Pith. sign in

REVIEW 4 major objections 4 minor 58 references

Parametrization of zero-skewness unpolarized GPDs

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Combining the VS24 parametrization with JHA21 quark distributions reproduces measured nucleon form factors and gives a proton radius of 0.853 fm.

desk verdict A transparent but incremental GPD parametrization paper whose central claim rests on visual comparison; two concrete equation errors need fixing before it can be trusted. read the letter →

arxiv 2507.11177 v2 pith:HWCSLP7D submitted 2025-07-15 hep-ph hep-lat

Hossein Vaziri Mohammad Reza Shojaei ID This is my paper · ORCID
classification hep-phhep-lat
keywords generalizedpartondistributionszeroskewnessnucleonelectromagneticformfactorsgravitationaldistributionfunctionsprotonelectricradiusflavorseparationVS24ansatz
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 establish that the zero-skewness unpolarized generalized parton distributions of the nucleon can be parametrized by the VS24 ansatz, and that using the JHA21 parton distribution functions at N3LO as input produces better agreement with measured electromagnetic form factors than other parametrizations. From that parametrization the authors derive flavor-separated Dirac and Pauli form factors for up and down quarks, the proton and neutron Sachs form factors, and the first-$x$-moment gravitational form factors $A_q(t)$ and $B_q(t)$ that no experiment has directly measured. They obtain a proton electric radius of $0.853\,\mathrm{fm}$, compatible with the experimentally determined $0.831\,\mathrm{fm}$, and find that the total valence-quark contribution to $A(t)$ at zero momentum transfer is nearly independent of the PDF set, around $0.43$--$0.46$. A sympathetic reading is that the paper provides a single functional family that connects deep-inelastic parton distributions to elastic electron scattering and, by extension, to the nucleon's mass and angular-momentum distributions, which is why the claim matters.

What carries the argument

The machine that carries the argument is the VS24 ansatz, a five-parameter exponential $t$-dependence for zero-skewness GPDs: $H^q(x,t)=q_v(x)\exp[-\alpha''' t(1-x)^\gamma\ln x+\beta x^{m'}\ln(1-bt)]$ and $E^q(x,t)=\varepsilon^q(x)\exp[-\alpha''' t(1-x)^\gamma\ln x+\beta x^{m'}\ln(1-bt)]$, where $\varepsilon^q(x)=(\kappa_q/N_q)(1-x)^{\eta_q}q_v(x)$ is the Pauli-type ansatz of Eq. (14). The parameters $\alpha'''$, $\beta$, $\gamma$, $\eta_u$, and $\eta_d$ are fitted to elastic form factor data with $b=2$ and $m'=0.65$ fixed. Inserting these GPDs into the sum rules $F_1(t)=\sum_q e_q\int_0^1 dx\,H^q(x,t)$ and $F_2(t)=\sum_q e_q\int_0^1 dx\,E^q(x,t)$ yields the electromagnetic form factors, and the first $x$-moments $A_q(t)=\int_0^1 dx\,xH^q(x,t)$ and $B_q(t)=\int_0^1 dx\,xE^q(x,t)$ yield the gravitational form factors. Thus the one functional family carries the full chain from PDF input to electron-scattering observables to mass distributions.

What would settle it

Measure the proton gravitational form factor $A(t)$ at several nonzero $-t$ values with better precision than current lattice results and compare with the VS24+JHA21 curve: the model predicts a specific slope for $A_{u+d}(t)$, and a systematic deviation would falsify the parametrization. A cheaper out-of-sample check is a precise measurement of the neutron electric form factor $G_E^n$ at $-t>5\,\mathrm{GeV}^2$, where the VS24 curves are not constrained by the fit data.

Watch

Extended reading notes

Core claim

The paper's central claim is that the VS24 exponential ansatz, Eqs. (22)--(23), together with the JHA21 N3LO PDFs, yields the flavor-separated zero-skewness GPDs $H^q$ and $E^q$ whose sum-rule integrals reproduce the nucleon electromagnetic form factors more closely than the same ansatz with KKA10 PDFs or than the other ansatz families considered. This is demonstrated by comparing quark-level and nucleon-level Dirac and Pauli form factors with extracted experimental points from electron-proton inelastic scattering over $-t$ from 0 to 5 GeV$^2$. The same parametrization gives gravitational form factors $A_q(t)$ and $B_q(t)$: their flavor-summed value at $t=0$ is $A_{u+d}(0)\approx0.426$ with JHA21 inputs, within a few percent of the values obtained with six other PDF sets, and the $t$-dependence is qualitatively consistent with lattice QCD. It also yields a proton electric radius $r_{E,p}=0.853\,\mathrm{fm}$, which the authors place next to the experimental value $0.831\,\mathrm{fm}$.

Load-bearing premise

The result stands or falls with the assumption that the VS24 exponential functional form, once its free parameters are tuned to the data, is flexible enough to represent the true zero-skewness GPDs over the whole fitted range of momentum transfer; if the true GPDs have a different shape, the agreement with the measured form factors is an artifact of curve fitting, and the derived gravitational form factors inherit the bias.

Editorial extensions

If this is right

  • The flavor-separated Dirac and Pauli form factors $F_1^q(t)$ and $F_2^q(t)$ from VS24+JHA21 provide ready inputs for impact-parameter-space pictures of up- and down-quark charge and magnetization distributions in the proton.
  • The predicted gravitational form factors $A_q(t)$ and $B_q(t)$ for individual flavors give concrete targets for future lattice QCD calculations and for any experimental program that can access the energy-momentum tensor of the nucleon.
  • The computed proton electric radius $r_{E,p}=0.853\,\mathrm{fm}$ is close to the experimental $0.831\,\mathrm{fm}$, supporting the VS24 parametrization's low-$|t|$ behavior.
  • The near-constancy of $A_{u+d}(0)\approx0.43$--$0.46$ across seven PDF sets indicates that the valence-quark mass fraction at zero momentum transfer is stable, while the slope with $t$ does depend on the PDF choice.

Reading between the lines

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

  • Editorial extension: applying the same VS24 machinery to gluon GPDs at zero skewness would test whether the exponential $t$-dependence is a general feature of the nucleon or an artifact of the valence-quark fit; a gluon version is not derived in the paper.
  • Editorial extension: the paper does not isolate whether the $0.853$ fm radius reflects the ansatz or the input PDFs; refitting at fixed PDF while varying the ansatz, and vice versa, would separate those sources.
  • Editorial extension: the neutron electric form factor, which the paper finds particularly well described, is the cleanest out-of-sample discriminator; a future precise $G_E^n$ point at $-t>5$ GeV$^2$ would test the parametrization where it was not fitted.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper presents a flavor-separated parametrization of zero-skewness unpolarized quark GPDs H and E using the VS24 ansatz, combined with several PDF sets (mainly KKA10 and JHA21 at N3LO). The authors compute nucleon electromagnetic form factors F1, F2 and Sachs form factors GE, GM, compare them with elastic scattering data, then derive gravitational form factors A(t), B(t) and the proton electric charge radius. The central quantitative claim is that VS24 combined with JHA21 PDFs shows better agreement with electron-proton scattering form factor data than VS24 combined with KKA10 PDFs, based on visual comparison of Figs. 3-6; the reported proton charge radius is 0.853154 fm, compared with the experimental 0.831 fm.

Significance. If the parametrization were quantitatively validated, it would provide a simple, analytically tractable flavor-separated description of nucleon electromagnetic and gravitational form factors, with a proton radius in the range of modern measurements. The paper gives no machine-checked proofs or public code; its numerical claims rest on standard integrals and fits. The gravitational form factor results are model outputs rather than independent predictions, and the radius is a derived consequence of the fitted parameters. The potential usefulness of the parametrization is undermined by the absence of any goodness-of-fit metric, by the internal inconsistencies in the printed formulas, and by the fact that the parameters are fitted to the same data used for the comparison.

major comments (4)
  1. [Section III, Table I and Figs. 3-6] The central claim that VS24+JHA21 shows better agreement with form factor data than VS24+KKA10 is supported only by visual inspection. No chi-square, likelihood, or other goodness-of-fit statistic is reported for any ansatz or PDF set. Moreover, the parameters in Table I are fitted to the same datasets (Refs. [44-46]) that are shown in the comparison figures, so the agreement is partly built in. Provide quantitative fit metrics, such as chi-square per degree of freedom, for each combination, and state clearly which data points were used in the fits.
  2. [Section V, Eqs. (36)-(37)] The printed formulas for the Dirac mean squared radii are not the correct derivatives of the VS24 ansatz. Differentiating Eq. (22) at t=0 yields an additional term -beta b x^{m'} from the derivative of ln(1-bt), and the factor -6 should be applied to the entire expression including that term. As written, the second term in Eqs. (36)-(37) vanishes at t=0 because ln(1-bt)|_{t=0}=0, and the reported value r_E,p = 0.853154 fm cannot be reproduced from the printed formula. Correct the equations and verify that the numerical radius was computed with the correct slope of F_1^p(t).
  3. [Section III, Eq. (25)] The neutron Dirac form factor is written as F_1^n(t) = e_d F_2^u(t) + e_d F_2^d(t). This expression uses the Pauli form factors F_2 rather than the Dirac form factors F_1, and both terms carry the same charge weight; the correct relation is F_1^n = e_u F_1^d + e_d F_1^u (with isospin-symmetric identification of quark form factors), which satisfies F_1^n(0)=0. This equation is load-bearing for the neutron form factor results in Figs. 5 and 6; state whether the corrected expression was actually used in the numerical calculation.
  4. [Section III, Eq. (28) and the sign of t] The paper states 'where t = Q^2 is the four-momentum transfer of the virtual photon'. In the space-like region t is negative, and the ansatz in Eqs. (22)-(23) only has the physically expected t-dependence if t is negative. The sign convention is essential for the behavior of the integrand as x -> 0 and for the reported slopes. Clarify the convention consistently: in Eqs. (8)-(11), (22)-(23), (31)-(34), and (35)-(37), and in the definition of tau in Eq. (28).
minor comments (4)
  1. [Table I and Eq. (22)] The parameter used in the VS24 ansatz is called alpha''' in Eq. (22) but alpha'' in Table I; use consistent notation.
  2. [Conclusion, paragraph 2] The text says 'F1 and F2 are the Pauli and Dirac form factors, respectively'; this is reversed. F1 is the Dirac form factor and F2 is the Pauli form factor.
  3. [Throughout] There are numerous typographical errors, including 'gravitional', 'INTRODUCTON', 'Ansatsez', 'T able', 'GP,n', and a duplicated 'As these figures show' in Section VI. A careful proofreading is needed.
  4. [Table II] The value G^n_E(0)=3.2 x 10^-13 is reported with no meaningful precision; since the symmetry requires G^n_E(0)=0, report 0 or a physically meaningful upper bound.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper fits a parameterized ansatz to form-factor data and then compares downstream integrals to independent benchmarks; the fit-to-data agreement is a validation of the parametrization, not a disguised prediction.

full rationale

The paper's derivation chain is explicit and non-circular. The PDFs and the VS24 functional form in Eqs. (22)-(23) are inputs; Table I states, 'The parameters of b and m′ are fixed, and the others have been calculated by fitting,' and the fitted parameters are obtained from elastic nucleon form-factor data. The curves in Figs. 3-6 are therefore the fitted curves, and the statement that VS24+JHA21 'show better agreement with the form factors obtained from electron-proton inelastic scattering experiments' is a fit-quality claim rather than an independent prediction. A fit reproducing the data it was fitted to is not a circular derivation unless the paper relabels it as a prediction; here the paper explicitly describes the parameters as fitted. The comparison between JHA21 and KKA10 has some independent content because the PDFs themselves come from external DIS fits, although the absence of a quantitative goodness-of-fit metric is a reporting weakness, not circularity. The gravitational form factors A(t), B(t) and the proton radius are integrals or derivatives of the fitted model computed via Eqs. (31)-(34) and (35)-(37); they are not fit parameters themselves, and they are compared with the independent MMNS lattice-QCD result, the GJLY calculation, and the Xiong et al. radius measurement. The authors' self-citations to their prior HS22/M-HS22/VS24 works supply the functional forms, but the parameters are re-fitted here to external data, so the self-citations are not load-bearing. Potential internal inconsistencies, such as the charge/Pauli structure in Eq. (25) and the apparent omission of the -β b x^m' term in the differentiated radius formula Eq. (36), are correctness risks rather than circularity. No step in the paper reduces to its inputs by construction in the sense required for a circularity finding.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles, forces, or conserved quantities. Its central outputs depend on seven free numbers (five fitted, two fixed) plus a phenomenological ansatz taken from the authors' earlier work. The PDF inputs and sum rules are external standards, but the key structural assumption is that the VS24 functional family is flexible enough to describe the true GPDs.

free parameters (7)
  • alpha''' (alpha'' in Table I) = 1.3473 +/- 0.00719 (JHA21); 1.3742 +/- 0.00717 (KKA10)
    t-slope parameter in the VS24 ansatz, Eq. (22); fitted to elastic form factor data [44-46].
  • beta = 1.51418 +/- 0.02556 (JHA21); 1.52378 +/- 0.02839 (KKA10)
    Shape parameter in the VS24 ansatz, Eq. (22); fitted to elastic form factor data.
  • gamma = 2.9823 +/- 0.01260 (JHA21); 0.05701 +/- 0.01494 (KKA10)
    Exponent in the (1-x)^gamma factor of the VS24 ansatz; fitted to elastic form factor data.
  • eta_u = 0.6931 +/- 0.00987 (JHA21); 0.71207 +/- 0.00991 (KKA10)
    Power in Eq. (14) relating the Pauli-type GPD to the u valence PDF; fitted to form factor data.
  • eta_d = 0.2782 +/- 0.01774 (JHA21); 0.19248 +/- 0.01606 (KKA10)
    Power in Eq. (14) relating the Pauli-type GPD to the d valence PDF; fitted to form factor data.
  • b = 2 (fixed)
    Fixed parameter in the VS24 ansatz, chosen by hand rather than fitted.
  • m' = 0.65 (fixed)
    Fixed parameter in the VS24 ansatz, chosen by hand rather than fitted.
assumptions (5)
  • standard math GPD sum rules connect first moments of H and E to electromagnetic form factors (Eqs. 8-11).
    Standard light-cone sum rules from Diehl and references therein; used without proof.
  • standard math Second moment sum rules connect GPD moments to gravitational form factors A(t), B(t) (Eqs. 31-34).
    Standard relation from the energy-momentum tensor matrix elements; used without proof.
  • domain assumption JHA21 and KKA10 N3LO PDFs are valid universal inputs.
    The PDFs are taken from prior global fits, with all their fit assumptions external to this paper.
  • domain assumption The VS24 exponential ansatz, Eqs. (22)-(23), and the E-GPD relation, Eq. (14), reproduce the true zero-skewness GPD t-dependence.
    The t-dependence of GPDs is not derived from QCD; the chosen functional form is a phenomenological model.
  • domain assumption Elastic form factor data from [44-46] are accurate and sufficient to fix the model parameters.
    All five continuous VS24 parameters are fitted to these datasets; the quality of the central claim depends on their reliability.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Parametrization of zero-skewness unpolarized GPDs." pith.science (2026). https://pith.science/paper/HWCSLP7D

@misc{pith2026250711177,
  author       = {Pith},
  title        = {Pith review of: Parametrization of zero-skewness unpolarized GPDs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HWCSLP7D}},
  note         = {Machine review of arXiv:2507.11177}
}
abstract

Recent parameterizations of parton distribution functions (PDFs) have led to the determination of the gravitional form factors of the nucleon's dependence on generalized parton distributions of nucleons in the limit $\xi$$\to 0$. This paper aims to obtain the flavor division of nucleon electromagnetic and gravitional form factors using the VS24 Ansatz and two PDFs at $N^3L0$ approximation in GPDs. The PDFs and GPDs formalism enable the calculation of various form factors of nucleons in different approximations, as well as the calculation of the electric radius of nucleons. The study, despite its high approximation complexity, enhances the accuracy of calculations and brings them closer to the experimental values.

Figures

Figures reproduced from arXiv: 2507.11177 by the authors.

Figure 1
Figure 1. a)HadronA + HadronB → 2P artons [26]. b) Deeply inelastic scattering [26]. relation could also be used as the definition [27, 28]. The technical definition of parton distribution functions is now ready to be studied. There are, in fact, two defini￾tions in current use: the MS definition, which is the most commonly used. There is also the DIS definition in which deeply inelastic scattering plays a privileged role [26… view at source ↗
Figure 2
Figure 2. The xuv and xdv of the CJ15 at NLO approximation [37], JR09 [38] at NNLO approximation, CT18 [39] at NNLO approximation, nCTEQ15 [40], KKA10 [23], JHA21 [24, 25], and MSTH [41] PDFs at NNNLO approximation as a function of x [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The F u,d 1 and F u,d 2 are multiplied by t as a function of −t. Comparison of the ER Ansatz [6], the MG Ansatz[35], the HS22 Ansatz [20], the M-HS22 Ansatz [19] with the VS24 Ansatz [22]. All of them make use of the KKA10 PDF [23]. Experimental data from [44] (triangle up), [45] (circle), and [46] (square) served as a basis for the extracted points. F n 2 (t) = edF u 2 (t) + euF d 2 (t). (27) where eu = 2/3 and ed … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The F u,d 1 and F u,d 2 are multiplied by t as a function of −t. Comparison of the ER Ansatz [6], the MG Ansatz[35], the HS22 Ansatz [20], the M-HS22 Ansatz [19] with the VS24 Ansatz [22]. The JHA21 PDF [24, 25] is used in all of them. The extracted points are based on…
Figure 5
Figure 5. Figure 5: The F p,n 1 and F p,n 2 are multiplied by t as a function of −t. Comparison of the ER Ansatz [6], the MG Ansatz [35], the HS22 Ansatz [20], the M-HS22 Ansatz [19], and the VS24 Ansatz [22]. The JHA21 PDF [24, 25] is used in all of them. The extracted points are based o…
Figure 6
Figure 6. Figure 6: The G p,n E and G p,n M as a function of −t. Comparison of the ER Ansatz [6], the MG Ansatz [35], the HS22 Ansatz [20], the M-HS22 Ansatz [19], and the VS24 Ansatz [22]. The JHA21 PDF [24, 25] is used in all of them. The extracted points are based on experimental data …
Figure 7
Figure 7. Figure 7: The proton GFF Au+d as a function of −t. The JHA21 PDF in the NNNLO approximation [24, 25], with combination of the VS24 Ansatz [22]. The results of MMNS (Lattice QCD) [52] are plotted. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -t[GeV2 ] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 …
Figure 8
Figure 8. Figure 8: The Au,d and Bu,d as a function of −t. The CJ15 parton distribution functions in the NLO approximation [37], the JR09 parton distribution functions in the NNLO approximation [38], the CT18 parton distribution functions in the NNLO approximation [39], the nCTEQ15 PDF in…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 26 canonical work pages

  1. [1]

    Abt et al

    I. Abt et al. , Phys. Rev. D 106, 079901 (2022)

    work page 2022

  2. [2]

    and ( 3), and some examples of different PDF charts as a function of x at different approximations are shown in Fig. ( 2). As these figures show, the behavior and physics of these functions are the same.As these figures show, the behavior and physics of these functions are the same. Since GPDs show the space inside the nucle- ons in three dimensions, we discu...

    work page

  3. [3]

    Halzen and A

    F. Halzen and A. D. Martin, Quarks & Leptons (Wiley, New York, 1984)

    1984

  4. [4]

    R. S. Thorne, A. D. Martin, W. J. Stirling and G. Watt, Eur. Phys. J. C 63, 189-285 (2009)

    work page 2009

  5. [5]

    M. N. Rosenbluth, Phys. Rev. D 79,079615 (1950)

    1950

  6. [6]

    Masjuan, E

    P. Masjuan, E. Ruiz Arriola and W. Broniowski, EPJ Web Conf. 73, 04021 (2014)

    work page 2014

  7. [7]

    Reza Shojaei, Eur

    M. Reza Shojaei, Eur. Phys. J. A 52, no.4, 111 (2016)

    2016

  8. [8]

    Guidal, M

    M. Guidal, M. V. Polyakov, A. V. Radyushkin and M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005)

    2005

Show all 58 references
  1. [9]

    G. A. Miller, B. M. K. Nefkens and I. Slaus, Phys. Rept. 194, 1-116 (1990)

    1990

  2. [10]

    Burkardt, Int

    M. Burkardt, Int. J. Mod. Phys. A 18, 173-208 (2003)

    2003

  3. [11]

    A. V. Radyushkin, Phys. Rev. D 83,076006 (2011)

    2011

  4. [12]

    Guidal, H

    M. Guidal, H. Moutarde and M. Vanderhaeghen, Rept. Prog. Phys. 76, 066202 (2013)

    2013

  5. [13]

    O. V. Selyugin and O. V. Teryaev, Phys. Atom. Nucl. 87, no.4, 518-522 (2024)

    2024

  6. [14]

    Hashamipour, M

    H. Hashamipour, M. Goharipour, K. Azizi and S. V. Goloskokov, Phys. Rev. D 105, no.5, 054002 (2022)

    2022

  7. [15]

    Haji Hosseini Mojeni and M

    H. Haji Hosseini Mojeni and M. R. Shojaei, Eur. Phys. J. Plus 137,no.8, 938 (2022)

    2022

  8. [16]

    Sattary Nikkhoo and M

    N. Sattary Nikkhoo and M. R. Shojaei, Phys. Rev. C 97, no.5, 055211 (2018)

    2018

  9. [17]

    X. D. Ji, Phys. Rev. Lett. 78, 610-613 (1997)

    1997

  10. [18]

    Muller, D

    D. Muller, D. Robaschik, B. Geyer, F. M. Dittes and J. Horejsi, Fortsch. Phys. 42, 101-141 (1994)

    1994

  11. [19]

    Vaziri and M

    H. Vaziri and M. Reza Shojaei, Phys. Rev. C 107, no.5, 055204 (2023)

    2023

  12. [20]

    A. V. Radyushkin, Phys. Rev. D 56, 5524-5557 (1997)

    1997

  13. [21]

    N. S. Nikkhoo and M. R. Shojaei, Int. J. Mod. Phys. E 24, no.11, 1550086 (2015)

    2015

  14. [22]

    Haji Hosseini Mojeni and M

    H. Haji Hosseini Mojeni and M. R. Shojaei, Phys. Rev. C 105, no.2, 025202 (2022)

    2022

  15. [23]

    A. N. Khorramian, H. Khanpour and S. A. Tehrani, Phys. Rev. D 81, 014013 (2010)

    2010

  16. [24]

    Vaziri and M

    H. Vaziri and M. R. Shojaei, Eur. Phys. J. Plus. 139, no.10, 905 (2024) ’

    2024

  17. [25]

    Blümlein and M

    J. Blümlein and M. Saragnese, Phys. Lett. B 820, 136589 (2021) ’

    2021

  18. [26]

    Blumlein, H

    J. Blumlein, H. Bottcher and A. Guffanti, Nucl. Phys. B 774, 182-207 (2007)

    2007

  19. [27]

    Diehl, Phys

    M. Diehl, Phys. Rept. 388, 41-277 (2003) ’

    2003

  20. [28]

    In each of the paper’s figures, we have analyzed the pa- rameters of VS24 Ansatz for the upper and lower limits

    were used to arrive at this conclusion. In each of the paper’s figures, we have analyzed the pa- rameters of VS24 Ansatz for the upper and lower limits. Furthermore, using the necessary Ansatz, we computed these form factors in q2 = 0 and compared them with the form factors der...

  21. [29]

    D. E. Soper, Nucl. Phys. B Proc. Suppl 53, 69-80 (1997)

    1997

  22. [30]

    Sattary Nikkhoo and M

    N. Sattary Nikkhoo and M. R. Shojaei, j.nuclphysa 138, (2018)

    2018

  23. [31]

    A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, Eur. Phys. J. C 63, 189-285 (2009)

    2009

  24. [32]

    P. M. Nadolsky, H. L. Lai, Q. H. Cao, J. Huston, J. Pumplin, D. Stump, W. K. Tung and C. P. Yuan, Phys. Rev. D 78, 013004 (2008)

    2008

  25. [33]

    R. D. Ball et al. [NNPDF], Nucl. Phys. B 809, 1-63 (2009) . [arXiv:0808.1231 [hep-ph]]. 12

    2009 arXiv

  26. [34]

    F. D. Aaron et al. [H1 and ZEUS], JHEP 01, 109 (2010)

    2010

  27. [35]

    Alekhin, J

    S. Alekhin, J. Blumlein, S. Klein and S. Moch, Phys. Rev. D 81, 014032 (2010)

    2010

  28. [36]

    J. E. Madriz Aguilar, Eur. Phys. J. C 53, 133-138 (2008)

    2008

  29. [37]

    O. V. Selyugin and O. V. Teryaev, Phys. Rev. D 79, 033003 (2009)

    2009

  30. [38]

    H. H. H. Mojeni and M. R. Shojaei, J. Exp. Theor. Phys. 131, , no.6, 910-916 (2020)

    2020

  31. [39]

    Accardi, L

    A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens and N. Sato, Phys. Rev. D 93, no.11, 114017 (2016) . [

    2016

  32. [40]

    Jimenez-Delgado and E

    P. Jimenez-Delgado and E. Reya, Phys. Rev. D 79, 074023 (2009)

    2009

  33. [41]

    T. J. Hou, J. Gao, T. J. Hobbs, K. Xie, S. Dulat, M. Guzzi, J. Huston, P. Nadol- sky, J. Pumplin and C. Schmidt, et al. Phys. Rev. D 103, no.1, 014013 (2021)

    2021

  34. [42]

    Kovarik, A

    K. Kovarik, A. Kusina, T. Jezo, D. B. Clark, C. Keppel, F. Lyonnet, J. G. Morfin, F. I. Ol- ness, J. F. Owens and I. Schienbein, et al. Phys. Rev. D 93, no.8, 085037 (2016)

    2016

  35. [43]

    McGowan, T

    J. McGowan, T. Cridge, L. A. Harland-Lang, R. S. Thorne Eur. Phys. J. C 83, 185 (2023)

    2023

  36. [44]

    M. R. Shojaei and N. S. Nikkhoo, Nucl. Phys. A 943, 137-146 (2015)

    2015

  37. [45]

    Y. Guo, X. Ji, Y. Liu and J. Yang, Phys. Rev. D 108, no.3, 034003 (2023)

    2023

  38. [46]

    I. A. Qattan and J. Arrington, Phys. Rev. C 86, 065210 (2012)

    2012

  39. [47]

    G. D. Cates, C. W. de Jager, S. Riordan and B. Wojt- sekhowski, Phys. Rev. Lett. 106,252003 (2011)

    2011

  40. [48]

    Diehl and P

    M. Diehl and P. Kroll, Eur. Phys. J. C 73, no.4, 2397 (2013)

    2013

  41. [49]

    F. J. Ernst, R. G. Sachs and K. C. Wali, Phys. Rev. 119, 1105-1114 (1960)

    1960

  42. [50]

    S. D. Drell and T. M. Yan, Phys. Rev. Lett. 24, 181-185 (1970)

    1970

  43. [51]

    N. S. Nikkhoo and M. R. Shojaei, Int. J. Mod. Phys. A. 32, no.17, 1750097 (2017)

    2017

  44. [52]

    D. H. Beck and R. D. McKeown, Ann. Rev. Nucl. Part. Sci. 51, 189-217 (2001)

    2001

  45. [53]

    Hohler, E

    G. Hohler, E. Pietarinen, I. Sabba Stefanescu, F. Borkowski, G. G. Simon, V. H. Walther and R. D. Wendling, Nucl. Phys. B. 114, 505-534 (1976)

    1976

  46. [54]

    J. More, A. Mukherjee, S. Nair and S. Saha, Phys. Rev. D 105, , no.5, 056017 (2022)

    2022

  47. [55]

    Garcia Martin-Caro, M

    A. Garcia Martin-Caro, M. Huidobro and Y. Hatta, Phys. Rev. D. 108 no.3, 034014 (2023)

    2023

  48. [56]

    Pagels, Phys

    H. Pagels, Phys. Rev. 144, 1250-1260 (1966)

    1966

  49. [57]

    Selyugin, EPJ Web Conf

    O. Selyugin, EPJ Web Conf. 222, 03018 (2019)

    2019

  50. [58]

    Xiong, A

    W. Xiong, A. Gasparian, H. Gao, D. Dutta, M. Khan- daker, N. Liyanage, E. Pasyuk, C. Peng, X. Bai and L. Ye, et al. Nature. 575, no.7781, 147-150 (2019)

    2019

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.