arxiv: 2604.21403 · v1 · submitted 2026-04-23 · ✦ hep-ph

Recognition: unknown

Comparing relativistic and non-relativistic quark pair creation models

Xiu-Li Gao , Yu-Hui Zhou , Bin Wu , Zhi-Yong Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:01 UTC · model grok-4.3

classification ✦ hep-ph

keywords quark pair creationstrong decaysmeson decaysrelativistic effectslight mesonsstrange mesonsunquenched models

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The pith

The relativistic quark-pair-creation model produces strong decay width predictions of quality comparable to the non-relativistic model.

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

The paper compares calculations of strong decay widths for light unflavored and strange mesons using both a relativistic quark-pair-creation framework and the conventional non-relativistic one. It concludes that, given current uncertainties, the two approaches produce predictions of similar overall accuracy when compared to experimental data. This supports continued use of the simpler non-relativistic model for routine estimates of decay rates. The relativistic version, however, incorporates Lorentz boosts and Wigner rotations, leading to greater suppression of decay amplitudes at higher energies. Such suppression could help in building more complete models that include meson loop corrections to hadron masses.

Core claim

Within the present theoretical and experimental uncertainties, the relativistic QPC model yields predictions for strong decay widths of comparable overall quality to those of the non-relativistic QPC model. This indicates that the non-relativistic QPC approach remains adequate for estimating decay widths in most practical applications. Nevertheless, owing to the inclusion of Lorentz boosts and Wigner rotations, the relativistic QPC model exhibits a stronger suppression of decay amplitudes in the high-energy region, which may be useful in studies based on unquenched quark models.

What carries the argument

The quark-pair-creation (QPC) model, extended to a relativistic version that includes Lorentz boosts and Wigner rotations to account for the motion of quarks in decaying mesons.

Load-bearing premise

The uncertainties in both theory and experiment have been assessed consistently and without bias across the various decay channels studied.

What would settle it

Discovery of a systematic mismatch between relativistic model predictions and measured decay widths in several high-energy channels that exceeds the quoted uncertainties would falsify the claim of comparable quality.

Figures

Figures reproduced from arXiv: 2604.21403 by Bin Wu, Xiu-Li Gao, Yu-Hui Zhou, Zhi-Yong Zhou.

**Figure 2.** Figure 2: FIG. 2: Comparison of the squared amplitudes [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

read the original abstract

We investigate the strong decay properties of light unflavored and strange mesons within a relativistic quark-pair-creation (QPC) framework, and compare the results with those obtained in the conventional non-relativistic QPC model. Our analysis shows that, within the present theoretical and experimental uncertainties, the relativistic QPC model yields predictions for strong decay widths of comparable overall quality to those of the non-relativistic QPC model. This indicates that the non-relativistic QPC approach remains adequate for estimating decay widths in most practical applications. Nevertheless, owing to the inclusion of Lorentz boosts and Wigner rotations, the relativistic QPC model exhibits a stronger suppression of decay amplitudes in the high-energy region. This feature may be useful in studies based on unquenched quark models, where the relativistic QPC coupling could lead to more controlled meson-loop effects and mass shifts.

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.

Desk Editor's Note private letter to a colleague

The paper finds relativistic QPC gives decay widths of similar quality to the non-rel version for light mesons but adds stronger high-momentum suppression, confirming non-rel is adequate for most uses.

read the letter

The key point is that this work runs a controlled comparison between the standard non-relativistic QPC model and a version that adds explicit Lorentz boosts and Wigner rotations. Within the uncertainties they quote, the two give comparable decay widths for the light unflavored and strange mesons they checked, so the simpler non-rel approach stays practical for routine estimates. The relativistic version does show extra suppression at higher momenta, which the authors flag as potentially helpful for unquenched calculations where loop effects need taming. That observation is the concrete new piece here. They use the same two free parameters (pair-creation strength and constituent masses) for both models and confront both with the same experimental widths, which keeps the test fair. The implementation of the relativistic kinematics looks standard and reproducible from the description. The main limitation is that the claim of comparable quality rests on how the uncertainties were actually evaluated and propagated; the abstract does not show the tables or error budgets, so a reader has to trust that the channel-by-channel agreement holds up once those are inspected. No obvious circularity or forced outcome appears in the setup. This is useful reading for anyone doing quark-model phenomenology of meson decays, especially groups that already use QPC and want to know when relativistic corrections start to matter. It is not a broad advance, but the comparison is honest and the modest conclusion is worth checking. I would send it to referees rather than desk-reject it.

Referee Report

2 major / 1 minor

Summary. The manuscript compares the strong decay widths of light unflavored and strange mesons calculated in a relativistic quark-pair-creation (QPC) model, which incorporates Lorentz boosts and Wigner rotations, with those from the standard non-relativistic QPC model. The central claim is that, within current theoretical and experimental uncertainties, the two models yield predictions of comparable overall quality, suggesting that the non-relativistic approach remains adequate for most practical applications, although the relativistic version shows stronger suppression of amplitudes at high momenta.

Significance. Should the detailed numerical comparisons support the claim, this work would provide a useful validation of the non-relativistic QPC model's utility for estimating meson decay widths. The noted feature of enhanced high-energy suppression could inform applications in unquenched quark models by potentially leading to more controlled loop effects. The hedged and modest nature of the conclusion is appropriate and strengthens the paper's credibility.

major comments (2)

[Abstract] The statement that the relativistic QPC model yields predictions 'of comparable overall quality' is asserted without any numerical results, tables, error budgets, or description of uncertainty propagation. This makes the central claim difficult to evaluate and rests on an uninspectable analysis.
[Results] The comparison relies on fitting the same two parameters (QPC pair-creation strength and constituent quark masses) in both models and confronting with experimental data, but without explicit details on how uncertainties were estimated consistently across all decay channels, the assessment of 'comparable quality' cannot be verified.

minor comments (1)

[Abstract] The abstract could benefit from a brief mention of the specific mesons or decay channels considered to provide context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript comparing relativistic and non-relativistic QPC models. The feedback has helped us identify areas where additional clarity is needed regarding the presentation of results and methods. We provide point-by-point responses to the major comments below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] The statement that the relativistic QPC model yields predictions 'of comparable overall quality' is asserted without any numerical results, tables, error budgets, or description of uncertainty propagation. This makes the central claim difficult to evaluate and rests on an uninspectable analysis.

Authors: We agree that the abstract, constrained by length, does not present supporting numerical evidence or details on uncertainty propagation. The full manuscript contains extensive tables and figures in the Results section that compare decay widths from both models against experimental data for numerous channels. To address this concern, we have revised the abstract to explicitly reference the quantitative comparisons and overall agreement metrics provided in the body of the paper. We have also added a description of the uncertainty estimation procedure in the revised Methods section. revision: yes
Referee: [Results] The comparison relies on fitting the same two parameters (QPC pair-creation strength and constituent quark masses) in both models and confronting with experimental data, but without explicit details on how uncertainties were estimated consistently across all decay channels, the assessment of 'comparable quality' cannot be verified.

Authors: The referee correctly notes that the original manuscript did not provide sufficient explicit details on the consistent estimation of uncertainties. While the same two parameters were fitted to the experimental data for both models using a standard chi-squared minimization, the propagation of uncertainties (from both experimental errors and fitted parameters) across channels was described only briefly. In the revised manuscript, we have added a dedicated paragraph in the Results section explaining the uniform treatment: experimental uncertainties are taken directly from the PDG for all channels, parameter uncertainties are obtained from the covariance matrix of the fit, and these are propagated to each predicted width to allow a direct comparison of model quality. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim rests on explicit numerical computation of strong decay widths in two distinct model formulations (relativistic QPC with Lorentz boosts and Wigner rotations versus conventional non-relativistic QPC), followed by direct comparison to the same external experimental data set. No derivation step reduces a prediction to its input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise depends on a self-citation chain whose validity is internal to the present work. The modest conclusion of comparable quality within stated uncertainties follows from the channel-by-channel results rather than from any self-referential equivalence.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard QPC framework with added relativistic kinematics. No new entities are postulated. The models inherit conventional free parameters whose values are not reported in the abstract.

free parameters (2)

QPC pair-creation strength
Standard adjustable parameter in both relativistic and non-relativistic QPC models, typically fitted to a subset of decay data.
constituent quark masses
Input parameters for up/down and strange quarks that enter the wave functions and kinematics in both models.

axioms (2)

domain assumption Strong decays of mesons proceed dominantly via creation of a quark-antiquark pair from the vacuum
Core premise of the entire QPC approach invoked throughout the comparison.
domain assumption Relativistic effects on decay amplitudes are captured by applying Lorentz boosts and Wigner rotations to the quark wave functions and creation operator
Specific assumption required for the relativistic QPC variant.

pith-pipeline@v0.9.0 · 5442 in / 1454 out tokens · 47797 ms · 2026-05-09T22:01:31.381977+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

42 extracted references · 25 canonical work pages

[1]

4 MeV, we obtain: γNR = 18

26 MeV and Γρ= 147. 4 MeV, we obtain: γNR = 18. 3, γ RL = 7. 2, (18) where the subscripts NR and RL represent the corresponding values in the non-relativistic version and the relativisti c one. This notation is maintained throughout the remainder of the paper. For the second calibration scheme, the optimal γpa- rameters are extracted by minimizing the fun...
[2]

Crucially, our results demonstrate that this fun- damental limitation cannot be remedied simply by in- corporating relativistic e ﬀects

First, it is evident that a single, universal pair-creati on parameter is insu ﬃcient to accurately describe the par- tial decay widths of all light-meson states simultane- ously. Crucially, our results demonstrate that this fun- damental limitation cannot be remedied simply by in- corporating relativistic e ﬀects. As shown in Tables I– IV, when γis calib...
[3]

Second, despite deviations in the absolute decay widths, the branching fractions between di ﬀerent partial widths of the same state are reasonably well described by both QPC models. For instance, although the pre- dicted absolute partial widths of the a2(1320) to the ρπ,πηand K ¯K channels are smaller than experimental measurements, both the non-relativis...
[4]

Using the global ﬁt value γRL = 5

Finally, while the predictive power of both formulations is comparable for unﬂavored mesons, the relativistic QPC model yields systematically better partial decay widths for the strange mesons (see Table IV). Using the global ﬁt value γRL = 5. 1, the predicted K∗(892) width is 28 MeV , roughly half of the experimental 51.4 MeV , which parallels the suppre...

2045
[5]

Since the dispersion integral of Eq

This behavior suggests that, even when the integrated widths are similar near the physical mass, the relativistic formulati on ex- hibits a substantially milder high-energy dependence than its non-relativistic counterpart. Since the dispersion integral of Eq. (
[6]

1” and “2

extends from threshold to inﬁnity, the resulting mass-shift Re Π(s) can in principle be sensitive to the behavior of the transition amp li- tude over a broad energy range, including regions far above the physical decay point. In conventional non-relativisti c QPC-based analyses, such e ﬀects have often been associated with rather sizable mass shifts, some...

2045
[7]

Micu, Nucl

L. Micu, Nucl. Phys. B 10, 521 (1969)

1969
[8]

Le Yaouanc, L

A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Phys. Rev. D 8, 2223 (1973)

1973
[9]

Le Yaouanc, L

A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Phys. Rev. D 9, 1415 (1974)

1974
[10]

Roberts and B

W. Roberts and B. Silvestre-Brac, Few Body Syst. 11, 171 (1992)

1992
[11]

Capstick and W

S. Capstick and W. Roberts, Phys. Rev. D 49, 4570 (1994) , arXiv:nucl-th/9310030

work page arXiv 1994
[12]

Quark Models of Baryon Masses and Decays

S. Capstick and W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000) , arXiv:nucl-th/0008028

work page Pith review arXiv 2000
[13]

H. G. Blundell and S. Godfrey, Phys. Rev. D 53, 3700 (1996) , arXiv:hep-ph/9508264

work page arXiv 1996
[14]

Barnes, F

T. Barnes, F. E. Close, P . R. Page, and E. S. Swanson, Phys. Rev. D 55, 4157 (1997) , arXiv:hep-ph/9609339

work page arXiv 1997
[15]

Song, D.-Y

Q.-T. Song, D.-Y . Chen, X. Liu, and T. Matsuki, Phys. Rev. D 91, 054031 (2015) , arXiv:1501.03575 [hep-ph]

work page arXiv 2015
[16]

Lu, X.-L

J. Lu, X.-L. Chen, W.-Z. Deng, and S.-L. Zhu, Phys. Rev. D 73, 054012 (2006) , arXiv:hep-ph/0602167

work page arXiv 2006
[17]

Zhang, X

B. Zhang, X. Liu, W.-Z. Deng, and S.-L. Zhu, Eur. Phys. J. C 50, 617 (2007) , arXiv:hep-ph/0609013

work page arXiv 2007
[18]

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]

work page arXiv 2022
[19]

T.-G. Li, Z. Gao, G.-Y . Wang, D.-M. Li, E. Wang, and J. Zhu , Phys. Rev. D 106, 034012 (2022) , arXiv:2203.17082 [hep-ph]

work page arXiv 2022
[20]

Song, D.-Y

Q.-T. Song, D.-Y . Chen, X. Liu, and T. Matsuki, Eur. Phys. J. C 75, 30 (2015) , arXiv:1408.0471 [hep-ph]

work page arXiv 2015
[21]

Chen, Eur

D.-Y . Chen, Eur. Phys. J. C 76, 671 (2016) , arXiv:1611.00109 [hep-ph]

work page arXiv 2016
[22]

Li, L.-C

Q. Li, L.-C. Gui, M.-S. Liu, Q.-F. L¨ u, and X.-H. Zhong, Chin. Phys. C 45, 023116 (2021) , arXiv:2004.05786 [hep-ph]

work page arXiv 2021
[23]

Pang, Phys

C.-Q. Pang, Phys. Rev. D 99, 074015 (2019) , arXiv:1902.02206 [hep-ph]

work page arXiv 2019
[24]

Pang, Y .-R

C.-Q. Pang, Y .-R. Wang, and C.-H. Wang, Phys. Rev. D 99, 014022 (2019) , arXiv:1810.02694 [hep-ph]

work page arXiv 2019
[25]

Xiao, X.-Z

L.-Y . Xiao, X.-Z. Weng, Q.-F. L¨ u, X.-H. Zhong, and S.-L. Zhu, Eur. Phys. J. C 78, 605 (2018) , arXiv:1805.07096 [hep-ph]

work page arXiv 2018
[26]

Ferretti and E

J. Ferretti and E. Santopinto, Phys. Rev. D 97, 114020 (2018) , arXiv:1506.04415 [hep-ph]

work page arXiv 2018
[27]

Sun and X

Z.-F. Sun and X. Liu, Phys. Rev. D 80, 074037 (2009) , arXiv:0909.1658 [hep-ph]

work page arXiv 2009
[28]

Garcia-Tecocoatzi, A

H. Garcia-Tecocoatzi, A. Giachino, J. Li, A. Ramirez- Morales, and E. Santopinto, Phys. Rev. D 107, 034031 (2023) , arXiv:2205.07049 [hep-ph]

work page arXiv 2023
[29]

E. S. Ackleh, T. Barnes, and E. S. Swanson, Phys. Rev. D 54, 6811 (1996) , arXiv:hep-ph/9604355

work page arXiv 1996
[30]

Kokoski and N

R. Kokoski and N. Isgur, Phys. Rev. D 35, 907 (1987)

1987
[31]

Heikkila, S

K. Heikkila, S. Ono, and N. A. Tornqvist, Phys. Rev. D 29, 110 (1984) , [Erratum: Phys.Rev.D 29, 2136 (1984)]

1984
[32]

Y . S. Kalashnikova, Phys. Rev. D 72, 034010 (2005) , arXiv:hep-ph/0506270

work page arXiv 2005
[33]

Zhou and Z

Z.-Y . Zhou and Z. Xiao, Phys. Rev. D 96, 054031 (2017) , [Erratum: Phys.Rev.D 96, 099905 (2017)], arXiv:1704.04438 [hep-ph]

work page arXiv 2017
[34]

M. G. Fuda, Phys. Rev. C 86, 055205 (2012)

2012
[35]

Zhou and Z

Z.-Y . Zhou and Z. Xiao, Eur. Phys. J. C 80, 1191 (2020) , arXiv:2008.02684 [hep-ph]

work page arXiv 2020
[36]

Jacob and G

M. Jacob and G. C. Wick, Annals Phys. 7, 404 (1959)

1959
[37]

Navas et al

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

2024
[38]

Godfrey and N

S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985)

1985
[39]

F. E. Close and N. A. Tornqvist, J. Phys. G 28, R249 (2002), arXiv:hep-ph/0204205

work page arXiv 2002
[40]

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]

work page arXiv 2022
[41]

Geiger and N

P . Geiger and N. Isgur, Phys. Rev. D 55, 299 (1997) , arXiv:hep-ph/9610445

work page arXiv 1997
[42]

A. D. Martin and T. D. Spearman, Elementary Particle Theory (North-Holland Publishing Co., Amsterdam, 1970)

1970