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REVIEW 2 major objections 6 minor 27 references

Hadron structure via Generalized Parton Distributions

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Lattice QCD can now compute x-dependent generalized parton distributions—including twist-3 ones—from first principles, giving access to hadron structure that experiments currently cannot reach.

desk verdict A competent, honest conference proceedings review of the quasi-distribution approach to lattice GPDs: nothing new in results, but the caveats are stated clearly and the asymmetric-frame discussion is useful. read the letter →

arxiv 2502.00481 v1 pith:BPULBBZB submitted 2025-02-01 hep-lat hep-ph

Shohini Bhattacharya This is my paper · ORCID
classification hep-lathep-ph
keywords generalizedpartondistributionsquasi-distributionapproachlatticeQCDperturbativematchingnucleontomographytwist-3GPDsasymmetricframehadronstructure
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 review argues that the quasi-distribution approach has matured into a practical way to compute the x-dependent generalized parton distributions (GPDs) of pions and protons directly from lattice QCD. The central claim is that Euclidean correlators computed at finite hadron momentum can be matched perturbatively to light-cone GPDs because the two objects share identical infrared singularities, so the only cost is a power correction of order $1/P_3^2$. If the claim is right, lattice QCD gives first-principles access to quantities—the full x-shape of GPDs, twist-3 quark-gluon-quark correlations, and spatial tomographies—that are extremely difficult to extract from experiments like deeply virtual Compton scattering. This matters because GPDs encode how momentum and spatial distributions of quarks are correlated inside the proton, and are central to the physics program of an upcoming electron-ion collider.

What carries the argument

The central object is the quasi-GPD, a matrix element of a spatial (non-light-cone) quark bilinear at finite hadron momentum $P_3$, which is computable on a Euclidean lattice. Its connection to the physical light-cone GPD is carried by the matching formula (Eq. 9), which is valid because the infrared singularities of the quasi- and light-cone distributions are identical; the matching coefficient $C(x/y, \xi/y, \mu/P_3)$ is known to one loop. A second piece of machinery is the Lorentz-covariant decomposition of the quark correlator into eight frame-independent amplitudes (Eq. 10), which lets one construct any quasi-GPD in a preferred frame from matrix elements computed in an asymmetric frame, and supports a Lorentz-invariant definition of quasi-GPDs that has no explicit extra amplitudes.

What would settle it

Take a quasi-GPD computed at several increasing boost momenta $P_3$ (for example 1.5, 2.0, and 2.5 GeV), apply the one-loop matching to each, and check whether the resulting light-cone GPD is independent of $P_3$ within the estimated power corrections; if the matched curves drift systematically with $P_3$, the power-correction assumption is false.

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Extended reading notes

Core claim

The paper's central discovery, assembled from recent lattice results, is that the quasi-distribution approach—originally introduced for parton distribution functions—works for GPDs: after performing the transverse-momentum integral at finite boost momentum $P_3$, the quasi-GPD has exactly the same infrared pole structure as the light-cone GPD, so a perturbative matching formula (Eq. 9) converts the lattice-calculated quasi-GPD into the light-cone GPD up to power corrections of order $\Lambda_{\mathrm{QCD}}^2/P_3^2$, $M_N^2/P_3^2$, and $t/P_3^2$. The review presents the first $x$-dependent twist-2 GPDs for the pion and proton, the first twist-3 GPD calculations, and a Lorentz-covariant amplitude formalism that allows quasi-GPDs to be computed in asymmetric frames with a Lorentz-invariant definition that reduces power corrections and computational cost.

Load-bearing premise

The entire approach rests on the assumption that at the finite boost momenta achievable on a lattice, the power corrections of order $\Lambda_{\mathrm{QCD}}^2/P_3^2$, $M_N^2/P_3^2$, and $t/P_3^2$ are small enough that the matched result is a faithful representation of the true light-cone GPD.

Editorial extensions

If this is right

  • Lattice QCD can provide the full $x$-dependence of all eight twist-2 GPDs and twist-3 combinations from first principles, independent of experimental input.
  • From these GPDs one can derive impact-parameter distributions (nucleon tomography) and, via the total angular momentum sum rule, the angular momentum carried by quarks.
  • Twist-3 GPDs, which encode quark-gluon-quark correlations, become accessible even though they appear suppressed by the hard scale in experiments.
  • The asymmetric-frame, Lorentz-invariant formulation reduces computational cost and allows a broader range of momentum transfer $t$, improving the spatial resolution of parton densities.
  • Matching lattice GPDs with upcoming electron-ion collider data can give a complementary picture of nucleon structure and help refine phenomenological extractions.

Reading between the lines

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

  • A practical test of the method is to compare the matched results from the traditional $\gamma^0$ operator and the Lorentz-invariant definition at the same $P_3$; agreement within the estimated power corrections would validate the approach, while systematic disagreement would signal that power corrections are not under control.
  • The same matching machinery should extend to gluon GPDs and to other hadrons, but that requires higher-loop matching coefficients and a careful renormalization of the extra operators—steps not yet carried out.
  • If lattice GPDs reach high enough precision before the electron-ion collider turns on, they could serve as model-independent benchmarks for global fits of GPDs, potentially reducing the model dependence in deep inelastic scattering analyses.
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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

2 major / 6 minor

Summary. This is the LATTICE2024 proceedings article of S. Bhattacharya, reviewing the quasi-distribution (large-momentum) approach to computing x-dependent Generalized Parton Distributions (GPDs) from lattice QCD. Section 2 defines the light-cone GPD correlator and motivates GPDs through nucleon tomography, quark angular momentum, the gravitational form factors of the energy-momentum tensor, and recent connections to chiral and trace anomalies. Section 3 carries out a one-loop quark-target-model calculation of the PDF and the quasi-PDF, uses it to argue that the infrared singularities of the two objects coincide, and states the matching formulas for PDFs and GPDs, Eqs. (8) and (9), including power corrections of order Lambda_QCD^2/P3^2, M_N^2/P3^2, and t/P3^2. Section 4 summarizes lattice results for twist-2 and twist-3 GPDs of the pion and proton, discusses the x=+-xi discontinuities as power-correction artifacts, and presents the asymmetric-frame amplitude formalism that grants access to a broader range of t. Section 5 sets the lattice program beside phenomenological extractions and the future EIC. The review is organized primarily around the author's own published results but cites the complementary pseudo-distribution and Compton-amplitude approaches.

Significance. If the reviewed program is sound, it provides a first-principles route to x-dependent GPDs, including twist-3 distributions that are currently beyond experimental reach, and the asymmetric-frame formalism is a practical methodological advance that reduces computational cost and extends the accessible t-range for tomography. The manuscript is appropriately self-critical at several load-bearing points: it flags the x=+-xi discontinuities in Fig. 3 as artifacts of power corrections (Section 4.1); it concedes in Section 4.3 that the a-priori expectation of faster convergence for Lorentz-invariant quasi-GPD definitions is likely too simplistic and that empirical convergence is definition-dependent; and it states that GPD matching is known only to one loop (Section 3). This candor makes the review internally consistent, and the central equations (Eqs. (5), (7), (8), (9)) agree with known one-loop results in the literature. The weakest point is not technical but rhetorical: the abstract and Section 5 frame the results more assertively than the caveats in Section 4.3 permit, so the required changes are to the claims' wording rather than to the underlying science.

major comments (2)
  1. [Section 4.3 / Eq. (9) / abstract] The central claim, that Euclidean quasi-GPDs matched with Eq. (9) yield the physical light-cone GPDs, is conditional on the power corrections O(Lambda_QCD^2/P3^2, M_N^2/P3^2, t/P3^2) being numerically small after one-loop matching, yet the proceedings display no systematic test of the P3 dependence of the matched distributions in Figs. 2-4 and 6. Section 4.3 itself reports that the Lorentz-invariant definition does not universally improve convergence: H is not substantially affected, and H-tilde converges better with the traditional definition. This leaves the status of the plotted curves as light-cone GPDs an assertion rather than a demonstrated result, and the concern is sharper for the twist-3 results in Section 4.2, whose matching is known only at one loop. I ask that the abstract and Section 5 state explicitly that the presented x-dependent GPDs still contain uncontrolled O(1/P3^2) effects and that systematic P3-extrapolation tests remain to be completed, or, alternatively, that one quantitative P3-dependence comparison from Refs. [18, 21, 22] be included so that the first-principles framing is tied to actual convergence evidence.
  2. [Section 4.2 / Fig. 4] The interpretation of the right panel of Fig. 4 rests on the statement that the norm of the twist-3 GPD G-tilde_1 is expected to vanish at xi=0, which the text presents as an expectation rather than a demonstrated property. On top of that assumption, the paragraph concludes that the data provide a glimpse of the twist-2 GPD E-tilde at xi=0 and that E-tilde exhibits a pronounced t-dependence near the origin, so that the pion-pole dominance picture E-tilde^u - E-tilde^d ~ 1/(t - m_pi^2) is being realized at the level of the GPD for the first time. Because the plotted quantity is the combination E-tilde + G-tilde_1 and the extraction of E-tilde is conditional on the assumed vanishing of G-tilde_1, I recommend either reporting this result as consistent with pion-pole dominance or adding a sentence in Section 4.2 that makes the conditionality of the E-tilde extraction explicit.
minor comments (6)
  1. [Section 3 / Eq. (7)] The x>1 and x<0 branches of Eq. (7) are typeset in a way that is easy to misread (the argument of the logarithm appears as 'x-1/x'), and no reference is given for this one-loop result; please typeset the logarithms unambiguously, for example as ln(x/(x-1)), and cite the original quark-target calculation.
  2. [Section 3 / after Eq. (8)] The relation p3=(x/xi)P3 introduced after Eq. (8) is unclear in the context of the PDF matching formula, where the convolution variable is x/y and the hadron momentum is P3; the sentence should either explain what p3 and xi refer to here or be deleted.
  3. [Figures 2-6] The captions omit the kinematic parameters (P3, xi, and lattice spacing) and do not cite the source references; because Section 4.3 hinges on the P3 dependence of different quasi-GPD definitions, adding P3 values and the originating references to the captions would materially help the reader.
  4. [References] Reference [26] has a typo ('hree-dimensional' should be 'Three-dimensional'), and references [6] and [24] are cited only by arXiv identifier without journal information; please complete the bibliographic data where available.
  5. [Section 2] The moment relation A(t)+xi^2 D(t) = integral dx x H(x,xi,t) uses a specific convention for the D-term normalization; a parenthetical convention statement or a pointer to Ref. [4] would prevent confusion, since conventions in the literature differ by factors such as 4 in the D-term.
  6. [Section 4.1] The explanation that the vanishing t-sensitivity as x goes to 1 aligns with the power-counting analysis suggested in Ref. [19] would be clearer with one sentence summarizing that power counting, since Ref. [19] is not otherwise described.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the matching claim rests on an explicit one-loop calculation and external references, with only minor non-load-bearing self-citations.

full rationale

The paper's central claim—that Euclidean quasi-GPDs can be matched to light-cone GPDs—is not circular. Section 3 derives the IR structure explicitly in a one-loop quark-target model: Eq. (5) gives the light-cone result and Eq. (7) gives the quasi-PDF, and the text observes that the IR pole structures are identical, both containing the term -(1-x) ln m_g^2. The matching formula in Eqs. (8)-(9) is then presented as a consequence of this independent perturbative calculation, with matching coefficients attributed to external Refs. [7-11]. No parameter is fitted to a subset of data and renamed a prediction; the lattice results in Section 4 are actual numerical computations from peer-reviewed papers, not fits to the matching formula. The paper's self-citations (e.g., Refs. [2,13,21-26]) are numerous but not load-bearing for the central derivation. The Lorentz-invariant quasi-GPD construction in Section 4.3 is presented with explicit equations (10)-(17) and is explicitly hedged: the paper notes that the expectation of faster convergence is 'likely too simplistic' and that convergence 'may, in reality, be governed by the underlying dynamics,' with the traditional definition sometimes converging better. Thus no claimed prediction reduces by construction to its input. Score 2 reflects the presence of minor self-citations without circular loading.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The review introduces no new free parameters and no invented entities. Its central message relies on three working assumptions of the quasi-distribution/lattice approach: LaMET factorization, control of lattice systematics, and one-loop matching accuracy. These are standard domain assumptions of the field, but they are assumed rather than established in this paper.

assumptions (3)
  • domain assumption Quasi-distribution (LaMET) factorization: finite-momentum Euclidean quasi-PDFs and quasi-GPDs can be matched to light-cone quantities via a perturbative coefficient function, with power corrections suppressed by P3^2.
    Invoked in Section 3, Eqs. (8)-(9). The entire lattice extraction program relies on this factorization theorem, which the paper cites but does not prove.
  • domain assumption Lattice QCD at finite lattice spacing and finite hadron momentum P3 provides a faithful discretization of the Euclidean correlators needed for the quasi-distribution approach.
    Section 3 notes that the maximum P3 is constrained by lattice spacing and that statistical noise grows with momentum; the method assumes these systematics can be controlled.
  • domain assumption One-loop matching is sufficient for the GPD results quoted in Section 4.
    The paper states that GPD matching is only known up to one-loop order (Section 3). The quoted lattice extractions assume this order is adequate, which is a working assumption of the field.

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Cite this review

Pith. "Pith review of Hadron structure via Generalized Parton Distributions." pith.science (2026). https://pith.science/paper/BPULBBZB

@misc{pith2026250200481,
  author       = {Pith},
  title        = {Pith review of: Hadron structure via Generalized Parton Distributions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BPULBBZB}},
  note         = {Machine review of arXiv:2502.00481}
}
read the original abstract

Recent advancements have made it possible to approximate light-cone correlation functions in lattice QCD by computing their Euclidean counterparts. In these proceedings, we review key developments in this approach and explore their direct implications for Generalized Parton Distributions (GPDs). Furthermore, we emphasize the pivotal role of GPDs in uncovering the internal structure of hadrons and beyond.

Figures

Figures reproduced from arXiv: 2502.00481 by the authors.

Figure 1
Figure 1. Hierarchy of parton distri￾butions, emphasizing the central role of GPDs in bridging parton distribu￾tion functions (PDFs) and form factors (FFs). The non-perturbative structure of nucleons is encoded in various distribution functions, each offering a different perspective on how quarks and gluons are arranged within nucleons. The most fundamental are parton distribution func￾tions (PDFs), which provide a one-dimens… view at source ↗
Figure 2
Figure 2. Left: Pion GPD as a function of 𝑥 for 𝜉 = 0 at various values of 𝑡. Right: Proton GPD as a function of 𝑥 for both 𝜉 = 0 and 𝜉 ≠ 0, with different values of 𝑡 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Left: Proton helicity GPDs 𝐻˜ and 𝐸˜ at 𝜉 ≠ 0 as a function of 𝑥. Right: Proton transversity GPD 𝐻𝑇 at both 𝜉 = 0 and 𝜉 ≠ 0 for different values of 𝑡 as a function of 𝑥. given that, at the time, no GPD extractions from experimental data existed for the full 𝑥-dependence. A recurring question arising from these plots concerns the meaning of the discontinuities at 𝑥 = ±𝜉. These discontinuities are not physical but rat… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Left: Proton twist-2 GPD 𝐻˜ and twist-3 combination 𝐻˜ + 𝐺˜ 2 as functions of 𝑥, compared against each other at 𝜉 = 0. Right: Proton twist-3 GPD combination 𝐸˜ + 𝐺˜ 1 at 𝜉 = 0 as a function of 𝑥 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Left: Symmetric frame of reference for calculating GPDs. Note the symmetric appearance of momentum transfer Δ between incoming and outgoing nucleon states. Right: Asymmetric frame of reference for calculating GPDs. Note that the momentum transfer is only on one of the …
Figure 6
Figure 6. Figure 6: Left: The unpolarized proton GPD 𝐸, derived within the amplitude formalism from an asymmetric frame using the Lorentz-invariant definition. We present this specific example of the 𝐸 GPD because the Lorentz-invariant definition yields a more precise result compared to t…

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Works this paper leans on

27 extracted references · 3 canonical work pages

  1. [1]

    Diehl,Generalized parton distributions, Phys

    M. Diehl,Generalized parton distributions, Phys. Rept.388, (2003) 41, [hep-ph/0307382]

    arXiv 2003

  2. [2]

    Bhattacharya, K

    S. Bhattacharya, K. Cichy, M. Constantinou, X. Gao, A. Metz, J. Miller, S. Mukherjee, P. Petreczky, F. Steffens and Y. Zhao,Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO, Phys. Rev. D108, (2023) 014507, [2305.11117]

    arXiv 2023

  3. [3]

    X. D. Ji,Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett.78, (1997) 610, [hep-ph/9603249]

    arXiv 1997

  4. [4]

    M. V. Polyakov and A. G. Shuvaev,On‘dual’ parametrizations of generalized parton distri- butions, hep-ph/0207153

    arXiv

  5. [5]

    Bhattacharya, Y

    S. Bhattacharya, Y. Hatta and W. Vogelsang,Chiral and trace anomalies in deeply virtual Compton scattering. II. QCD factorization and beyond, Phys. Rev. D108, (2023) 014029, [2305.09431]

    arXiv 2023

  6. [6]

    Tarasov and R

    A. Tarasov and R. Venugopalan,The role of the chiral anomaly in polarized deeply inelastic scattering III: Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass, 2501.10519

    arXiv

  7. [7]

    Ji, Parton Physics on a Euclidean Lattice, Phys

    X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110, (2013) 262002, [1305.1539]

    arXiv 2013

  8. [8]

    X. Ji, A. Schäfer, X. Xiong and J. H. Zhang,One-Loop Matching for Generalized Parton Distributions, Phys. Rev. D92, (2015) 014039, [1506.00248]

    arXiv 2015

Show all 27 references
  1. [9]

    Y. S. Liu, W. Wang, J. Xu, Q. A. Zhang, J. H. Zhang, S. Zhao and Y. Zhao,Matching generalized parton quasidistributions in the RI/MOM scheme, Phys. Rev. D100, (2019) 034006, [1902.00307]. 12 Hadron structure via GPDs Shohini Bhattacharya

    2019 arXiv

  2. [10]

    F. Yao, Y. Ji and J. H. Zhang,Connecting Euclidean to light-cone correlations: from flavor nonsingletinforwardkinematicstoflavorsingletinnon-forwardkinematics ,JHEP 11,(2023) 021, [2212.14415]

    2023 arXiv

  3. [11]

    Z. Y. Li, Y. Q. Ma and J. W. Qiu,Extraction of Next-to-Next-to-Leading-Order Parton Dis- tribution Functions from Lattice QCD Calculations, Phys. Rev. Lett.126, (2021) 072001, [2006.12370]

    2021 arXiv

  4. [12]

    A. V. Radyushkin,Generalized parton distributions and pseudodistributions, Phys. Rev. D 100, (2019) 116011, [1909.08474]

    2019 arXiv

  5. [13]

    Bhattacharya, K

    S. Bhattacharya, K. Cichy, M. Constantinou, A. Metz, N. Nurminen and F. Steffens,Gener- alized parton distributions from the pseudodistribution approach on the lattice, Phys. Rev. D 110, (2024) 054502, [2405.04414]

    2024 arXiv

  6. [14]

    Dutrieuxet al.[HadStruc], Towards unpolarized GPDs from pseudo-distributions, JHEP 08, (2024) 162, [2405.10304]

    H. Dutrieuxet al.[HadStruc], Towards unpolarized GPDs from pseudo-distributions, JHEP 08, (2024) 162, [2405.10304]

    2024 arXiv

  7. [15]

    Hannaford-Gunnet al.[CSSM/QCDSF/UKQCD],Reconstructing generalized parton dis- tributions from the lattice off-forward Compton amplitude, Phys

    A. Hannaford-Gunnet al.[CSSM/QCDSF/UKQCD],Reconstructing generalized parton dis- tributions from the lattice off-forward Compton amplitude, Phys. Rev. D110, (2024) 014509, [2405.06256]

    2024 arXiv

  8. [16]

    Cichy, Progress in 𝑥-dependent partonic distributions from lattice QCD, PoS LAT- TICE2021, (2022) 017, [2110.07440]

    K. Cichy, Progress in 𝑥-dependent partonic distributions from lattice QCD, PoS LAT- TICE2021, (2022) 017, [2110.07440]

    2022 arXiv

  9. [17]

    J.W.Chen,H.W.LinandJ.H.Zhang, PiongeneralizedpartondistributionfromlatticeQCD , Nucl. Phys. B952, (2020) 114940, [1904.12376]

    2020 arXiv

  10. [18]

    Alexandrou, K

    C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato and F. Steffens,Unpolarized and helicity generalized parton distributions of the proton within lattice QCD, Phys. Rev. Lett.125, (2020) 262001, [2008.10573]

    2020 arXiv

  11. [19]

    Yuan, Generalized parton distributions at x —> 1, Phys

    F. Yuan, Generalized parton distributions at x —> 1, Phys. Rev. D69, (2004) 051501, [hep-ph/0311288]

    2004 arXiv

  12. [20]

    Alexandrou, K

    C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato and F. Steffens,Transversity GPDs of the proton from lattice QCD, Phys. Rev. D105, (2022) 034501, [2108.10789]

    2022 arXiv

  13. [21]

    S.Bhattacharya,K.Cichy,M.Constantinou,J.Dodson,A.Metz,A.ScapellatoandF.Steffens, Chiral-even axial twist-3 GPDs of the proton from lattice QCD, Phys. Rev. D108, (2023) 054501, [2306.05533]

    2023 arXiv

  14. [22]

    Bhattacharya, K

    S. Bhattacharya, K. Cichy, M. Constantinou, J. Dodson, X. Gao, A. Metz, S. Mukherjee, A. Scapellato, F. Steffens and Y. Zhao,Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Unpolarized quarks, Phys. Rev. D106, (2022) 114512, [2209.05373]. 1...

    2022 arXiv

  15. [23]

    Petreczky and F

    S.Bhattacharya,K.Cichy,M.Constantinou,J.Dodson,X.Gao,A.Metz,J.Miller,S.Mukher- jee, P. Petreczky and F. Steffens,et al. Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case, Phys. Rev. D109, (2024) 034508, [2310.13114]

    2024 arXiv

  16. [24]

    Bhattacharya, K

    S. Bhattacharya, K. Cichy, M. Constantinou, X. Gao, A. Metz, J. Miller, S. Mukherjee, P. Petreczky, F. Steffens and Y. Zhao,Moments of Axial-Vector GPD from Lattice QCD: Quark Helicity, Orbital Angular Momentum, and Spin-Orbit Correlation, 2410.03539

    arXiv

  17. [25]

    Scapellato and F

    K.Cichy,S.Bhattacharya,M.Constantinou,J.Dodson,X.Gao,A.Metz,J.Miller,S.Mukher- jee, A. Scapellato and F. Steffens,et al. Generalized Parton Distributions from Lattice QCD, Acta Phys. Polon. Supp.16, (2023) 7-A6, [2304.14970]

    2023 arXiv

  18. [26]

    H. T. Ding, X. Gao, S. Mukherjee, P. Petreczky, Q. Shi, S. Syritsyn and Y. Zhao, hree-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions, 2407.03516

    arXiv

  19. [27]

    K.Cichy,M.Constantinou,P.SznajderandJ.Wagner, Nucleontomographyandtotalangular momentum of valence quarks from synergy between lattice QCD and elastic scattering data, Phys. Rev. D110, (2024) 114025, [2409.17955]. 14

    2024 arXiv

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