The $\rho$-meson electromagnetic form factors within the light-front quark model

Shuai Xu; Xiao-Nan Li; Xing-Gang Wu

REVIEW 3 major objections 4 minor 1 cited by

The $\rho$-meson electromagnetic form factors within the light-front quark model

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read Replacing the meson mass by the invariant mass removes the zero-mode problem and makes four form-factor prescriptions agree.

desk verdict A useful numerical extension of the type-II M→M0 prescription to rho-meson EMFFs; the consistency claim is somewhat stronger than the evidence in the region of maximal residual angular-condition violation. read the letter →

arxiv 2505.02419 v1 pith:AIIXNM5K submitted 2025-05-05 hep-ph

Shuai Xu , Xiao-Nan Li , Xing-Gang Wu This is my paper · ORCID

classification hep-ph

keywords rhomesonelectromagneticformfactorslight-frontquarkmodelzero-modecontributionangularconditiontype-IIreplacementinvariantmassspin-1mesons

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 argues that one formal replacement—substituting the physical meson mass $M$ by the invariant mass $M_0$—removes the zero-mode contribution from the helicity-zero matrix element $S^+_{00}$ in the light-front quark model and largely restores the angular condition that different form-factor prescriptions must satisfy. With that replacement, the four standard prescriptions for the rho-meson charge, magnetic and quadrupole form factors give consistent curves, whereas without it they disagree and the angular condition is violated by up to about $0.53$ near $Q^2=10\,\mathrm{GeV}^2$. The payoff is an unambiguous determination of the rho meson's electromagnetic structure—charge radius, magnetic moment, quadrupole moment—from the model, with the same recipe applicable to other spin-1 particles. The authors also find that the replacement weakens the relativistic or interaction effects inside the bound state, as seen in smaller magnetic and quadrupole moments.

What carries the argument

The central object is the type-II replacement, Eq. (9): in every light-front formula the physical meson mass $M$ is replaced by the invariant mass $M_0$, with $M_0^2=(m_1^2+k_\perp^2)/x+(m_2^2+k_\perp^2)/\bar{x}$. This additive replacement is what absorbs the zero-mode contribution into the valence part of $S^+_{00}$. The second object is the angular condition $\Delta(Q^2)=(1+2\eta)S^+_{11}-\sqrt{8\eta}S^+_{10}+S^+_{1-1}-S^+_{00}=0$, whose degree of violation decides whether different form-factor prescriptions agree.

What would settle it

Evaluate the four prescriptions after $M\to M_0$ with the quoted parameter uncertainties propagated through every step and compare the spread in $G_C$, $G_M$ and $G_Q$ at $Q^2\sim10\,\mathrm{GeV}^2$; if the prescription spread exceeds the propagated uncertainty, the claim that the residual violation is negligible is wrong. A complementary check is to compute the angular condition maximum for a spin-1 meson with a much larger mass difference $M-M_0$ and see whether the maximum stays near $0.1$ or grows.

Watch

Extended reading notes

Core claim

The paper's central claim is that in the standard light-front quark model the rho-meson electromagnetic form factors become unambiguous once the physical mass $M$ is replaced by the invariant mass $M_0$ in all formulas. With this replacement, the zero-mode contribution to the helicity zero-to-zero matrix element $S^+_{00}$ is either absent or fully absorbed into the valence contribution, so the valence and full results coincide. The angular condition $\Delta(Q^2)$ then drops from a maximal violation of about $0.53$ to about $0.13$ near $Q^2=10\,\mathrm{GeV}^2$, vanishes exactly at $Q^2=0$, and the four standard prescriptions (GK, CCKP, BH, FFS) yield consistent charge, magnetic and quadrupole form factors. The residual violation is treated as negligible for the form factors, and the same mechanism is expected to work for other spin-1 particles.

Load-bearing premise

The entire consistency claim rests on the premise that the residual angular-condition violation after $M\to M_0$, which peaks near $0.13$ at $Q^2\sim 10\,\mathrm{GeV}^2$, is small enough that the differences among the four prescriptions fall inside the input parameter uncertainties; the paper supports this by curve overlap rather than by a full propagation of $m_q=0.25\pm0.04\,\mathrm{GeV}$ and $\beta=0.3124\pm0.0060\,\mathrm{GeV}$.

Editorial extensions

If this is right

Under the $M\to M_0$ replacement, the GK, CCKP, BH and FFS prescriptions give consistent rho-meson form factors, with exact agreement at $Q^2=0$ and overlap for $Q^2\lesssim0.5\,\mathrm{GeV}^2$.
The rho meson's charge radius from the consistent prescription is about $0.47\,\mathrm{fm}^2$, its magnetic moment about $2.13$, and its quadrupole moment about $0.010$; the radius is about 25% larger than earlier estimates.
For the heavy meson $\Upsilon(1S)$, the same replacement suppresses the angular-condition violation to below $0.02$, showing that the effect weakens as the quark mass grows.
The same zero-mode absorption through $M\to M_0$ is expected to apply to other spin-1 bound states in the light-front quark model.

Reading between the lines

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

A quantitative uncertainty propagation, which the paper does not perform, would settle whether the residual violation near $Q^2=10\,\mathrm{GeV}^2$ is genuinely inside the model's noise; without it, the consistency claim is plausible but not demonstrated to that precision.
If the residual violation survives full uncertainty propagation, the natural next explanation—which the paper leaves open—is a missing two-body current or higher Fock-state contribution rather than the zero-mode; this can be tested by adding such terms to the current.
The success of $M\to M_0$ may be specific to weakly bound, equal-mass configurations: for spin-1 systems with strong binding or asymmetric quark masses, the residual angular-condition violation could be larger, so the recipe should be re-tested case by case.

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.

Desk Editor's Note

read the letter

Read this one. It is a straightforward extension of the type-II/M→M0 prescription to rho-meson electromagnetic form factors in the light-front quark model. The new content is the demonstration that this replacement kills the zero-mode contribution to S+00 numerically and cuts the angular-condition violation from ~0.53 to ~0.13 maximum, so that four standard prescriptions (GK, CCKP, BH, FFS) give nearly coincident GC, GM, GQ. That is a genuinely useful result for people who work on LFQM; it confirms earlier hints from decay constants and weak transitions and extends the program to EM observables.

The paper is honest about its own limits: it says the zero-mode cancellation is numerically verified, not proven analytically, and it acknowledges that the residual ∆≠0 needs other explanations. The citation pattern is fair; the relevant previous type-II papers are cited and the zero-binding limit observation from Ref. [12] is credited. No fitting to the target form factors is done, so circularity is not an issue.

The soft spots are real but not fatal. The stress-test concern lands: the maximum residual ∆ is near Q²≈10 GeV², yet the form-factor plots stop at Q²=5 GeV². So the claim that the residual violation can be "safely neglected" is not directly supported in the region where the violation is largest. The authors say the prescription differences are "limited in the uncertainty from inputs," but they never propagate mq=0.25±0.04 GeV and β=0.3124±0.0060 GeV through the four prescriptions, nor do they compare the inter-prescription spread with those uncertainties. For GQ, which is a small quantity, this matters most. That said, the low-Q² overlap and the improvement at intermediate Q² are visible in the figures, and the claim that the replacement improves consistency is solid.

This is a subfield-level contribution, not a breakthrough. It deserves a serious referee, though, because the numerical claim is specific and testable, and the gap between the residual angular-condition violation and the actual form-factor spread can be closed with modest additional work (extend the plots to Q²=10 GeV² and add uncertainty bands). I would not desk-reject it. I would send it to review with a request to quantify the residual spread. I wouldn't cite it myself, but I'd bring it to the group if anyone works on light-front models.

Referee Report

3 major / 4 minor

Summary. The paper studies the electromagnetic form factors (EMFFs) of the ρ meson in the light-front quark model (LFQM), focusing on the so-called type-II replacement M→M₀. The authors argue that under this replacement the zero-mode contribution to the helicity zero-to-zero matrix element S⁺₀₀ vanishes, and that the angular condition Δ(Q²) is substantially improved, with its maximum dropping from about 0.53 to about 0.13 near Q²≈10 GeV². As a consequence, they claim that four standard prescriptions for the ρ-meson form factors—Grach–Kondratyuk (GK), Chung–Coester–Keister–Polyzou (CCKP), Brodsky–Hiller (BH), and Frankfurt–Frederico–Strikman (FFS)—give consistent results for G_C, G_M, and G_Q. Static quantities (charge radius, magnetic moment, quadrupole moment) are also computed and compared with previous work. The main stated conclusion is that the M→M₀ replacement weakens the apparent relativistic effects in the zero-binding limit and that the residual angular-condition violation needs some other explanation beyond zero modes.

Significance. If the central claim holds, the paper provides a practical resolution of the long-standing self-consistency problem in light-front calculations of spin-1 electromagnetic form factors: the M→M₀ replacement, previously proposed for decay constants and weak transition form factors, would also cure the prescription dependence of ρ-meson EMFFs. The numerical demonstration is internally coherent and the reduction of Δ from ≈0.53 to ≈0.13 is a concrete, falsifiable quantitative result. The paper also usefully tests an imported prescription rather than fitting new parameters, and it explicitly states the limitations of the zero-mode argument. The main weakness is that the consistency claim is not quantitatively connected to the region where the residual angular-condition violation is largest, because the form-factor plots stop at Q²=5 GeV² while Δ peaks near Q²=10 GeV², and the input uncertainties are not propagated through the four prescriptions.

major comments (3)

[Sec. III.B, Fig. 2 and Sec. IV.A, Figs. 4–6] The central claim that the four prescriptions are consistent after M→M₀ rests on the statement that the residual angular-condition violation, with maximum Δ≈0.13 near Q²≈10 GeV², can be safely neglected. However, all form-factor plots are shown only up to Q²=5 GeV², so the curves are never displayed in the region where the violation is maximal. The text asserts that the deviations are 'limited in the uncertainty from inputs' without propagating the quoted uncertainties m_q=0.25±0.04 GeV and β=0.3124±0.0060 GeV through the four prescriptions. Please either extend the form-factor plots to the full range of Fig. 2, add uncertainty bands, or compare the inter-prescription spread quantitatively with the input-parameter uncertainty; otherwise the consistency claim is only supported for Q²≲5 GeV².
[Sec. III.A, Eq. (10), Fig. 1 and Introduction] The statement that ∫₀¹Λ(x)dx vanishes 'exactly' for the type-II scheme, and hence that the zero-mode contribution to S⁺₀₀ is zero, is supported only by numerical integration of Fig. 1. The Introduction itself concedes that the conclusion is 'not rigorous but just a verification through a few of quantities.' Please either provide an analytic derivation of the cancellation or phrase the conclusion as numerical evidence, with an explicit estimate of the numerical precision of the integration.
[Sec. IV.B, Table I] The static properties under SLF(M→M₀) shift outside the previously quoted ranges: the charge radius is 0.47 fm² versus 0.35–0.40 fm², the quadrupole moment is 0.010 fm² versus 0.024–0.058 fm², and the magnetic moment is 2.13 versus 2.14–2.48. The text only notes the 25% increase in ⟨r²⟩ and does not comment on the fact that the quadrupole moment lies outside the previous range. Please discuss whether these shifts are consistent with the claim that the replacement weakens relativistic effects and with the phenomenological acceptability of the model. In addition, the table leaves the CCKP and BH charge radius entries as '—'; the reason for these omissions should be explained.

minor comments (4)

[Sec. I, first paragraph] 'phenomenal researches' should read 'phenomenological researches', and 'residue' should be 'residual' in the abstract and conclusions.
[Sec. II, Eq. (3) and Fig. 4 legend] The notation S⁺₁₋₁ should be written consistently; also, the Fig. 4 legend uses 'CCPK' while the text uses 'CCKP'.
[Sec. IV.A, Eq. (11) and Table I] Equation (11) defines ⟨r²⟩ and Q̄ by limits as Q²→0; please state the numerical extrapolation procedure used to evaluate these limits from the computed form factors.
[Sec. III.B, Fig. 3] The Υ(1S) calculation is introduced without stating the input parameters (quark mass and β) used for that meson; please provide them for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the target form factors are not used to fit any input, the M→M0 prescription is externally proposed and tested, and the key zero-mode and angular-condition results are re-derived here.

full rationale

The paper calculates ρ-meson EMFFs with fixed LFQM inputs (mq=0.25±0.04 GeV, β=0.3124±0.0060 GeV) taken from prior fits to fπ and fρ; these fits do not include the target EMFF data, so the form factors are not being used to calibrate the model. The central manipulation, the 'M→M0' (type-II) replacement, originates with Choi and Ji [20] and is applied here as a proposed external prescription, not invented or fitted to make the angular condition vanish. The claimed zero-mode cancellation in S+00 is directly verified by the computed function Λ(x) in Fig. 1, and the angular-condition improvement is shown by the independent Δ(Q²) calculation in Fig. 2. The consistency of the four prescriptions is then checked by evaluating their explicit linear combinations of matrix elements in Figs. 4-6. Reliance on Refs. [22,23,34], which include one of the present authors, is present but not load-bearing: Ref. [22] is only the source of the fitted decay-constant parameters, and the zero-mode/type-II conclusion is re-derived in this work rather than merely cited. The paper honestly states its limitation that the residual violation Δ≈0.13 at Q²≈10 GeV² is not strictly zero and 'needs other explanations,' and that the earlier conclusion was 'not rigorous but just a verification'; these are acknowledged caveats, not circular reductions. No equation in the derivation is equivalent to its input by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard LFQM machinery plus one ad hoc but previously proposed prescription, the type-II M-to-M0 replacement, which is validated numerically rather than proven. The only fitted numbers are the quark mass and the wavefunction scale, both taken from earlier fits to pion and rho decay constants; the target form factors are not used to set them. No new particles, forces, or conserved quantities are introduced.

free parameters (2)

Constituent quark mass m_q = 0.25 +/- 0.04 GeV
Taken from the fit to f_pi and f_rho in Ref. [22] (Sec. III numerical inputs). It sets the quark kinematics and wavefunction shape for the rho meson; it is not fitted to the EMFFs reported here.
Harmonic oscillator scale beta_q qbar = 0.3124 +/- 0.0060 GeV
Taken from the same fit to f_pi and f_rho in Ref. [22]. It controls the transverse momentum width of the meson wavefunction and directly affects the Q2 behavior of the form factors.

assumptions (5)

ad hoc to paper Type-II replacement (M to M0) is a valid prescription that exactly accounts for or absorbs the zero-mode contribution to the S+00 matrix element.
Introduced in Eq. (9) and used throughout Sec. III. The paper verifies this numerically through Lambda(x) in Eq. (10) and Fig. 1 but does not derive it; the main consistency claims stand or fall on this imported prescription.
domain assumption The one-body current approximation, without explicit two-body currents, is adequate; all missing covariance effects are captured by zero modes plus the replacement.
States in Sec. II that the one-body current breaks rotational covariance; the zero-mode formalism of Sec. III A assumes this truncation is sufficient. No two-body currents are computed.
domain assumption The good plus component in the Drell-Yan frame (q+=0) is sufficient to define the four independent matrix elements and the physical form factors.
Sec. II adopts this frame and the plus component; standard in LFQM but a modeling choice.
domain assumption The effective vertex function chi_M and wavefunction normalization are matched between the covariant and standard light-front quark models as in Refs. [20,22,23].
Sec. III, first paragraph, imports this matching without re-derivation.
standard math The angular condition Delta(Q2)=0 is the correct criterion for rotational covariance and for consistency of the four form-factor prescriptions.
Eq. (3) follows from rotational covariance of the matrix elements; it is a standard relation in the cited deuteron and vector meson literature.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The $\rho$-meson electromagnetic form factors within the light-front quark model." pith.science (2026). https://pith.science/paper/AIIXNM5K

@misc{pith2026250502419,
  author       = {Pith},
  title        = {Pith review of: The $\rho$-meson electromagnetic form factors within the light-front quark model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AIIXNM5K}},
  note         = {Machine review of arXiv:2505.02419}
}

abstract

In this paper, we study the $\rho$-meson electromagnetic form factors (EMFFs) within the framework of light-front quark model (LFQM). The physical form factors $G_{C,M,Q}(Q^2)$ of $\rho$-meson as well as the charged square radius $\langle r^2\rangle$, the magnetic moment $\mu$ and the quadrupole moment $\bar Q$ are calculated, which describe the behaviors of EMFFs at zero momentum transfer. Using the type-II replacement, we find that the zero-mode does contribute zero to the matrix element $S_{00}^+$. It is found that the ``$M\to M_{0}$" replacement improves angular condition remarkably, which permits different prescriptions of $\rho$-meson EMFFs give the consistent results. The residue tiny violation of angular condition needs other explanations than the zero-mode contributions. Our results indicate that the relativistic effects or interaction internal structure are weaken in the zero-binding limit. This work is also applied for the other spin-1 particles.

Figures

Figures reproduced from arXiv: 2505.02419 by the authors.

**Figure 4.** FIG. 4. The charge form factor [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** FIG. 5. The magnetic form factor [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

Figures from the paper (1 more)

**Figure 6.** Figure 6: FIG. 6. The quadrupole form factor [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The Electromagnetic Form Factors of Pseudoscalar Mesons within the Light-Front Quark Model
hep-ph 2025-07 conditional novelty 5.0 of 10

A light-front quark model with Gaussian wavefunctions, calibrated on decay constants, reproduces pion and kaon form factors and predicts systematic quark-mass-asymmetry trends for heavier meson radii.

Reference graph

Works this paper leans on

38 extracted references · 35 canonical work pages · cited by 1 Pith paper

[12]

Covariant analysis of the light-front quark model,

W. Jaus, “Covariant analysis of the light-front quark model,” Phys. Rev. D 60, 054026 (1999)

work page 1999
[1]

the self-consistency

It is found that the “M→ M0” replacement improves angular condition remarkably, which permits different prescriptions of ρ-meson EMFFs give the consistent results. The residue tiny violation of angular condition needs other explanations than the zero-mode contributions. Our results indicate that the relativistic effects or interaction internal structure a...

arXiv 2025
[2]

Charge Form-Factors of Quark Model Pions,

P. L. Chung, F. Coester and W. N. Polyzou, “Charge Form-Factors of Quark Model Pions,” Phys. Lett. B205, 545 (1988)

work page 1988
[3]

The result is independent to the conventions for calculating

+ 5 p 2ηS+ 10 1 In deed, we take the BL convention and there is an additional “1/2” factor in P− = 1 2 (P 0 − P 3). The result is independent to the conventions for calculating. 2 It is an abstruse task to recovered the complete rotational co- variance via an in-depth way, and in the paper, we will adopt the same approximation for rotational covariance. 3...

work page
[4]

good” component “ µ = +

+ 2 p 2ηS+ 10 − (η + 2)S+ 1−1]. (5) The third one is suggested by Brodsky and Hiller [4] GBH C (q2) = 1 3(1 +η)[(3− 2η)S+ 00 + 8 p 2ηS+ 10 + 2(2η− 1)S+ 1−1], GBH M (q2) = 2 (1 + 2η)[S+ 00 + 2η− 1√2η S+ 10−S+ 1−1], GBH Q (q2) = 2 √ 2 3(1 + 2η)[−ηS+ 00 + p 2ηS+ 10− (η + 1)S+ 1−1], (6) where S+ 00 is treated as the dominant one at large Q2 by perturbative QC...

work page
[5]

Relativistic constituent quark model of nucleon form-factors,

P. L. Chung and F. Coester, “Relativistic constituent quark model of nucleon form-factors,” Phys. Rev. D 44, 229 (1991)

work page 1991
[6]

Pion electromagnetic current in the light cone formal- ism,

J. P. C. B. de Melo, H. W. L. Naus and T. Frederico, “Pion electromagnetic current in the light cone formal- ism,” Phys. Rev. C 59, 2278 (1999)

work page 1999
[7]

Relativis- tic calculation of the deuteron quadrupole and magnetic moments,

P. L. Chung, B. D. Keister and F. Coester, “Relativis- tic calculation of the deuteron quadrupole and magnetic moments,” Phys. Rev. C 39, 1544 (1989)

work page 1989

Show all 38 references

[8]

Universal properties of the electromagnetic interactions of spin one systems,

S. J. Brodsky and J. R. Hiller, “Universal properties of the electromagnetic interactions of spin one systems,” Phys. Rev. D 46, 2141 (1992)

1992
[9]

Covariant and light-front approaches to the rho meson electromagnetic form-factors,

J. P. B. C. de Melo and T. Frederico, “Covariant and light-front approaches to the rho meson electromagnetic form-factors,” Phys. Rev. C 55, 2043 (1997)

1997
[10]

Electro- magnetic transition form-factor of pseudoscalar meson and eta - eta-prime mixing,

J. Cao, F. G. Cao, T. Huang and B. Q. Ma, “Electro- magnetic transition form-factor of pseudoscalar meson and eta - eta-prime mixing,” Phys. Rev. D 58, 113006 (1998)

1998
[11]

Actually, those four S+ h′′h′ are not independent if the rotational covariance is completely satisfied but not just hold for the rotation about ˆz. If the rotational co- variance is completely satisfied, they should be restrained by an additive relation equation, which is the ...
[13]

Consistent treatment of spin 1 mesons in the light-front quark model,

W. Jaus, “Consistent treatment of spin 1 mesons in the light-front quark model,” Phys. Rev. D 67, 094010 (2003)

2003
[14]

Mixing angles and electromag- netic properties of ground state pseudoscalar and vector meson nonets in the light cone quark model,

H. M. Choi and C. R. Ji, “Mixing angles and electromag- netic properties of ground state pseudoscalar and vector meson nonets in the light cone quark model,” Phys. Rev. D 59, 074015 (1999)

1999
[15]

Pion form-factor in the k(T) factorization formalism,

T. Huang, X. G. Wu and X. H. Wu, “Pion form-factor in the k(T) factorization formalism,” Phys. Rev. D 70, 053007 (2004)

2004
[16]

Electromagnetic structure of the rho meson in the light-front quark model,

H. M. Choi and C. R. Ji, “Electromagnetic structure of the rho meson in the light-front quark model,” Phys. Rev. D 70, 053015 (2004)

2004
[17]

Is the Structure in the Deuteron Mag- netic Form-factor at Q2 Approximately = 2-GeV**2 a New Evidence for Nuclear Core?,

L. L. Frankfurt, I. L. Grach, L. A. Kondratyuk and M. I. Strikman, “Is the Structure in the Deuteron Mag- netic Form-factor at Q2 Approximately = 2-GeV**2 a New Evidence for Nuclear Core?,” Phys. Rev. Lett. 62, 387 (1989)

1989
[18]

Electromagnetic Form-factor Of Deuteron In Relativistic Dynamics. Two Nucleon And Six Quark Components,

I. L. Grach and L. A. Kondratyuk, “Electromagnetic Form-factor Of Deuteron In Relativistic Dynamics. Two Nucleon And Six Quark Components,” Sov. J. Nucl. Phys. 39, 198 (1984)

1984
[19]

Hamiltonian Light Front Dynamics of Elastic elec- tron Deuteron Scattering,

P. L. Chung, W. N. Polyzou, F. Coester and B. D. Keis- ter, “Hamiltonian Light Front Dynamics of Elastic elec- tron Deuteron Scattering,” Phys. Rev. C37, 2000 (1988)

1988
[20]

The Vec- tor meson form-factor analysis in light-front dynamics,

B. L. G. Bakker, H. M. Choi and C. R. Ji, “The Vec- tor meson form-factor analysis in light-front dynamics,” Phys. Rev. D 65, 116001 (2002)

2002
[21]

Semileptonic Decays of B and d Mesons in the Light Front Formalism,

W. Jaus, “Semileptonic Decays of B and d Mesons in the Light Front Formalism,” Phys. Rev. D 41, 3394 (1990)

1990
[22]

Semileptonic, radiative, and pionic decays of B, B* and D, D* mesons,

W. Jaus, “Semileptonic, radiative, and pionic decays of B, B* and D, D* mesons,” Phys. Rev. D 53, 1349 (1996); Erratum: [Phys. Rev. D 54, 5904 (1996)]

1996
[23]

Covariant light-front approach for s wave and p wave mesons: Its application to decay constants and form-factors,

H. Y. Cheng, C. K. Chua and C. W. Hwang, “Covariant light-front approach for s wave and p wave mesons: Its application to decay constants and form-factors,” Phys. Rev. D 69, 074025 (2004)

2004
[24]

Self-consistent covariant de- scription of vector meson decay constants and chirality- even quark-antiquark distribution amplitudes up to twist-3 in the light-front quark model,

H. M. Choi and C. R. Ji, “Self-consistent covariant de- scription of vector meson decay constants and chirality- even quark-antiquark distribution amplitudes up to twist-3 in the light-front quark model,” Phys. Rev. D 89, 033011 (2014)

2014
[25]

Two-particle twist-3 distribu- tion amplitudes of the pion and kaon in the light-front quark model,

H. M. Choi and C. R. Ji, “Two-particle twist-3 distribu- tion amplitudes of the pion and kaon in the light-front quark model,” Phys. Rev. D 95, 056002 (2017)

2017
[26]

Self- consistency and covariance of light-front quark models: testing viaP ,V andA meson decay constants, andP→ P weak transition form factors,

Q. Chang, X. N. Li, X. Q. Li, F. Su and Y. D. Yang, “Self- consistency and covariance of light-front quark models: testing viaP ,V andA meson decay constants, andP→ P weak transition form factors,” [arXiv:1810.00296 [hep- ph]]. Phys. Rev. D 98, 114018 (2018)

2018 arXiv
[27]

Revisiting the form factors of P→V transition within the light-front quark models,

Q. Chang, X. N. Li and L. T. Wang, “Revisiting the form factors of P→V transition within the light-front quark models,” Eur. Phys. J. C 79, 422 (2019). 8

2019
[28]

Exact light cone wave function representation of matrix elements of electroweak currents,

S. J. Brodsky and D. S. Hwang, “Exact light cone wave function representation of matrix elements of electroweak currents,” Nucl. Phys. B 543, 239 (1999)

1999
[29]

Quantum field theories in the infinite mo- mentum frame. 4. Scattering matrix of vector and Dirac fields and perturbation theory,

T. M. Yan, “Quantum field theories in the infinite mo- mentum frame. 4. Scattering matrix of vector and Dirac fields and perturbation theory,” Phys. Rev. D 7, 1780 (1973)

1973
[30]

Pairs in the light-front and covariance,

J. P. B. C. de Melo, J. H. O. Sales, T. Frederico and P. U. Sauer, “Pairs in the light-front and covariance,” Nucl. Phys. A 631, 574C (1998)

1998
[31]

Covariance of light-front models: Pair cur- rent,

J. P. B. C. de Melo, T. Frederico, H. W. L. Naus and P. U. Sauer, “Covariance of light-front models: Pair cur- rent,” Nucl. Phys. A 660, 219 (1999)

1999
[32]

Nonvanishing zero modes in the light-front current,

H. M. Choi and C. R. Ji, “Nonvanishing zero modes in the light-front current,” Phys. Rev. D 58, 071901 (1998)

1998
[33]

Explicitly covariant light-front dynam- ics and relativistic few body systems,

J. Carbonell, B. Desplanques, V. A. Karmanov and J. F. Mathiot, “Explicitly covariant light-front dynam- ics and relativistic few body systems,” [nucl-th/9804029]. Phys. Rept. 300, 215 (1998)

1998 arXiv
[34]

Elas- tic electron-Deuteron Scattering at High-Energy,

R. G. Arnold, C. E. Carlson and F. Gross, “Elas- tic electron-Deuteron Scattering at High-Energy,” Phys. Rev. C 21, 1426 (1980)

1980
[35]

Rotational covariance and light-front cur- rent matrix elements,

B. D. Keister, “Rotational covariance and light-front cur- rent matrix elements,” Phys. Rev. D 49, 1500 (1994)

1994
[36]

Electromagnetic form-factors of the rho meson in a light-front constituent quark model,

F. Cardarelli, I. L. Grach, I. M. Narodetsky, G. Salme and S. Simula, “Electromagnetic form-factors of the rho meson in a light-front constituent quark model,” Phys. Lett. B 349, 393 (1995)

1995
[37]

Deuteron form-factors in the light cone quantum me- chanics ’good’ component approach,

L. L. Frankfurt, M. Strikman and T. Frederico, “Deuteron form-factors in the light cone quantum me- chanics ’good’ component approach,” Phys. Rev. C 48, 2182 (1993)

1993
[38]

Form factors of V′→V′′ transition within the light-front quark models,

Q. Chang, L. T. Wang and X. N. Li, “Form factors of V′→V′′ transition within the light-front quark models,” JHEP 1912, 102 (2019)

2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [12]

Covariant analysis of the light-front quark model,

W. Jaus, “Covariant analysis of the light-front quark model,” Phys. Rev. D 60, 054026 (1999)

work page 1999

[2] [1]

the self-consistency

It is found that the “M→ M0” replacement improves angular condition remarkably, which permits different prescriptions of ρ-meson EMFFs give the consistent results. The residue tiny violation of angular condition needs other explanations than the zero-mode contributions. Our results indicate that the relativistic effects or interaction internal structure a...

arXiv 2025

[3] [2]

Charge Form-Factors of Quark Model Pions,

P. L. Chung, F. Coester and W. N. Polyzou, “Charge Form-Factors of Quark Model Pions,” Phys. Lett. B205, 545 (1988)

work page 1988

[4] [3]

The result is independent to the conventions for calculating

+ 5 p 2ηS+ 10 1 In deed, we take the BL convention and there is an additional “1/2” factor in P− = 1 2 (P 0 − P 3). The result is independent to the conventions for calculating. 2 It is an abstruse task to recovered the complete rotational co- variance via an in-depth way, and in the paper, we will adopt the same approximation for rotational covariance. 3...

work page

[5] [4]

good” component “ µ = +

+ 2 p 2ηS+ 10 − (η + 2)S+ 1−1]. (5) The third one is suggested by Brodsky and Hiller [4] GBH C (q2) = 1 3(1 +η)[(3− 2η)S+ 00 + 8 p 2ηS+ 10 + 2(2η− 1)S+ 1−1], GBH M (q2) = 2 (1 + 2η)[S+ 00 + 2η− 1√2η S+ 10−S+ 1−1], GBH Q (q2) = 2 √ 2 3(1 + 2η)[−ηS+ 00 + p 2ηS+ 10− (η + 1)S+ 1−1], (6) where S+ 00 is treated as the dominant one at large Q2 by perturbative QC...

work page

[6] [5]

Relativistic constituent quark model of nucleon form-factors,

P. L. Chung and F. Coester, “Relativistic constituent quark model of nucleon form-factors,” Phys. Rev. D 44, 229 (1991)

work page 1991

[7] [6]

Pion electromagnetic current in the light cone formal- ism,

J. P. C. B. de Melo, H. W. L. Naus and T. Frederico, “Pion electromagnetic current in the light cone formal- ism,” Phys. Rev. C 59, 2278 (1999)

work page 1999

[8] [7]

Relativis- tic calculation of the deuteron quadrupole and magnetic moments,

P. L. Chung, B. D. Keister and F. Coester, “Relativis- tic calculation of the deuteron quadrupole and magnetic moments,” Phys. Rev. C 39, 1544 (1989)

work page 1989