag et al ., (ACCMOR Collaboration), Phys. Lett. B 278, 480 (1992)

    1992

  2. [10]

    Abachi et al ., Phys

    S. Abachi et al ., Phys. Lett. B 212, 533 (1988)

    1988

  3. [11]

    Albrecht et al ., (ARGUS Collaboration), Z.Phys.C 66, 63 (1995)

    H. Albrecht et al ., (ARGUS Collaboration), Z.Phys.C 66, 63 (1995)

    1995

  4. [12]

    Butler et al ., (CLEO Collaboration), Phys

    F. Butler et al ., (CLEO Collaboration), Phys. Rev. Lett. 69, 2041 (1992)

    1992

  5. [13]

    Navas et al ., (Particle Data Group), Phys

    S. Navas et al ., (Particle Data Group), Phys. Rev. D 110, 3, 030001 (2024)

    2024

  6. [14]

    Bartelt et al ., (CLEO Collaboration), Phys

    J. Bartelt et al ., (CLEO Collaboration), Phys. Rev. Lett. 80, 3919 (1998)

    1998

  7. [15]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, T. M. Yan, Phys. Rev. D 21, 203 (1980)

    1980

  8. [16]

    G. A. Miller, P. Singer, Phys. Rev. D 37, 2564 (1988)

    1988

  9. [17]

    R. L. Thews, A. N. Kamal, Phys. Rev. D 32, 810 (1985)

    1985

  10. [18]

    T. N. Pham, Phys. Rev. D 25, 2955 (1982)

    1982

  11. [19]

    P. L. Cho, H. Georgi, Phys. Lett. B 296, 408 (1992) (Phys. Lett. B 300, 410 (1993) (erratum))

    1992

  12. [20]

    complete

    [25] [23] [43] [44] [24] Ours Ex[13] Γ( D∗(2010)+ → D0π +) 25 32 ± 5 56.6 62.53 65 55 . 8 56 . 5 ± 1. 6 Γ( D∗(2010)+ → D+π 0) 11 15 ± 2 25.8 28.30 30 25 . 8 25 . 6 ± 1. 0 Γ( D∗(2007)0 → D0π 0) 23 ± 3 16 22 ± 2 36.9 43.40 42 34 . 6 Γ( D∗ (2010)+→D0π+) Γ( D∗ (2010)+→D+π0) 2.27 2...

    2010

  13. [21]

    Angelos, G

    L. Angelos, G. P. Lepage, Phys. Rev. D 45, R3021 (1992)

    1992

  14. [22]

    Zhu, W.-Y

    S.-L. Zhu, W.-Y. P. Hwang, Z.-S. Yang, Mod. Phys. Lett. A 12, 3027 (1997)

    1997

  15. [23]

    Cheng, C.-Y

    H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.-C. Lin, T.-M. Y an, H.-L. Yu, Phys. Rev. D 47, 1030 (1993)

    1993

  16. [24]

    P. J. O’Donnell, Q. P. Xu, Phys. Lett. B 336, 113 (1994)

    1994

  17. [25]

    T. M. Aliev, D. A. Demir, E. Iltan, N. K. Pak, Phys. Rev. D 54, 857 (1996)

    1996

  18. [26]

    Di Pierro, E

    M. Di Pierro, E. Eichten, Phys. Rev. D 64, 114004 (2001)

    2001

  19. [27]

    F. E. Close, E. S. Swanson, Phys. Rev. D 72, 094004 (2005)

    2005

  20. [28]

    E. E. Salpeter, H. A. Bethe, Phys. Rev. 84, 1232 (1951)

    1951

  21. [29]

    E. E. Salpeter, Phys. Rev. 87, 328 (1952)

    1952

  22. [30]

    Wang, G.-L

    T.-H. Wang, G.-L. Wang, H.-F. Fu, W.-L. Ju, JHEP 07, 120 (2013)

    2013

  23. [31]

    X.-Z. Tan, T. Wang, Y. Jiang, S.-C. Li, Q. Li, G.-L. Wang, C.-H. Chao, Eur. Phys. J. C 78, 583 (2018)

    2018

  24. [32]

    Z.-H. Wang, Y. Zhang, T.-H. Wang, Y. Jiang, Q. Li, G.-L. W ang, Chin. Phys. C 42, 123101 (2018)

    2018

  25. [33]

    Wang, G.-L

    T.-H. Wang, G.-L. Wang, Phys. Lett. B 697, 233 (2011)

    2011

  26. [34]

    Wang, G.-L

    T.-H. Wang, G.-L. Wang, Y. Jiang, W.-L. Ju, J. Phys. G 40, 035003 (2013)

    2013

  27. [35]

    S.-Y. Pei, W. Li, T.-T. Liu, M. Han, G.-L. Wang, T.-H. Wan g, Phys. Rev. D 108, 033003 (2023)

    2023

  28. [36]

    Mandelstam, Proc

    S. Mandelstam, Proc. R. Soc. Lond. A 233, 248 (1955)

    1955

  29. [37]

    Chang, C

    C.-H. Chang, C. S. Kim, G.-L. Wang, Phys. Lett. B 623, 218 (2005)

    2005

  30. [38]

    C. S. Kim, G.-L. Wang, Phys. Lett. B 584, 285 (2004). Phys. Lett. B 634, 564 (2006) (erra- tum)

    2004

  31. [39]

    Chang, J.-K

    C.-H. Chang, J.-K. Chen, G.-L. Wang, Commun. Theor. Phy s. 46, 467 (2006)

    2006

  32. [40]

    Wang, Phys

    G.-L. Wang, Phys. Lett. B 633, 492 (2006)

    2006

  33. [41]

    Wang, T.-H

    G.-L. Wang, T.-H. Wang, Q. Li, C.-H. Chang, JHEP 05, 006 (2022)

    2022

  34. [42]

    Li, S.-Y

    W. Li, S.-Y. Pei, T. Wang, T.-F. Feng, G.-L. Wang, Phys. R ev. D 109, 036011 (2024)

    2024

  35. [43]

    S.-Y. Pei, W. Li, T. Wang, G.-L. Wang, JHEP 08, 191 (2024)

    2024

  36. [44]

    Chang, G.-L

    C.-H. Chang, G.-L. Wang, Sci. China Phys. Mech. Astron. 53, 2005 (2010)

    2010

  37. [45]

    Cheung, C.-W

    C.-Y. Cheung, C.-W. Hwang, JHEP 04, 177 (2014)

    2014

  38. [46]

    Jaus, Phys

    W. Jaus, Phys. Rev. D 53, 1349 (1996). Phys. Rev. D 54, 5904 (1996) (erratum)

    1996

  39. [47]

    V. H. Kher, A. K. Rai, J. Phys. Conf. Ser. 934, 1, 012036 (2017)

    2017

  40. [48]

    Devlani, A

    N. Devlani, A. K. Rai, Int. J. Theor. Phys. 52, 2196 (2013)

    2013

  41. [49]

    Becirevic, F

    D. Becirevic, F. Sanfilippo, Phys. Lett. B 721, 94 (2013)

    2013

  42. [50]

    J. L. Rosner, Phys. Rev. D 88, 3, 034034 (2013)

    2013

  43. [51]

    Becirevic, B

    D. Becirevic, B. Haas, Eur. Phys. J. C 71, 1734 (2011)

    2011

  44. [52]

    Li, S.-Y

    W. Li, S.-Y. Pei, T. Wang, Y.-L. Wang, T.-F. Feng, G.-L. W ang, Phys. Rev. D 107, 113002 (2023)

    2023

  45. [53]

    Du, S.-Y

    X.-Y. Du, S.-Y. Pei, W. Li, M. Jia, Q. Li, T. Wang, B. Wang, G.-L. Wang, Phys. Rev. D 110, 113009 (2024)

    2024

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